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OtiooHt OR Td Ae cs ba » ve i PREFACE. = ~ THE present work aims at embracing a full course of Logie, both Formal and Inductive. In an introductory chapter, are set forth such doctrines of psychology as have a bearing on Logic, the nature of knowledge in general, and the classification of the sciences ; the intention being to avoid doctrinal digressions in the course of the work. Although preparatory to the under- standing of what follows, this chapter may be passed over lightly on a first perusal of the work. The part on Deduction contains the usual doctrines of the Syllogism, with the additions of Hamilton, and a full abstract of the novel and elaborate schemes of De Morgan and Boole. The Inductive portion comprises the methods of induc- tive research, and all those collateral topics brought for- ward by Mr. Mill, as part of the problem of Induction ; various modifications being made in the manner of state- ment, the order of topics, and the proportion of the hand- ling. The greatest innovation is the rendering of Cause by the new doctrine called the Conservation, Persistence, or Correlation of Force. Mr. Mill’s view of the relation of Deduction and Indue- tion is fully adopted, as being the solution of the otherwise inextricable puzzle of the syllogism, and the means of giving unity and comprehensiveness to Logic. iv PREFACE, A separate division is appropriated to the Logie of the Sciences, with the view of still further exemplifying the logical methods, and of throwing light upon various points in the sciences themselves. The review comprises all the theoretical or fundamental sciences—Mathematies, Physics, Chemistry, Biology, and Psychology ; the sciences of Classi- fication, or Natural History ; and two leading Practical sciences—Politics and Medicine. The department of Definition is, for the first time, brought, under, a methodical scheme, and rendered of co- ordinate value with Deduction and Induction, as a branch of logical method. The modes of defining, as a generalizing process, are given under two canons, a positive and a negative ; and attention is called to the chief obstacles— uncertainty in the denotation of words, and the gradual transition of qualities into their opposites, In discussing Fallacies, I have canvassed the grounds for the usual practice of detaching the violations of logical rules from, the exposition of the rules themselves; and have endeavoured to show that the only portions of the subject proper to reserve for separate handling, are the Fallacious tendencies of the Mind, and Fallacies of Con- fusion, As these are subjects of great moment, and admit of wide illustration, both are considered with some minute- ness. None of the controversies in the subject are overlooked ; but it has been deemed advisable to separate them from the main body of the work. In an Appendix, are em- braced the various Classifications of the Sciences, the Pro- vince of Logic, the Classification of Nameable Things, the Universal Postulate, the meanings of Analysis and Syn- thesis, the Theories of Induction, the Art of Discovery, and the maxims of Historical Evidence. ‘T'o adapt the work to an elementary course of Logic, PREFACE, Vv the parts to be omitted are the Additions to the Syllogism, the Logic of the Sciences, and the chapters in the Appen- dix. The junior student, or the candidate for a pass examination, without attempting to master or commit these reserved portions, might yet find their perusal of service in understanding the rest. There is a general conviction that the utility of the purely Formal Logic is but small; and that the rules of Induction should be exemplified even in the most limited . course of logical discipline. I would suggest that an in- creased attention should be bestowed on Definition and Classification, with reference both to scientific study and to matters not ordinarily called scientific. As I may be open to the charge of presumption in appearing as a rival to Mr. Mill, I will venture the remark, that an attempt to carry out still more thoroughly the enlarged scheme of logical method, seems the one thing hitherto wanting to the success of his great work. ABERDEEN, March, 1870 \ i, : ‘ . — : o ‘ = % ~*~ * * i { | . = ' - 2 7 - s — ’ ~ “ “a q 8 _ A = a os vee ; * oe . = ang 8 5 o ee pas 2 ¢ie$ bale tom ee NN TS. INTRODUCTION . : ; ‘ : ‘ y G ‘ ‘ BOOK 1. NAMES, NOTIONS, AND PROPOSITIONS. P. a Names or Terms i ; : : ¥ IL. Classes, Notions, or Concepts IIL. Propositions . ° 7 BOOK II. DEDUCTION. I. The Syllogism . IL. Recent Additions to the Syllogism — 3 Ill. Functions and Value of the Syllogism IV. Trains of Reasoning and Deductive Sciences , V. Demonstration—Axioms—Necessary Truth : : BOOK III. INDUOTION. ‘Meaning and Scope of Induction . The Ground of pe aay of N ature—Laws of Na- ture ‘ III. Induction of Coexistence V. Law of Causation . Elimination of Cause and Effect—Observation and Experiment VL The Experimental Methods ‘ d j : VU. Examples of the Methods VIII. Frustration of the Methods IX. Chance, and its Elimination ‘ ‘ X. Induction aided by Deduction . XI. Secondary Laws—Empirical and Derivative . Explanation of Nature . ; XIfl. Hypotheses XIV. Approximate Generalizations and Probable "Evidence : XV. Analogy : ‘ : ° XVI. Credibility and Incredibility ; ; ; ‘ PAGE 42 43 133 178 207 214 219 231 238 241 245 271 279 297 306 814 825 332 346 358 365 370 378 Vili CONTENTS. BOOK IV. DEFINITION. CHAP. I. Canons of Definition . : II. General Names > : III Classification ; . ° BOOK V. LOGIC OF THE SCIENCES. I, Logic of Mathematics . ; II. Logic of Physics. : ° Ill. Logic of Chemistry IV. Logic of Biology . V. Logic of Psychology VI. Sciences of Classification . VII. Logic of Practice VIII. Logic of Politics IX. Logic of Medicine BOOK VI. FALLACIES. I. Mill’s Classification of Fallacies II. The Position of Fallacies . Ill. Fallacious Tendencies of the Mind . IV. Fallacies of Confusion . : V. Logical Fallacies. ‘ . APPENDIX. A.—Classifications of the Sciences B.—The Province of Logic C.—Enumeration of Things D.—The Universal Postulate . EK —Aristotelian and Scholastic Fallacies F.—Analysis and Synthesis G.—Growth of the Logic of Induction H.—Art of Discovery x : ‘ I.—Historical Evidence : : K.—Explanation of Some Logical Terms . PaGE 384 401 414 . 429 451 472 488 505 522 545 547 575 599 608 606 616 625 627 689 652 664 673 687 697 707 715 o> a8 ~~ » rh : e sn agit pie fa (EAS Toe -* Ge peireiss. PART TF. 3 Raye yUOTro nye oer INTRODUCTION. 1. Loaic may be briefly described as a body of doctrines and rules having reference to Truth. The functions of Logic will be afterwards given with par- ticularity and precision. For the present we remark that it concerns the Truth of things, no matter what the subject be. While in one aspect it is theoretical, in the prevailing aim it is practical. In this introductory chapter we are to consider the following topics. _ (1) The Psychological data or groundwork of Logic. (2) The First Principles of Logic. (3) The Classification of the Sciences. (4) The different views of the Province of Logie. (5) The Divisions of Logic. PSYCHOLOGICAL DATA OF LOGIC. 2. Logic, under every view, involves frequent references to the laws and workings of the mind; and the more so the more we extend its province. In the common Logic of the Schools, the Syllogistic or Deductive Logic, explanations are usually given of the intel- lectual processes named Perception or Simple Apprehension, Abstraction or the formation of concepts or notions, Judgment or the laying down of propositions, and Reasoning or the drawing of inferences or conclusions from premises. In the Inductive Logic, an enquiry is instituted into our 2 PSYCHOLOGICAL DATA OF LOGIC. idea of Cause; in connection with which, notice is taken of the controversy respecting the Origin of our Knowledge in the Mind, namely, as to whether it be wholly derived from experience, or whether any portion of it (as Cause, the Axioms of Mathematics, &c.) be intuitive, instinctive, or innate. It is considered a part of Logic to set forth the theory and the limits of the Explanation of phenomena; for which pur- pose a reference must be made to the structure of the mental powers. This was the avowed aim of Locke, in his Essay on the Understanding, one of the greatest contributions to the science of mind. Under such circumstances, the most satisfactory course ap- pears to be to bring forward and expound, once for all, at the commencement, whatever portions of Psychology are in any way implicated with the rules and methods of Logic. Butthe exposition must necessarily be brief. | Discrimination or Relativity. 3. In order to make us feel, there must be a change of impression ; whence all feeling is two-sided. This is the law of Discrimination or Relativity. , Observation shows that unbroken continuance of the same impression is attended with unconsciousness; and that the greater the change or transition, the greater ths consciousness. An unvarying touch, or a monotonous sound ceases to be felt ; in an even temperature, we lose all consciousness of heat or cold. Still more convincing are the instances showing that changes affect us in proportion to their greatness and sudden- ness. Abrupt transitions are stimulating and exciting ; the first exposure to sun-light after being in the dark, the first mouthful of water when we are thirsty, the moment of transi- tion from poverty to wealth—are accompanied with the highest degree of feeling ; after which there is a gradual subsidence of the excitement. | Hence the fact of our being under some agency of sense or feeling does not of itself attest our mode of feeling; there must farther be given the condition immediately, and for some time previous. That a man is the possessor of a thou- sand pounds to-day is not a sufficient criterion of his feel- ings as regards worldly abundance. If a year ago, the same man possessed nothing, he feels in a way totally different from bim that has fallen to that amount from a fortune of ten thou- sand pounds. DISCRIMINATION OR RELATIVITY. 3 _ 4. As regards Knowledge, there must likewise be a tran- sition, or change ; and the act of knowing includes always two things. When we consider our mental states as Ae: the same law holds. We know heat by a transition from cold; light, by passing out of the dark; up, by contrast to down. There is no such thing as an absolute knowledge of any one property ; we could not know ‘motion,’ if we were debarred from knowing ‘rest.’ Noonecould understand the meaning ofa straight line, without being shown a line not straight, a bent or crooked line, We may attend more to one member of the couple than to the other. In this way only can we think of an individual property. We may be thinking more of the heat than of the cold, of the straight than of the crooked; the one may be the explicit, the other the implicit subject of our thoughts. As our transitions may be in two directions—from heat to cold, and from cold to heat—we have a difference of feeling in the two cases. We are more conscious of heat, when passing to a higher temperature, and of cold when passing toa lower. The state we have passed to is our explicit consciousness, the state we have passed from is our implicit consciousness. The principle of Relativity has wide andimportant bearings in Logic. It will appear in Naming; in Definition; in Pro- positions or Affirmation. It will be appealed to in rectifying a large class of Fallacies—the fallacies of the suppressed rela- tive, or of the Absolute. Agreement or Sinvilarity. 5, When an impression is repeated, after an interval, we are affected with a new and peculiar consciousness, the shock or consciousness of Agreement in difference. We see a candle flame; it is withdrawn; after a time, it is brought back. We have now, in addition to the luminous effect of the presentation, a shock or feeling of agreement, identity, repetition ; a state no less concerned in our intellec- tual operations than the shock of difference or discrimination. We are constantly experiencing the repetition of former im- pressions, in circumstances more or less altered, and we are affected with a greater shock according to the greatness of the alteration. The degree or intensity of the consciousness of Agreement may vary through a wide range, from the slight 4 PSYCHOLOGICAL DATA OF LOGIC. recognition of a new day to the flash of a great discovery of identification, like Newton’s assimilating the fall of a stone to the deflection of the moon towards the earth, Knowledge as conjoining Difference and Agreement. 6. Our knowledge of a fact is the Discrimination of it from differing facts, and the Agreement or identification of it with agreeing facts. The only other element in knowledge is the Retentive power of the mind, or memory, which is implied in these two powers. Our knowledge of heat is (1) a series of shocks of Difference or discrimination between heat and cold, and (2) the Agree- ments or repetitions of the same shocks under change of circumstances. z Besides the transition heat-cold, which is the primary cog- nition of heat, we make other transitions into other sensations. - We have occasion to pass from a sensation of warmth toa sensation of light, and the difference of the two brings out a new discriminative consciousness, and gives a new meaning to warmth, and also to light; heat is no longer simply the con- trast of cold, it is also the contrast of the feeling of luminosity. So, every new sensation that we pass to from heat, with con- — sciousness of difference, gives a new negative meaning to heat; it isnot taste, nor smell, nor hardness, nor sound, Again, our mental impression, knowledge, or idea of a shilling, is the sum of all its differences from the things that we have contrasted it with, and of all its agreements with the things that we have compared it to. We call it round; sig- nifying that it differs from things called square, oblong, oval, &c.; that it agrees with other things called round—that we have been frequently struck with the identity of this figure in many different combinations, So with the weight of the shilling. We know weight by difference, and by agreement ; we recognise a shilling as heavier than some things, lighter than others; which is difference; and as identical with a third class, which is agreement. The knowledge, idea, or recollection of any concrete object, is thus the aggregate of those mental exercises of Discrimination and Agreement, fixed and retained in the mind by the power called retentiveness, or memory ; by which power of retention we are able to discriminate and compare VARIETIES OF KNOWLEDGE. 5 present impressions with past, and to accumulate a vast stock of mental effects or deposits, called ideas, knowledge, thought. Knowledge is of two kinds, called Object and Subject. 7. The knowledge ofa shilling, of a house, of a mountain, of a star, is said to be objective; it relates to the object, or the outer, world. The knowledge of a pleasure or a pain, or of the succession of ideas in the mind, relates to the subject, or the internal, world. We have a great accumulation of both kinds of knowledge ; some minds abounding more in one, some more in the other. Knowledge as (1) Individual and Conerete, or (2) General and Abstract. 8. The knowledge of a table in a room, at a particular time, is in the highest degree individual or concrete. The knowledge relating to any table, at any time, is said to be general and abstract. By the mental power of Agreement or Similarity, we bring to mind different individual tables, attending to their points of community, in spite of many diversities. We affirm properties common to them all, This is the generalising power of the mind. It is one of the most signal functions of our intelligence, and is purely an outgoing of the fundamental power named Agreement, or Similarity. Dispute as to the Character of General Knowledge, called also Abstract Ideas, 9. In General Knowledge, strictly so called, there is nothing but the fact of agreement among a number of separate particulars; which agreement is signified by the use of a common name. A general name, as ‘circle,’ ‘round,’ ‘animal,’ ‘ wise,’ is applied to things agreeing in a certain respect, while differing in other respects, to signify their agreement. It has been supposed that the points of community of agreeing things exist apart from the things. This view is called Realism. It was believed by a certain school of philosophers, deriving from Plato, that there exists, in the universe of being, a Circle in general, or circular Form without substance, size, or colour; that in like manner, there are archetypal Forms of Man, of 6 PSYCHOLOGICAL DATA OF LOGIC. Just, of Good, &c. After a severe controversy, which raged in the scholastic period, this view was abandoned. Realism is still exemplified, however, in the doctrine of an Independent External World, and also in the doctrine of the separate existence of Mind or Soul. In strictness, the External World is known only as perceived by our senses; Mind is known only as conjoined with body. | Another mode of regarding the fact of community in diversity, is to suppose that the mind can represent to it- self in a notion, the points of agreement by themselves, and can leave entirely out of sight the points of differ- ence. Thisis Conceptualism. | Although there is no pure circle in existence, we are sup- posed able to think of the round figure to the exclusion of the other properties of the individual circles—material, colour, size. This too is incorrect. It exaggerates the mind’s power of giving a preference of attention to some of the attributes of a concrete object, as a wheel, or a shilling. We may think much of the roundness, and little of the size; but we cannot think of the roundness, without thinking of some size or colour. The usual mode of thinking an abstraction, or of concen- trating the mind upon one property, is to think alternately of the different objects possessing the property. We can best — think of roundness, by having in view various round things, differing in material, size, colour, &c. The effect of the mind’s passing and repassing between the individuals, is that the roundness starts into great prominence, and the other proper- ties fall into the background, without, however, being extin- guished. The great fact constantly underlying Abstraction, is the mustering of individuals agreeing in the midst of differ- ence. We are in the habit of using single individuals to typify a multitude; as in the diagrams of Euclid. We do not, in geometrical reasoning, think of a great number of circular things ; we can study the circle upon one figure, provided we take care to affirm nothing as to size, colour, or material, which facts are inseparable even from the barest diagram. When the logician speaks of a Notion, Concept, or Abstract Idea, he must not be understood as implying anything be- yond the agreement of a certain number of things in a given manner. THE INDIVIDUAL AND THE GENERAL. 7 Our idea of an Individual a conflux of Generalities. 10. What we term the Perception of an individual, as a given tree, is not simply a sense impression of the moment, it is an aggregation of many generalized impressions. When we look at a tree, we are affected by a great number of different influences—colours, shape, size, &c. Now, every distinguishable impression recalls the previous stamps of the same, by Agreement or Similarity ; and the idea of the tree is not an original sense presentation, but a compound of this with old presentations. Every feature of the tree suggests a classification upon that point; the green and brown colours are felt only as the collective impressions of those shades of colour. In our minds, therefore, the Concrete and the Abstract are inextricably blended. Of a pure concrete, not also resolved into classifications or abstractions, we have no experience. Our knowledge proceeds in both ways at once; individuals giving generals and generals re-acting upon individuals. If there was one concrete thing in the world, having no property in common with any other known concrete thing, we might, by gazing upon that, and comparing it with ftself, possess an idea of a concrete individuality, where no generality was im- plicated ; but sucha concrete would be very different from any concrete known to us. We are not in the position to imagine such an idea. 11. The speciality of a concrete Individual is that itis a definite aggregate not confounded with other individuals. The number of general properties pointing to the individual must be such as to give it a definite or special character, instead of leaving it indefinite or common. The tree that I now look at, is individualized by a concurrence of properties never realized before ; or if not by such concurrence itself, by its surroundings, and all the circumstances of time and place, accompanying its perception. A _ shilling is individualized by its adjuncts of place and time. 12. The distinction between Presentation and Represent- ation, is the distinction between a definite conflux of generalities, and an indefinite conflux. A shilling in the hand is a Presentation. A shilling as a general coin of the realm is Representative; it is common to 8 PSYCHOLOGICAL DATA OF LOGIC. many places and times and circumstances, and not bound down to one definite situation and one definite moment. 13. The names of Individuals usually correspond to their character as a conflux of generals. In a few instances, we have names that bear no reference to generalities, as when a certain individual man is named—Coesar. These are proper, or meaningless names; the bare symbols for separating the thing from other things. But in the vast majority of instances, the name follows the manner of conceiy- ing the thing—that is, by specifying the concurring generalities. A large gothic building; a stout man of forty; a cubical crystal, with a certain hardness and specific gravity, found in a certain formation :—are examples of designations in strict accordance with the ideas of the things. Philology confirms this. The primitive names of such con- crete objects as sun, moon, father, mother, have all a gene- ralized meaning; ‘moon ’ is the measurer, ‘father’ is the feeder, and soon. There seems to be no possibility of con- ceiving individuals without classifying and generalizing at the same time ; and the one name means both an individual and a general. The intellectual function of Agreement, or Similarity, as the basis of Reasoning. 14. Reasoning, in every form, supposes the operation of Similarity—the assimilating of one thing to some other thing. Mi The most general type of Reasoning is to infer from one particular fact to another particular fact of the same kind ; the likeness being both the means of suggestion, and the jus- tification of the transfer of properties. We throw a stone into a pool; it makes a splashing noise, sinks to the bottom, and diffuses a series of waves from the point where it fell. We infer or reason, or presume, that another stone thrown into the same pool will be followed by the same series of effects; and we may extend the inference to another pool, or to any mass of liquid. ‘This is to infer, to reason, to transcend our actual experience, to make an affirmation respecting the un- known. Now, the mind is prompted by the likeness of the cases to take this step in advance, to anticipate what is to happen. One would not infer that a handful of dried leaves KINDS OF REASONING. 9 would produce all the consequences of throwing the stone; we never expect either through our instinctive belief, or through our experience of the world, that the same effects will arise under different circumstances. This mode of Reasoning is in constant use, and extends to the animal intelligence. An animal accustomed to find a shelter under a bush, reasons from one bush to another bush, being moved solely by the resemblance of the second to the first. A dog is deterred by the menacing movement of a strange per- son wielding a strange stick: the partial resemblance to former experiences is enough to rouse its fears. A second mode of Reasoning is when by the help of general language, we infer from one or a few cases, to all cases of the kind; as when we conclude, after a certain number of trials, that all stones sink in water, that all matter of vegetable origin is combustible, that all animals are generated from other animals. This is Induction, in the more technical sense—the inferring not from particulars to other particulars, but from particulars to universals. The mental process is still Simi- larity, or the process whereby one thing suggests other resembling things. Itis by similarity that we assemble in the mind all kindred facts that have ever come under our knowledge; we then are able to compare the points of agree- ment, with a view to an accurate general statement, in other words, an Inductive proposition. The third kind of Reasoning, called Deductive, is also based on the tracing of resemblance. When we infer that, because all stones sink in water, a certain body will sink (which is Deduction), it is because that body resembles the rest, or has the points of community indicated by the general word ‘stone.’ When we have mastered a general principle, it is by similarity that we discover cases to apply it to, and so ex- tend our knowledge deductively. Origin. of owr Knowledge in Haperience. 15. Our knowledge of the world, both of matter and of mind, is the result of our conscious Experience. As regards the Material, outer, or object world, we gain _ our knowledge through the ordinary Senses, coupled with our Movements, under the three laws of our INTELLIGENCE— viz., Difference, Agreement, and Retentiveness. We see, hear, touch, taste, smell; we have our active energies aroused by things resisting, by movements, and by things extended; we 10 PSYCHOLOGICAL DATA OF LOGIC. discriminate and identify impressions ; we acquire permanent recollections, and associate things presented in combination ; and, by all these processes (exemplified at full length in Mental Science, or Psychology) we lay up our stock of imagery, ideas, or thoughts, of the world of sensible experience, As regards the Mind, or the knowledge of our inner life the senses do not avail us. We are directly and immediately conscious of our feelings, thoughts, and volitions, and acquire a store of permanent recollections of these also. We remem- ber our different pleasures and pains, and the order of their occurrence; we learn not merely things, but our ideas of things, und the laws of the rise and succession of these ideas. Thus, it is a fact of our mental or subjective life, that we easily recall to mind whatever strongly engaged our attention in the reality. 16. It has been alleged that some parts of our knowledge, instead of being the result of experience, like the greater portion, are intuztive or inherent to the mind, apart from the operation of the senses upon actual things, or the par- ticular phenomena of the subjective consciousness. | At different stages in the progress of Philosophy, there have been given different lists of intuitive, or &@ priort elements of knowledge. At the present day the controversy turns chiefly on these four notions—Time, Space, Substance, Cause. It is maintained that there is in these notions something that experience could not give; so that some different origin must be sought for them. On the other side, the supporters of the Experience theory hold that the Moving energies, with the Senses and Self-Con- sciousness, aided by the intellectual functions, can account for all these notions, For example, True is an abstraction: and, like all other abstractions, is, properly speaking, a certain mode of likeness among individual things or feelings of the mind. All our experiences, whether object or subject, are regarded by us as more or less enduring ; the attribute of Time is the assimilation or classification of enduring states, as enduring. Apart from these actual experiences of differences and agreements of enduring things, there can be no such thing as Time, unless on the exploded doctrine of Realism, nor any self-subsisting notion of Time, unless on the erroneous theory of Conceptual- ism. In the absence of objects and states continuing or enduring, an intuition of Time is a self-contradiction ; in the ALLEGED INTUITIVE KNOWLEDGE. 11 presence of such experiences of enduring things, discriminated and compared on the point of endurance, we cannot but have an idea of Time. Next as-to Spacr, or Extension, the fact common to all Matter, and not pertaining to mind. Extension belongs both to solid matter, and to the intervals between the masses of solid matter, which intervals are measured by the same sensibilities, namely, the muscular feelings of motion, sup- ported by the passive sensations. The @ priort philosophers allege that Space comes from no experience, but is already inherent in the mind before any- thing is perceived; being the condition of our perceiving things external. In opposition to this view, it is contended that Space in the abstract is merely the community or similarity of extended bodies, and of the intervals between them, commonly called empty space. We compare all those things on this particular point of agreement; we occasionally think of them under this comparison ; aud in so doing we are thinking of Space. This is the only view compatible with Nominalism. An innate form of Space is a species of Conceptualism. The pure intuition of Space is said to be the source of our knowledge and belief of the Axioms of Geometry, this being held to have a character that no experience can explain. In the case of these Axioms, the a priori revelation takes the form of Principles, and not of mere Notions; but the fact is the same, although differently viewed. ‘That two straight lines cannot enclose a space ;’ ‘that things equal to the same thing are equal to one another:’ are held by those that contend for an intuition of space, to be intuitive. The idea of Cause is included among the alleged intuitions. It may be expressed either as a mere Notion or as a Principle, namely, ‘ that every effect must have a cause.’ An equivalent proposition is, ‘that nature is uniform or that what has been will be.’ The contention is, that while, by experience, we might become aware that particular effects follow the law of Cause, or of Uniformity, we could not from experience know that every effect has and must have a cause, that what has been will always be. The idea of Supstance means that, underlying all the phenomenon or appearances of Matter and of Mind, there is an unknown or unknowable substratum, called Substance, Noumenon, Permanent Existence. This idea we cannot pos- sibly obtain from experience ; the very statement of it, shows 12 PSYCHOLUGICAL DATA OF LOGIC. that it passes beyond experience; yet some philosophers con- tend that we are obliged to assume and believe in it. As applied to Mind, Substance is another name for Personal Identity, or the supposed continuity of each one’s mental existence—the canvass that receives and holds together all the feelings, thoughts, volitions, that make up the stream of our conscious life, According to the counter doctrine on this head, the notion of Substance is fictitious, incompetent, and unnecessary. The real meaning of Substance, as applied to matter, is the point of community of all material bodies, the most highly general- ized fact respecting them ; otherwise expressed by Resistance, Inertia, Momentum, the Mechanical property of matter. The meaning of Substance as applied to Mind is the most highly generalized property or properties of mind—the facts wherein all minds agree on comparison, and which caused them to receive the common designation Mind, as opposed to not-mind, or matter. These generalized points of community are Feeling, Volition, and Intellect, the three facts attaching in various degrees to whatever is accounted Mind. | The nature of Belief as applied to the controversy respect- ing the origin of Knowledge. 17. There is a natural tendency to believe much more than we have any experience of. The primitive disposition of the mind as regards belief is" to suppose that whatever is will continue, that what exists here and now, exists everywhere and at all times. This in- born credulity is checked and abridged by our experience ; we soon discover that we have been assuming too much; and by degrees we abate our confidence and adapt our views to the reality of things. The following are common examples of the tendency. Be- fore experience, we believe that as we feel now, we shall always feel; that other people feel as we do; that what hap- pens to us happens to all; that whatever any one tells us is true. By the natural impetuosity of the mind, we form these assurances ; experience did not create them, but rather mode- rates and checks them. That we should treat any partial experience as universal, being thus a consequence of blind .instinctive forwardness, is no proof of what really happens in nature. As we are so liable to extend our assertions beyond the facts, we should be par- BELIEF PASSES BEYOND EXPERIENCE. 13 ticularly on our guard against universal declarations, This is one of the weaknesses of human nature, and a leading source of fallacy and error. To make the application to the particular case of causation. We are very ready to fall into statements as to the universality of cause and effect; but so we do with many other things, where we find ourselves utterly wrong. The real evidence of the Law of Causation must be something different from our being disposed to believe it. Nothing can be affirmed as true, except on the warrant of expervence. 18. As the natural disposition to believe carries us into falsehood, we must, notwithstanding our instincts, cling to experience as the only standard of truth. This inevitably follows from the nature and sources of Belief. Even the supporters of innate principles, at the pre- sent day, admit that these principles cannot arise except along with the actual things ; a qualification that subjects the innate notions as completely to the measure of experience, as if there was nothing innate about them. Our intuition of Cause is supposed to show itself only when we have observed a number of examples of cause and effect; it is, therefore, involved and implicated with our experience to such a degree as to be deprived of an independent standing. There is no means of discovering what the intuitions would dictate of themselves. For all purposes of logical certainty, therefore, they must be put out of account; regard must be had solely to observation, and experience. Our Knowledge is Limited by our Sensibilities, 19. We are able to know what things affect our various sensibilities, or what may be compounded of these; and our knowledge extends no farther. We have a certain number of sensibilities, namely, in the Senses (Passive), and in the Muscles (Active); and when any of these is affected we have knowledge or experience ; we know sight, sounds, touches, tastes, smells, and various organic affections; we know resistance and movement. We know various emotional states, love, anger, fear, &e. We have many experiences from the discrimination and 14 FIRST PRINCIPLES OF LOGIC. the agreement of our various states. In these, we have our alphabet of the knowable. We can then combine a num- ber of primitive feelings into a constructive aggregate, as when we attain to the idea of an orange, or of a man, or of the entire globe. But we cannot by any effort pass out of the compass of these primitive sensibilities. Supposing the universe to contain powers and properties that do not im- press one or other of our senses, as at present constituted, we can never by any means be made cognisant of such properties. On this ground the notion of a Substance distinct from all attributes is a thing unknowable. We can know body by its sensible properties, and mind by our conscious feelings, thoughts, and volitions; and we can know nothing beyond. FIRST PRINCIPLES OF LOGIC. 20. In Logic, there are certain general principles, consti- tuting it a science properly so called, and lying at the foundation of its practical rules and methods. These principles are variously expressed. They are termed Laws of Thought, and fundamental Axioms of Reasoning. From embracing these highest of all generalities, which pene- trate into every science, and from laying down rules on scien- tific method, Logic has been designated ‘ scientia scientiarum’ —the science that comprehends all sciences. The First Principles may be arranged thus :— I. The Principlé of Consts'rency, or Necessary Truth. II, The Principles of Depuction, III. The Principle of Inpuction. I.— Principle of Consistency—Necessary Truth. 21. It is a fundamental requisite of reasoning, as well as of communication by speech, that what is affirmed in one form of words shall be affirmed in another. Language often contains equivalent expressions for the same fact. There are synonymous names as ‘ round,’ ‘ circular;’ a round thing is the same as acircular thing. ‘ Matter is heavy,’ ‘matter gravitates’ are the same fact in different words; if the one is true, so is the other, by virtue of mere consistency. Again, there are forms that enable us to affirm many separate facts in one sweeping statement ; instead of affirming in detail, Mercury moves in an ellipse, Venus moves in an ellipse, &e., PRINCIPLE OF CONSISTENCY. 15 we can put forth the one condensed affirmation—all the planets have elliptic orbits. Having advanced this general statement, we are required by consistency to maintain each separate particular, the orbit of Saturn is elliptical, and so on. It is obvious that without this consistency, there could be no intelligent communication between one human being and another. Unless the affirmer adheres to his affirmation, how- ever he may vary the language, no one can divine what he means; there is no possibility of discussion or reasoning. To these self-consistent, although variously worded, affirma- tions is applied the descripion ‘ Necessary Truth.’ ‘ All matter is heavy, therefore any one piece of matter is heavy’ is called a necessary inference. A more exact designation would be an equivalent, inplicated, or self-consistent assertion. There is a vital contrast between passing from one form to another form of expressing the same fact, and passing from one fact to another distinct fact. When we say-—because both A and B are mortal, therefore, A ismortal—we merely repeat ourselves; when we say, because A is mortal, therefore B is mortal—we make the affirmation of one fact, the ground of an affirmation of a different fact. In order to the one leap, we need only to know the meaning of language; in order to the other, we must consult the facts of the world. The supposition has been advanced that truths of implica- tion or consistency, inappropriately called ‘ Necessary,’ are drawn out from their equivalent statements by a peculiar innate power of the mind, distinct from the powers of observing the order of nature ; that without a special instinct they could not be evolved, nor reposed in with the absolute credence that we give tothem. There are no sufficient grounds for the sup- position. We should be disposed to consistency of statement, without any special instinct. The impossibiity of carrying on intercourse by language, on any other footing, compels us to be consistent in our statements ; at least up to a certain point, for we are not always so. There is no instinct needed but the © broad instinct of self-preservation ; were it not for this we should probably care very little about observing the conditions of necessary truth. If we could go on as well by maintaining an opinion in oue form of words, while denying it in another, there appears to be nothing in our mental constitution that would secure us against contradicting ourselves. Our facul- ties as laid down by those philosophers that derive all our knowledge from experience alone, taken together with our practical necessities, seem quite sufficient to make us ad- 2 16 FIRST PRINCIPLES OF LOGIC. here to our statements under all variety ot forms and expres- sions.* 22. There are certain maxims of Consistency known by the title ‘Laws of Thought’; they are the principles of Identity, Contradiction, and HKacluded Middle. | The principle of Identity is given in the form “Ais A”; a thing is what it is; manis man. According to Plato, “The Idea is equal to itself.” ‘ Properly speaking this is not the case contemplated under the principle of Consistency ; it is not the same fact in other language, but the same fact in the same language. That the same meaning expressed by the same word or words, is the same, would appear to be an utter superfluity of affirmation ; what we want to be guarded against is mistaking the same fact in a different form of language. This obvious criticism is evaded by giving the law an inter- pretation that supposes difference in the statement. The meaning is said to be that the thing A, although differently worded, is still A; whichis merely an awkward way of stating the general maxim of Consistency. If A equals, or includes, a, b, c, d, &c., then we may say, in slightly different words, A is equal to the whole series of what it includes; a whole is the sum of its parts; a complex attribute is the aggregate of the component attributes. The Principle of Contradiction. ‘The same thing cannot be A and not-A ;’ this room cannot be both hot and not-hot, that is, cold. Consistency requires that when we affirm a definite fact, we do not at the same time deny it; having made an assertion, we are to abide by that. The principle may be carried one step farther. By the law of Relativity, every thing that can be thought of, every affirmation that can be made, has an opposite or counter notion or affirmation ; to the thing that we call a ‘straight’ line, there corresponds a negative or oppo- site called a ‘bent’ or crooked line. Now thorough-going consistency requires that when we affirm a certain thing to be * Only some of the a priori philosophers, as Leibnitz, contend for the existence of an intuitive faculty in order to apprehend these judgments of mere consistency. Kant, and others after him, confine the characteristics of necessity, and of intuitive origin, to certain synthetic judgments, where the two things given are distinct, and not mutually implicated facts. It was the peculiarity of Kant to maintain that there are such synthetic eae a priori transcending our actual experience: he instanced, in ee the proposition that ‘two straight lines cannot enclose a space.’ CONTRADICTION AND EXCLUDED MIDDLE, 17 @ straight line, we must be prepared also to deny that it is a bent line ; when we call this man wise, we must also deny that he is foolish. This is an equivalent form that plays a great part in Logic. Viewed thus, the Law of Contradiction has a pregnant meaning, which can hardly be said of the Law of Identity. The Principle of Hacluded Middle. ‘A thing must either be or not be ;’ ‘of contradictories one must be true, and the other false.’ This law grew out of the distinction of propositions into those of total, or universal, and those of partial or particular quantity—all men and some men.’ When a proposition of universal quantity is opposed by one of particular quantity, the opposition is not thorough-going; there is not a perfect and entire contrariety. Perfect contrariety is between, ‘ all men are mortal’ and ‘no men are mortal ;’ partial or incomplete con- trariety is ‘all men are mortal,’ ‘some men are not mortal;’ and ‘no men are mortal,’ ‘some men are mortal.’ Between this last species of opposition, there is no middle affirmation ; if one is not true, if it is not true that all men are mortal, then it must be true that some men are not mortal; we have no third alternative. But in the thorough-going contrariety— ‘all diamonds are precious,’ ‘no diamonds are precious,’ there is @ middle ground of compromise ; the fact may- be that some — diamonds are precious and some not. Thus, the Law of Excluded Middle is an incident of partial or incomplete con- trariety. It was enunciated by Aristotle as following from the classification of propositions according to quantity. It is too much honoured by the dignity of a primary law of thought. The Principle of Consistency, inadequately rendered by these Laws of Thought, may be assigned as the basis of the logical department entitled ‘Immediate Inference’ (as opposed to Mediate Inference or Syllogism), ‘ Inferences improperly so called,’ ‘Equivalent Propositional Forms.’ Whatever be the general designation, the details are fully agreed upon; the doctrine of the Conversion of Propositions is one of the leading topics. First Principles of Deduction. 23. In Deduction, there is the application of a general proposition to a particular case coming under it. The following is a deduction :—‘ All arsenic is poison ; now this substance is arsenic; therefore, this substance is poison.’ This is something more than consistency, implication, or 18 FIRST PRINCIPLES OF LOGIC. equivalence of phraseology. There would be equivalence of affirmation in saying ‘all arsenic is poison; therefore, some arsenic is poison.’ In the present case, however, we have another step to take ; we need a second and distinct assertion, ‘ this substance is arsenic,’ before we can conclude, ‘ this sub- stance is poison. Instead of deriving an affirmation from a prior affirmation, by change of language, we derive an affirma- tion from two prior affirmations ; and these have to be related one to another in a proper form, in order that we may draw the conclusion. This process is called Mediate Inference; there being an — intermediate link or stepping-stone between the primary pro- position and the conclusion. We cannot, by mere Consistency, resolve ‘ All arsenic is poison’ into ‘the substance in this bottle is poison ;’ ‘no matter is destructible,’ mto ‘no ether is destructible’; there is in both cases a missing link, Until we show that the substance in the bottle is arsenic, and that ether is matter, we cannot draw the special conclusions above given. 24, The Axiom, or First Principle, at the basis of De- duction, is expressed in a variety of forms, which are ‘reducible substantially to two :— (1.) Whatever is true of a whole class is true of what can be brought under the class. (2.) Things co-existing with the same thing co-exist with one another. There are corresponding forms for negative reasoning. The first form is the one suitable to the exposition of the syllogism. It sets forth the deductive type of reasoning, as consisting of a general principle brought to bear upon a case or cases, fonnd to come under it, The second form can be shown to be equivalent to the first. It has the advantage of making prominent the mediate charac- ter of deductive inference, so as to contrast it with immediate inference, or mere identical propositions under the Law of Consistency. Two things not known in themselves to co- exist, are shown to co-exist by each co-existing with some third thing. Mere consistency will not include this case. The principle is admitted as soon as it is understood ; but solely because each one’s experience bears it out. The obverse forms, for negative reasoning, are—(1) What is denied of a whole class is denied of whatever can be AXIOMS OF DEDUCTION. 19 brought under the class; (2) One thing co-existing with a second thing, with which second thing a third thing does not co-exist, is not co-existent with that third thing. 25. The Axioms of Deduction suppose the Uniformity of Nature. This is obvious, if the axioms are based on experience. We have observed, in a large number of instances, that things con- ciding with the same thing coincide with one another; but we have not observed it in all instances; we have not observed it in what took place before we were born, in what is beyond our reach, or in what is still to happen. Yet, from the cases we have observed, we do not hesitate to extend the principle to the unobserved cases. We thus assume that ‘nature is uniform ;’ that what we find to-day, all circumstances being the same, we shall find to-morrow. Again, we may deny that the axioms are experimental, and call them intuitive. The case is not altered. The intuition still supposes nature’s uniformity ; the thing intuitively con- ceived and believed is not true, unless nature be uniform. Thus, on either supposition as to our knowledge of the Logical _ (and Mathematical) Axioms, the truth, still deeper, and more comprehensive, is that nature is uniform. The so-called axioms, therefore, are not ultimate principles; they are only secondary, proximate, or derivative; they proceed from a stem bearing other branches besides them. If they are true, more is true. The wider principle will next be stated, for the sake of its other consequences. First Principle of I: nduetion. 26. When we infer from a fact known, to another un- known, we make a real inference, for which there must be some guarantee. The sole guarantee is the Uniformity of Nature. Putting a piece of wood into the fire and seeing it consumed, we infer that another piece will be consumed in like manner. This is to take for granted that what has happened will, in the same circumstances, happen again; in other words, that Nature is Uniform. The Uniformities of Nature fall under (1) Uniformities of Co-existence, and (2) Uniformity of Succession. It is a uni- formity of Co-existence that ‘inert matter gravitates,’ that the distinctive property of matter called ‘ Inertness’ is asso- 20 FIRST PRINCIPLES OF LOGIO. ciated, through all nature at all times, with the property of weight or Gravitation. The evidence for Uniformities of Co-existence is special observation of each separate uniformity. From seeing two things coupled together in a few instances, we canndt presume that they are always coupled together; we must observe the coupling in various times, places, and circumstances. If, after a sufficient search, we find no single contradictory instance, we affirm the union to prevail through all nature. 27. In Uniformities of Succession, there has been dis- covered a daw of Uniformity that shortens the labour on enquiry in this department. It is called the Law of Cause and Kffect, or Causation. We may express it thus :— ‘Every event is uniformly preceded by some other event :’ ‘To every event there is some antecedent, which happening, it will happen,’ To say that ‘ Every effect must have a cause,’ is begging the question ; the word cause implies an effect, and the word effect implies a cause. The correct mode of expression is, ‘ To every event there corresponds a prior event, which happening, it will happen ; and which failing, it will not happen.’ ‘ The antecedent may be, and often is, a whole assemblage of circum- stances; as in the case of Health, an effect depending on many conditions. Since there are effects produced by a plurality of Causes, the principle of Uniformity is limited and qualified by that circum- stance. Thus, Death may be caused by starvation, by a violent blow, by poison, &c. It is therefore proper to say that given any of these conditions in sufficient amount, death will follow ; but the occurrence of death does not prove that there has been starvation; it proves only that one of the producing agencies has been present. In the Inductive enquiry into nature, all the causes that may produce each effect are sought out. From the Law of Causation, we deduce consequences such as these :—‘ If the cause be absent, the effect will be absent’—- ‘cessante causa, cessat et effectus,’ ‘If the cause be present the effect will be present,” ‘Whatever agent cannot be removed without the cessation of the effect, must be the cause or part of the cause,’ ‘Whatever agent can be removed without the cessation of the effect is not the cause,’ ‘The cause and effect vary proportionately.’ LAW OF CAUSATION. 21 These various aspects or implications of the Law of Causa- tion are the maxims serving to eliminate and to prove cause and effect in the phenomena of nature. 28. The Law of Uniform Causation appears in a form still more pregnant with consequences, namely, the Law of the Persistence, Conservation, Correlation, or Equivalence of Force. This is a generalization only recently effected. Galileo and Newton may be considered as having established the Law of the Persistence or Conservation of Mechanical Force, that is, force applied to matter in masses. If one ball strikes another and puts it in motion, the force imparted to the second is exactly what is lost to the first. Lavoisier established the persistence of ponderable matter, showing that no atom of matter could be destroyed, and none created. In burning and in evaporation, the particles merely change their positions; they do not abandon their material properties of inertia and gravity. In the present day, evidence has been obtained to show that other forces besides mechanical force, namely, Heat, Chemical Force, Electricity, Nerve Force, have the same numerical persistence; they can neither be created nor destroyed ; They can, however, be mutually converted, at a definite rate. Heat can give birth to Mechanical Force ; Chemical Force can evolve Heat; Electricity is convertible into all the other modes. In this conversion, nothing is lost, and nothing is created ; when heat becomes a mechanical prime mover in the steam engine, it disappears as heat. When mechanical force is seemingly destroyed, as when a cannon ball spends itself on an unyielding mass of stone, the whole momentum of the ball is transformed into heat; at the place of encounter, both the ball and the stone are raised in temperature, exactly in propor- tion to the momentum arrested. This great law of the quantitative persistence of Force, or Momentum, deserves an eminent place in the Inductive Logic. It encompasses and pervades all the natural sciences, each one of which is but a partial development of it. NATURE AND CLASSIFICATION OF KNOWLEDGE. 29. Knowledge is made up of affirmations respecting the order of the world. These affirmations are the subject of Belief, of which the ultimate criterion is Action. 22 NATURE AND CLASSIFICATION OF KNOWLEDGE. Twice two is four; the sun rises and sets; unsupported bodies fall to the ground; heat causes water to boil; animal bodies are nourished by food and air; harmony is agreeable to the mind :—are affirmations, or Knowledge, respecting the universe. We believe them, and show our belief by acting on them. When we desire water to boil, we apply heat; which is our belief of the affirmation. 30. The first requisite of Knowledge is that it shall be brue. An Affirmation is true when, on actual trial, it corresponds to the fact. This is the direct proof. Indirectly, we may test the truth of affirmations by comparing one with another. Wherever there is contradiction, there must be falsehood. 31. Knowledge is either Particular or General. An Affirmation respecting a certain individual thing, as ‘this house is stable,’ ‘ Cesar was brave,’ ‘a certain patient will not recover ’—is a particular or individual affirmation ; it is limited to one subject. An affirmation respecting a whole class or species of things—as ‘an erection is stable when the line of the centre of gravity falls within the base’; ‘all great — generals are brave’; ‘the stiffening of the limbs is a sign of death ’;—are general: affirmations; they extend to instances beyond number. 32. Owing to the frequent recurrence of the same things and the same processes, we can attain to numerous genera- lities. If every individual thing in nature were throughout unique, resembling no other thing, each would need a law to itself. If, instead of a common substance ‘water’ in all seas, rivers, and fountains, there were a thousand different substances, we should have to multiply affirmations accordingly. If, instead of the sixty-three elementary bodies known to us at present, the globe were made up of six thousand elements with their compounds, there would be a great increase in the bulk of our knowledge. If instead of sixty-three, there had been six, we should have been able to comprehend all physical knowledge in comparatively few affirmations. 33. It is desirable to attain knowledge in the highest possible degree of generality. TRUTH AND GENERALITY. 23 The reason is obvious, A general affirmation is a great many particular affirmations in one. It is a vast economy of the human understanding. a he < + _ a as noth £ 7 2 “fe opr eree y id tae! eytt 4Gl ESET ICA ORG BO OS v. s* ‘3 * [oer ry et + 7 hbedyl tee rost gave GS (3s GUAzeE As : a t : i 7 : . af Ps 5st t ietneauy suit -HE- a hee 5 C98 Pre % petrcant ts WSS 34 D. ; 7 s fas é : : 7 x y eygi'y 5 i ‘ Lig \ ‘ - sereweRels VFI WOLD ou { 7 ‘ ry t . at tidvtadts Ou i JiSs 7 bees Ca $x Of aa 6 pert du iolh of ‘ : r) rae hee gee TH pI : rf 4, od jo ora sat brit 7 yy “oi OES =a webakt su ; #4 hi ; ; * ts * ! THis TAs! He ua Tamed ey < Ey x Zi / * 3 > ; . . ’ . ; . :% § >» : : a eax ¢ — 7s 4 . ' ee : e - * , 2 a, BOOK Il. DEDUCTION. CHAPTER L THE SYLLOGISM. 1. The Sytioaism is the fully expressed form of a De- ductive Inference, that is, an inference from the General to the Particular. “ When a step of reasoning or argumentation consists in as- signing, as the proof of an affirmation (or denial), some more general affirmation, it admits of being stated in a peculiar form, in which there is sometimes greater facility in judging of its soundness. The peculiarity of the form of statement consists mainly in this, that everything belonging to the rea- soning is set forth explicitly. Thus, when any one maintains that Mathematics is useful as a mental discipline, and assigns as the proof, that all the exact sciences are useful as mental discipline, the reasoning, which is Deductive, and not Induc- tive, contains these two assertions :—(1) All the exact sciences are useful as mental discipline; (2) Mathematics is an exact science. Both these are indispensable to the conclusion * Mathematics is a mental discipline.’ The first is the general principle, the second an intermediate proposition for applying the general principle to the casein hand. Very often, one of the two propositions is left unexpressed. In the example: ‘this man is a rogue, therefore he is not to be trusted,’ there is an ellipsis of the general principle—‘ rogues are not to be trusted.’ In the form ‘you cannot trust rogues, therefore you cannot trust this man,’ the omission is in the second or apply- ing proposition-—‘ this man is a rogue.’ Say RRS SEL CU Te ERT 134 THE SYLLOGISM. A Deductive reasoning fully and formally expressed is a Syllogism. The following arrangement— (1) All men are fallible, (2) John is a man, (8) John is fallible— : is a regular deductive reasoning, or an argumentation in th syllogistic or complete form. The two first propositions combine to make the proof of the third; they are called the Premises of the reasoning or syllogism ; the third is the point to be proved, and is called the Conclusion. We shall see hereafter that, in the departures made from the regular form of the syllogism, the order of the propositions may be reversed ; the applying proposition coming first, and the grounding proposition second. But whatever form the syllo- gism may assume, one feature can never be absent—a general proposition. This is indispensable. Unless one of the premises be more general than the conclusion, the argument is not deductive. 2. A Syllogism is said to contain three, and only three Terms; the Subject and the Predicate of the Conelusion, and another Term, occurring in both Premises; the Sub- ject of the Conclusion is the Minor Term; the Predicate of the Conclusion, the Major Term ; the term occurring in both Premises, is the Middle Term. By ‘ Terms’ are meant the expressed notions entering into the subjects and predicates of the propositions, A proposition couples or unites two Terms. ‘ X is Y’ contains the two terms X and Y affirmatively conjoined. ‘ Men are not gods’ contains the two terms ‘men’ and ‘gods’ under a negative copula, — In seeking out the Terms, we begin with the proposition to be proved, that is, the conclusion. The sudject of the conclusion is the Minor or smaller term, the predicate the Major or greater term. The propriety of these designations is grounded on the circumstance, formerly adverted to, that in propositions generally, the predicate covers the subject, and other subjects besides; ‘kings are fallible,’ and many other beings besides kings are fallible ; hence ‘kings’ are a smaller group forming part of a larger group ‘fallible ;’ in compass or extent, there- fore, ‘kings’ are a Minor term, ‘ fallible’ a Major term.’* *Sir W. Hamilton complains that these designations are false and erroueous becanse they do not apply to the terms as considered in Com- prehension, There are more men than kings, and so the designations are — THE THREE TERMS. 135 The Middle Term must be sought not in the conclusion, but in the Premises, or proving propositions, and must appear in both. Thus, in the syllogism— ‘Men are fallible, Kings are men, Kings are fallible. The term, absent from the conclusion, and present in both premises, is ‘ men,’ the subject of the first and the predicate of the second. It is called ‘ middle’ because it is the medium or instrumentality for bringing together in the conclusion, the major and minor terms; they being separated in the premises. Also, as regards extent, compass, or denotation, it is inter- mediate thus :—The minor * kings’ is less in extent than ‘ men;’ men are more numerous than kings. Again, ‘men’ is less in extent than ‘fallible beings;’ there being many fallible beings besides men. So ‘men’ being more extensive than the minor term ‘ kings,’ and less extensive than the major term ‘ fallible beings,’ is properly a middle or intermediate term. The grada- tion is represented in a diagram thus :— Fallible, 3 ‘ 3 major, Men, . B : é middle, Kings, : ; j minor. Although the syllogism contains three propositions, each with two terms, making six terms in all; yet, in virtue of the double occurence of each, there are in reality only three terms, ‘The example shows :— The Middle term in both premises. The Minor term in the conclusion and in one premise. The Major term in the conclusion and in one premise. __ 3. In the Syllogism, there are Three, and only three, Propositions, namely, the two Premises and the Conclusion. The Premise containing the Major Term and the Middle Term, is called the Major Premise ; the Premise contain- ing the Middle Term and the Minor Term, is called the Minor Premise. In the foregoing example, the Premise first in order contains applicable to the extension of the terms; but, he argues, more attributes are connoted by the term ‘kings’ than by the term men, and so major and minor are inapplicable to the comprehension. In criticism of this view, it may be said that confessedly the designations major and minor are applicable to the terms viewed in their compass or extension, that these terms are used in that sense, that they cannot be used without confusion in both senses, and that Hamilton has shown no good reason for invert- ing the common usige. eis 136 THE SYLLOGISM. the Major term ‘fallible,’ together with the Middle term, ‘men, —‘ men are fallible;’ this is the Major Premise. The Premise second in order contains the Middle term, ‘ men,’ and the Minor term, ‘ kings,’—‘ kings are men ’—and is the Mior Premise. We find it convenient to represent the forms of the syllogism by letters or symbols, thus :—Let X be the minor term, Y, the middle term, Z, the major term; then— All Y is Z All X is Y All X is Z } is a syllogistic form on the basis of affirmation ; that is to say, the universal proposition in the first premise is affirmative, and the conclusion is affirmative. An example on the basis of negation is— No Y is Z All X is Y No X is Z, or, by Hamilton’s still more expressive symbols,— S (subject of conclusion, mimor term), M (middle term), P (predicate of conclusion, major term) ; All M is P No Mis P All S is M All § is M All S is P No S is P. 4, Syllogisms, or Syllogistic forms, are divided into FIGURES, according to the position of the Middle Term. There are, in all, Four Figures, | | The First Figure is exemplified in the forms hitherto em- ployed. In it, the Middle Term is Subject in the Major Pre- mise, Predicate in the Minor Premise. . Yis Z M is P M — Wi =) Sane, —M X is Z Sis P ; | The idea implied under ‘ Figure’ is borrowed from. the Figures of Rhetoric, which are departures, for effect, from the — the plain and ordinary forms of speech. On this analogy, however, as remarked by Hamilton, there ought to be some one regular or stundurd form, from which all other forms are deviations or departures, thence properly called ‘ Figures.’ Such standard form is what is mis-named the ‘First Figure,’ which is the pure type of a deductive argument The Major or First Premise is the universal proposition indispensable in pee THE FIGURES. 137 deduction, the Minor or Second Premise is an affirmative pro- position, whatever may be its quantity. As to order, the Uni- versal is placed first, as being of the two premises the funda- mental or chief; the use of the second premise, the minor, being to apply the first to a particular case. ‘ All thieves are deserving of punishment,’ is applied to a particular instance, by means of an affirmation bringing the instance within the sweep of the rule, that is, declaring such a one to be a thief. This is the function of the minor. In the Second Figure, or the first departure from the normal syllogism, the middie term is predicate in both premises “is Y PisM —M XisY SisM —M Here there is an obvious inversion of the. natural order of things. In the major premise, Z is Y, P is M, the largest term is made the subject, and the middle term the predicate, of the proposition. Ifthe proposition be affirmative, this change is not compatible with universality, and therefore the proposition can- uot be the major in the same sense as in the standard syllogism. If the proposition be negative, there is only a harmless con- version ; we may, for ‘ no Y is Z,’ substitute ‘no Z is Y ;’ ‘no men are gods,’ ‘no gods are men.’ This is an insignificant and, for the most part, useless alteration of the negative form of the standard syllogism. Two of the four forms of the Figure (called Moods) are fashioned out of this trivial altera- tion. The two other forms containing affirmative majors in- volve still greater changes of the standard furm. In one, the major is not the universal proposition required as the basis of the deduction, but the applying proposition, which in the first figure is the second or minor premise. In the conciuding form, there is a much greater distortion, consequent on present- ing the normal premises in obverted forms, In the Third Figure, the middle term is subject in both premises. WA, 2 M is P M— Y is X Mis§ M— Here the major stands as in the first, or normal figure. The minor has ity terms transposed; the middle term is subject, and the minor term predicate. As before, this is a harmless change, if the proposition be a universal negative ; in which case, however, the minor prémise must be the universal or ground- img proposition, and not the applying proposition ; so that, as compared with the standard form, there is an inversion of the order of the premises. Ifthe minor be affirmative, either it ae > _— 138 THE SYLLOGISM. must be particular, or there is some distortion, rendering the terms different in fact from what they are in appearance. In the Fourth figure, the position of the middle term is the first figure reversed ; ; it is predicate in major, and subject in minor. ZLisY PisM —M Yis X Mis§S M — This double inversion of the order of the terms implies still greater deviations from the primary form. The inversion is possible by such devices as above described for the smaller inversions in the second and third figures. d. Each Figure has a certain number of distinct fhe called the Moods, or modes of the figure. The variation of mood is determined by the variety of the propositions con- tained, as regards Quantity, and Quality. The order of the terms is fixed for each Figure; but the propositions constituting the premises and the conclusion may, within certain limits, be of one or other of the four forms, A, I, E, O. The First Figure, the normal syllogism, has Four Moods, The First Mood is composed of three universal affirmations. All YisZ) A, A, A All men are fallible. All Xis Y (Barbara) All kings are men. All X is Z All kings are fallible. In the Second Mood, The Major is a universal negative —E, The Minor The Conclusion a universal negative _k. No Y isZ) H, A. E No men are gods, All X is Y (Cedurent) All kings are men, No X is Z No kings are gods. The Third Mood is the first, with a particular minor, and particular conclusion :— All Y is Z Ae toed All men are fallible. Some X is Y ' (Dari) Some beings are men. Some X is Z Some beings are fallible. The Fourth Mood is a similar variation on the second; par- ticular minor and particular conclusion {— No Y is Z HK, I, O No men are gods. Some X is Y (Ferio) Some beings are men. Some X is not Z Some beings are not gods. FIRST FIGURE. 139 These four moods are obviously reducible to two; the third and fourth being mere unessential varieties of the first and second. The two comprehensive forms may be stated thus :— All Y is Z No Y is Z Allor some Xis Y All or some X is Y All or some XisZ§ No Xis Z. . Some X is not Z. _ The first form is the normal type of all deduction for an affirmative conclusion ; the second, the type for a negative conclusion. They present the deductive process in its regular order :— First, a universal proposition, as the ground proposition of the reasoning (Major premise) ; Secondly, an afiirmative and applying proposition (Minor premise) ; Lastly, the universal truth applied to the particular case (the Conclusion). We desire to prove that kings are fallible, by applying to them the principle of the fallibility of all men. The major states the principle, the minor applies it. And so for a negative con- clusion, There cannot be any valid deduction whatsoever but must conform to the foregoing type; whatever variation may be made, this is at the bottom. The Seconp Figure has likewise four Moods. In the First Mood, The Major is a universal negative —H. The Minor a universal affirmative—A. The Conclusion a universal negative —EH. All X is Y > (Cesare) All kings are men. No X is Z No kings are gods. | This is a case where advantage is taken of the simple con- version of the universal negative to make a trivial departure from the standard (negative) syllogism. Only a slight change is necessary to reconvert the present mood to the second mood of the First Figure ; for ‘No Yis Z’ ‘No menare gods,’ we are at liberty to substitute ‘No Z is Y,’ ‘No gods are men,’ which is the whole difference. No Zis Y H, A, EK, No gods are men. In the Second Mood, The Major _ is a universal affirmative—A, The Minor @ universal negative—H, 140 THE SYLLOGISM. The conclusion a universal negative—H. All Zis Y ) A, E, E, All kings are men. No X is Y > (Camestres) No gods are men. No X is Z No gods are kings. A much greater variation from the standard (negative) is observable here. The grounding proposition, which must be universal, is the minor premise: so that there is an inversion of the normal order of the premises. Moreover, the same pro- position has been converted simply, from the form ‘ No men are gods ;” and the conclusion is likewise the converse of the conclusion in the regular syllogism. By first restoring the order of the premises, and next re-converting two universal negations, we have the normal negative syllogism (Celarent). No men are gods. All kings are men. No kings are gods. The grounding universal is the negative proposition, ‘ no men are gods’—the applying proposition is ‘all kings are men.’ In the Third Mood, The Major is a universal negative —H, The Minor a particular affirmative—I, The Conclusion a particular negative —O, Some X is Y (Festino) Some beings are men. Some Xis not Z Some beings are not gods. Here we remark the same trivial departure from one of the standard forms, as in the first mood. The universal negative— the major in the fourth mood of the first figure (Ferio)—is simply converted (No Y is Z, into No Z is Y; no men are gods, into no gods are men), No Gis Y bi I,QO Nogods are men. In the Fourth and last Mood, there is a more serious dis- tortion. The Major is a universal affirmative—A, The Minor a particular negative —O, The Conclusion a particular negative —O, All Z is Y A,O,O All gods are men. Some X is not Y >(Baroko) Some beings are not men. Some X is not Z Some beings are not gods. A glance at the premises shows us that they are not at bottom what they appear on the surface. There is indeed a universal proposition in the major premise, which might auswer for the ground proposition ; but then the other pre- SECOND FIGURE. 14] mise, in that case the applying proposition, is negative, which is not allowable. The real fact is that the affirmative major, is a negative (universal) in disguise, and the negative minor, E an affirmative in disguise. The disguises may be laid open, thus— All Z is Y No not-Y is Z Some X isnot Y Some X is not-Y Some X isnot Z Some X is not Z The true middle term instead of being Y, is the negative of _Y; or not-Y (U—Y) This is the key to the distortion. The remedy consists in (1) obverting and converting the major—All Z is Y, which becomes No not-Y is Z; and (2) in obverting the minor—Some X is not Y, Some X i is not-Y. There thus emerges a form of the third mood of the first figure (Ferio), with not-Y, as the middle term. This mood cannot be reduced to a mood of the First Figure without Obversion. The older logicians sought to establish its validity by a cumbrous process technically known as Reductio ad impossibile. They showed that the conclusion cannot be supposed false, without leading to a contradiction of one of the premises, which are given as unimpeachable. Thus :— AllZ is Y Some X is not Y Some X is not Z If ‘Some X is not Z’ be declared false, the universal ‘ All X is Z,’— which is its contradictory,—must be admitted as true. Taking this new proposition, ‘All Xis Z’ along with the major of the original syllogism, ‘ All Z is Y,’ we reach the conclusion that ‘All X is Y.’ Thus :— All Z is Y AllX is Z All X is Y is a syllogism in Barbara, But we know from the original premises that ‘Some X is not Y ;’ it cannot therefore be true that ‘All X is Y.’ One of the premises of the above Burbara must be unsound. The major ‘ All Z is Y,’ is one of the origi- nal premises, granted as true; the error must lie on the minor, ‘All X is Z.’ Now this is the proposition taken on trial; and its truth being shown to be incompatible with the truth of the original premises, its contradictory, ‘Some X is not Z’ must be true. And ‘Some X is not Z’ is the conclusion in question; which is thus shown to be valid. The Tuirp Ficure has six Moods. 142 THE SYLLOGISM. In the First Mood, The Maju is a universal affirmative—A. The Minor a universal affirmative—A. The Conclusion a particular affirmative—lI. All Y is Z A, A, I All men are fallible. AllY is X }+(Darapti) All men are living beings. Some X is Z Some living beings are fallible. The only departure, in this instance, from the standard syllogism (with a particular minor, Dariv) is the universality . of the minor, All Y is X. By simple conversion, this premise becomes Some X is Y, and the syllogism is then the same as the third mood of the regular syllogism. This figure is quoted as a useful form. Certain reason- ings are considered to fall more readily into the above ar- rangement, than into the corresponding mood of the First Figure. The Second Mood contains an inversion of the order of the Premises. This distortion is altogether gratuitous; it serves no purpose but to seem a variety. Some Y is Z)I, A, I Some men are kings. All Yis X }+(Disamis) All men are fallible beings. Some X is Z Some fallible beings are kings. Here, if we redress the order of the premises, and simply convert the new minor—Some Y is Z, into Some Z is Y,— there arises a regular affirmative syllogism, with a particular minor (Daviz) ; there being only the speciality that the minor and the major terms have changed places, thus :— All Y is X All men are fallible beings. Some Zis Y Some kings are men. From this the conclusion would be ‘Some Z is X,’ ‘some kings are fallible beings,’ which, however, by simple con- version, gives ‘Some X is Z,’ ‘some fallible beings are men.’ : The Third Mood is one of the trival variations of syllogistic orm. All Y is Z A, I, I, All men are fallible. Some Y is X }(Datisi), Some men are kings. Some X is Z Some kings are fallible beings. There is no departure here, from the regular syllogism (affirmative, with particular minor Darii), but in the minor premise, which is Some Y is X, instead of its equivalent, Some A198.) ; THIRD FIGURE. 143 The Fourth Mood is exactly the counterpart of the previous mood, with a negative major. No Y is Z K, A,O. No men are gods. All Y is X (Felapton) All men are living beings. Some X isnot Z Some living beings are not gods, This differs from the negative mood of the first figure, with a particular minor (Ferzo), only in having a universal minor, which, by conversion, becomes particular, Some X is Y ; the syllogism is then exactly the fourth mood of the standard syllogism. The Fifth Mood is, in point of distortion, the parallel of the last mood of the Second Figure (Baroko). Both the premises appear different from what they are in reality. Some Y is not Z) O, A, O, Some men are not kings. All Y is X (Bokardo) All men are fallible. Some X is not Z Some fallible beings are not kings. If we look for a universal premise, to supply the ground proposition, we seem to find it in the minor; but then the other premise is negative, and therefore is not the applying proposition. As in Baroko, we must transfigure both pre- mises. ‘The present major is made affirmative, by obversion,— ‘Some Y is not-Z,’ and is then converted, ‘Some not-Z is Y.’ This is taken as the minor premise, the other being the major, thus :— All Y is X All men are fallible. Some not-Z is Y Some not-kings are men. which are the premises of the regular syllogism (affirmative, with particular minor, Darii):and would give as a conclusion, Some not-Zis X, Some not-kings are fallible, or, by conversion and obversion, Some X is not Z, Some fallible beings are kings. As in the case of Barvko, the older logicians could not refer this mood to the First Figure, and applied as a test of its validity the Reductio ad impossibile. The process need not be repeated at length. We assume the universal contrary to the conclu- sion, and taking it along with the given minor, evolve a pro- position that contradicts the given major: and argue, as under Baroko, that the universal contrary of the conclusion must be false, and therefore the conclusion itself valid. The Sizth and last Mood is the negative counterpart of the third, and should have been placed after the fourth; it is an equally trivial departure from the regular syllogism (negative, with particular premise, erio). 144 THE SYLLOGISM. No Y is Z HK, I, O, No men are gods. Some Y is X (Ferison) Some men are living beings. Some X is not Z Some living beings are not gods, The simple conversion of the minor ‘Some Y is X,’ into ‘Some Xis Y,’ ‘some living beings are men,’ —reproduces Ferio, in the standard figure. . The Fourrn Ficure has five Moods. In this figure, there is an inversion of both premises as compared with the regular syllogism. This, of course, produces apparently a great degree of distortion ; but there is very little in reality. In three of the moods, the inversion is caused by the transposition cf the — premises ; this rectified, they need only the simple conversion of one or more of the propositions to make them standard syllogisms. Thus, to take the Furst Mood, which has universal affirmative premises, and particular conclusion :— All Zis Y | Aetievd All kings are men. All Yis X }(Bramantip) All men are fallible. Some X is Z j Some fallible beings are kings. Transpose the premises, and there emerges a standard syllo- gism (affirmative, with universal minor, Barbara)— All Y is X All men are fallible. All Zis Y All kings are men. The conclusion from these premises is— All Z is X All kings are fallible. This conclusion, converted by limitation, gives— Some X is Z Some fallible beings are kings. The Second Mood is, if possible, still closer to a regular syllogism, when the order of the premises is changed. All Z is Y ) A, H, EH, All kings are men. No Y isX (Camenes) No men are gods. No X is Z No gods are kings. Restore the order of the Premises :— No Y is X No men are gods. All Zis Y All kings are men. These are the premises of the regular syllogism (negative, with universal minor, Celarent), and the conclusion is No Zis X No kings are gods, Whence No X is Z No gods are kings. The Third Mood is constructed on a similar plan; the devia tion from regularity being caused by transposed premises :— + a ae FOURTH FIGURE. 145 Some Zis Y)I, A,I Some living beings are men. All Yis X }+(Dimaris) All men are fallible. Some X is Z Some fallible objects are living beings With re-transposed premises,— All Y is X All men are fallible. Some Zis Y Some living beings are men. Whence by Darii, in the standard Figure, the conclusion is,— Some Z is X Some living beings are fallible. - Or Some X is Z Some fallible objects are living beings. The fourth and fifth Moods attain their peculiar form, not through the inverted order, but through the conversion, of the Premises. The Fourth runs thus .— No Zis Y ) E, A,O No gods are men. All Y isX (Fesapo) All men are living beings. Some X is not Z Some living beings are not gods. Convert both premises, the major simply, the minor by limita- tion :— No Y is Z No men are gods. Some Xis Y Some living beings are men. These are the premises of the negative form in the first figure, with particular minor (Ferio), whence Some X is not Z Some living beings are not gods, The Fifth and last Mood differs from the fourth only in having a particular minor; the universality of the minor in the fourth being superfluous, as leading to no stronger conclu- sion than the present form, The process of assimilation to Ferio is precisely the same— No Zis Y EH, I, O, No gods are men. Some Y is X (Fresison) Some men are living beings. Some X is not Z J- Some living beings are not gods. Convert both premises simply :— No Y is Z No men are gods. Some X is Y Some living beings are men. The premises are now in Ferto, whence, Some X is not Z Some living beings are not gods. The modes of the Fourth Figure, are thus, with the appear- ance of great inversion, mere varieties of the primary Figure. The transposition of the order of the premises is the most insignificant of all the alterations made on a syllogism. It signifies nothing to the reasoning, in what order the premises are stated. The three first moods depart from the standard moods in very little besides. The two last moods, as has 146 THE SYLLOGISM. been seen, present both premises converted ; and the first of the two is superfluous, even as a form. The prime importance of the Syllogism attaches to its standard forms, that is, to the First Figure. In it we learn the essential structure of each valid deduction—a universal ground proposition, affirmative or negative, and an applying proposition, which must be affirmative. These appear, in the standard syllogism, in the order stated—first, the ground proposition (the major premise), secondly, the applying propo- sition (the minor premise). In the subsequent figures, these are sometimes transposed; and, in two forms, Baroko and Bokardo, they are greatly disguised. The ground proposition is called by Hamilton the sumption, the applying proposition, the subsumption (more strictly, the subsunwng proposition). It is not easy at first sight to point out any of the forms of the 2nd, 3rd, or 4th Figures that are of special importance in the conduct of reasoning or argumentation. The Fourth Figure is the least important of all; next, perhaps, the second, which, with the exception of Baroko, scarcely disguises the standard forms. The Third Figure is useful in overthrowing universal oppositions, by exceptions or contradictory particulars. It was pointed out by Aristotle, that in the First Figure only have we conclusions in all the forms, A, E, I, O. The Second _ Figure is restricted to negative conclusions; the Third Figure, to particulars, The Fourth Figure, which Aristotle did not re- cognize, does not admit of a universally affirmative conclusion. In explanation of the possible uses of the Figures after the first, two circumstances may be remarked that lead to depart- ures from the typical form. In the first place, the order of subject and predicate in either premise, and consequently the figure wherein the syllogism naturally falls, may vary with the idea uppermost in the mind of the reasoner. ‘ The best form of Government is Government by a plurality of persons,” and “Government by a plurality of persons is the best form of Government,” are variations of the same statement that would cause a variation of Figure. In the second place, the extent of the middle term relatively to the extent of the major and minor, gives rise to variations. When the middle term is larger than either major or minor, it naturally forms the predicate both of the major and of the minor premise, producing a syllo- gism of the Second Figure. When, again, the middle term is smaller than either, it naturally forms the subject of both pre- mises, producing a syllogism of the Third Figure, _ . THE MNEMONIC LINES, 147 Tt has been shown in the detailed explanation above given, that the fifteen moods of the three last Figures are strict equivalents of the Moods of the First Figure, and therefcre have the same validity as these standard moods. The demon- stration of this equivalence is technically called the Repucrioy of the syllogisms, or their revocation to the primitive forms of affirmative and negative predication. The necessity of Reduc- tion depends upon the nature of the proximate canons adopted for the syllogism. If those canons are applicable only to the First Figure, then, before we can test the validity of irregular moods, we must reduce them to moods of the First Figure. Ifthe proximate canons are applicable directly to all syllogistic moods, reduction is unnecessary. Order of the Premises. Many logicians have inverted the order of the premises, commencing with the minor. Thus— All X is Y All Y is Z All X is Z. This is the form that seems most convenient and convincing, in a chain of reasoning, as in the Sorites. It suits the particu- lar form of the syllogistic axiom, expressed by ‘the mark of a mark is a mark of the thing;’ X is a mark of Y, Y is a mark of Z; hence X isa mark of Z. It, however, disguises the gennine type of Deductive Reasoning, which ought to be exhibited in the standard syllogism, even, if we depart from it in the other figures. The universal proposition is rightly put forward as the foundation of the reasoning, to which should follow the applying premise, or the minor. In the moods of the 2nd, 3rd, and 4th Figures, inversion of premises occurs as one form of departure from the First or regular figure. Aristotle’s mode of writing Barbara is— A is predicated of all B B is predicated of all C A is predicated of all C— where the minor is given first, and the propositions inverted in the wording; ‘A is predicated of all B,’ is the same as All Bis A. 6. The Mnemonic Lines of the Syllogism contain the statement of the different moods, with the manner of reduc- ing to the First Figure, those of the three last Figures. To each of the moods, as described, a technical name has been appended, Barbara, Celarent, &c. These words have 148 THE SYLLOGISM. been constructed for showing the constituent propositions of each mood, and how the moods of the 2nd, 8rd, and 4th Figures may be transmuted into moods of the lst Figure; as in the process actually gone through in the foregoing explana- tion. The names are made up in lines of Latin hexameter verse. Among artificial aids to memory, they stand unrivalled ;:— Fig. 1. bArbArA, cE]ArEnt, dArII, fErlOgue, prioris. Fig. 2. cHsArk, cAmEstrHs, fEstInO, bArOkO, secundae. Vig. 8. tertia, dArAptl, dIsAmIs, dAtIsI, fHlAptOn, bOkArdO, fErIsO, habet: quarta insuper addit. Fig. 4. brAmAntIp, cAmEnKs, dImArIs, fEsApO, frEsIsOn, Hach of these names represents a mood; the three capital letters in each standing for the three propositions, as symbo- iized in their Quantity and Quality by the forms A, H, I, O. Of the smaller letters, or consonants, 7, ”, t, are meaningless or dumb letters. The consonants that commence each name —b, c, d, f—indicate the moods in the First Figure that the several moods in the other Figures are reduced to; Bramantip is reduced to Barbara, Cesare to Celarent, and so on. The consonants m, s, p, and k, which signify the processes of Reduc- tion: m indicating that the premises have to be transposed ; s indicating simple conversion ; p conversion by limitation, or per accidens; while k is the symbol of reductio ad impossibile. The application of eack is to the vowel immediately preceding. hus, in Bramantip :— All Z is Y All Y is X Some X is Z— we learn from m that to obtain the form of Barbara, the first mood of the First Figure, we must transpose the premises. And as we should then see ourselves entitled to conclude ‘ All Z is X,’ it has further to be signified by p, that to obtain the conclusion ‘Some X is Z,’ we must make a limited conver- sion. So in Fesapo to obtain Ferio of the First Figure, we must convert E simply, and A by limitation. Although the method of reduction ad impossibile may be applied to any of the irregular moods, the letter / occurs only in two, Baroko and Bokardo, these being the only two that the logicians found irreducible by the processes of transposition and conversion. 7. The rules or Canons of valid reasoning are variously stated. They are proximate rules, being derived from the fundamental axioms of all Deduction, CANONS OF THE SYLLOGISM. 149 Common Canons.—These are six in number.* (1) Every Syllogism has Three, and only three, Terms. (2) There must be T'hree, and only three, Propositions. (3) The Middle Term must be distributed once, at least, in the premises. That is to say, the Middle Term must be a universal in one or other of the premises. It must be the subject of a univer- sal proposition (4/1 Y is Z, No Y is Z), or else the predicate of a negative proposition No X is Y, Some X is not Y. As the subject of a particular proposition (Some Y is Z, Some Y is not-Z), and as the predicate of an affirmative proposition (All X is Y, Some X is Y), the middle term Y is particular, or un- distributed. By a reference to the nineteen valid syllogisms, it will be seen that in each of them the middle term is distributed once in the premises. Thus, in the First Figure throughout, it is the subject of the major, which is a universal (All Y is Z, No Y is Z). This is as it ought to be in the standard syl- logism. In the Second Figure, it is distributed three times in the major, and once in the minor (Some X is not-Y). In the Ist, 2nd, 4th, and 5th moods of the Third Figure, it is distributed in the minor; being also distributed in the major, in the Ist and 4th. In the Fourth Figure, it is distributed in the minor, in all the moods but the last. In the following couples, there is no distribution of the middle term (Y), and consequently none of the couples could stand as premises in a valid deduction, All Z is Y Some Z is Y All Z is Y All X is Y Some X is Y Some Zis ¥ Some Y is Z, Some Y is not Z All Zis Y All X is Y, All X is Y Some Y is not X. A pretended syllogism, in such forms as these, or any form where the rule does not hold, is said to exemplify the fallacy of undistributed middle. Such are the following :— Some Y is Z Some men are kings. All X is Y All cooking animals are men. All X is Z All cooking animals are kings. Other examples will occur afterwards. (4) No term undistributed in the premises must be distributed in the conclusion. In other words, there must not be a greater * After Whately, who gives them as a condensation of the twelve canons of Aldrich. 150 THE SYLLOGISM. quantity attaching to any term in the conclusion, than is attached to the same term in the premises. If X be particular in the premises, so must it be in the conclusion ; the same with “ This condition, likewise, is fulfilled in the valid syllogisms. hus :— All Y is Z No Y is Z. All X is Y Some X is Y. All X is Z Some X is not Z. In the first of the two, the subject of the conclusion is universal in the minor premise, and may therefore be universal in the conclusion ; in the second, it is particular in the minor, and must be particular in the conclusion. Iu both, the predi- cate of the conclusion is particular in the premises, and must be particular in the conclusion. So if, in Dart, a universal conclusion were drawn, it would be invalid. All Y is Z All men are mortal. Some X is Y Some extended things are men. All X is Z All extended things are mortal. We may have premises, free from the last-named vice of undistributed middle, yet made to yield a false conclusion by overstepping the present rule, or raising a term of particular quantity, in the premises, to the rank of universal quantity in the conclusion. To this error is given the name, Illicit process ; and according as the unduly extended term occurs ir the major or in the minor premise, the error is called illicit process of the major or illicit process of the minor. In the foregoing instance, the illicit process is in the minor. We give an instance of illicit process of the major. All Y is Z All men are fallible. Some X is not Y Some beings are not men. No X is Z No beings are fallible. The major term ‘fallible,’ being the predicate of an affir- mative proposition, is particular or undistributed ; in the con- clusion, it is the predicate of a negative proposition, and is therefore distributed. (5.) There can be no conclusion drawn from negative premises. No Y is Z No men are gods NoXis Y No trees are men ° do not supply the materials for a deductive inference. The reason of this is already apparent from what has been said as to the applying proposition, which must always ajirm. To know only that two things are each excluded from a third thing is to know nothing concerning their mutual relation. (6.) If one premise be negative, the ‘conclusion must be negatine, HAMILTON’S CANONS. 151 This is illustrated throughout the series of valid syllogisms. If one premise be negative, all that is predicated concerning one of the terms is its exclusion in whole or in part from the middle term: we cannot, therefore, conclude through the medium of the middle term anything about its total or partial co-extension with the other term. _ In order to facilitate the detection of unsound syllogisms, the two following rules, directly deducible from these canons, are also enounced. A. There is no inference from particular premises. Some Y is Z Some Y is Z Some X is Y Some X is not-Y give no conclusion. The first example contains an undistri- buted middle; and the weakest inference drawn from the second (Some X is not Z) would contain an illicit process of the major. B. If one premise is particular, the conclusion must be par- ticular. As in Darit, Ferio, &c. Any attempt to extract a universal conclusion where both premises are not universal would incur either undistributed middle or illicit process. This last canon, and also the Sixth, are embraced in one statement—‘ The conclusion always follows the weaker part.’ 8. Hamilton’s Canons. These are three in number, The first contains the 1st and 2nd of the foregoing list (Three Terms and Three Propositions). The two others are as follows :— II. Of the Premises, the Sumption must in Quantity be defimite (i.e. universal or singular); the Subsumptioa in Quality affirmative. As Hamilton means by the Sumption the universal or ground proposition, and by the Subsumption, the applying or subsuming proposition, this is declaring the characters of the standard syllogism. It appears that, through all the mutations of syllogistic moods, there must always be one universal proposition (or else a definite singular), and one affirmative proposition. (The meaning of the alternative, a singular propo- sition will appear afterwards). III. The conclusion must correspond in quality with the Sumption, and in guantity with the Subsumption. Whatever be the quality of the Universal or ground propo- sition, that must be the quality of the conclusion; the one 152 THE SYLLOGISM. being affirmative the other is affirmative; the one negative, the other is negative. Again, the quantit y of the Applying proposition is the true quantity of the conclusion; universal giving universal, and particular giving particular. These two rules of Hamilton’s are given as the equivalent for Whately’s four last. They have the advantage of placing ina due prominence the fundamental structure of deductive reasoning, which is altogether invisible in the foregoing canons; - but they are uot readily applicable to the more distorted figures. Before using them, we must first discover which term contains the sumption, and which the subsumption; and for this, we must refer to the directions given respecting the irregular moods. In short, we must first redress the inver- sions and distortions of the irregular moods, which is substan- tially to go through the process of reducing each to the first figure. 9. The rules of the syllogism given in the form of separate canons for each figure. For the First or standard Figure, the canons of Hamilton are the most suitable expression. For each of the other Figures, special canons may be framed according to the nature of the F igure. . Thus, in the second Figure, it can be shown that, (1) One premise ts neg gate. (2) The major premise is wniversal, The proof is easy. (1) If both premises were affirmative, the middle term being the predicate of both premises, it would be undistributed. Again, (2) ifthe major were particular, the weakest conclusion that could be drawn, Some X is not Z, involves illicit process of the major. It follows from the first of the two rules (One premise must be negative) that, in this Figure, it is possible to prove negative conclusions only. In the Third Figure, the canons are, (1) The minor premise is affirmative. (2) The conclusion is particular. If the minor premise were negative, the conclusion must be negative, and the major term affirmative, which would involve an illicit process of the major. Again, the conclusion must be particular, whether the syllogisms be affirmative or negative. The minor premise being affirmative, there cannot be @ uni- SPECIAL CANONS OF THE FIGURES. 153 versal affirmative conclusion without illicit minor. In a uni- versal negative conclusion both terms are distributed: and they cannot both be distributed in the premises, unless both premises were negative, which could not be. In the fourth Figure, (1) Ln the negative moods, the major is universal. Some Z is not Y, Some Z is Y All Y is X, No Y is X - could not yield even particular conclusions, without illicit process of the major. We should have to infer—Some X is not Z: and Z is undistributed in the premises in consequence of the particularity of the major. (2) Uf the major is affirmative, the minor is universal. A particular minor to an affirmative major would give All Z is Y, All Zis Y Some Y is X, Some Y is not X both forms containing undistributed middle. (3) If the minor is negative, both premises are universal. Try ' All Zis Y, Some Z is Y, Some Y is not X, No Y is X. There is, in the first form, undistributed middle; and in the second, the weakest conclusion, Some X is not Z, contains illicit process of the major. This rule is implied in the two preceding. By the First rule, the Major is universal, because the mood is negative. By the Second rule, the Minor is universal, because the major is affirmative. (4) Ifthe minor is affirmative, the conclusion is particular. With minor affirmative, we have— . All Z is Y, NoZis Y All Y is X, All Y is X, In both cases, a universal conclusion would be attended with illicit process of the minor. 10. That the valid moods are those above given, and no more, is shown by testing all the other possil.e moods ac- cording to the syllogistic canons. The possible moods may be arrived at by computing the possible groups of threes that can be made out of the four pro- positional forms—A, I, E, O. Now, taking the premises alone, there are sixteen different couples that can be made from these four letters. A,A I, A HE, A O, A AI (41) EI (6,1 154 THE SYLLOGISM. A,E I, E (E,E) (0,5) A,O (1,0) (8,0) (0,0). Of these sixteen forms, we can reject at once, as inad- missible, first, those that have both propositions particular— II, 10, OI, OO. Wecan farther reject those that have both negative—E H, E O, O E (O O is rejected on the pre- vious ground). After these seven rejections, there are nine forms remaining. For a farther sifting, two methods are open to us. First, let us try whether every one of the nine couples may stand as premises to conclusions of all the forms, A, I, H, O. A, A, A (A, I, A) (A, B, A) to AnQ,A) A, Ayddovos aaj ©) ody eal (A, A, EH) (A,I, B) A, E, H (A, O, B) - (A, A, O) (A, I, O) A, E, O A, O, O and so on through the remaining five forms. Now, by applying the canon that requires a particular con- clusion when one of the premises is particular, we exclude two in the second column—A I A, A I H, and two in the fourth— AOA, AOE. By applying the canon that requires a nega- tive conclusion when one of the premises is negative, we ex~ clude, in the third column, A E A, A E 1; in the fourth column, A O J (also A O A excluded on the previous ground), Although no express canon is laid down requiring an aflirma- tive conclusion from affirmative premises, such canon could be proved to be valid ; and by means of it, two exclusions would be made in the first column—A A H, A A O, and one farther exclusion in the second. Hence, of the sixteen forms, six only survive these successive purgations By a similar operation, extended to the remaining twenty forms, it would appear that there are in all twelve forms admissible ;— AAA, AAI AEH, AEO, All, AOQ HAH, EAO, EIO, IAD, LEO 40a If these twelve forms were each admissible in all the Figures, there would still be forty-eight valid syllogisms. But, by stating them under the successive figures, their ranks are thinned still farther. Thus, in the First Figure, A A I and> A EO are superfluous because they infer a smaller conclu- sion when a larger could be drawn; with the premises A A, we can infer A (Barbara); with A E, we infer EH (Celarent). Of the remaining ten, six would involve violations of funda- mental canons, as may be seen by expressing them in full, Two examples are enough. Thus, A E E gives— All Y is Z All men are mortal SIFTING OF THE VALID MOODS. 155 No X is Y No molluscs are men No X is Z No molluscs are mortal which contains illicit process of the major. The same would hap- pen under a particular conclusion, as in A, H, O. Again, 1,A, 1— Some Y is Z Some fishes are sharks All X is Y All salmons are fishes * Some X is Z Some salmon are sharks— has the middle term undistributed. By operating in this manner, we reduce the valid moods of the First Figure to the four formerly given—A A A, E A H, AITEIO. : The same process repeated for the remaining figures has the result of reducing the admissible forms to those actually given in the scheme of the syllogism. ! The other method of elimination is to apply the special canons of the figures to the nine forms of unobjectionable premises, A A, Al, &c. By the canons of the standard syllo- gism, the major is universal and the minor affirmative ; whence the forms, A E, A O,J A, O A, are rejected at once ; and there remain only the four, A A, AI, HK A, EI, corresponding to the four moods of the First Figure. For the Second Figure, the canons (One premise is negative; the major is universal) exclude A A, AI, I A,I H, OA; leaving A E (Camestres), AO (Baroko), E A (Cesare), EK I (Festino). For the Third Figure, the first canon (The minor is affirmative) excludes A E, A O, IE; and there remain A A (Darapti), A I { Datisi), I A (Disa- mis), EH A (Felapton), EH I (Lerison), O A (Bokardo). For the Fourth Figure, the first canon (In the negative moods, the major is universal) excludes I H,O A. The second canon (If the major is affirmative, the minor is universal) excludes AI, AO. The remainder are A A (Bramantip), AB (Camenes), I A (Dimaris), EH A (fesapo), EK I (Fresison). AXIOM OF THE SYLLOGISM. 11. Logicians have aimed at reducing the whole of the special canons or rules of the Syllogism to one comprehen- sive Law or Principle. The oldest form of this principle is that named the Dictnm de omni et nullo. ‘ Whatever is affirmed or denied of a class, is affirmed or denied of any patt of that class,’ As stated, this maxim seems merely one of the forms of Im- mediate Inference :—‘all men are mortal,’ hence ‘this man, ten men, some men, are mortal.’ ‘his, however, is not the 156 AXIOM OF THE SYLLOGISM. form actually assumed by the syllogism. We have to prove that some object is mortal, not expressly named a man, but designated by some other title, as ‘king.’ We cannot say ‘men are mortal,’ therefore ‘ kings are mortal ;’ such an infer- ence can be made only through an intermediate assertion, ‘kings are men.’ | Another defect has been pointed out in the diclwm: namely that it proceeds upon the old erroneous view of a proposition, the reference of a thing to qa class. This, however, might be got over by understanding ‘ class’ to mean the class indefindte, marked by the connotation of the class name. Practically, such must be the case; we have no means of pointing out the class ‘men,’ except as the possessors of human attributes. _ Considering the dictwm as the basis of all Deductive Reason- ing, we might amend it thus :—‘ whatever is true of a whole class (ciass indefinite, fixed by connotation), is true of whatever thing can be affirmed to come under or belong to the class (as ascertained by connotation).’ This supposes the need of a second affirmation, the minor proposition, and is no longer an immediate inference. 12. The defects of the dictum are supposed to be remedied by this form :— Attributes, or Things, co-existing with the same Attri- butes or ‘l'hings, co-exist with one another (Affirmative). If the attributes of a king co-exist with those of a man, and the attributes of a man co-exist with the attribute ‘ fallibility,’ the attributes of a king co-exist, or co-inhere with the attribute fallibility. | There is a close resemblance between the present form and the mathematical axiom—Things equal to the same thing, are | equal, The two are alike axioms of mediation; they connect two things by a common third. | The negative form is stated thus :—‘ One thing co-existing with a second thing, with which second thing a third thing — does not co-exist, is not co-existent with that third thing; which resembles the axiom—Things unequal to the same thing, — are unequal, This mode of stating the axiom has often been adopted by logicians :—.Vota note est nota rei ipsius ; Things that agree in the same third, agree among themselves. For the negative form —repugnans note, repugnat rei ipsi; Things whereof the one agrees, the other does not agree, with the same third, do not agree among themselves. ¥ NOTA NOTA. 157 The advantages of the form are indicated by the remarks already made. It gives very great prominence to the fact of mediation in Deductive Inference, and thus draws a broad line between it, and Immediate or Apparent Inference. It also accommodates itself to such a case as Darapti, with a singular subject, thus, 7 Socrates was wise. Socrates was poor. Some wise men have been poor. Now, the treating of a Singular proposition as a universal, which is necessary to make the above a regular syllogistic form, has always seemed a great anomaly in the syllogism. Indeed, it is asubversion of the theory of Deductive Reasoning, as supposed to consist in the application of a general or uni- versal principle to a case coming under it. But, if we accept the present form of the axiom, the above syllogism is rendered with apparent ease. ‘Wise’ co-exists with ‘Socrates ;’ ‘Poor’ co-exists with Socrates; therefore ‘ Wise’ and ‘ Poor’ co-exists with one another ; that is, ‘ Some wise persons are poor.’ A farther advantage of the same form consists in following out the the ‘ Connotation’ theory of Propositions. The exten- sion of the several propositions is completely banished from it, and nothing but Connotation or Comprehension left. It is no longer ‘all A is B,’ but the attribute A co-exists with the attribute B,’andsoon. From the same cause, a seeming facility is given in chains of reasoning, which can be rendered thus: —A is a mark of B, B of C, C of D; wherefore A is a mark of D. Notwithstanding so many advantages, this form of the axiom now described is unworkable as a basis of the syllogism. The fatal defect consists in this, that it is ill adapted to bring out the difference between total and partial coincidence of terms, the observation of which is the essential precaution in syllogizing correctly. If all terms were co-extensive, the axiom would flow on admirably; A carries B, all B and none but B; B carries C in the same manner; whence A carries B, without limita- tion or reserve. But, in point of fact, we know that while A carries B, other things carry B also, whence a process of limita- tion is required, in transferring A to C through B :—A (in com- mon with otber things) carries B; B (in common with other things) carries C; whence A (in common with other things) carries C. The axiom provides no means of making this limi- tation ; if we were to follow A literally, we should be led to suppose A and C co-extensive: for such is the only obvious 158 AXIOM OF THE SYLLOGISM. meaning of ‘the attribute A coincides with the attribute is Unless the predicate is quantified, as Hamilton recommends, the propositional form in Extension—‘ all men are mortal,’ does not explicitly suggest that ‘men are buta part of mortals ;’ yet we can readily conceive the fact when reminded of it ; the extent of ‘mortal beings’ is greater than the extent of ‘ men.’ But the proposition stated in pure connotation or comprelhen- sion, as the present axiom requires,—‘ the attributes of men co- exist with the attribute mortality’—is difficult to adapt to the fact that mortals are more numerous than man. We should have to make a still greater circumlocution :—the attributes of men co-exist, but are not the only attributes that co-exist, with the attribute ‘mortality.’ So, the attributes of a king co-exist, but are not the only attributes that co-exist, with the attributes of men. The conclusion would then be—The attributes of a king co-exist, but are not the only attributes that co-exist, with the attribute ‘ mortality.’ Now, as the axiom ‘attributes co-existing with the same: attribute co-exist with one another’ does not suggest these necessary limita- tions, it is not, as worded, an explicit basis for the syllogism, _ It is only the same objection, otherwise put, that the axiom does not accomniodate itself to the type of Deductive Reason- ing, as contrasted with Induction—the application of a general principle to a special case. Anything, that fails to make pro- minent this circumstance is not adapted as a foundation for the syllogism. The scientific processes of Induction and Deduction are habitually conceived on the basis of Extension; it is only thus that we readily appreciate the greater or less generality of propositions. Hence the proper view of the syllogism, as of the notion and the proposition, is to base it on Extension, but to determine the extension by Connotation or Comprehension. ‘ All men are mortal’ is best understood as the conerete population of human beings, defined and determined by the class attributes of humanity. This double point of view com- plies with all the exigencies of reasoning, and is not advan- tageously surrendered in favour of the statement of propositions in pure comprehension. The result of the comparison of the two axiomatic state- ments is, that the Dictwm de omni et nullo, properly guarded, is the most suitable and exact repr esentation of the cepeintind feature of Deductive Reasoning or Syllogism. The case of Singular Propositions, held for the nonce to be . ai SINGULAR PROPOSITIONS. 159 universal, is a grave exception to the Deductive process as we have uniformly described it. On-examining such cases, however, we may see good reason for banishing them from the syllogism. Let us take the example already quoted :— Socrates is poor Socrates is wise Some poor men are wise. Properly, the conclusion is, ‘one poor man is wise.’ Now, if ‘ wise,’ ‘poor,’ and ‘a man,’ are attributes belonging to the mean- ing of the word Socrates; there is then no march of reasoning at all, We have given, in Socrates, inter alia, the facts ‘wise,’ ‘ poor,’ and ‘a man, and we merely repeat the concurrence, which is selected from the whole aggregate of properties making up the whole, ‘Socrates.’ The case is one under the head ‘ Greater and Less Connotation,’ in Equivalent Propositional Forms, or Immedi- ate Inference. But the example in this form does not do justice to the syllogism of singulars. We must suppose both propositions to be real, the predicates being in no way involved in the subject. Thus :— Socrates was the master of Plato Socrates fought at Delium The master of Plato fought at Delium. It may fairly be doubted whether the transitions, in this instance, are anything more than equivalent forms. For the proposition, ‘Socrates was the master of Plato, and fought at Delium,’ compounded out of the two premises, is obviously nothing more than a grammatical abbreviation. No one can say that there is here any change of meaning, or anything beyond a verbal modification of the original form. The next step is, ‘the master of Plato fought at Delium,’ which is the previous statement cut down by the omission of ‘Socrates.’ It contents itself with reproducing a part of the meaning, or saying less than had been previously said. The full equivalent of the affirmation is ‘the master of Plato fought at Delium, and the master of Plato was Socrates ;’ the new form omits the last piece of information, and gives only the first. Now, we never consider that we have made a real inference,.a step in advance, when we repeat /ess than we are entitled to say, or drop from a complex statement some portion not desired at the moment. Such an operation keeps strictly within the domain of Equivalence or Immediate Inference. In no way, therefore, can a syllogism with two singular premises be viewed as a genuine syllogistic or deductive inference. 13. The Proof of the Axiom is uncontradicted experi- ence. The Dictum is not a mere rule of consistency, exacting the admission, in equivalent forms, of all that has been conceded in one form. It is a mediate process, and the mediation has to be justified by an appeal to the facts. As far as proof goes, 8 160 AXIOM OF THE SYLLOGISM. it resembles in character the second form above given— Things co-existing with the same thing, co-exist,’ and the mathema- tical axiom ‘ Things equal to the same thing are equal.’ All the three principles stand upon the same foundation ; some philosophers refer them to intuition, others to experience ; but the mode of proof for one is the mode for all.. The dictum seems to approach nearest to a mere rule of consistency ; yet the fact of mediation makes all the difference; ‘ the identical of an identical is identical ’ is a new step and needs a new jus-— tification. Nobody would accept even so obvious an inference —as ‘men are mortal, kings are men, kings are mortal,’ with- out first verifying upon examples the peculiar kind of transi- tion involved. Weare so alive to the snares lurking in the most obvious and plausible forms of language, that we do not trust any of them without the check of actual trials. Nothing could seem more satisfactory than ‘ A co-exists with B, B with C, therefore A co-exists with C wholly and unconditionally,’ yet until we have elaborately fenced the operation against the simple conversion of a universal, the conclusion is unwarranted. Viewing together the Mathematical axiom of Equality and the axiom of the Syllogism, Mr. de Morgan remarks :—‘ In both there is a law of thought appealed to on primary subjective testimony of consciousness ;’ ‘ equal of equal is equal’ in the one; ‘ identical of identical is identical’ in the other. The two laws are equally necessary, equally self-evident, equally incapable of being resolved into simpler elements. 14. There are other modes of stating the Axiom. Hamil- ton has two forms. The first is for what he calls Informal Reasoning :—In so far as two notions (notions proper or individuals) either both agree, or one agreeing the other does not, with a common third notion; in so far, these notions do or do not agree with one another. . _ This is simply one way of wording the Nota note, and is liable to the objections urged against that form. There is no provision for distinguishing total from partial agreement, and therefore no basis for the working of the syllogism. The words ‘agreement’ and ‘ disagreement’ are less apt than ‘co- existence’ and ‘non-coexistence’ for expressing the axiom; they have the defects inherent in the ‘judgment’ theory of Propositions. 15. For the Figured Sylogism, where the terms are re- lated as subject and predicate of propositions in a given : os OI ae 2 T HAMILTON’S FORMS, 16] order, Hamilton enounces this form:—What worse re- lation of subject and predicate subsists between either of two terms and a common third term, with which one, at least, is positively related; that relation subsists between the terms themselves. The peculiar phraseology ‘ What worse relation’ is a man- ner of saying that the conclusion must carry the weakest re- lationship signified by the premises. If there be a negative in the premises, there must be a negative in the conclusion ; if there be particularity in the premises, there must be particu- larity in the conclusion. The same thing is otherwise ex- pressed—‘ The conclusion must follow the weaker part.’ This is the Axiom given in Extension, and is in accordance with the Dictwm, although not stated with the same generality. It more resembles one of the canons for working out the syllo- gistic details, itself resting on the Dictum. 16. The first of Hamilton’s two forms is expressed otherwise thus (Thomson) :—The agreement or disagree- ment of one conception with another, is ascertained by a third conception, inasmuch as this, wholly or by the same part, agrees with both, or with only one of the conceptions to be compared. This form appears to be based upon Comprehension, or the Nota note, but endeavours to introduce the limitations requisite for discriminating total and partial quantity. The phraseology, however,—‘ conception, &c.’—is ambiguous; it may express either extension or comprehension—‘ men’ or the attributes ‘human.’ If, taken in extension (which is most probable), is closely reproduces Hamilton’s second form, and puts stress upon the difference between total and partial coincidence. Nevertheless, it does not rise to the sweep of the Dictuin, in declaring the paramount circumstance of deductive reason- ing,—the carrying out of a general law to particular cases. lf ‘conception’ means attributes, comprehension, or conno- tation, the phraseology would indicate Hamilton’s syllogism of Comprehension, and would not suggest the common syllogism. The attributes * king’ and the attribute ‘mortal’ agree (better ‘ coincide’) by agreeing (coinciding) with the same part of the attributes ‘human.’ Hamilton’s syllogism is more explicit ; thu:—The attributes ‘king’ contain the attributes ‘man;’ the attributes ‘man’ contain the attribute ‘mortal ;’ the att:ibutes ‘king’ contain the attribute ‘ mortal.’ .- Oe eee ree el a Pl 162 AXIOM OF THE SYLLOGISM. 17. In the comprehensive scheme of De Morgan, the axiom is a generalization of many special axioms. The syllogism is treated as the composition of two relations into one ; the axiom is ‘ the relation of a relation is a rela tion compounded of the two,’ or The truth of this is seen, and its application controlled, by the special instances of relationship. One of these instances is the axiom of the common syliogism. Others are the mathe- matical axioms, ‘ Equal of equal is equal,’ and ‘greater of greater is still greater’ (a fortiori). Among more special in- stances are ‘ antecedent and consequent,’ ‘ancestor and descendant. | Ss 18. It has been supposed by some that the common axiom, as expressed by the ‘dictum de omni et nullo,’ is a consequence of the Laws of Thought (Identity, Contradic-. tion and Excluded Middle). Hamilton maintains that categorical syllogisms are regulated by the fundamental laws of Identity and Contradiction. He interprets the law of Identity as the identity of a whole and the sum of its parts, whence he considers it right to infer that what belongs to a whole belongs to its part. Mr. Mansel agrees with Hamilton in referring the syllogistic laws to the same principles. . The effect of this doctrine is to abolish the difference be- tween Immediate and Mediate Inference, by bringing mediate inference under Immediate, or under the law of Consisteney. On the face of it, the supposition is unlikely ; and accordingly it has been denied by other logicians. Thus, Mr. de Morgan (Syllabus, p. 47) remarks of the attempts to reduce the syllog- ism to the three so-called Laws of Thought, ‘When any one attempts to show how, I shall be able to judge of the process; as it is, I find that others do not go beyond the simple asser- tion, and that I myself can detect the petitio principit in every | one of my own attempts.’ a The law of Consistency requires us to concede that what is true of a class is true of every individual in the class; ‘all men are fallible,’ ‘ the half of men are fallible, this man is fallible’? ; here there is no transition, it is the same fact, repeated only to a less extent. But when we say ‘kings are men,’ ‘ kings are fallible,’ there is a transition to a different subject, a subject not present to the mind as a part of the original whole, but 4 brought under it by a second assertion, Now a distinct axiom, | 7 DERIVATION OF SPECIAL CANONS. 163 is needed to transfer the attribute under this new case. The axiom may be in its nature self-evident, but the conclusions regulated by it are not identical with either of the premises, as an immediate inference, properly so called, is identical with the original form. 19. The special canons of the Syllogism are derivable from the Axiom. (1) It easily follows from the Dictum, as explained, that there are three terms, and no more. There is a Universal Pro- position containing a subject and a predicate, an applying or Interpreting proposition, adding a third term, and repeating one of the terms of the universal:—All or no Y is Z, All X is Y. The conclusion contains no new term-—All X is Z. Whence there are three terms in all. (2) The same examination shows that there are three and no more than three propositions ;—the Universal, the Inter- preting Proposition, and the Conclusion. (3) The third special canon is—‘ The middle term must be distributed once in the premises.’ Distribution or Universal Quantity in the middle term is essential to the total coincidence or non-coincidence of at least one of the other terms with the middle term ; without which the two extreme terms could not be shown either to coincide, or not to coincide, in whole or in part. ‘Some men are fallible,’ ‘kings are some men,’—would not bring about a coincidence between ‘ fallibility’ and ‘ kings ;’ one portion of men might be fallible, and a different portion might be kings. This is obviated if fallibility adheres to all men ; it must then adhere to whatever objects are found to be men. (4) The fourth special canon is—-‘ No term undistributed in the premises must. be distributed in the conclusion.’ It may be brought under the Dictum thus:—The distribution of a term in the conclusion means universal or total coincidence with the other term of the conclusion ;—* All X is Z’ means that X is wholly coincident with, wholly included in Z. Now X and Z are brought together by a middle term Y; and if X did not wholly coincide with Y in the first instance, it could not be transferred, in total coincidence, to Z. If we had only some X is Y, even although all Y is Z, we could not declare all X to be Z. There is carried over to Z ouiy so much of X as goes with Y ; if that be the whole, the whole is carried ; if a part, part iscarried. If ‘all men are fallible,’ and ‘some beings are men,’ only some beings are fallible, namely, as many as are men, 164 AXIOM OF THE SYLLOGISM, (5) ‘ From negative premises, there is no inference.” Nega- tive premises do not comply with the essential fact of the in- terpreting proposition, which is to declare that a given case comes under the sweep of the rule. -Whether the universal be affirmative or negative, the applying proposition must, from its nature, be affirmative. No Y is Z,no X is Y, could not be the means of bringing X under Z, or of bringing these two terms together in a conclusion ; we could not, from such pre- mises, infer even No X is Z. ‘No matter is destructible’ re- quires to be followed up with ‘ether is matter’ to prove that ‘no ether is indestructible.’ (6) ‘If one premise be negative, the conclusion is negative,’ ex- presses exactly what happens in the negative form of the axiom. In the enlarged scheme of De Morgan, some of these rules are violated in appearance, but only in appearance. Thus from ‘two negative premises’ he draws a conclusion in the affirmative. This, however, arises from the elasticity of ex- pression allowed by the use of contrary forms. Every affirma- tive proposition may be given as a negative; and there may be the semblance of negation, with the reality of affirmation in conformity with the axiom. Thus— AllYisZ =z No/Yisnot% All XisY = No X is not Y. All X is Z All X is Z. 20. The axioms—‘ Equals added to equals, give equal sums, and the argumentum a fortiori, if received as axioms in Logic, are distinct from the axiom of the Syllogism, and must be independently proved. | The argumentum a fortiort is represented thus:—If A is greater than B, and B greater than C, still greater is A than C. This, and the other axiom stated, are purely mathematical in their character; they serve for the comparing of quautitics as equal or unequal. They rest on their own special evidence of fact. | It will be seen that Boole draws the Syllogism under the axiom that suffices for the reduction of equations. He assumes that the analogy of the logical method and the algebraical is sufficiently close to allow of the substitution. The conflicting opinions as to the evidence of axioms gener- ally, whether of logic, of mathematics, or of other sciences, will be discussed in a succeeding chapter. ~ TESTING OF ARGUMENTS, 165 EXAMPLES OF THE SYLLOGISM. 21. The chief application of the theory and the forms of the syllogism is to detect fallacies in deductive reasonings. There are certain forms of deductive reasoning or argument, that are specious to appearance, and fallacious in reality ; and the analysis of the syllogism is useful in disclosing the fallaci- ousness. 22. The course of procedure, in dealing with an argu- ment in any way uncertain or perplexed, is as follows :— I. Ascertain what is the conclusion, or the point to be proved. State this distinctly in a proposition so as to dis- tinguish the Subject (minor term of the syllogism) and the Predicate (major term). Il. Find out the middée term of the argument. In a valid syllogism there must be a middle term, and only one: and it must be something not occurring in the conclusion. IIf. Find out some proposition connecting the middle term with the major term; this is the major premise of the syllogism. Also some proposition connecting the middle term with the minor term; giving the mimor premise of the syllogism. IV. The two premises and the conclusion being stated in form and order, the validity may be judged according to the laws of.the syllogism. (1) If the deduction coincides with any of the valid moods, it is valid; if not, not. (2) It being seen what Figure the argument comes under, it may be tested by the special canons of that figure. (3) The general canons of the syllogism may be applied to discover errors, if there be any such. Any one of these three modes may be adopted at choice ; inasmuch as each of them singly is conclusive. The easiest remembered mode of testing a syllogism, when once in form, is by the six general canons of the syllogism. Of these, the two that are most usually violated in sophistical reasonings are the 3rd (Distribution of the Middle Term) and the 4th (‘The quantity of the terms in the conclusion not greater than in the Premises). An argument with negative premises (5) would deceive no one. It would also be obvious, without much Logic, that one premise being negative, the conclusion must be negative (6). 23. As an alternative, we may discard the consideration 166 EXAMPLES OF THE SYLLOGISM. of the separate Figures, and reduce every argument at once to the standard form of Deduction. From the very nature of deductive reasoning, the conclusion is a special application of some more general proposition. This more general proposition must be found in the premises 3 itis the ground proposition ; in Hamilton’s phraseology, the Sumption. There must also be found another proposition declaring its applicability to a particular case, namely, the case given inthe conclusion. ‘These two indispensable proposi- tions may occur under distorted forms, which we must be able to redress by the methods already pointed out, that is, by obversion and conversion, as the case may be. Also, the eonclusion may require to be obverted or converted, or both. By such methods, we may evade all the variations of figure, and come at once to the regular type of deduction. EXAMPLES. All men are mortal All Y is Z7.—(A) No dogs are men No X is Y.—(E) 7; 1st Fig. No dogs are mortal No X is Z.—(E) (1) This syllogism is in the First Figure, but there is no mood in that Figure containing the propositions A, EH, E. (2) Otherwise: The major term, mortal, is distributed in the conclusion, and not in the premises ; there is illicit process of the major. (3) Or lastly : It contradicts the canon of the normal syllo- gism, whereby the minor is declared to be affirmative. All planets are round All Z is Y.—A A wheel is round All X is Y.—A }2nd Fig, A wheel is a planet All X is Z.—A (1) There is no such mood in the Second Figure, (2) The middle term, ‘ round,’ is undistributed. (3) There is a violation of the special canon of the Second Figure—One premise must be negative. ‘Every honest man attends to his business; this person attends to his business ; this person is an honest man.’ This is the exact counterpart of the foregoing. The conclusion being ‘this person is an honest man ;’ the minor term is ‘ this person,’ the major, ‘an honest man.’ The middle term is ‘attends to his business.’ The major premise (major and middle), ‘Every honest man attends to his business,’ A; the minor premise, ‘this man attends to his business,’ A (a definite 7) ?.? i eee a FALLACY OF CONVERSION. 167 individual may be considered as either A or I). Onany one of the three grounds given in the foregoing example, the reason- ing is fallacious. These. two examples are regarded by logicians as‘of a type calculated to mislead, and therefore exemplifying the use of the laws of the syllogism. It is interesting to enquire what circumstance gives them their fallacious plausibility. With this view, we may proceed by the alternative method above pointed out, namely, by ascertaining whether these be the regular premises of deduction. To prove that a wheel is a planet, we must have a more general proposition, of which this shall be a particular case. Such a proposition would be ‘all round bodies are planets:’ We should then require an applying or subsuming proposition, namely, ‘wheels are round bodies.’ With these two proposi- tions, the conclusion would be legitimate, that wheels are planets. Looking at the premises given, however, we do not find a proposition corresponding to the first, or the general proposition. It is stated, not that ‘all round bodies are planets,’ but only that ‘all planets are round,’ a different proposition. The confounding of the two is effected by the simple conversion of a universal affirmative; by arguing from ‘all planets are round,’ that ‘all round bodies are planets,’ which we can do only if there are no round things but planets. In short, the fallacy, traced to its root, isa fallacy of conversion ; and if we are liable to be deceived by such syllogisms as the pre- sent, it is because we are liable to slip into this fallacy. There is something in the form of the universal affirmative that throws us off our guard; from the expression All X is Y, we are apt to assume the co-extension of X and Y, unless cautioned and educated to the contrary. In cases where the co-extension exists, and only in such cases, could the argument in question give a sound conclusion. Thus— All matter gravitates. Air gravitates. Air is matter. Now, by the same process as before, it is shown that the general proposition needed for this conclusion is ‘ All gravi- tating things are matter,’ which happens to be true, but is not justified by the assertion in the major, ‘all matter gravitates ;’ for there might be other gravitating things. So in the second example ‘ Every honest man attends to his business,’ &c., we should require the terms ‘ honest man’ and ‘attention to business’ to be co-extensive, which they are not. dy cy. ee . 7 . A +. : . 168 EXAMPLES OF THE SYLLOGISM. Whatever tendency we have to be deceived by such reasonings depends solely upon the intellectual weakness of presuming co-extension of terms, in universal affirmations. Hume says:—‘ We have no perfect idea of anything but a perception. A substance is entirely different from a perception. We have therefore no idea of substance. ’ The first step is to resolve the conclusion into its two terms. As often happens, in Logic, these terms are not the grammati- cal subject and grammatical predicate ; a transformation must be given to suit the tenor of the premises. Comparing the first proposition with the last, we see that the mor term, or subject of the conclusion, must be ‘having an idea;’ the major term is ‘substance. The affirmation is negative ; literally, our ‘ having an idea’ is not true of substance. It is denied that substance is one of the things included under having an idea. The next point is to single out the middle term, namely, ‘ perception.’ Joined with the major and minor terms respectively, this yields as premises— No ‘having an idea’ is not perception. All substance is not perception. No ‘having an idea’ is true of substance. In the present form, the reasoning is wholly inadmissible ; the premises are both negative. We might, however, obvert the middle term ‘perception,’ and regard not-perception as the true middle (like changing ‘ not wise’ into not-wise, or foolish). We have thus— No ‘ having an idea’ is poP neta ae E All substance is not-perception A | 2nd Fig. (Cesare). No ‘having an idea’ is substance. H; In this form the argument is sound. It is often desirable to express arguments of great subtlety, such as the present, in the standard form of deduction. The requisite transmutation would have to be effected thus. The conclusion, ‘ “‘ having an idea” is not true of substance,’ is to - be converted ‘No substance is included in our having an idea,’ For this, the universal proposition would be a proposi- tion of denial more comprehensive than substance :—No not- perception is included in our having an idea, The minor is then, All substance is not-perception ; whence we conelude according to the regular form for the negative deduction. From the middle term being a negation, however, this, can never be an easy form of argument; and more especially so in 3 1 4 * = eee et ie a 2 oe Lee el wc ro EXAMPLES OF THE SYLLOGISM. 169 the present argument, where perception is as wide as exist- ence, and has only a formal, and not a real obverse. Thus, then, we have, in the First Figure, as Ceiwrent— Nothing that is not a perception (no not-perccption) can be perfectly conceived, : Substance is not a perception (a not-perception), A. Substance cannot be perfectly conceived. E. ‘None but Whites are civilized; the Hindoos are not Whites ; therefore they are not civilized.’ ~ Ina syllogism thus :— . No not-Whites are civilized E The Hindoos are not Whites A > (Celarent), The Hindoos are not civilized E A correct argument, the middle term being ‘ not- Whites,’ for which the positive equivalent would be the remaining members of the Universe, ‘races of men ’ (Black, brown, yellow, &c.) This would give a more intelligible form :— No communities of the black, browu, or yellow races are civilized ; The Hindoos are of the black or brown races, The Hindoos are not civilized. * Abstinence from the eating of blood had reference to the divine institution of sacrifices; one of the precepts delivered to Noah was abstinence from the eating of blood; therefore, one of the precepts delivered to Noah contained the divine institution of sacrifices ’ (Whately). Although prolix in the wording, there is little distortion in this example. The minor term is obviously ‘one of the precepts delivered to Noah,’ the major, ‘contained or had reference to the divine institution of sacrifices.’ The middle term is ‘ abstinence from the eating of blood ;’ and the arrange- ment is exactly as in the standard syllogism. ‘Few treatises of science convey important truths, without any intermixture of error, in a perspicuous and interesting form; and therefore, though a treatise would deserve much attention which should possess such excellence, it is plain that few treatises of science deserve much attention.’ (Whately). The conclusion gives as minor term ‘few treatises of science,’ as major ‘ deserve much attention.” The middle term is ‘convey important truths, &c.’ The major premise, there- fore, is— 170 EXAMPLES OF THE SYLLOGISM, All treatises of science that convey &c., deserve attention: The minor premise— . Few treatises of science are works conveying important, &. The conclusion— Few treatises of science deserve attention (Dari). It was formerly remarked (p. 82) that for Some, in the minor term, we may have—Few, most, many, one, two,—provided that the same quantity is used in the premises and in the conclusion, . ‘Enoch (according to the testimony of Scripture) pleased God ; but without faith it is impossible to please Him ; there- fore Enoch had faith’ (Whately). The minor and major terms are obyious. The middle is ‘pleasing God.’ The major premise is—‘ pleasing God is im- possible without faith,’ which is a circumlocution by way of expressing emphatically the proposition ‘pleasing God is having faith ’—‘ all persons that please God have faith.’ The minor premise being ‘noch pleased God,’ the conclusion fol- lows from the regular type of deduction: It was said by some one during the Reform discussions of 1867 :—‘ Every reasonable man wishes the Reform Bill to pass. Idon’t.’ There was but one inference. The speaker was not a reasonable man (Camestres). This is a good example to show that an effective argument may be given out of the First Figure. If we follow the ordinary method of reduction in this case, we find ourselves in a difficulty. Camestres is usually reduced to the First Figure by transposing the premises and simply converting the original minor: if we do so in this case, we find a singular proposition in the major premise, which cannot be converted without doing great violence to the ordinary forms of language, and cannot stand as the grounding pro- position conceived as a general rule. The general rule in this case is obviously the existing major—‘ Every reasonable man wishes the Reform Bill to pass.’ But if we view this as the general rule, then we appear to have a negative applying pro- position—‘ I don’t.’ Looking more closely at the premises, we see that the true nature of the predication is disguised. The major proposition is really negative, and the minor really affir- mative. The remedy for the distortion is to obvert the major into—' No reasonable man wishes the Reform Bill to fail ;’ or ‘No man that wishes the Reform Bill to fail is reasonable.’ EXAMPLES OF THE SYLLOGISM. 171 The minor when altered to correspond becomes—‘ I do ;’ and we have a syllogism in Celarent, Another example of this same mood, Camestres, illustrates the occurrence in ordinary reasoning of other syllogistic forms than the moods of the standard figure. We are presented with the assertion that ‘No despotism is a good form of govern- ment,’ and on asking the ground of such an assertion, are told—‘ Hvery good form of government promotes the intelli- gence of its subjects, and no despotism does that.’ This is an argument in Camestres. Every good form of government promotes Af ee the intelligence of its subjects. Es No despotism promotes, &c. No despotism is a good form of govern- \ om ment. The above statement of the Major is the natural statement of the proposition ; the order of subject and predicate is such as a reasoner would naturally observe. ‘That it promotes the in- telligence of its subject: is affirmed of every good form of government; the order of the terms conforms to the usual arrangement of having the largest term in the predicate ; other agencies than good government promote the intelligence of the people. As in the former Camestres, this syllogism cannot be reduced to the First Figure by the process indicated in the Mnemonic letters without putting the real Major, or grounding proposi- tion, in the Minor place. We may retain the present order without violating the rule that the applying proposition must be affirmative. For the present major, affirmative in form, is obviously negative in its bearing; while the minor, negative in form, is really of an affirmative nature, asserting that a despotic form of government possesses the character contem- plated in the ground proposition as precluding the title of good. By obverting the predicate of the major, the middle term, we manifest the real character of the premises :— No form of government that fails to promote the intelli- gence of its subjects is a good from of government. : A despotism fails to promote the intelligence of its subjects. No despotism is a good form of government. In speaking of the general uses of the Figures, we remarked that the Third Figure is sometimes useful in making good an unobtrusive and timid contradictory. The three first moods 172 EXAMPLES OF THE SYLLOGISM. supply mild contraries to a universal negative; the two last mild contraries to a universal affirmative. We give an ex- ample of each. Suppose a speaker to maintain absolutely and without reservation that speculation is of no value. His position in logical fourm is—‘ No speculation is valuable.’ We subvert this and extort from the speaker a concession that his position is too extreme, when we obtain his assent to the two proposi- tions—‘ Some truths affecting human conduct are speculations’, and ‘ All truths affecting human conduct are valuable.’ These two propositions involve the sub-contrary of the extreme negative ;—namely, Some speculations are valuable. They are given in the order of subject and predicate natural to the occasion, and they fall into the Third Figure. They serve as premises either for Disamis, or Datisi, according to the order we observe in enouncing them. Thus :— Some truths affecting human conduct } 47, are speculations All truths affecting human conduct ree are valuable Some speculations are valuable Is This is a syllogism in Disamis. But it is to be observed that we invert the normal order of the major and minor terms in the conclusion. The most natural form is Datisi—thus:— | All truths affecting human conduct are valuable ‘ Laat Some truths affecting human conduct are speculations Some speculations are valuable I If our opponent should concede that all truths affecting human conduct are speculations, we should have a syllogism in Darapti. In that case, our partial contradiction would seem peculiarly bland, because our premises would then be superfluously strong, and we should have the appearance of remitting something in the conclusion. Our next example illustrates the partial subversion of a universal affirmative by making good its sub-contrary, a particular negative. It is maintained that no attention should be given to what isnot practical. This may assume the logical form of a universal aflirmation,—‘ Everything that is unprac- tical should be neglected.’ Desiring to Contradict this in mild form, we may use the following argument :— i eae perms a , ae. ARNAULD’S UNIVERSAL TEST. 173 No truth applicable to practice should be fF] neglected. Every truth applicable to practice may % seem unpractical. P Some seemingly unpractical truths should) ,5 not be neglected. 33 This isa syllogism in Felapton. The major—‘ Some truths applicable to practice should not be neglected,’ would equally suit our purpose, and with the above minor wonld give a Bokardo. In such cases as the above, itis difficult to say which is the grounding proposition. There is no violation of the essential nature of Deduction in regarding a particular proposition, or approximate generalization, as the ground of the argument. To make the reasoning a genuine deduction, it is required only that the grounding proposition be more general than the conclusion. Arnauld’s Universal Test. It may be worth while to give an example of Arnauld’s mode of testing a deductive argument without reference to its logical form. He directs the pupil simply to observe whether the conclusion is contained in the premises. He gives the following example of his method : — *T am in doubt whether this reasoning be good :— The duty of a Christian is not to praise those that conmit criminal actions. Now those that engage ina duel commit a criminal action. Therefore it is the duty of a Christian not to praise those that engage in duels. * Now I need not trouble myself as to the figure or mood to which this may be reduced. It is sufficient for me to consider whether the conclusion be contained in one of the two first propositions, and if the other show this. And I find at once that the first proposition, since it differs in nothing from the conclusion, except that there is in the one, those that com- mit criminal actions, and in the other those that engage in duels, —that in which there is commit criminal actions, will contain that in which there is engage in duels, provided that conumitting criminal actions contains engaging in duels. ‘ Now it is clear by the sense that the term those that commit criminal actions is taken universally, and that it extends to all those that commit any such actions whatever; and thus the 174 EXAMPLES OF THE SYLLOGISM. minor, Those that engage in a duel commit a criminal action, showing that to engage in a duel is contained under this term, commit criminal actions, shows also that the first proposition contains the conclusion.’ This test of Arnauld’s is the simplest of application to premises not couched in syliogistic terms. It is easily applied in any case: the only change of form that could aid in the scrutiny, would be to make the containing proposition of the same form with the conclusion. To the following arguments, the student may supply such grounding propositions as would give them validity :— A true philosopher is independent of the caprices of fortune, for he places his chief happiness in moral and intellectual ex- cellence. A slave is a human being, therefore he should not be held in bondage. Not being thirsty, he cannot be suffering from fever. The Reformation was accompanied and followed by many disturbances, and is therefore to be condemned. Solon must be considered a wise legislator, seeing that he adapted his laws to the temper of the Athenians. He was too impulsive a man not to have committed many errors. Educated among savages, he could not be expected to know the customs of polite society. Not every advice is prudent, for many advices are not safe. Many assertions that are open to doubt are nevertheless worthy of attention, for many assertions that are open to doubt may be true. ‘Napoleon never cared for anybody but himself.” In modi- fied opposition to this, it may be urged that, after all, ‘he was human.’ Supposing this rejoinder is intended to establish that Napoleon had some disinterested affections, what ground- ing proposition does it require ? In like manner, subvert the assertion, ‘ Napoleon never knew fear,’ Volcanic eruptions, earthquakes, and plagues cannot be interpreted as a warning to evil-doers, for they involve alike the innocent and the guilty. Some dogs are useful animals, for is not the retriever useful ? All zeal is not virtuous, there being a zeal that has no dis- cretion, ‘Table-turning,’ (you may say,) ‘is a thiny I don’t under MISCELLANEOUS EXERCISES, 175 stand.’ Admitting this, I ask you to construct in an affirma- tive form, an argument which would entitle you, logically, yet not convincingly, to deny the existence of table-turning. _ (Spalding). Miscellaneous Syllogisms. ‘Suppose a man says, ‘I dislike all foreigners;’ find a premise which, with his own assertion, would entitle him to say also, ‘ No foreigner deserves to be liked.’ (Spalding). All cold is to be expelled by heat: this person’s disorder is a cold; and must therefore be expelled by heat. No carnivorous animals have four stomachs: all ruminants have four stomachs: no ruminants are carnivorous, Some men of inferior ability are legislators. All peers are legislators, and some peers are men of inferior ability. ‘No war is long popular: for every war increases taxation ; and the popularity of anything that touches our pockets is very short-lived.’ (Spalding). He that will not learn cannot become learned. This being so, there are many clever young men that we cannot expect to become learned. There is some anger that is not blameworthy. What pre- mise do you need for the conclusion,—‘ Some passions are not blamewortby.’ ‘No truth is without result; yet many truths are misunder- stood.’ What is the conclusion P Some deserve to be imitated that are nevertheless fools. Whoever speaks the truth deserves to be imitated. Humanity is a moral virtue: the study of polite letters is humanity ; the study of polite letters is a moral virtue. White is a good fellow : if, therefore, linen is white, it is a ood fellow. ‘ He that says you are an animal speaks truly : he that says you are a goose, says you are an animal; he that says you are a goose speaks truly.” (Arnauld), ‘You are not what I am: I am aman: therefore yon are not a man.’ (Arnauld). One symptom of the plague is fever; this man has fever; therefore he has the plague. Some objects of great beauty answer no other perceptible purpose, but to gratify the sight: many flowers have great beauty ; and many of them accordingly answer no other pur- pose but to gratify tl.e sight. . Every good statesman is favourable to progress. Some © * a 176 EXAMPLES OF THE SYLLOGISM. members of Parliament, not being favourable to progress, are not good statesmen. ‘ Unpleasant things are not always injurious ; afflictions are often salutary.’ Sup ply the missing premise. John is taller va Williain ; William is taller than Charles ; John is taller than Charles. ‘Of two evils the less is to be preferred ; occasional turbu- lence, therefore being a less evil than rigid despotism, is to be _ preferred to it.’ (Whatley). All fixed stars twinkle ; yonder star twinkles ; therefore it is fixed. All that do not act foolishly are respectable; all fools act foolishly ; no fools are respectable. ‘Most men that make a parade of honesty are dishonest ; this man makes a parade of honesty.’ Can we conclude that he is dishonest ? Ill doers are ill dreaders. This man dreads evil, and is, therefore, a scoundrel. All aristocracies are self-willed ; some self-willed people are not cruel; some aristocracies are not cruel. Some democracies are not persistent in their designs; the Government of the United States is a democracy ; the Govern- ment of the United States is not persistent in its designs. All plants contain cellular tissue ; no animals are plants; no animals contain cellular tissue. ‘I snatch at the conclusion that every eager desire is an evil thing; since I know that the desire of evil is evil, and that not a few eager desires have evil objects.’ (Spalding). A good marksman must have a steady hand; George has a steady hand ; therefore, George is a good marksman. Flotation is possible only in liquids, and so not possible in this water, which is frozen. Poetry is not Science. The characteristics of Science are truth and generality, and Poetry possesses neither. Nothing that is not possible for man to do has ever been done by man. Raising the dead is not possible for man, and, consequently, has never been done by man. ‘If I know that Messieurs A. B. and C. are not only learned, men but also silly ones, will you allow me to draw any infer- ence ?’ (Spalding). Irrational prejudice is symptomatic of a weak mind, and we sometimes see it in very learned men. State this in syllogistic form, and draw the legitimate conclusion. One who misapplies riches deserves poverty ; which one who a EXAMPLES OF CHAINS OF REASONING. 177 is benevolent does not deserve. Is the legitimate conclusion consonant with fact? ‘If a rule never is, and a principle always is, a law admitting no exception, judge that a rule must be something different from a principle.” (Spalding). No branch of science can be made absolutely perfect, yet all branches of science are worthy of diligent culture. What inference do you draw from this ? ‘What was it that first gained him the public ear? It cer tainly was not the pure Saxon-English in which his sentences are clothed, for, alas! we find that many writers who neglect their grammar even, secure an immence audience, to the de- light of their publishers, and their own gratification.’ _ ‘It has been supposed by some philosophers, that electricity is the real agent by which the nerves act upon the muscles. But there are many objections to such a view; and this very im- portant one among the rest,—that electricity may be trans- mitted along a nervous trunk which has been compressed by a string tied tightly round it, whilst the passage of ordinary nervous power is as completely checked by this process as if the nerve had been divided.’ The following are examples of chains of reasoning, resolvable into consecutive syllogisms. ‘The concept ‘ horse’ cannot, if it remain a concept, that is, @ universal attribution, be represented in imagination ; but ex- cept it be represented in imagination, it cannot be applied to any object; and except it be so applied, it cannot be realized in thought.’ (Hamilton). ‘But, to prove that moral sentiments are instinctive or inscrutable, it is boldly asserted, by the advocates of the hypothesis in question, that the moral sentiments of all men are precisely alike. ‘The argument, in favour of the hypothesis, which is raised on this hardy assertion, may be stated briefly in the following manner ;— No opinion or sentiment which is a result of observa- tion and induction is held or felt by all mankind. Observation and induction, as applied to the same subject, lead different men to different conclusions. But the judgments which are passed internally upon the rectitude or pravity of actions, or the moral sentiments or feelings which actions excite, are precisely alike with all men. Consequently, our moral sentiments or feelings were not gotten by our inductions from 178 RECENT ADDITIONS TO THE SYLLOGISM. the tendencies of the actions which excite them: nor were these sentiments or feelings gotten by inductions of others, and then impressed upon our minds by human authority and ex- ample. Consequently, our moral sentiments are instinctive, or are ultimate or inscrutable facts.’ (Austin.) ‘The general object which all laws have, or ought to have, in common, is to augment the total happiness of the commun- ity ; and therefore, in the first place, to exclude, as far as may be, every thing that tends to subtract from that happiness: in other words, to exclude mischief. But all punishment is mischief: all punishment in itself is evil. Upon the principle of utility, if it ought at all to be admitted, it ought only to be admitted in as far as it promises to exclude some greater evil.’ (Bentham), ‘If our intellectual part is common, the reason also, in respect of which we are rational beings, is common: if this is so, com- mon also is the reason which commands us what to do, and what not to do; if this is so, there is a common law also; if this is so, we are fellow-citizens ; if this is so, we are members of some political community; if this is so, the world is in a manner a state.’ (Marcus Antoninus). It is not to be sup- posed that all these transitions make distinct syllogisms ; some are at best but immediate or equivalent transitions. CHAPTER II. RECENT ADDITIONS TO THE SYLLOGISM. HAMILTON’S ADDITIONS. Sir Witt1am Hamiton’s extensions of the theory and the forms of the syllogism are chiefly based on the Quantification of the Predicate, and on the full development of the two modes of Quantity—LHxtension and Comprehension. He has also much criticism in detail on many parts of the syllogistice theory, It has been seen (p. 86) that the thorough quantification of the predicate yields four new propositional forms, making eight in all. Two of these, the affirmative forms, ‘ All X is all Y,’ ‘Some X is all Y,’ which are held by De Morgan and by Mill, . ° 4 Rai i a Nia ae QUANTIFICATION OF THE PREDICATE. 179 to be compound propositions, have been adopted by some other logicians, as Thomson (‘Laws of Thought’) and Spalding. The remaining two forms—the negative ‘ All X is not some Y,’ _ *Some X is not all Y’ have been set aside as not occurring in actual instances. _ The addition of two new forms greatly increases the number of possible syllogistic moods. By trying all the combinations of three propositions out of six, and by rejecting all that violate laws of the syllogism, and all that repeat others, Dr. Thomson makes out 22 moods in the First Figure, 20 moods in the Second Figure, 20 moods in the Third Figure; so that apart from the Fourth Figure, of which no account is taken, there are 62 moods. We give, as examples, some of the new moods. U U U contains three universal affirmatives with universal predicates. All Y is all Z All X is all Y All X is all Z a syllogism, to which there is no counterpart in nature, unless the terms are merely different names for the same thing; as ‘all water is all oxide of hydrogen.” We may find a proposi- tion whose terms are of co-equal extent to constitute a major, (all matter are all gravitating things); but we shall probably never be able to couple with this a minor also co-extensive in its terms, if these terms really mean different things. U E Bis an example, constituting an exception to the canon requiring the minor in the First Figure, or normal deductive syllogism, to be affirmative. All Y is all Z All matter is all gravitating things NoX is Y No mind is matter NoXis Z No mind gravitates Here the quantification of Z (universal) avoids illicit process of the major. It is not pretended that any useful form grows out of these additions to the syllogistic moods; and even as a formal exercise, no one has thought it worth while to state them im full; far less to provide examples of them in the concrete. Only Hamilton himself (followed by Professor Spencer Baynes) has endeavoured to enumerate the syllogistic moods growing out of the eight quantified propositional forms. He even gives the number variously. The earliest statement is thirty-six valid moods, for each figure (excluding the Fourth), that is, twelve affirmative, and twenty-four negative. Dr. Thomson has tabulated the forms, agreeing with Hamilton so “¢, eee es 180 HAMILTON'S ADDITIONS OF THE SYLLOGISM. far, but deducting from Hamilton’s complete list as useless though possible varieties, 14 moods in the first figure, 16 in the second, and 16 in the third. He thus reduces Hamilton’s 108 moods to 62. In a later statement Hamilton gives 42 _ syllogisms, reducible to 21. Syllogisms viewed either in Extension or in Comprehension. It is a great point with Hamilton to show that the common syl- logism is defective, from not being expressed both in Extension and in Comprehension. He complains that all logicians, with the doubtful exception of Aristotle, have limited their con- sideration to reasoning as given in the quantity of Extension. He exemplifies the difference of the two syllogisms thus .— Hatenston. Comprehension. Bis A Cis B Cis B Bis A Cis A Cis A All men are mortal Caius is a man Caius is a man All men are mortal Caius is mortal Caius is mortal In the first example the class ‘mortal’ contains under it the class man; in the second example, the attributes of ‘man’ contain in them the attribute ‘ mortal.’ The following is an example in Celarent, Hatension. Comprehension. No men are gods Kings are men All kings are men Men are not gods No kings are gods Kings are not gods The second form (Comprehension) may be read thus :— The attributes of a king contain the attributes of a man. The attributes of a man do not contain the attributes of a god. The attributes of a king do not contain the attributes charac- teristic of a god. It is to be remarked, with reference to this scheme of double syllogisms, according as the terms are taken in extent, or in intent—breadth or depth—that the two modes express one and the same meaning; and that the really fundamental. meaning is Intent, or the Connotation of the Terms employed. The real meaning of the last example is, first, that the attributes connoted by the term, man, fail to accompany, or are incompatible with, the attributes connoted by the term, ‘god’ (major); that the attributes connoted by ‘king’ are accompanied with the attributes connoted by ‘man.’ The other form, however, falls readiest into common language, the form of Extension, that is, of inclusion or exclusion of i ee ae een eee ii ae ale SYLLOGISMS IN COMPREHENSION, _ 181 classes; men are out of the class of gods; kings are in the class men; therefore, kings are out of the class gods. This is a more concrete and intelligible form; still, it is not the contrast or the opposite of the other. We do not _ think of this form justly, correctly, unless we conceive the terms as determined by their connotation. The extent is bounded solely by the intent. lt is not as if we had a com- plete list of men, and a complete list of kings, and saw the kings inserted among the men, while the list of men had nothing in common with the list of gods. This is the full and literal rendering of the reasoning in extension ; and the very statement of it is enough to show that we do ‘not reason so. When we speak of a class, we do so in a figurative manner ; we suppose an actual array of individuals when there is no such array; there being only the defining mark, the connota- tion of them, to define them whenever they appear. The extent of ‘man’ is the imaginary aggregate of all objects agreeing in the marks connoted by the term, the defining characteristics of man; if we lose sight of this condition for a moment, we have nothing fixed in our grasp. Accordingly, comprehension is inseparable from extension in every case; it is an ever present fact, without our topsy-turvying the syllogism, or constituting a parallel array of moods to match the moods in extension. Hamilton’s forms in comprehension depend solely on his in- troducing the idea of ‘ containing and contained’ into the sroups of attributes signified by the terms of the proposition. A king has more attributes than a man; the individual person ‘Frederick the Second’ has more attributes thana king. Thus, Frederick is the largest term, in point of number of attributes, man is the smallest. Hence we may, by straining a metaphor, apply the relation of whole and part, containing and contained, to this circumstance, as well as tothe groups (in extension) men, kings, Frederick; and may carry the analogy so far as to construct syllogisms to match. But no new or distinct meaning is conveyed ; and there is not even a more intelligible , rendering of an old meaning. Hamilton, in discussing the conditions of the Distinctness of Notions, remarks justly that the highest degree of distinctness cannot be attained without fixing the Comprehension, in other words, the meaning, definition, or connotation of the term. (Lectures on Logic 1.168). He remarks also that the quantity of Extension is a creation of the mind itself, and only created through, as abstracted from, the quantity of comprehension ; wn 182 DE MORGAN’S ADDITIONS TO THE SYLLOGISM. whereas the quantity of comprehension is at once given in the nature of things (p. 218). All which tends to the conclusion that the comprehension is what we think of in a notion; and consequently the comprehension cannot be left out of the ac- count in any syllogistic form. It is the power behind the throne, even when extension is the ostensible reigning circum- stance. In objecting to the Fourth Figure, Hamilton grounds his dislike on the circumstance, that the premises proceed in the whole of comprehension, while the conclusion is drawn in the counter whole of extension. He explains the matter thus. The scheme of the Figure is— Pis M Mis§S Sis P Now in the premises P is contained under M; and M con- tained under S; whence in the conclusion we should expect P to be contained under 8. In this, however, we are disappointed ; for the reasoning suddenly turns round in the conclusion, and affirms S as a part of P. [Not strictly correct; for Sis qualified by “some,’ which may still leave it the larger term; ‘Some 8 is P.’] If we had an affirmative syllogism in the form All P is M All kings are men All Mis § All men are fallible All S$ is P All fallible beings are kings we should have an illegitimate inference; which might no doubt be evaded if the conclusion could be read thus— All the attributes of fallible beings are contained in the at tributes of Kings. But no one ever reads the figure in this way, DE MORGANS ADDITIONS. We have seen Mr. De Morgan’s views as to Terms, and his enumeration of Fundamental Propositions. Before proceeding to view his enlargements of the Oy Opiate we shall advert’ to his remarks on the CopuLa. He complains that the ‘is’ of logicians is not confined to one strict meaning. It professes to be a word of the highest abstraction, a formal mode of joining two terms, carrying no meaning, and obeying no law, except such as is barely neces- sary to make the forms of inference hold good. ‘ X is Y* com- mits us to nothing specific. Yet, at times, logicians employ it in the sense of identity, The best description of its employ- COPULAR RELATIONS. 183 ment, he considers to be—‘ agreement in some understood, and, for the occasion, unvarying particular.’ He supposes that a copular symbol had been used, instead _ of ‘is;’ the effect of which would have been to stamp upvn the copula the character of an abstraction, as is done by the use of symbols, X, Y, Z, for terms. Had such a symbol been used, the copwlar conditions would have been stated. These are twoin number. The first is transitiveness ; meaning that if X stands in a certain relation to Y, and Y in the same re- lation to Z, X stands in the given relation to Z. Very many copule show this transitive relation ;—is,—rules,— lifts,— draws,—leads to,—is superior to, —is ancestor to,—is brother of,—.joins,—depends on,—is greater than,—is equal to,—is less than,—agrees with (in a given particular), &. The second condition is convertibility, in which the relation is its own correlation; whatever X is to Y, Yisto X. Ina certain number of the foregoing examples, there occur con- vertible relations; is,—is brother of,—joins (if a middle verb),—is equal to,—agrees with. There are cases of con- vertibility without the transitive character ; converses with,— is in the habit of meeting,—is cousin of,—is in controversy with, &c. Again, there are copula not convertible, but correlative; A gives to B; B receives from A. These forms also are duly reasoned upon; and syllogisms might be constructed aecord- ingly. Hvery X gives toa Y; Some Xs give to no Ys; No X gives to a Y; Every X receives froma Y ; Some Xs receive from no Ys,—are examples of the propositional forms. They are all capable of conversion, by substituting the correlative copula. The admission of Relation in general, Mr. De Morgan con- tends, and of the composition of relation, makes logic more in alliance with ordinary thinking. ‘The reduction of all relations by ‘is’—‘mind acts on matter, mind is a thing acting on matter,’—is a systematic evasion, hostile to the pro- gress of the science. Logicians are aware that the form ‘ A equals B, B equals C, therefore A equals C’ is not reducible to the syllogism. So with the relation of ‘ greater than,’ in the argument a fortiori. Yet, to the ordinary mind, these inferences are as natural, as forcible, and as prompt, as the syllogistic inference. Mr. De Morgan, therefore, would propose to include all such forms in one sweep by a generalized copula of relation, which would be formally embodied and symbolized in propositions. Thus— 9 184 DE MORGAN’S ADDITIONS TO THE SYLLOGISM. Every X has a relation to some Y Kvery Y has a relation to some Z from which the inference would be that ‘very X has a com- pound relation to some Z;’ the compound of the relations X ~ to Y,and Y to Z Under this form, we reason, John can coutrol Thomas; Thomas can control William; John can control William. Under the general and comprehensive copular relation, specific modes might be developed for specific purposes. The Logical copula in common use is the equival- ent of ‘ fastened to,’ ‘connected with,’ ‘co-exists with,’ and may be considered for logical purposes the most important. The copula of equality and inequality is developed in Mathe- matics, and an inference according to it would probably be called a mathematical inference. The converse copular relation, ‘ causes,’ would be singled out on account of its great importance :—A causes B, B is caused by A. We practically construct syllogisms from these propositions, without passing through our minds the formal transformation to—A is the cause of C. | These remarks of Mr. De Morgan’s are undoubtedly just and cogent; and they are highly valuable in the way of eman- cipating the student trom the Aristotelian limits, as well as for pointing out the vagueness and vacillation of the ordinary copula. Still, we could hardly afford the labour of following out the technical developments of half-a-dozen distinct forms of copula. It is well to see that such developments are not merely competent in themselves, but needed to formulate the whole compass of our habitual thinking and reasoning. Being, however, aware of this fact, we must be content with con- structing one scheme adapted to the most useful and most frequently recurring relationship ; which scheme we should then regard as an example of the rest, one out of many, Any one having Mr. De Morgan’s genius for the construction of forms might do well to develop a variety of copular relations ; from these such selections might be made as would extend the inferential grasp of the ordinary student. Mr. De Morgan’s Extensions of the Syllogistic forms are avowedly based upon the full recognition of contraries, as laid out in his scheme of eight fundamental propositions. Also, by providing symbols for contraries he can exhibit all denials as assertions; No X is Y, is All X is y (U—Y). Hence, the unit syllogism may be represented in an affirmative form— If an X be a Y, if that same Y be a Z, then the X is a Z.’ mee ee a nary? a. SYLLOGISTIC FORMS. 185 All syllogisms are derivable from the following combinations of Premises :— (1) All Xs are Ys, and all Ys are Zs. Tho conclusion is All Xs are Zs; the unit syllogism. This is the inversion of the Aristotelian order of premises, but it is in the author’s view the proper and the natural order. (2) Some Xs are Ys, all Ys are Zs; some Xs are Zs. The unit syllogism is here, as it were, cut down to the form,—‘ as often as there are Xs in the first premise, there are in the con- clusion.’ (3) Some Xsare all Ys, some Ys are Zs ; conclusion—some Xs are Zs. In point of form, this is the previous case inverted. The universal middle term (all Ys) is transferred from the second premise to the first. (4) Some Xs are all Ys, All Ys are Zs; Some Xs are Zs. Here, although there is an additional universal middle, all Ys, occurring in both premises, there is no stronger conclusion than in the two preceding cases, where the middle term is universal (or distributed) only once. These are all the possible couples of affirmative premises apart from any cognisance of contrary terms. Now, all negations may be rendered as affirmations about contraries ; and therefore the application of these cases to all combinations of propositions, direct or contrary, will give all possible valid syllogisms. Taking X, Y, Z, and their contraries x, y, z, there are eight combinations of threes:—X Y Z,x Y Z,x y Z, xyz, XY 4z, XyZ,Xyz,xYz. Toeach of these the four modes of inference ean be applied; and when x, y, z, are read as the contraries of X, Y, Z, we obtain the proper expression of the syllogism. Thus, the first or unit syllogism, applied to x y Z, gives Hvery x is y, Hvery y is Z; therefore, Every x is Z This unfolded, by giving the equivalents of the contrary terms x, y, in the forms X, Y, the whole syllogism may be read thus :— Kivery x is y (All not-X is not-Y) is the same as No Y is not X, or Every Y is X, or Some Xs are all Ys. livery y is Z (Every not-Y is Z) is the same as Everything is either Y or Z(one of De Morgan’s new propositional forms). In like manner, the conclusion Every x is Z, (Every not-X is Z) is Everything is either X or Z. The syllogism then is :— Some Xs are all Ys (Every Y is X). Everything is either Y or Z. Everything is either X or Z. A syllogism not in the Aristotelian figures. From the very SM UPN Srey et 186 DE MORGAN’S ADDITIONS TO THE SYLLOGISM, wide compass of the form, Everything is either Y or Z, there can be few applications of such a syllogism. Some extended things are all material things. Everything is either material or pertaining to mind. Everything is either extended or pertaining to mind. The remaining seven forms being expressed and unfolded in like manner, there would arise the eight forms. of wniversal syllogism, that is wniversal premises with universal conclu- sion. Again, apply case second to the same eight forms—Some Xs are Ys, all Ys are Zs; some Xs are Zs ; and there emerge eight minor-particular syllogisms, particular conclusion with the minor (or first) premise particular. Apply case third—Some Xs are all Ys, some Ys are Zs; some Xs are Zs—and we have eight major-particular syllogisms, particular conclusion with the major (or second) premise par- ticular. Apply case fourth—Some Xs are all Ys, All Ys are Zs, Some Xs are Zs—and we have eight strengthened particular syllogisms, wniversal premises with particular conclusion By a strengthened syllogism, the author means one whose premises are stronger than they need be to bear out the conclusion. The above 32 forms are those that give inference, out of 64 possible combinations of the premises. The remaining 32 forms could be drawn out by representing the eight proposi- tional arrangements, X Y Z, x Y Z, &c., in four varieties of premises, which the author states. Thus: (1) Some Xs are some Ys, Some Xs are all Ys; (2) All Xs are some Ys, Some Xs aresome Ys; (8) Some Xs are some Ys, Some things are neither Xs nor Ys; (4) Some Xs are Ys; All Xs are not some Ys. From none of these combinations of premises could any inference be drawn. The test of validity, and the rule of inference, the author expresses thus :— ' There is inference (1) When both the premises are uni- versal. (2) When, one premise only being particular, the middle term has different quantities in the two premises. Hither of these cases happening, the conclusion is found by erasing the middle term and its quantities. Premises of like quality give an ajirmative conclusion; of different quality, a negative. A universal conclusion follows only from universals with the middle term differently quantified in the two. From two particular premises nothing follows. A particular premise having the concluding term strengthened i RULES OF INFERENCE. 187 (that is, made universal), the conclusion is also strengthencd, und the syllogism becomes universal; for example, Darii, by this process, would become Barbara. With the middle term strengthened, the conclusion is not strengthened, and there being, therefore, a surplus of affirmation in the premises, the syllogism forms what the author calls a strengthened particular syllogism, Thus, Darapti, in the third figure— All Y is Z All Y is X Some X is Z— has the middle term universal in both premises, when once is enough , there would be inference with ‘Some Y is X’ in the minor. Felapton and fesapo are other examples. A different case is exemplified in Bramantip. The two universals—‘ All Z is Y, All Y is X,’ yield the universal ‘all Z is X,’ which, for the sake of a different order of the terms in the concl usion, is converted and weakened into the particular ‘Some X is Z.’ This is termed by the author a weakened universal. Hach form of proposition has corresponding to it certain opponent forms. ‘Thus, if the propositions A, B, gives C, they cannot give ¢ (the contrary of C). Hence A and C being true, B is false or B true; that is A, c, give B, that is to say, either premise joined with the contrary of the conclusion gives the con- trary of the other premise. Thus, there are two opponent forms to every syllogism. And the syllogisms may be so grouped in threes, that each one of any three may have the two others for opponents. Barbara has, for opponent forms, Baroko and Bokardo. Mr. De Morgan considers it of importance to remark that the adjective for expressing universal quantity—‘ All’ means two things, which should be kept distinct. It may be ‘ All’ collectively, the entire collection or aggregate of individuals; this he calls the cwmular form ; and it may be ‘all’ distribu- tively, in the sense of ‘every one,’ or ‘any one,’ however taken, which he calls the exemplar mode. He holds that the language of Aristotle, and of his immediate followers, was exemplar and not cumular; zas dv6pwrros, he contends, is each or every man, not all man. ‘ All man,’ as a comprehensive genus, has parts,—for example, the sevoral species or varieties of men ; ‘every man’ has no parts, but makes assertions about every individual of the genus man. The exemplar mode is that used in geometrical proof. A proposition in Euclid assumes some one case, and the demon- 188 DE MORGAN’S ADDITIONS TO THE SYLLOGISM. stration is such that nothing prevents the one chosen from being any one. It would be useful in geometry, to admit the form ‘any one X is any one Y.’ In negation, the exemplar form is needed. ‘ All men are not fishes,’ does not deny the proposition, ‘ All men are fishes.’ The denial would, however, be given in ‘Every man is not any fish.’* | Properly speaking, the cumular proposition can be found proved only through exemplars; hence the exemplar precedes in the order of thought; a circumstance justifying its adoption as the basis of a logical system. According to it, quantily 1s mode of selection by example; universal is replaced by wholly indefinite; particular by not wholly indefinite. The forms of the propositions would be modified thus :— Any one X is any one Y. X and Y singular and identical. Some one X is not some one Y. KHither X not singular, or Y not singular ; or if both singular, not identical. Any one X is 8ome one Y. All Xs are some Ys. Some one X is not any one Y. Some Xs are not (all) Ys. Some one X is any one Y. Some Xs are all Ys. Any one X is not some one Y. All Xs are not some Ys. Any one X is notany one Y. All Xs are not (all) Ys. Some one X is not some one Y. Some Xs are some Ys. The ‘ Numerically Definite Syllogism ’ is a scheme of infer- ence which supposes exact numbers to be given. If in 100 instances of any thing, 70 are Xs, and 30, Ys, then at least 20 Xs must be Ys. The author develops at great length a symbolical scheme founded on this assumption. Syllogisms with numerically definite quantity occur rarely, if ever, in common thought. But it is not unfrequent to find forms where the number of instances of one term is the whole number of instances of the other term ;—‘ For every Z there * Mr. Mill, in a controversial note to his chapter on the Functions of the Syllogism, makes the following remark:—The language of ratiocination would, I think, be brought into closer agreement with the real nature of the process, if the general propositions employed in reasonittg, instead of being in the form All men are mortal, or Every man is mortal, were expressed in the form Any man is mortal. This mode of expression, exhibiting as the type of all reasoning from experience “ The men A, B, C, &c. are so and so, therefore amy man is 80 and so,” would much better manifest the true idea— that inductive reason- ing is always, at the bottom, inference from particulars to particulars, and that the whole function of general propositions in reasoning, is to vonch for the legitimacy of such inferences. THE ARISTOTELIAN SYSTEM COMPARED, 189 is an X that is Y; some Zs are not Ys;’ ‘For every man in the house there is a person that is aged ; some of the men are not aged ;’ from which it follows, but not by any common form of syllogism, that ‘some persons in the house are not men.’ To this case the author applies the designation ‘syllogism of transposed quantity.’ Of terms in common use the only one that gives syllogisms of this character is ‘ most :-—‘ Most Ys are Xs; most Ys are Zs; th refore some Xs are Zs,’ Adverting to the distinction of Figure, he styles the First the figure of direct transition; the Fourth, which is nothing but the first with a converted conclusion, the figure of inverted transition; the Second, the figure of veference to (the middle term); the Third, the figure of reference form (the middle term). Apart from the conversion of the conclusion, the Fourth Figure is the most natural order, as it takes up what was left off with—‘ X is in Y, Y is in Z, therefore X is in Z;’ this is the first figure, according to the simplest arrangement of the premises. In the author’s system, however, Figure attains importance only through a wider view of the copular relation. Mr. De Morgan compares his system with the Aristotelian, of which he regards it as an extension, through the single de- vice of adding contraries to the matters of predication. (Hamil- ton also claims to extend Aristotle, but on a different principle). Accordingly the Aristotelian syllogisms may be all collected from the preceding system, by the following modifications. 1. The exclusion of all idea of a limited universe, of contrary names, and of the propositions, ‘ Every thing is either X or Y,’ — ‘Some things are neither Xsnor Ys.’ 2. The exclusion of the form of conversion, ‘Some Xs areall Ys.’ 3. The exclusion of every copula except the transitive and convertible copula. 4. The regardivg of the identical pairs—No X is Y, No Y is X, and Some X is Y, Some Y is X—as distinct propositions of themselves determining distinction of figure and mood; as Celarent and Cesare, Ferio and Ferison, &c. 5. The-introduc- ing of the distinction of figure. 6. The writing of the major and minor propositions first and second, instead of second and first. Farther, in the Aristotelian scheme, there are four funda- mental syllogisms in the first figure, each of which has an opponent in the second, and ‘an opponent in the third. The opponents of Barbara are Buroko and Bokardo, There are three fundamental syllogisms in the fourth figure (Dimaris, 190 BOOLE’S ADDITIONS TO THE SYLLOGISM. Camenes, Fresison), each of which has the two others for op- ponents. Altogether there are fifteen fundamental! syllogisms. The remaining four are—three strengthened particular syllo- gisms, Darapti (III), Felapton (III), Fesapo (IV), and one weakened universal; Bramantip (IV). The Aristotelian rule that the middle term must be distri- buted once fails with the introduction of contraries. The rule to be substituted is—All pairs of universals are conclusive, but a universal and a particular require that the middle term should also be a universal and a particular,—universal in one premise and particular in the other. The rule that when both premises are negative, there is no syllogism, also fails. In the system completed by contraries, there are eight such syllogisms ; as many, in fact, as with pre- mises both affirmative. But in these cases, as before re- marked, the premises are not both negative in reality. Again, on the rule ‘that two particular premises can give no conclusion,’ the author brings forward as a legitimate inference, ‘Most Ys are Xs, most Ys are Zs, therefore some Xs are Zs; most men wear coats, most men wear waistcoats, therefore some men wear both coats and waistcoats,’ He develops this form at length into a symbolical scheme, under the name of ‘ The numerically definite syllogism.’ Mr. De Morgan’s system, on the whole, is characterized by an immense multiplication, not only of symbolical forms, but of verbal designations for the relationships growing out of the syllogism. BOOLE’S ADDITIONS. The late Professor Boole, of Cork, published two works on Formal Logic. The first and smaller, entitled—‘ The Mathematical Analysis of Logic,’ comprised an Algebraic rendering of the syllogism, showing how all the moods might be symbolically deduced. The second and larger work, en- titled—* An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Proba- bilities,’ takes a much wider sweep, and is an entirely new application of the symbolical methods of Algebra, to Inference, both Immediate and Mediate ; the largest share of attention being given to the first, or the so- called Immediate Inference The author also extends the same nomenclature and handling to Probabilities. Besides the novel employment of symbolical processes of the Algebraic kind, the work is intended to bear fruit in other Cr Tee CONNEXION OF LOOIC AND MATHEMATICS. 191 ways. In using the title ‘ Laws of Thought,’ tho author in- dicates that one purpose of his theory of Reasoning is to throw light upon the workings of the Intellect. He considers that our views of the Science of Logic must materially influence, perhaps mainly determine, our opinions upon the nature of the intellectual faculties. For example, whether reasoning con- sists merely in the application of certain first or necessary truths, originally imprinted on the mind, whether the mind is itself a seat of law [whatever that may mean], or whether all reasoning is of particulars, concerns not Logic merely, but also the theory of the intellectual faculties. It cannot be said, how- ever, that the author has been able to decide which alternative is the correct one. He farther proposes to elucidate the subtle connexion be- tween Logic and Mathematics; how far a common theory is applicable to both kinds of reasoning, and how far the likeness fails. He hoids that the ultimate laws of Logic are mathe- matical in their form, that they are, except in a single point, identical with the general laws of Number. The exhibition of Logic in the form of a Calculus is not arbitrary: the ultimate Jaws of thought render that mode possible, and forbid the perfect manifestation of the science in any other form. It is not of the essence of Mathematics to be conversant with the ideas of number and quantity. The author does not design to supersede, by symbolic processes, the common forms of reason- ing; nevertheless, cases may arise where the value of scientific procedure, even in things confessedly within the scope of ordinary reasoning, may be felt aud acknowledged. The author’s scheme starts with the consideration of Lan- guage as an instrument, not of communication merely, but of Reasoning; it being his intention to substitute, for ordinary language, a set of symbols adapted to perform this function in a more effective manner. The signs composing Language, with a view to Reasoning especially, are characterized in the following definition :—‘ A sign is an arbitrary mark, having a fixed interpretation, and susceptible of combination with other signs in subjection to fixed laws dependent upon their mutual interpretation.’ The first part is obvious; a sign, in its primary invention is purely arbitrary ; ‘house’ and ‘domus’ are equally good for the purposes of language. It is also obvious that each sign should possess a fixed interpretation, that there should never be any ambiguity of meauing. Ordinary language is greatly liable to 192 BOOLE’S ADDITIONS TO THE SYLLOGISM. this infirmity; hence, one of its defects as an instrument of reasoning. Lastly, signs must be susceptible of combination with other signs, which combinations must have fixed laws depending upon their mutual interpretation. The author proceeds to explain his artificial symbols for superseding, by a higher mechanism, the vocables of our ordi- nary speech. The symbols, and their connecting signs of operation, are borrowed from Algebra, and are manipulated by the algebraic processes, after allowances are made for the difference between the material of Logic, and the material of Mathematics (Number and Quantity). All the operations of Language, as an instrument of Reason- ing, may be conducted by a system of signs composed of the following elements :— First, Literal symbols, as a, y, 2, &c., representing things as subjects of our conceptions. For the object ‘man’ we may use x, for a ‘ brute,’ y, for the quality ‘ living,’ z, and so on. Second. Signs of operation, as +, —, X, standing for the operations whereby conceptions are combined, or, when com- bined are resolved into their elements ; ‘men and brutes’ may be represented by « + y. Third. The sign of identity =. These symbols of Logic are used according to definite laws, partly agreeing with, and partly differing from, the laws of the corresponding symbols in the science of Algebra. The first class of symbols above given are the appellative or descriptive signs, expressing either concrete things, or the qualities of things; that is to say, they are the equivalents of the two appellative parts of speech, the Noun and the Adjec- tive. Thus, let a denote ‘men,’ or all men; and let y denote the adjective good ; then all good men would be expressed by some suitable combination of « and y, Now the suitable com- bination, for the case of a thing qualified by an attribute, or of {wo or more co-inhering attributes is a product @ X y, or ay. Why this, and not the sum a + y, is the proper symbol, the author does not specifically explain; the means, as in other symbolical sciences, are left to be justified by the end, namely, arriving at true results. Soif # stands for ‘ white’ or ‘white things,’ y for sheep, x y stands for ‘ white sheep ;’ and if z stands for ‘horned,’ z « y will represent ‘horned white sheep.’ In this symbolism, the order of the symbols is unimportant, just as the order of the adjective and the sub- stantive is indifferent as regards the meaning; ‘good man,’ ‘vir bonus’ are equally accepted by the mind to suggest that oe . lo SYMBOLS FUR PARTS AND WHOLE. 193 the conception ‘man’ is to be limited by the conception *good.’’ Hence we may use at pleasure x y, andy a; « y 2, and zy a, &c. It is a law of speech that an appellative gains nothing (ex- cept perHaps rhetorically) by repetition or duplication ; ‘ good, good, is the same as good; ‘horse, horse,’ is the same as horse. To adapt this to symbols, « ¢ would amount to no more than w; that is, using = (as in Algebra) for equivalence, or iden- tity, « “= 2 Here Logic and Algebra are at variance, and the methods of manipulating logical symbols must vary ac- cordiugly. The author shows that the form « = », or # = #, has still deeper meanings. Next as to signs for collecting parts into a whole (quantity in extension) or for separating a whole into parts. These cor- respond to the conjunctions ‘and,’ ‘ or,’ in common speech— ‘trees and minerals;’ ‘barren mountains, or fertile vales.’ The sign of addition is now used; let x be ‘trees’ and y ‘minerals ;’ the conjoined expression is + y. This employ- ment of the sign is so closely allied to addition in arithmetic, that it may be worked upon the same principle. Again, let « stand for men, y for women, and z for European; then ‘Huropean men and (European) women’ would be represented by z(@ + y) = 4a+ zy. Addition implies subtraction. ‘ All men except Europeans’ will be expressed by a—y. ‘ White men except white Asiatics’ (% men, y Asiatics, z white), 2(w—y) = em—a2y With a view to Propositions, it is necessary to consider the rendering of the copula. For this purpose all propositions have to be reduced to the form ‘is’ or ‘are ;’ ‘ Cesar conquered the Gauls,’ must be resolyed into ‘ Cesar is he that conquered the Gauls.’ This is the copula of identity, the most generalized form of relationship of subject and predicate. It may be ex- pressed by the symbol =; and the meaning so far coincides with the Algebraic meaning, that the Logical equation is little different from the Algebraic equation. Take the Proposition, ‘The stars are the suns and the planets.’ Let stars be represented by 2, suns, by y, and planets, by z; then, : = z Whence we can deduce, «—y=—=z2z(The stars, except the suns, are planets), or, «© — z = y (The stars, except the planets, are suns). Thus, in the Logical equation, we may apply the mathe- 194 BOOLE’S ADDITIONS TO THE SYLILOGISM. matical axioms ‘equals added to equals give equal sums; ‘equals taken from equals give equal differences.’ If two classes of things, * and y, be identical, that is, if all members of the one are members of the other, then such members of the one class as possess a given property, z, will be identical with the members of the other that possess the same property. Hence, if we have the equation oe Yy: then, whatever class or property 2 may represent, we have also oe =Sz Yy. In point of form, this coincides with the algebraic law—if both members of an equation be multiplied by the same quantity, the products are equal. % The analogy, however, does not extend to division, For, supposing the members of a class ~, possessing the property z, are identical with the members of a class y, possessing the same property, it does not follow that the members of the class x universally are identical with the members of the class y. Hence, it cannot be inferred from the equation 42% =2Y, that the equation == is also true. Thus, the process of division, as applied to equations in Algebra, has no formal equivalent in Logic. Multiplication sufficiently represents the combination or com- position of conceptions, but division does not appear to repre- sent their decomposition or abstraction. The want of analogy on this point, however, is not total. Even in Algebra, the rule of division does not hold throughout ; for example, it does not apply when the divisor is z=0O. Through this one loophole, the author is able to restore the consistency of the algebraical and the logical processes. Reverting to the equation x = & ‘ he remarks that only two values of 2 will comply with it; namely, 0 and 1. For 0? = 0, and 1*=—1; and of no other numbers is the relation true. Hence, in an Algebra, whose symbols a, y, z, &c., never knew any values but 0 and 1, the laws of operation would coincide with the laws of operation in Logic. The two sciences are divided by no other difference than the manner of interpretation. , In chapter III., Boole professes to derive the laws of the symbols of Logic, above assumed, from the laws of the opera- SYMBOLS FOR COMPLEX SUBJECTS. 195 tion of the mind. He proceeds thus :—In every discourse, there is a limit to the subjects considered ; in other words, _ a unwerse. [He is here at one with De Morgan]. Thus the term ‘men’ is used with. reference to a certain implied exten- sion, on the part of the speaker ; it may be all men whatsoever ; or it may be a more limited universe, as civilized men, men in the vigour of life, and so on. The term ‘ men’ raises in the mind of the hearer the beings so intended to be comprised. Let us next consider the employment of an adjective in addition. Suppose ‘men’ to be spoken of in the widest sense, the uni- verse ‘all men;’ then the application of the adjective ‘ good’ prescribes the operation of selecting from the universe all objects possessing the further quality ‘good ;’ such selection corresponds to the combination—good men. Thus, the office of an adjective is not to add the quality, ‘ good’ for instance, to all the universe, men, but to select, from the universe, individuals according to the idea prescribed in the word. The intellectual faculties employed in these successive operations may be sup- posed to be those denominated Conception or Imagination, and Attention ; or perhaps the entire act may be summed up in one function of Conception. Hach step in the process may be characterized as a definite act of conception. Now, the syllogism above adopted exactly corresponds to this operation. The symbol z directs attention upon a certain universe, men for example; the symbol y, good or white, di- rects us to search that universe for individuals owning the pro- perty named ; and the combination y x, or * y, expresses the selection—good men or white men. This symbol will not fall under the relations expressed by a sum ; its meaning is a group qualified by the conjoined conceptions x and y, not an aggregate made up by adding the universe x to the universe y. In this way does Boole consider that he has established his positions: (1) that the operations of the mind are subject to general laws, and (2) that these laws are mathematical in their form; whence the laws of the symbols of Logic are deducible from the opera- tions of the mind in reasoning. He then proceeds to determine the logical value and signifi- cance of the symbols 0 and 1, to which quantities Algebra has to be cut down, in order to become Formal Logic. The sym- bol 0 corresponds to Nothing; the symbol 1 corresponds to the universe of discourse. Nothing and Universe are the two limits of extension—none and all. Whatever the class y may be, the individuals common to it and to the class 0, or Nothing, are Nothing or none. That is, Ox ¥y=—0,or0y=0 ay a a 196 BOOLE’S ADDITIONS TO THE SYLLOGISM. Again, the symbol 1, satisfies the law of equation, _xXy=yorly sy whatever y may represent. ‘The class represented by 1, there- fore must be ‘the Universe,’ the only class cuntaining all the individuals that exist in any class, . Now as tocontraries, If x represent any class of objects, 1—« will represent the contrary, or supplementary class, what remains when z is withdrawn from the Universe of discourse 1. Ifa be ‘men’ in the universe ‘animals,’ 1 —~ is the not- men, the remaining members, or the brutes. This coincides with De Morgan’s symbolism, U—z« for the contrary of a. The author next offers from his fundamental logical equa- tion, 2”? = x, or x —«* = 0, a formal proof of the Law of Con- tradiction, thus :—The equation admits of the form z(1—z)—=0 which, being interpreted according to the meaning of the symbols, is that a class determined at once by 2, and by its contrary 1 — a, is the same as 0 or Nothing; that is, does not exist. Advancing farther into the consideration of Propositions (chap. IV.), the author divides these into ‘ primary’ or simple, and ‘secondary’ or complex; the one relating to things, the other to propositions. Under the last named class are included hypotheticals, &c. He begins by propounding a general method for expressing any ‘term’ that may enter into a primary proposition. The method is merely the appli- cation of his symbols as already explained. Thus, let # repre- sent opaque substances, y polished substances, z stones ; then “xy z = opaque polished stones. . Now as 1 — z represents substances that are the contrary of | stones, or are not stones, 9 a y (1 — z) = opaque polished substances that are not stones ; Oo w« (1—y) (1 —2)= opaque substances, not polished, and not stones, Again, for the case of collections of things,—or objects con- joined by ‘and,’ ‘or,’—the sign of addition must be added, as above explained. The sign ‘or’ gives a disjunctive form; all #’s are either y’s or z’s; and this has two meanings not dis- criminated by the use of ‘or,’ but differently rendered in the formula. It is a question whether x may, or may not be both yandz. ‘ He is either a rogue or fool;’ he may or may not be both, so far as this expression goes, although the more Se ee COMPLEX TERMS. 197 usual rendering would be ‘not both.’ The two ways of sym- bolic expression are the following. (1) Things that are either w’s or y’s, are things that if «’s are not y’s, and if y’s are not ws; that is x(1—y)+y(l—2). (2) Things that are either «’s, or if not a’s, then y’s. x+y (1—2). This admits the supposition of being both « and y, a suppo- sition more explicitly given in the enlarged equivalent form. ey + 2«(l—y)+y (l—z), where we have all three alternatives : zy expressing the concur. rence of both#z andy. If heis not a rogue heisa fool, « fool, y rogue, « (1—vy); if he is not a fool he is a rogue, y (1 — 2); he is a fool and a rogue together, w y. To take a more complex example, exhibiting the full power of the method; let * = hard, y = elastic, e = metals; and we shall have the following results: non-elastic metals = z (1 — y). Elastic substances, together with non-elastic metals, y +z 1 — y). Hard substances except metals, « — z. Metallic substances, except those neither hard nor elastic, een) (l—y) orz4 Pee ony To take a still more complicated examples: ‘ Hard substance, except such (hard substances) as are metallic and non-elastic, and such (hard substances) as are elastic and non-metallic.’ Hard substances being represented by #; substances hard, metallic, and non-elastic, are « z (1 — y); substances hard, _ elastic, and non-metallic, are z y (1--z), and the whole expres- sion is z—fe a(l—y)+ay (1—z) or ~— «x z(1—y)—a# y (1—z). Such is the expression of Terms. To form Propositions, the sign = is used for the copula of identity. Thus, to ex- press identity between ‘ Fixed Stars’ and ‘ Suns,’ or to express that ‘ All fixed stars are suns,’ and ‘ All suns are fixed stars,’ { Hamilton’s universal with universal predicate], ime is This is the form applicable to the verbal proposition or de- finition ; and the author exemplifies it by such. For example, Senior’s definition of wealth, as consisting in things trans- ferable, limited in supply, and either productive of pleasure 198 BOOLE’S ADDITIONS TO THE SYLLOGISM. or preventive of pain, is symbolized thus. Let w = wealth; t = things transferable; s ~ limited in supply; p = pro- ductive of pleasure; r = preventive of pain. Now it is to be remarked that the conjunction ‘and’ is not necessary and might be misleading; ‘and’ conjoining two adjectives ‘ great and good men,’ is very different from ‘and’ coupling two groups ‘great men and good men;’ the first is « y z the second « zg + y z We farther remark that the disjunctive ‘or’ in ‘ productive of pleasure or preventive of pain,’ means things that ‘if not productive of pleasure are preventive of pain ;’ and that, ‘if not preventive of pain are productive of pleasure ;’ and does not suppose any class of things to be both at once. With these explanations, the definition is embodied — in the formula, w= st \p(1—7) + r (l—p) ; Passing now to [teal Propositions, as—‘ men are mortal,’ we need a mode of rendering particular terms; ‘ All men are sone mortal beings.’ Let v represent an indefinite class, some of whose members are mortal beings; and let « stand for the the entire class ‘ mortal beings ;’ then v 2 will represent ‘some mortal beings.’ Hence if y stand for men, the equation sought is— YT Us The qualifying symbol v is thus the mark of particularity in every case. In the proposition, ‘ the planets are either primary or secondary’ (some primary bodies or else some secondary bodies), Let # represent planets (the subject) ; y = primary bodies; z = secondary bodies ; then, assuming that the planets cannot be both primary and secondary, the equation of the proposition is =v fy (1 = 4) +2(1—y).} A more simple form, stating the same proposition, is xv (y +2). For, the meaning obviously is, that the planets fall exhaust- ively under the two heads, primary aud secondary; that is, are made up of some primary and some secondary bodies, Such is the symbolism applicable to affirmative real proposi- tions, where the predicate, as a rule, must be sapposed to surpass the subject. The author next shows how to express negative propositions. . ee. ee oa ee ee EXPRESSION OF PROPOSITIONS. 199 Suppose the case, ‘No men are perfect beings,’ a universal negative. Here, we make an assertion to the effect that ‘ all men’ are ‘not perfect beings.’ The meaning may then be expressed thus :—All men (subject) are (copula) not any part of perfect (predicate). Let y represent ‘ men,’ and # *‘ perfect beings.’ ‘ Not perfect beings’ are repr esented by she negative form 1—z ; and ‘some not perfect beings,’ by this form, quali- fied by the sign of particularity, v. Hence, the equation is y =v (l—2). Thus, to express the form No as are ys, we have to convert it into ‘ All ws are not (any part of) ys.’ A particular negative proposition, ‘some men are not wise,’ is resolvable into ‘some men’ (subject) ‘are’ (copula) ‘ not wise’ (predicate). Putting, then, y for ‘men,’ « for ‘ wise,’ and v for an indefinite containing some individuals of the class qualified by it, we have for ‘some men, vy, for ‘not any part of the wise,’ v (1 —-~), or the equation vy =v(l— 2). So much for the eattil odd expression of primary or simple propositions. Itis next to be seen how these forms are turned to account in furnishing immediate infereuces, or in exhaust- ing all the equivalent propositional forms of each; in which operation the eamigy principally expends the force of his method. With this view, permission must be given to work the several equations after the algebraical model, with the restrictions already stated. The reader must be satisfied from the ex- planations afforded that the signs used have the same force in Logic as in Algebra. The conditions of valid reasoning are then those three :—First, that a fixed interpretation be as- signed to the symbols; secondly, that the formal processes of solution or demonstration be conducted in obedience to the laws laid down as to the meanings of the signs of operation ; thirdly, that the final result be interpreted in the same way as the original data. Having once clothed the logical meaning in the algebraic dress, the author claims to proceed exactly as if he had to deal with an algebraic equation wherein the symbols have only the two meanings and 1. The exhaustive renderings of each proposition are to be gained by a process of ‘development,’ which is explained at length, and is strictly after the manner of Algebra, with the conditions of value specified. The skeleton of the form of _ development is furnished from these considerations :—Suppose we are considering a class of things with refereuce to the point 200 BOOLE’S ADDITIONS TO THE SYLLOGISM. whether its members possess or do not possess a property < ; as avimals, with reference to, humanity. Suppose next that the members possessing the property 2, possess also a property wu; and that the members not possessing the property a are subject to a condition v. On these suppositions the class in its totality is represented by : uetyv(1—2). ; Any function of x, f (x), whereiu « is a logical symbol, susceptible only of the values 0 and 1, is said to be developed, when it is reduced to the form a x + b (1 — 2), a and b being so determined as to make the result equivalent to the function whence it is derived. The following out of this development is purely algebraical, and occupies a good many pages of the work. To a student versed in ordinary Algebraical equations, the whole is sufliciently intelligible. We shall here indicate merely the results and applications. The following is given asan example. Itis a definition with two defining marks. ‘Clean beasts are such as both divide the hoof and chew the cud.’ Let 2 = clean beasts, y = beasts dividing the hoof, % —= beasts chewing the cud, The definition will then be represented by the equation “= y 2, which may be reduced to the form xr—y2z2=—0, Here a function of x, y, and z, namely « — y z has to be developed according to the methods laid down. As a speci- men, we may transcribe the development ; Oxy + ay (1 —2)+a(1—y)2+x2(1—y) (1—2z) —(1—a) ya + 0 (1—2x) y (1 —z) + 0(1—ax) (l— y)z + 0 (1—z)(1— y) (1—a). Now all those terms that are multiplied by 0 necessarily vanish and the remaining terms are * xy (1—z)=0,axz (1—y)=0, x2 (1 —y)(1—z) =0,(1— 2x) yz=0. Which equations all express the denial, or nothingness, of the combinations given in the left side of each. Thus 2 y (1 — «) = 0 means that there cannot be beasts that are clean (x) and that divide the hoof (y), and that do not chew the cud (1 —z). So the last of the four, (1 — x) y e=0, indi- cates that there are no beasts unclean (1 — #) and yet divid- ing the hoof (y), and chewing the cud (2). These equivalent forms are somewhat obvious in themselves without the aid of analysis; but the author evolves more complicated equivalents, such as these :—‘ Unclean beasts are EQUIVALENT FORMS. 201 all that divide the hoof without chewing the cud, all that chew the eud without dividing the hoof, and all that neitber divide the hoof nor chew the cud.’ he reader may be curious to _ see the corresponding equation :— 1—a#=y(l—2)+2(1—y) +(1—y) (l—a2). It is obvious, from this instance, that, out of a definition containing three or four defining marks (Senior’s definition of wealth, for example), a great many equivalent forms are deriv- able. Whether there be any important form that the unassisted mind might not evolve, is not quite apparent. It is possible, however, that cases might arise where the symbolical method would yield equivalents too recondite for an intellect with only the ordinary logical training. The author extends his analysis so as to comprise a more difficult order of examples, typified thus. Suppose the analysis of a particular class of substances has conducted us to the following general conclusions, namely :— First. Wherever the properties A and B are combined, either the property C or the property D is present also; but they are not present jointly. Secondly. Wherever B and C are combined, A and D are either both present or both absent. Thirdly. Wherever A and B are both absent, C and D are both absent also; and vice versa, where C and D are both absent, A and D are both absent also. Let it then be required from these conditions to determine what may be concluded in any particular instance from the presence of the property A, with respect to the presence or absence of the properties B and C, paying no regard to the property D. ‘The working of the corresponding equations leads to this answer :— Wherever A is present, there either C is present and B absent, or C is absent. And, inversely, wherever C is present and A is absent, there A is present. Several other curious combinations might be quoted, still growing out of the equivalence of simple propositions. We are next led to the consideration of Secondary Propositions (hypotheticals, &c.), which the author symbolizes by introduc- ing the idea of Time as their peculiarity, A simple, unqualified proposition (affirmative) holds through all time; a negative, through no time; a qualified proposition holds only through a certain limited time. The symbol 1 may represent an unqualified truth, as being true through the whole universe of time; (0 will stand for an unqualified negation, something true for no time. Let X represent a certain proposition, and let 202 BOOLE’S ADDITONS TO THE SYLLOGISM. represent the time of its being true. So, if Y represent another proposition, y may be taken for the time of its being true. Taking both propositions together, « +- y will denote the aggregate of the times when both X and Y are respectively true, those times being separated from each other. Again, x — y may denote a remainder of time left when the time y is taken from the time %, it being supposed that a includes y. So, « = y will indicate that X and Y are true for identical times. Further, « y indicates the portion of time when X and Y are both true. Now, as x denotes the time of X’s being true, 1 — # will denote the time that X is false. So # (1 — y) will denote the time when X is true and Y is false: and so on. The same system is to be applied to any number of symbols. To express the proposition ‘ X is true’ (there being no limit or qualification), we have e== di To express the proposition ‘ X is false—? ® =-0. To express—‘ Hither the proposition X is true or the propo- sition Y is true (not both).’ First, ‘When X is true Y is false,’ is signified by (1 —y); ‘when Y is true X is false,’ — is signified by y (1 — 2): the equation then is a(l1—y)+y(l—2)=1. Next to express the conditional Proposition, ‘ If the proposi- tion Y is true, the proposition X is true.’ This implies that whenever Y is true, X is true; or that the time of the truth of X covers the whole time of the truth of Y, and possibly more. Hence X is at least equal to, if not larger than Y. Conse- quently some form must be given, implying that Y is contained in X: a form analogous to that required for a universal affir- mative proposition. Let v represent an indefinite portion of . time, such as to express the unknown part of a whole, ‘some, it may be—all,’ and the equation required is yY— ve. It is unnecessary to exemplify the symbolism for the more complicated cases. The author is so far carried away by the success of his expedient for expressing compound or secondary propositions by a reference to time, that he speculates on an analogous mode of expressing the primary propositions by a referesice to space; and thinks that he thus lends some coun- tenanve to the doctrine that Space and Time are ‘ forms of the human understanding.’ A chapter is devoted to the treatment of the secondary pro- ¥ _ENUMERATION OF PROPOSITIONS, — 203 positions, by way of exhausting their whole implication, in the manner previously shewn for the primary propositions; the effect being, however, merely to deduce the usual consequences of disjunctive and of conditional assumptions. It is to be remarked that the process is still one of immediate inference, confirming the view that in hypothetical syllogisms so-called, there is no real or mediate inference. In order to exhibit the value of the symbolical evolution of equivalent forms, Boole selects for analysis two specimens of metaphysical argumentation, sufficiently perplexing to test the powers of a logical method. They are (1) a portion of Samuel Clarke’s ‘ Demonstration of the Being and Attributes of God,’ and (2) Spinoza’s argument to prove the identity of God and the Universe. He confessed that one main difficulty in dealing with those arguments is to extricate the real premises of the authors; he might have added the farther difficulty of assign- ing definite and consistent meanings to the very abstract terms made use of by them—necessity, existence, eternity, cause, &c. But the premises once obtained, it is possible to embody them in symbols, and then to extract all their equivalents by solving the corresponding equations. 'The method may be commended as an interesting effort, varying and corroborating the method followed by a logical and acute mind working upon the ipsa corpora of the premises, without symbolism. We have now reviewed the larger half of Boole’s work, and as yet have seen no mention of the syllogism. A short chapter is all that is bestowed upon mediate inference; which, how- ever, is a mere carrying out of the algebraic method, with the modifications demanded by the nature of the case. He begins by accepting De Morgan’s additions to the four types of propositions in the common Logic. He lays out the eight forms, with his equations for them: expressing the four new forms by supplying a contrary subject to each of the old forms. The parallelism is shown thus A — All Ys are Xs y= ve (1) (A) All not-Ys are Xs l—y=ve (2) E No Ys are Xs y = v(1—2) (3) (E) No not-Ys are Xs 1l1—y=v(1—2) (4) = { All Xs are Ys eCm=vy I Some Ys are Xs vy = Ue (5) (1) Some not-Ys are Xs v(l—y) = ve (6) 204 BOOLE’S ADDITIONS TO THE SYLLOGISM. — J Some Xs are not Ys vy =o(1—y} O Some Ys are not Xs vy =v(l— a) a (O) Some not-Ys are not-Xs v(l—y)=v(l—a2) (8 The second form of E coincides with A by mere transposition of letters. The second form of I is O, in like manner. The second form of O (O) is the only new form—Some not-Ys are not-Xs, some things are neither Ys nor Xs. This is one of De Morgan’s two disjunctives; his other disjunctive—no not-X is not Y, every thing is either X or Y—does not appear in the above list. The laws of Conversion follow from the symbolical forms. The proposition ‘ All Ys are Xs’ being represented by y = v x, we have only to read v x = y, Some Xs are Ys. To convert the same proposition by negation (obversion and con- version), we deduce, by eliminating », y(l—2)=0 which gives by solution with reference to 1 — 2, 0 1—2#=5 (1 —y); whose interpretation is ‘ All not-Xs are not-Ys. [This opera- tion contains methods and symbols not explained in the fore- going abstract |. So far as Conversion goes, the author merely continues his former methods of reducing and interpreting equations ; as we might expect from considering that conversion is merely one variety of Immediate or Equivalent Inference. The sYLLOGiIsm demands a step in advance. The two premises must be em- bodied in two equations, with a common middle term, and that term must be made to disappear in a third formed out of these two. Thus, All Xs are Ys e=vy All Ys are Zs y = v's. Whence, by substituting for y, in the first equation, its value in the second, we have All Xs are Zs 2 ues. The form v v’z shows that # is a part of a part of 2. Sowith © all other cases ; it is requisite merely to eliminate the middle term y. The method might be easily carried through the whole of the ordinary syllogisms ; as well as applied to the un- figured and fallacious forms. But the author proceeds to deduce the general rules of the syllogism by an equation com- prehending all the forms of valid reasoning. He gives as the results of the analysis these rules: ‘when one middle term, at a ae RULES OF THE SYLLOGISM. 205 least is universal, equate the extremes.’ ‘In case of unlike middle terms (one positive and the other negative), with one universal extreme, change the quantity and quality of that extreme, and equate the result to the other extreme: and with two universal middle terms, change the quantity and the quality of either extreme, and equate the result to the other extreme unchanged.’ Suppose the case— All Ys are Xs All Zs are Ys. This belongs to the first rule. ‘All Ys’ is the universal middle term; the extremes being equated give as the conclu- sion, All Zs are Xs. Suppose next— All Xs are Ys No Zs are Ys. The proper expression of these premises is— All Xs are Ys All Zs are not-Ys. They belong to the case of unlike middle terms, and have one universal extreme. Whence, by application of the rule, we change the quality and the quantity of that extreme, and equate it with the other extreme— All Xs are not Zs, or No Xs are Zs. Commencing from the other universal extreme, we obtain the equivalent result— No Zs are Xs, A third case— All Ys are Xs All not-Ys are Zs. Here the terms are of unlike quality. There are two uni- versal middle terms, and, by the rule, we change the quantity and the quality of either extreme (Some Xs into All not-Xs), and equate with the other extreme (Some Zs). All not-Xs are Zs. The two last examples are selected by the author as present- ing syllogisms that would not be regarded as valid in the Scholastic Logic, which virtually requires that the subject of a proposition should be positive. [As often remarked already, the want of a thorough-going recognition of contraries is the defect of the Aristotelian scheme]. The cases are, however, perfectly legitimate in themselves, and the rules for determin- ing them are undoubtedly the most general canons of syllogistie 206 BOOLE’S ADDITIONS TO THE SYLLOGISM. inference. The analysis employed, the author contends, is not properly of the syllogism, but of a much more general mode of combining propositions to yield results; and he gives an imaginary case to illustrate this wider import. Without pursuing the syllogism farther, Boole now dis- cusses the vexed question as to the fundamental type of de- ductive reasoning, and takes issue with Whately and with Mill, who agree in this that all valid ratiocination is ultimately the inferring of propositions from others of a more generat kind; the syllogism being a full and adequate formal repre- sentation of the process. Now, as the Syllogism is a species of elimination, the question resolves itself into these two deter- minations, namely, first, whether all elimination is reducible to Syllogism; and, secondly, whether deductive reasoning consists only of elimination. To the first question, he replies, that it is always theoreti- cally possible so to resolve and to combine propositions that — elimination may subsequently be effected by the syllogistic canons, but that the process of reduction would, in many cases, be constrained and unnatural, and would involve operations that are not syllogistic. To the second question, he replies that reasoning cannot, ex- cept by arbitrary restriction, be confined to elimination. It cannot be less than the ageregate of the methods founded on the Laws of Thought, and the process of elimination, import- ant as it is, is only one process among others. He farther remarks that, of all the Laws of Thought, the one of fundamental importance in Logic, is the Law of Con- tradiction, to which Leibnitz also assigned the same position. All persons that have attained a just notion of the Rela- tivity of Knowledge, would agree with Boole in the prime im- portance thus given to Contrariety or Contradiction; but this merely goes the length of Equivalence or Immediate Inference. It prepares the way for Syllogism, and is the main key to the useful enlargements of the syllogism ; but it does not touch what is essential to deduction. The axiom, or ‘law of thought,’ at the foundation of mediate inference must be something else. and if it is not the axiom assigned in the previous chapter of this work, itis an axiom yet to be sought Passing from Boole’s somewhat vague generalities to his actual method, which con- sists in combining two equations standing for the premises of the syllogism, into a third standing for the conclusion ; and adverting to the maxim that justifies the process of reduction, ee os ae _— AXIOM OF THE SYLLOGISM. 207 we seem to see that it is the same maxim as enters into a pro- blem of equations with two or more unknown quantities ; as for example, given «+ y= a,x — y — 8, to find wand y. Grant that the conditions of a logical syllogism are fairly ex- pressed by Boole’s symbols, and that the algebraic reduction is suitable and relevant to the case, then the logical axiom is the algebraic axiom that permits the substituting for y in one equation, of its equivalent in the other; as when we obtain from &—y = b, y = x — J, and insert this value of y in the equa- tion « + y=a. The axiom of direct application to the case would be that, for any quantity, its equivalent may be substituted in an equation; in other words, the substitution, for any quantity, of its equivalent, does not change the value of the equation. This is a various reading of the axiom of mediate equality—things equal to the same thing are equal to one another; an axiom to which Mr. Mill compares, in point of form, the axiom of the syllogism. If one thing is equal to a second, and the second equal to a third, the first is also equal to the third. In a combination containing A and B, we may introduce in room of B its equivalent C. A large portion of the work is devoted to Probabilities, in handling which, the author continues the symbolism employed in the previous portion of the work. It is generally admitted that he has made important additions to the theory of this subject, the common ground of Mathematics and of Logie. CHAPTER III. FUNCTIONS AND VALUE OF THE SYLLOGISM. 1. It is the peculiarity of the Syllogism, that the conclu- sion does not advance beyond the premises. This circum- stance has been viewed in two lights. On the one hand, it is regarded as the characteristic excellence of the Syllogism. On the other hand, it is represented as constituting a pelitio principit. In the syllogism ‘men are mortal, kings are men, kings are mortal.’ the conclusion seems already affirmed in the premises. 10 SOLE ee 208 FUNCTIONS AND VALUE OF TH# SYLLOGISM. By virtue of the universal major, coupled with the interpreting minor, there is distinctly involved in the premises the fact that , kings are mortal.’ (1) To this circumstance has been attributed ‘the peculiar ee dignity, and certainty of syllogistic inference. When the two premises are supplied, the conclusion cannot be refused without self-contradiction. There is nothing precarious in the leap from the premises to the conclusion. The same circumstance has been represented in a more dis- advantageous light. The allegation is made that mere repeti- tion is not inference; that to reproduce in a new form what is already given may be highly convenient (as in the various kinds of Immediate Inference), but is no march, no progress from the known to the unknown. (2) There remains a far more serious charge, and one that takes us direct to the root of Formal Reasoning. Supposing there were any doubt as to the conclusion that kings are mortal, by what right do we proclaim, in the major, that all men are mortal, kings included ?P It would be requisite, seemingly, to establish the onesie before we can establish the major. Ina order to say, ‘ All men are mortal,’ we must have found, in some other way, that all kings, and all peoples are mortal. So that the conclusion first contributes its quota to the major premise, and then takes it back again. This is the deadlock of the syllogism, the cirouri aia ad has brought down upon it the charge of ‘ reasoning in a circle’ (petitio principit). In point of fact, we can hardly produce a more glaring case of that fallacy. The extrication from the puzzle is due to Mr. John Stuart Mill, and the consequence has been a total revolution in Logie. 2. The major premise of a syllogism (in the regular figure) may, so far as the evidence is concerned, be divided into two parts; the one part containing the instances observec, and the other part containing the instances not observed, but inferred. The major premise, ‘ All men are mortal,’ consists of two very different statements. The first is, that a certain number of men have actually died. The evidence for these is actual observation, the highest of all evidence. The second statement is, that the men now living. and the men yet to be born, will die ; for which there is not the evidence of observation. In the same manuer may we analyze any other general REASONING IS FROM PARTICULARS TO PARTICULARS. 209 affirmation or negation. The proposition ‘transparent bodies bend light’ is made up of the bodies that have been actually experimented on, and of bodies that have not been experi- mented on; in the one case, the predicate is affirmed on the evidence of fact; in the other case, the predicate is affirmed by virtue of the inductive leap from the known to the unknown. Thus, the ordinary form of the general proposition confounds together the observed with the unobserved; the indiscriminate fusion of the two is what has perplexed the theory of the syllogism. 3. In affirming a general proposition, real Inference is exhausted. When we have said ‘All men are mortal,’ we have made the greatest possible stretch of inference. We have affirmed mortality of all men, of every class, in every age, past and future. We have incurred the utmost peril of the inductive hazard. Whatever justification needs to be offered for the inference in hand, must be advanced as a security for the major premise. | 4. The type of reasoning that best discloses the real process is reasoning from Particulars to Particulars. The basis of fact in every argument may be stated\to be the particulars actually known from experience; as the mor- tality of the men that have died. The inference is usually to some other particulars unobserved, as ‘the present inhabitants of London will die.’ The real evidence for the mortality of the men now living is the death of their predecessors. A, B, and C, have died ; D, now living, will die. The practice of reasoning at once from certain particulars experienced, to some other particular as yet unexperienced, (there being a similarity in the cases) is not only the usual, but the most obvious and ready method. We feel that the real force of every reasoning lies not in the general statement, but in the actual facts; and we are as much moved by the facts in their particularity, as when they are given in a gene- rality. That boiling water will scald the hand, is sufficiently proved by its having done so in innumerable past instances ; the deterring force lies in these actual instances. We are in- fluenced by individual precedents, as strongly as by rules. This is seen extensively in all professions. The experience of a professional man consists of the cases he has actually ob- 210 FUNCTIONS AND VALUE OF THE SYLLOGISM. served ; these he remembers as particulars, and when a new example i is presented, he at once assimilates that with the pre- vious particulars, and infers accordingly. When Dr. Mead was called in to the last illness of Queen Mary, he pronounced the disease to be small pox; his knowledge of that ailment was the remembrance of a series of patients previously wit- nessed by him; the queen’s symptoms resembled those, and he drew the inference. 5. Wherever we may infer from a certain number of particulars given, to one other particular, we may infer to a whole class, or make the inference general. If we can infer, from the men that have died, that the pre- sent Pope will die, it is by virtue of a sufficient amount of re- semblance between them and him; and we must be prepared to make the same inference in all other cases where the re- semblance holds. We may, therefore, say once for all, whoever resembles past generations of human beings, in the points wherein the pope resembles them, will die. The justification — of one is the justification of the whole. The inference to an individual case must ‘not be arbitrary ; it must be grounded on a resemblance, and be applicable wherever the resemblance i is found. In a general proposition, therefore, we state the points of resemblance that entitle us to infer from past particulars to a new particular; and in stating these points we render the in- ference at once general, and formally exhaustive. We mingle up in one statement the observed known, and the inferred unknown, the evidence and the conclusions. The use of general language enables us thus to rise beyond particular inferences. 6. Deductive Inference may be described as a BIA of Interpretation. Although the major premise covers the conclusion, it does nos point to it by name, but only by character. The premise ‘men are mortal’ does not specify kings, nor the living pope ; it indicates certain marks by which we are to judge whether kings and popes are to be pronounced mortal, namely, the marks of ‘men or humanity.’ Something, therafobera is want- ing in addition to the major premise, in order to the conclu- sion, the pope is mortal; we have to be assured that he is a man, that he conforms to the defining marks of human beings, To supply this requisite is the purpose of the minor premise, at Mae Pah. a. YS ae : oun r DEDUCTIVE INFERENCE IS INTERPRETATION 211 which declares that the pope possesses the attributes of men, or identifies him with the subject of the major premise. The necessity for such an affirmation rescues the syllogism from Immediate Inference or tautology. ‘ All men are mortal’ in- eludes ‘the pope is mortal,’ on the supposition that the pope is aman; and if this supposition is explicitly given in a distinct proposition, the pope is then brought within the sweep of the major premise : and the conclusion is established. After affirming a general proposition (or making a general denial) connecting or disconnecting a certain subject with a certain predicate—men and mortality— we have still to hunt out the particular cases of the subject, the things that possess its attributes. This is the real deduction, and it is a material and nota formal process. Itis an operation of comparing the actual individuals already pointed out by the generalized subject —actual and known men—with all future individuals as they occur, and of pronouncing agreement of the new with the old. The deductive inference that ‘ the pope is mortal,’ presupposes an examination (direct or indirect) of the pope’s personality. If this resembles the usual type of humanity, judged from the instances actually known to us, we identify him with the subject, ‘men,’ in our general proposition. The identity being considered satisfactory, we complete the syllogistic formula, and declare him to be mortal. The proposition ‘men are mortal,’ by its form of universality, imposes upon us, and leads us to suppose that we have in our grasp the whole human race. The correcter view is to regard it as an allegation respecting a certain number, with a power of including others as they come on the stage. The proposition assigns marks for the future identification of the beings that are to be declared mortal; and, as the identification proceeds, the minor premise is replenished with appropriate cases, and so brings forth the conclusion. The interpretation of a law or a command illustrates the purely deductive part of the operation of reasoning—the sup- plying of the minor. The law is given in general terms; cer- tain characters are assigned as belonging to the subject of the proposition. The administrator or judge ascertains whether any particular case has or has not the characters specified. If it has, a minor proposition is afforded, and a conclusion is drawn. This case also shows that the syllogism is the mere formal completing of an operation, not at all formal, but in the strict ‘sense material. The operation consists in comparing one par- 212 FUNCTIONS AND VALUE OF THE SYLLOGISM. ticular fact with other particular facts, through the medium of a general description. The wording of a law, however gene- ral be the terms, must be such as to suggest definite individual eases. When the law mentions heritable property, or person- alty, it must either state or suggest the particular things in- tended; and the question of the application to a given case turns upon the comparison of the case with the cases cited or suggested by the general term or definition. Hence, the business of the reasoner, in actual practice, 1s concrete com- parison, from which, in the last resort, he can never be ex- empted. This is riateriél deduction, which: in its essence, is the same as material induction, being the carrying out of the in- ductive operation, or the in-gathering of the details shadowed forth, but not actually seen, in the general proposition. Legal decisions are founded sometimes on statutes, some- times on precedents or previous decisions. There is no generic distincticn between the two modes. A statute has no meaning except the particular cases specified or suggested ; and a pre- cedent must involve a principle or rule. In both, the judge refers back to concrete particulars, which are viewed under a certain point of likeness or community. Another case is the application of general theorems furnished by the observations of others, such as the principles of science established by foregone researches. We may have had no share in arriving at the induction known as the atomic theory ; we have not even seen the facts, we receive them embodied and registered in the general statement of the law. We must understand the meaning of that statement; we must realize the kind of facts intended by it. When a case is started, a given compound of two substances, we must say, by concrete comparison, whether this compound has the characters of the compounds expressed as chemical compounds. For example, is the atmosphere a chemical compound? Does it agree with the general characters of chemical compounds, or with those typical instances that the general characters can do nothing but refer us to. This is a truly material deduction; it is that process of comparing instances that is the essence of the generalizing operation, as seen in induction. It exactly resembles generalization with a view to definition. 7. Although the deductive stage of induction is still an inference from particulars to particulars, which nothing can supersede, there are certain advantages in embodying the possible inferences in a formal generality. Powe. wae) UTILITY OF THE SYLLOGISM. 213 Mr. Mill remarks that the syllogistic form of inference, from generals to particulars, which supposes that each induction is made general, is ‘a collateral security for the correctness of the generalization itself.’ It is so in two ways. First. It increases the sense of responsibility on the part of the reasoner, by letting him know that his inference to one individual must equally apply to a large host of individuals. A common device for checking a rash inference is to point out the extent of the consequences involved. The legal decision against John Hampden, in the matter of thirty shillings of ship money, was portentous as affirming the king’s power to tax the nation without a parliament. Secondly. If an induction is unsound, the making it general is likely to. suggest contradictory instances. This is merely a modification of the same consequence. Any person attempting to justify a particular despotism must be prepared to say that, in all similar circumstances, despotism would be desirable. The remark is sometimes made, in the controversy as to the inspiration of the Bible, that even Milton was inspired; but, if so, then all great poets—Homer, Virgil, Dante, Chaucer, Shakespeare, Dryden, Byron, Shelley—must also own the gift of inspiration. Mr. Grote, in defending the received canon of the Platonic writings from the critics that would reject many of the Dia- logues, on the ground of their style being unworthy of Plato, points out the numerous Dialogues that would have to be sacrificed to this criterion, if each critic were allowed to reject for himself, and all rejections were admitted. 8. One great use of the syllogistic form is to analyze, bring to light, and present for separate consideration, the parts of a step or a chain of reasoning. This has been already exemplified in the applications of the syllogism to confused reasonings. It is advantageous to know that the truth of a conclusion by inference supposes the truth of two separate allegations, both alike necessary to the conclu- sion. To prove that A is C, by a mediate inference (B is C, A is B), two propositions have to be verified ; and the mind is aided in disentangling a perplexed argumentation, by knowing what to look out for. In stating the distinction between the two modes of reasoning, used both in Law and in Politics—reasoning from Precedents or Examples, and reasoning from Rules or Principles—Sir G. C, Lewis adverts to the great superiority of the last, the reasoning 214 TRAINS OF REASONING AND DEDUCTIVE SCIENCES. from Rules. The reason of the comparative obscurity of the argument from example or precedent, is that the principle involved is usually suppressed. ‘The reasoning is much more perspicuous when the general principle is stated first, the particular case is placed under it, and the conclusion is then drawn. In order to argue from one case to another, it is necessary to reject from each the circumstances immaterial to the matter in hand, and to compare those in which they agree. In complex cases, this process is often extremely difficult. Much sagacity and knowledge of the subject are required, in order to discriminate between material and immaterial facts—to reject enough, but not more than enough. For if immaterial facts are retained, the comparison becomes obscure and uncertain; if material facts are rejected, it becomes fallacious. This process, which, in the argument from precedent, must often be performed mentally, though it may be easy and sure to the experienced practician, perplexes the tiro. Hence, students of the law have great difficulty in collecting legal rules from cases, though they are soon able to apply a rule of law, laid down in general terms, to a particular case of practice.’ CHAPTER IV. TRAINS OF REASONING AND DEDUCTIVE SCIENCES. 1. A series of syllogisms may be connected in a chain. Logicians have always recognized compound reasonings. The Sorites is a connected chain of syllogisms. The conclusion of one syllogism may be the major premise to a second, and so on. The Sorites is usually stated in this form :— A is B, Bis C, Cis D, &c., therefore A is D. The regular form of proof (by the First Figure of the Syllo- gism is— B is C, A is B, therefore A is C. C is D, A is ©, therefore A is D, &e. It can scarcely ever happen that a proper deduction in this simple form can be protracted over two or three syllogisms. The application of a universal proposition to a particular case seldom needs to descend by three or more distinct steps: indeed, in by far the greater number of instances, the descent is made at once. No new logical principle, or modification of principle, is involved in these consecutive reasonings. Their lucid state. EXAMPLE OF A CHAIN. 215 ment is a matter of consideration for the expositor, but they present no speciality to the logician. Still, they are usually discussed in treatises on logic; and we may, following the example of Mr. Mill, take occasion from them to discuss two themes—the compatibility of the foregoing theory of the syllo- gism with such trains, and the nature of the Deductive Sciences. 2. A chain of Reasoning is reducible to a series of syllo- gisms, the major in each being an induction from par- ticulars, or a truth ultimately based in particulars. Thus, if we were to prove that intelligent beings, although they may be interrogated, are not to be experimented on like brute matter, we should have the following chain :—wherever there is intelligence, there is sensibility, in other words, suscepti- bility to pleasure and pain ; we are not at liberty to inflict pain ; now, most experiments that could be tried upon sentient crea- tures would be painful ; hence, intelligent beings are not fit subjects for experimental enquiry. Three syllogisms are con- cerned in this chain of reasoning. The majors are— (1) Society prohibits the infliction of pain. (2) All intelligent beings have sensibility to pain. (3) Experiments for ascertaining function in sentient beings lead to pain. Hach of these majors may be resolved, according to the method of the previous chapter, into particulars observed and particulars inferred, or left to be inferred, by virtue of identity. The first major (Society prohibits) is in the form of a command, the case where we may be supposed to be least concerned with the particulars, and most concerned with the general descrip- tion serving to identify the particulars. Still it must not be forgotten that the real force even of a command is embodied in the instances where it is enforced; the general state- ment means nothing, is nothing, except as referring us to these; the application of the rule is an inductive extension of these instances. The second major (intelligent beings have sensibility) takes in the observed coincidences of intelligence and sensibility, together with the future extensions of these by identification with the presence of intelligence—the first term of the couple. The third major is likewise an inductive gene- ralization, containing the observed particulars where experi- menting has ended in pain, together with the resembling inferred particulars. We may arrange the train of reasoning in syllogisms. Thus, --taking a different order— 216 TRAINS OF REASONING AND DEDUCTIVE SCIENCES. First Syllogism. Experiments for ascertaining function in sentient creatures lead to pain. The present proposal is an experiment for saver taney function. The present proposal will lead to pain (Barbara). Second Syllogism. Society prohibits the infliction of pain. The present proposal will lead to pain, Society prohibits the proposal to experiment on sentient beings (Cesare). Third Syllogism. Society prohibits experiments on sentient beings. All intelligent beings are sentient beings. Society prohibits experiments on intelligent beings, (Cesare). The form (Society prohibits, &c.), has the force of a nega- tive ; were it not so, the last syllogism would not be valid. The language of inference from particulars to particulars might be used in each of these syllogisms. Thus in the first : Experiments for ascertaining function in sensitive beings have been observed to lead to pain; the present case is an experi- ment for ascertaining function: the present case will lead to pain (as the observed cases have done). Similarly for the others. . The Deductive Sciences. 3. The Deductive Sciences are those where the labour mainly lies in applying or carrying out ascertained induc- tions, that is, in the discovery of minors to given majors. From the foregoing theory of the syllogism, it is apparent that every deduction supposes a previous induction. The Deductive Sciences, therefore, do not dispense with induction. Whereas, in the Inductive Sciences, such as Chemistry and Physiology, the chief labour consists in arriving at inductions ; in the Deductive Sciences, as Mathematics, the inductions are few and easily gained (being in fact sometimes called intui- tions) and the labour consists in carrying them out into their various applications, by bringing cases under them. We soon arrive at the inductions ‘things equal to the same thing are equal,’ or ‘the sums of equals are equal ;’ ‘ the differences of ae. wa a GEOMETRICAL DEDUCTION. 217 equals are equal : ’ but it was not easy to bring under the sweep of these inductions the proposition ‘a sphere is equal to two- thirds of the circumscribed cylinder.’ This is arrived at only after a long and circuitous process of successive deductions, based upon the invention of numerous diagrams. - If we take a comparatively simple case of geometric deduc- tion, the 47th of the First Book of Huclid, ‘the square des- cribed on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the two sides,’ we shall find that the proof can be accomplished by two main leaps—two syllogisms having axiomatic majors, and a preparatory syllo- gism having as its major a previously established derivative proposition. The rest of the process is not syllogistic. We first, by an ingeniously devised construction, establish two minors under the proposition—‘ A parallelogram and a triangle being on the same base and between the same parallels, the parallelogram is double of the triangle ;’ and then proceed to the main steps, the application of the axioms. We first apply the axiom—‘ The doubles of equals are equal,’ (a derivative from the axiom—‘The sums of equals are equal,’) to prove that the square described on one of the sides is equal to a part of the hypothenuse square, and that the square described on the other side is equal to the remaining part of the hypothen- use square. This being done, it needs but an easy application of the axiom—‘ The sums of equals are equal,’ to complete the proof. The deductive sciences circumvent their problems; they accomplish indirectly what there is no means of accomplishing directly. The science of mathematics instead of resting satis- fied with announcing its axioms and definitions, and leaving people to apply them at once, evolves a vast scheme of deductive properties, to any one of which we may repair in an emergency, instead of making a connexion at once with the fountain head. We measure a height by bringing the case under some theorem of Plane Trigonometry that chances to be adapted to the means at our command. The length and the complicacy of mathematical or other reasonings may be ascribed to these two circumstances. (1) There are many steps of mere Immediate Inference, as in applying Definitions. Thus, when Euclid shows that two figures coincide, he makes a formal appeal to the Definition of Equality (namely, Coincidence), and, by virtue of tliat declares them to be equal. This is seemingly a step in the reasoning ; it involves a distinct act of attention on the part of the stu- * «™ sv 6,37" “a 218 TRAINS OF REASONING AND DEDUCTIVE SCIENCES. dent, but it is not a deduction or syllogism. So, there may be steps involving other transitions to Equivalent Forms, as Ob- version, Conversion, &c. (2) Not only is a great deal of preparatory construction or scaffolding often required in order to bring the case under the sweep of a previous generality, but, when the construction is made, there jut out from every part of it separate inferences, and all these have to be made convergent to the purpose in hand. Moreover, many propositions start at once with a com- plicated hypothesis—‘ If a point be taken without a cirele (1), and straight lines be drawn from it to the circumference (2), whereof one passes through the centre (3),’ &c.; the proof in these cases is a convergent series of steps, each starting from a distinct member of the hypothesis. The process of Identification to supply a minor is difficult according to the complicacy of the subject of the major; as in Diseases, in Law, in Politics, &c. + sem of 4nd * a gl ail asl-s PUSHING OF DEDUCTIONS. 219 forees. A process of computation is substituted for a process _ of observation; the consequence is, in most instances, a great economy. The pushing of truths of induction to all their deductive applications is one great department of scientific research. The aptitude for the operation is almost purely intellectual. When a great law, such as Gravitation, has been established, _the following out of all its deductive consequences supplies work to several generations of men. The generalization of the present day, called the Persistence of Force, will give pro- bably an equal amount of occupation to the more purely de- ductive or speculative aptitudes of the scientific mind. The inductive laws that connect Mind with Body, when ascertained with precision, will admit of being deductively pushed in numerous ways, and will yield many facts at present discover- able only by separate observations. The doctrine of the Relativity of all Feeling and Thought hag not as yet been completely followed out to its consequences. CHAPTER V. DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH. 1. The kind of evidence named ‘ Demonstration’ has its sources in Induction. Demonstrative proof is only another name for Deductive proof, which, in the last resort,is Induction. The propositions of Euclid are said to be demonstrated ; and, as above seen, this means that the conclusions are proved by bringing each case under the sweep of the fundamental principles of the science. To make out Mathematical Demonstration inductive, it is requisite to show—(1) that the foundations of the Science (the axioms) are inductive; and (2) that the axiom of the Syllogism is inductive. The axioms of mathematics supply the principles, and the axiom of the syllogism justifies their application. In the question respecting the ultimate foundations of the so-called axioms, these are the chief examples in dispute. It is maintained, on one side, that the axioms of Mathematics, Ieee 220 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH. the axiom of the Syllogism, together with the axiom of Causn- tion, —are inductions from particular facts of experience; and on the other side, that they are of intuitive origin, and, in this origin, possess a higher certainty than can be given by experi- ence. * 2. The chief argument against the Inductive origin of these principles is that they are necessary, and no experi- ence can give the character of necessity. | The idea of ‘ necessity,’ as attaching to such truths as the mathematical axioms, dates from Leibnitz; it was re-stated, in a qualified form, by Kant, and persists in the minds of many to the present day. The term, however, is ambiguous, Meanings of Necessity. 3. I. In common speech, ‘ necessity * is a synonym of certainty ; and would apply to inductive truths. - | When speaking of anything that is certain to happen, we use among other words, the term ‘necessary.’ We should call the freezing of water, at 32°, a necessity, meaning that we are perfectly sure of its happening. We even say that vice isa necessary consequence of bad training. The necessity in such cases has admittedly nothing to do with intuitive perception. Experience is competent, in every instance, to give the strong assurance that the word signifies. So, we have only experience to rely upon in believing that the | sun must rise to-morrow. There could be nothing incompatible with this usage in terming all the inductive laws of nature ‘ necessary ’—the law of gravity, the laws of motion, the fundamental laws of organi- zation, and so on. But metaphysicians are accustomed to call these principles ‘contingent,’ as opposed to necessary; for al- though they are true, as the universe is now constituted, they might have been otherwise. The law of gravity might have been wanting ; the laws of organized beings might have been different. But, in no circumstance (it is said) could ‘two straight lines enclose a space ;’ this, therefore, is necessary in a more peculiar sense of the word, as will be next stated, * On the subject of Mathematical Evidence, other questions have been raised, namely, the place of the Definitions in the Science, and the su posed hypothetical character of definitions, These questions will be ad: verted to afterwards (Loatc or THE SCIEs crs, Mathematics), (quae NECESSITY AS IMPLICATION, Del 4, II. ‘Necessity’ more properly means implication ; ‘necessary truths’ in this sense are the truths demanded by Consistency. Their denial is a contradiction in terms. These truths have already been fully exemplified. (See InrrRopUCTION, and also EquivaLent PropositionaL Forms). That the less cannot contain the greater, is necessary ; it follows from the very meaning of less and greater ; it could not be contradicted without declaring the greater not to be the . greater. ‘The same thing cannot be in two places at once’ is necessary ; the meaning of a ‘place’ is some definite spot the negative of all other places; to say that a thing is ina particular place is to deny that it is in a second, or a third, or any other place. ‘Time isan eternal now!’ must be set down as self-contradictory. ‘Some of the axioms of Huclid are necessary in this sense. ‘A whole is greater than its part’ is implicated in the defini- tion of whole and part; it could not be contradicted without contradicting the definition, A whole is summed up by its parts; omit any of these, and the whole is not made up; the result is something less than the whole. ‘Things that coincide are equal’ is not an axiom but a de- finition ; it is the mark or test of equality, the only mark that ean be propounded in the last resort. Of all the alleged necessary truths, the one most frequently cited in the present controversy is—‘ Two straight lines can- not enclose a space.’ This was held by Kant to be a real pro- position, a synthetic judgment; in other words, the subject is not implied in the predicate; to it the criterion of ‘implica- tion’ wonld, therefore, not apply. | On the other hand, mathematicians are now probably unani- mous in regarding this as a corollary from the definition of the straight line, or as implicated in the very essence of straightness ; so that to deuy it would be a contradiction in terms. They would characterize it, in Kant’s own language, as an ‘analytic’ judgment. A very little reflection on the case proves that the mathematicians are right. Starting from the definition of the straight line—‘ when two lines are such that they cannot coincide in two points without coinciding alto- gether, they are called straight lines,’ we see that the very terms forbid the enclosing of a space; what meaning can we attach to ‘coinciding altogether,’ but the exclusion of non- coincidence, or of an intermediate space? Total coincidence, and an intervening space, are wholly incompatible ; if the one 922 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH. is true the other is false. The proposition is therefore neces- sary in the sense of implication, as much so as a ‘ straight line is not a bent line,’ ‘a whole is greater than its part.’ The axiom ‘Things eqnal to the same thing are equal to one another’ is not a truth of implication, and therefore is not a necessary truth in the present sense. The subject and the predicate express distinct properties, and the one does not in- volve the other. The axiom declares that mediate coincidence is to be held as carrying with it, or as making, mmediate coincidence ; but the two modes of coincidence are not iden- tical. It is immediate coincidence that makes equality, accord- ing to the definition of eqn: lity; the axiom extends this very uarrow, and often inapplicable test, and declares that coin- cidence through some third thing, a go-between, will be found in the end to be the same as actual coincidence, and is conse- quently to be accepted in all cases as a test of equality. If, therefore, this axiom is to be held as a necessary truth, some other meaning than the present must be assigned to necessity. 5. Necessary truths, in the foregoing signification, are so far independent of experience, that they are perceived to be true when the language is understood. They do not, how- ever, require any powers of intuitive perception. | As soon as we fully comprehend the notion of whole and part, we perceive that the whole is greater than the part ; we do not nced to make observations and experiments to prove it. We required concrete experience, in the first instance, to attain to the notion of whole and part; but the nution once arrived at implies that the whole is greater. In fact, we could not have the notion without an experience tantamount to this conclusion. When we know a fact, we know it, even when called by another name, which is all that is meant, at present, by necessary truth. When we have mastered the notion of _ straightness, we have also mastered that aspect of it expressed by the affirmation, ‘two straight lines cannot enclose a space,’ No intuitive or innate powers or perceptions are needed for such cases. Our ordinary intellectual powers enable us to pronounce, in more than one form, that an object is everything or anything that we have found it to be. We cannot have the full meaning of ‘ straightness’ without going throagh a com parison of straight objects among themselves, and with their opposites, bent or crooked objects. The result of this com- parison is, iter alia, that straightness in two lines is seen to INCONCEIVABILITY OF THE OPPOSITE. 223 be incompatible with enclosing a space ; the enclosure of space iuvolyes crookedness in at least one of the lines. 6. Ill. A third meaning and criterion of Necessity, is enconcewability of the opposite. It is maintained that ‘things equal to the same thing are equal to one another,’ because the mind is unable to conceive things agreeing with a common standard, and yet not agree- ing when directly compared. It is also maintained that we are unable to conceive ‘effects arising without a cause ;’ whence such propositions are declared to be true necessarily. The test of inconceivability of the opposite (stroagly urged by Whewell, and held with modifications by Spencer), is liable to serious objections. What we can, or cannot conceive, is mani- festly dependent, in a very large measure, on our education : the proof of which is that many truths inconceivable in one age and country are not only conceivable under a different state of education, but are so thoroughly engrained that their opposites are inconceivable. The Greeks held matter to be eternal and self-existent; many moderns hold that the self- existence of matter is inconceivable. Some maintain that mind is the only conceivable source of moving power or force ; others, regarding the action of mind upon matter as incon- ceivable, have contrived special hypotheses to get over the difficulty,—we may instance Malebranche’s doctrine of Divine Interference, and Leibnitz’s Pre-established Harmony. New- ton could not conceive gravity without a medium. With regard to truths of Implication, the difficulty of con- ceiving the opposite must be at its maximum. Yet self-con- tradiction is not an impossible operation, for it is often done. In Theology, people have even boasted of holding contradic- tory propositions. But where the subject does not imply the predicate, there is no self-contradiction, and the opposite of any such proposition may be conceived. That things medi- ately coinciding, should not immediately coincide, is conceiv- able ; for the facts are different; the difficulty that we feel is in contradicting our habitual experience on a matter so very familiar and tangible. Propositions of avowedly inductive origin may be so strongly associated that their opposites are all but impossible to con- ceive. It is scarcely in our power to conceive colour without extension; and yet the two are united solely by our experi- ence; they strike the mind through different avenues, and their incessant conjunction constitutes a practically indissoluble 224 DEMONSTRATION.—AXIOMS.—NECESSARY TRUTH. bond. We should have some difficulty in conceiving soot flakes, particles of dust, and small pieces of paper, falling to the ground plumb and swift like a stone. The Greek proverb for the impossible was water flowing back to its source. The Nature of Axioms, 7. The fundamental principles of the Deductive Sciences are called Axioms. Every Deductive Science must begin with certain funda-— mental assumptions. In Mathematics, andin Logic, these are deemed so self-evident, that no express effort is made to establish them. In Mechanics, the statement of the Laws of Motion is accompanied with a few examples to make them at once intelligible and evident. In Chemistry, the Atomic Theory is somewhat too far removed from ordinary compre- hension to be called a self-evident axiom, albeit the most fun- damental assumption contained in the science. The requisites of an axiom are, first, that it should be a real proposition, and not a definition ; and, secondly, that it should be independent of any other principle within the science. On the first of these two requirements, we should have to reject Euclid’s axioms—‘ Magnitudes that coincide are equal,’ and ‘ The whole is greater than its part.’ On the second requirement, we must reject,— The differences of equals are equal ; If equals be added to unequals, the wholes are unequal ; If equals be taken from aia the remainders are unequal ; Doubles of equals or of the same are equal ; Halves of equals or of the same are equal ; Two straight lines cannot be drawn through the same point, and parallel to the same straight line, without coinciding. It may be useful to give an explicit statement of these truths, but as they are all derivable from other axioms (together with Definitions), they should be appended to these others, as corollaries or inferences. If, in any instance, we set up a derwative proposition as an axiom, we break down the sole boundary between axioms and the propositions or theorems constituting the body of a science. 8. The only two Axioms of Mathematics, properly so called, are, the axiom of ‘ mediate coincidence,’ and the axiom of the ‘ equality of the sums of equals.’ These are Inductive truths. reeontnael i 4 " : 4 4 AXIOMS OF MATHEMATICS. 225 The excision of Definitions with their corollaries, and of Derivative Propositions, leaves only the two axioms now men- tioned—‘ Things equal to the same thing are equal,’ and ‘ The sums of equals are equal.’ These are real, and not essential or analytic, propositions: and they are ultimate within the science. They are two distinct tests of equality, over and above the defining test, immediate coincidence. From them, together with the definition, all other tests of equality are deducible. To say that they are Inductive truths, generalizations from our experience of the particular facts, is to say that they have the same origin as the great mass of our knowledge (not deductive). That day and night alternate, that water flows downward, that smoke ascends, that plants grow from seed, that animals die, that men seek pleasure and eschew pain,—are all obtained by a comparison of observed facts ; and this is the regular, the usual source of scientific generalities. The burden of proof lies upon those that would assign any other source to the two axioms named; some reasons must be given to show that they are exceptions to the prevailing rule. The chief reasons actually assigned are those already ex- amined, their Necessity, and the Inconceivability of their Op- posites. As corroborating these, or rather as putting in a different shape the supposed difficulty of referring the axioms to experience, it is said that the intensity of owr conviction that ‘things equal to the same thing are equal’ is greater than could arise from the accwmulated comparisons that we have instituted on actual things. The considerations that serve to obviate what force there is in this objection are the following. First, by the law of Belief already explained, every uncon- tradicted experience has, on its side, all the force of our primi- tive credulity. The initial believing impetus of the mind errs on the side of excess; and if nothing has happened to check it in a particular case, it will be found strong enough for anything. Secondly, our opportunities of comparing magnitudes are numerous and incessant ; they require only the very simplest and most accessible instruments. The child, having at com- mand, three equal chips of wood, cannot avoid making, in the course of an hour, scores of comparisons that exemplify the axiom of mediate equality. Thirdly, it is usual to remark, on the mathematical axioms generally, that the subjects of them—namely, magnitudes and forms—are with the greatest possible ease represented in ima- 226 DEMONSTRATION,—AXIOMS.—NECESSARY TRUTH. gination, so that we can make numerous ideal experiments, in addition to our comparison of actual things in the concrete 9. The Axioms of the Syllogism repose upon experience. In the form—‘ Attributes co-existing with the same attri- bute, co-exist,’ we have a principle closely resembling Euclid’s first axiom of Equality ; the character of the evidence for both must be the same. Now, so far is this axiom from being an absolute and intuitive certainty, that it is erroneous. Wemay illustrate it by a parallel form, ‘Things in contact with the same thing are in contact with one another ;’ which is plausible but fallacious. The dictum de omni et nullo cannot be exempted from the criterion of experience. It is not intelligible without much familiarity with examples of the generalizing process ; and, as, in the case of all other first principles, the same knowledge that makes it understood, suffices to verify it. However expressed, the Axioms of the Syllogism are, in the first place, Real Propositions, and not identical statements under the so-called Law of Identity, or Self-Consistency. And, in the second place, as Real Propositions, they are not intuitively suggested tothe mind; they grow up with our experience, and if our belief in them seems to outrun experience, the same thing happens to all our beliefs, 10. As regards the Law of Causation, usually ineluded among the so-called a prior elernents of ourknowledge, there is a strong primitive tendency to believe it in a crude form, while experience must adapt this belief to the actual facts. We have already seen that the primitive tendency of the mind is to believe, until checked, that what is now will continue, that what is here is the same everywhere. Neither experience nor any intellectual faculty creates this impetus; but experi- ence arrests and modifies it, till by degrees it adapts itself to the real occurrences. The headlong impulse is curbed in such matters as the surrounding temperature, luminosity, and visi- ble appearances ; it is left in possession of other matters, as the force of gravity. The instinct is important as giving the active element of belief; it is perfectly worthless as a guide to the things proper to be believed. So far as concerns the authority or evidence, for causation, experience is paramount over instinct ; apart from experience, the infant would for life be- lieve that all the water of the globe is of the temperature of its first bath. THE UNIFORMITY OF NATURE, T77 The crude impulse to believe that what is will continue, after the shock of many contradictions, is transformed into a belief in the uniformity of nature, as represented by the law of Causation. 11. The axiom underlying the axioms of Mathematics, and the axiom of the syllogism, is the axiom of the Uni- formity of Nature. The consideration of cause and effect brings us face to face with the most fundamental assumption of all human know- ledge, expressed by such language as ‘Nature is Uniform’ ‘the Future will resemble the Past’, ‘ Nature has fixed Laws.’ This axiom is the common ground of all inference, wh>ther avowedly inductive, or induction disguised under the forms of deduction. Without this assumption, experience can prove nothing. We may have found, in ten thousand instances, that magnitudes coinciding with the same magnitude also coincide when applied to one another; so far as these instances go, the fact is not to be disputed ; the evidence of actual trial is the highest we have. But they do not prove that it will happen in any untried instance. This must be received without proof ; it can repose on nothing more fundamental than itself. If we see n to offer any proof for it, we merely beg it in another shape. (See Apprenpix D.) winndo Liw Bt * - - 4; t } i t ‘ 5 ' ! ve if ‘ ’ % 7 wit Att J ? Ets . Pr . TWyvi: Sif ai | “¢ Ae be KSVIC BLL TS ; f oe : b ‘ i Ritywe ges Se ; 8 PS PTOI Le d j Li 1 te vt MJ 2 eo : : boat i : fivi 5 L ’ + wfihiv s+ . 2 d5 a ry t « ‘ y ms z tvits: bos oaneo lo Ona 16 nO ANOS lo nougqaeet ihre y Oe fi of? pel of ow ia sf } (Onhop ed ar a ; it 10 ovitosbanrg jab} tao lee 1 ovate } rasyw es nie M100 | ose ara my bee | . +} apt Se Tea 3 sheath pats tas (rit; : 3) ée2ge viogour + Tee 7 (AL ZIG¥ nwith ¢ ie be ee .) Pa eRe ee Oe ee -— es pea ~~ ee ofa" Pn rn ty ; RA ae eis 8 me as : Moe ' oe Rest eet 4, e + 5 ; wk ty ; Pree: ee PART IT. INDUOTION. os a uJ i of 1% zi one ele é i 4 A : 2 ; “ 1A ae : , oe Dae Ww BOOK IIL INDUCTION. CHAPTER I. MEANING AND SCOPE OF INDUCTION. 1. Induction is the arriving at General Propositions, by means of Observation or Fact. In an Induction, there are three essentials: —(1) the result must be a proposition—an affirmation of concurrence or non- concurrence—as opposed to a Notion: (2) the Proposition must be general, or applicable to all cases of a given kind: (3) the method must be an appeal to observation or Fact. (1) By Induction, we arrive at Propositions,—Affirmations of coincidence or non-coincidence of distinct properties ; we have to do, not with verbal, but with Real Predication. That ‘The boiling temperature destroys animal life,’ is an induction so far as being a proposition, affirmation, or real predication ; there are two distinct facts—boiling heat, and destruction of animal life—and these two facts are coupled in an affirmation of coincidence. To this essential of Induction, are opposed the cases where what we arrive at isa Notion or Definition. Sometimes we are liable to confound the two. This happens when we are attending too exclusively to the second characteristic of Induc- tion— generality. In the process of defining, we generalize a number of individuals, so as to obtain and express their point or points of community, which expressed community is a De- finition or Notion; as Heat, Knowledge, Justice. If such definitions, or expressed general notions, are absolutely limited to one indivisible fact or attribute, they are by that circum- stance decisively contrasted with inductions, which always join 11 232 MEANING AND SCOPE OF INDUCTION. at least two facts or attributes. Thus, the generalized notions of length, resistance, whiteness, heat, could not be confounded with inductions; there is clearly absent from these the con- joining or coupling of distinct properties. But we have seen many instances where a definition expresses a plurality of attributes concurring in the same subject, as in all the natural kinds—minerals, plants, animals—and in various other things. There is no small delicacy in placing the boundary between those generalities ending in plural notions, or definitions, and proper inductive generalizations. We have to ask whether or not the stress is laid on the circumstance of conjunction, whether it is made a question—are the properties conjoined or not, In definition, the conjunction is tacitly assumed; in induction, it is laid open to question; it has to be proved or disproved. (See p. 292), (2) The Propositions established by Induction are general. A single individual concurrence, as ‘ the wind is shaking the tree,’ is in its statement a proposition, but not an induction. On such individual statements, we base inductions, but one is not enough. If the coincidence recurs, we mark the recur- rence ; we are affected by the shock or flash of identity, a very important step in our knowledge. If, pursuing the sugges- tion, we remark that as often as the wind is high, the trees: are shaken; that the two things have concurred within the whole course of our observation; that the same concurrence has been uniform in the observation of all other persons whose experience we have been informed of,—we are then entitled to take a still wider sweep, and to say, ‘every time that a high wind has been observed, a waving of the trees has’ also been observed.’ . sat 4 Still, with all this multitude and uniformity of observations, there is no proper Induction. What then remains? The answer is, the extension of the concurrence from the observed to the unobserved cases—to the futwre which has not yet come within observation, to the pas/ before observation began, __ to the remote where there has been no access to observe. This — is the leap, the hazard of Induction, which is necessary to complete the process. Without this leap, our facts are barren ; they teach us what has been, after the event; whereas, — we want knowledge that shall instruct us before the event, — that shall impart what we have no means of observing. A complete induction, then, is a generalization that shall express what is conjoined everywhere, and at all times, superseding for ever the labour of fresh observation. it GORE IMPROPER INDUCTIONS. 933 We thus contrast Induction with that species of ‘ Induc- tions improperly so called,’ where a general statement merely sums up the observed particulars. If, after observing that each one of the planets shines by the sun’s light, we affirm that ‘all the planets shine by the sun’s light,’ we make a general proposition to appearance, but it falls short of an induction in the full sense of the term. The general statement is merely another way of expressing the par- ticulars ; it does not advance beyond them. But without such an advance there is no real inference, no march of information, no addition to our knowledge. Induction is the instrument of multiplying and extending knowledge; it teaches us how, from a few facts observed, to affirm a great many that have not been observed. If, from the observation of the planets now discovered, we make an assertion respecting all that have yet to be discovered, we make the leap implied in real or inductive inference. If the assertion had been made when only six planets were known, actual observation would have been the guarantee for those six, induction for the remaining bundred or upwards. Sc the proposition ‘all animals have a nervous system’ is an induction only when affirmed on the observation of a part of the animal species. If the representatives of every species had been examined before the statement was made, the pro- position would be proved by observation, and not by induction; the generality would be merely a literal repetition or summary of the particulars. This kind of improper induction is assumed in the attempt, made first by Aristotle and repeated by others, to bring Induction under the syllogism. Induction ‘is defined by Aristotle, “ proving the major term of the middle by means of the minor;” in which definition, the expressions major, middle, and minor, are used relatively to their extension, to designate respectively the attribute proved, the constituted species of which it is proved, and the aggregate of individuals by which the species is constituted.’ (Mansel’s Aldrich, Note G.), Thus— X, Y, Z, (minor) are B (major), X, Y, Z, are all A (middle), All A is B. This has the appearance, but only the appearance of a syllogism in thé Third Figure. It is liable to the criticism already made upon syllogisms with two singular premises. It is nota syllogism - at all, in any correct sense, but a mere process of equivalence. The two premises can be summed in one, by verbal or grammatical condensation ; and when that has been done, the conclusion is a mere repetition of part of the meaning of the combined statement. 234 MEANING AND SCOPE OF INDUCTION. A more ambitious form of the Inductive Syllogism is given by Aldrich and Whately, which trenches on Induction proper. The magnets that I have observed, together with those that I have not observed, attract iron, These magnets are all magnets, All magnets attract iron. | The major here obviously assumes the very point to be estab- lished, and makes the inductive leap. No formal logician is entitled to lay down a premise of this nature. The process altogether transcends syllogism or formal logic. In no sense is the Inductive Syllogism an admissible logical form, A truly inductive Proposition may be but a narrow genera- lity. That ‘the breeze always spreads the royal flag hoisted at Windsor Castle’ is a proper induction ; it covers the unseen, and the future as well as the seen. The still wider induction, ‘the breeze spreads all the flags of all nations,’ is not more essentially inductive, although of more value as knowledge. (3) An Inductive Proposition is based on the observation of facts. Many true propositions, instead of being based on a direct appeal to observation, are derived from other propo- sitions ; such are, with a few exceptions, the propositions of Mathematics, and many truths in all the other sciences. In this view, Induction is contrasted with Deduction. Induction is necessarily the prior source of truths; the Deductive pro- positions are obtained from Inductions, We must commence with observation of fact, and thence rise to Inductive gene- ralities, before we can proceed downwards in the way of deduction. 2 By the use of our observing faculties for the object world, and of self-consciousness for the mind, we not merely obtain our notions of things—stars, mountains, trees, men, pleasures —but also discern the conjunctions or connexions of things. A single conjunction excites little notice, but an iterated con- junction awakens our feeling of identity; we attend to the circumstance, and watch for the recurrence. If, in the midst of fluctuation, some one couple of things is found always associ- ated, we state the fact to ourselves as a natural conjunction, a _ law of nature; and the statement is an inductive proposition. A meteor flashing along the sky is an isolated circumstance ; we term it casual or accidental. The recurrence of a stream of meteors year after year, in the same month, is a coincidence, which we elevate into an induction, affirming it for the future as wellas for the past. oe The semblance of Induction is put on by certain operations , INDUCTION AND DEDUCTION CONFOUNDED. 235 purely Deductive. Of these Inductions improperly so called, two forms may be mentioned. First. There is a certain likeness to Induction in the demon- strations of Huclid; which are each made upon an exemplary diagram, and thence extended to all similar instances, by what — is termed parity of reasoning. When Euclid proves that the angles at the base of an isos- celes triangle are equal, he proves it upon a single diagram, and rests the general proposition upon the circumstance that the same result would be arrived at in every other case of the same sort. The resemblance to Induction les in extending what is found in one instance to all other instances. Yet the resemblance fails on vital points. In reality, such truths are not established by measuring the particular diagram, and recording that measure as an observed fact, to be taken with other facts similarly observed, in mak- ing up a general rule; as if we were, by means of an induction from the pyramids, to lay down a general law of pyramidical structure. The only use made of the figure is to provide a concrete reference in applying the general language of the demonstration. One triangle is as good as another for the purpose. We expressly omit from the reasoning all reference to the size of the triangle, to its material, to the size of the angle included by the two equal sides; consequently, our proof is independent of any one of these elements, and holds under all variations of each. The demonstration is to the effect that, guoad isosceles triangle, the affirmation is true; it is a perfectly general truth. The expression, ‘ the same might be proved of any other isosceles triangle,’ would be idle and superfluous; the fact is already proved of every such triangle. Secondly. The term Induction has been improperly applied to discoveries of identification to establish a minor—a purely deductive operation. When Kepler, after comparing a great many positions of Mars, came to the conclusion that all these places lay in an ellipse of certain dimensions, he made an advance from the known to the unknown, which is one criterion of induction. Without any farther observations, it was possible to assign . the place of the planet at any moment of time throughout the entire circuit. Yet, notwithstanding this remarkable peculiarity, the case is not an induction. It is, in fact, a deduction. We might term it a discoyery of identification to establish a minor. : Supposing that, in the time of Kepler, the geometrical pro- 236 MEANING AND SCOPF OF INDUCTION. positions of the ellipse had been still undiscovered, he cou!d not have established his law, nor applied it to fill in the inter- mediate places of the planet. What he really discovered was an identity between the series of observed positions of Mars and the path of an ellipse with the sun in the focus. It was by the help of the known properties of the ellipse that he made this identity. The identity once established, any or all of tne propositions of the ellipse could be applied to the orbit of Mars, and by these the orbit could be as it were drawn, so as to show the successive positions of Mars as he described his circuit. There could have been no inference from places observed, to places unobserved, except through the application of those laws respecting the ellipse, which had been dis- covered by the Greek geometers. The propositions of the ellipse supplied the major premise of the reasoning. Kepler’s observations supplied the minor premise; they showed that the places of Mars coincided with the places in an ellipse ; whereupon whatever was true of the ellipse was true of the orbit of Mars. 1 Similar instances of discoveries of Deduction could be cited. When after the inductive establishment of the laws of magnetism upon Iron, other substances were discovered to be magnetic as Nickel, Cobalt, Manganese, Chromium, &c., the magnetic laws were forthwith transferred deductively to these bodies. Franklin’s great discovery of the identity of lightning and electricity, enabled all the previously ascertained facts regarding electricity to be applied to the atmospheric charge. In contrast to the law of the elliptic orbits, we may quote Kepler’s third law—the relation of the periodic times to the mean distances, an induction in the proper sense of the word, There is still a mathematical element present, but that element is not the major proposition, to which Kepler supplied a minor. The numerical ratio merely expresses the point of concurrence of the particulars observed, it being the nature of that con- currence to be numerical. The basis of the induction was the agreement of the six planets in the numerical ratio; and the induction was brought out in its real character when new planets were discovered and the law applied to them at once, and before there was time to observe the fact in each indiyi- dual case. Of a similar nature to Kepler’s third law ‘s the law of the refraction of light, a proper induction set in mathematical lan- guage. From a number of positions of the incident and re- FUNDAMENTAL INDUCTIVE METHOD. IT fracted rays of light in various substances, Snell found that the relation of the two could be expressed by a definite numerical proportion of the sines of the angles, the proportion being constant for the same transparent medium. JHe had _ observed the relation in anumber of cases, and he inductively affirmed it in all. In like manner the establishment of the law of gravitation was an induction numerically expressed. 2. The sole method of attaining Inductive truths being the observation and the comparison of particulars, the sole evidence for such truths is Universal Agreement. A permanent or uniform concurrence can be established, in the last resort, only by the observation of its uniformity. That unsupported bodies fall to the ground, is a conjunction sug- gested by the observation of mankind, and proved by the unanimity of all observers in all times and places. “What is found true, wherever we have been able to carry our observa- tions, is to be accepted as universally true, until exceptions are discovered: This is to apply the Universal Postulate, the primary assumption at the root of all knowledge beyond the present—that what has never been contradicted (after sufficient search) is to be received as true. Through this method alone—of Universal Agreement in de- tail—can our most general and fundamental truths be dis- covered and proved. It is the only proper Inductive Method. By it are established the Axioms of Mathematics, the Axioms of the Syllogism, the Law of Gravity, the Law of Causation or of Conservation. Likewise on it we depend for the proof of all uniformities that, although not ultimate, are for the time unresolved into higher uniformities ; or what are termed Kmpi- rical Laws. CHAPTER IL THE GROUND OF INDUCTION—UNIFORMITY OF NATURE—LAWS OF NATURE. 1. As Induction proper infers from the known to the unknown ; it assumes that, under certain circumstances (to be specified), what has been will be. The same thing is otherwise expressed by affirming that Nature is Uni- form; that there are Laws of Nature. This great foundation of all possible inference is stated in many forms of language. ‘ Nature repeats itself,’ ‘the future will resemble the past,’ ‘the absent is like the present,’ ‘ the Universe is governed by Laws.’ In one great department, it is named Causation, or the Law of Cause and Hffect. : The principle is put in another light by the remark of Mr. Mill that the Uniformity of Nature is the ultimate major premise of every inductive inference. To prove that the present generation of men will die, we may construct a syllogism thus :—major—what has been in the past will continue (under given circumstances); minor—men have died in the past ; conclusion—men will continue to die. Nature is not uniform in all things. One day agrees with another in part, and differs in part. Human beings are born with a certain amount of uniformity, and also with a certain amount of difference. The law of uniformity, there- — fore, needs to be limited and qualified. 2. The course of the world is not a Uniformity, but Uniformities. ‘There are departments of uniformity, which — are radically distinct. The most pointed illustration of this statement is the Classification of the Sciences. Although, in early ages, men’s minds were strongly prepossessed with a supposed Unity of Nature, we now recognize a plurality of distinct kinds of phenomena, each kind having its own separate principles or laws. Thus, the facts and principles of Number are studied apart from the facts and principles of Life. LAWS OF NATURE. 239 The phrase ‘ Laws of Nature’ may be understood to imply (1) that Nature is uniform, and (2) that this uniformity is a plurality and not a unity. There are separate departments, each with its own uniformities or laws. That unsupported bodies fall to the ground, that fire is quenched by water, that men pursue pleasure—are said to be laws of nature; they are, however, generically different laws, and are distributed under distinct branches or departments of Science or Knowledge. The word ‘ Law’ is a metaphor taken from human society, where it supposes the relationship named authority and obedi- ence. Seeing that in all well-constituted societies, the decrees emanating from the sovereign authority are alike binding upou all citizens, in all times and places, they have the characteristic of uniformity ; and it is on this characteristic alone, that ‘law’ can be employed to signify the order of the natural world. The full definition of a law is inapplicable to physical sequences. The likeness fails in the essential point. In human authority, a certain beneficial result is aimed at by rules of conduct on the part of the subjects of the state ; which conduct is enforced by a penalty or punishment; and the penalty is directed with precision upon the wrong doer. In the order of the world, on the contrary, a man conforming to the physical sequences is safe, whatever be the extent of his violations of moral law. Night exposure may be more injurious to the policeman than to the thief; immunity is purchased not by virtuous conduct as regards others, but by prudential care as regards self. 8. The term ‘ Law of Nature’ is sometimes used in a more restricted sense, to express the highest generalities, or ultimate uniformities of nature. There being a constant wish to discover, not merely laws that shall be true, but laws of the highest and most command- ing generality, such laws are more emphatically termed ‘The Laws of Nature’—the most centralized and all-compre- hending expressions of the order of nature. This more imposing character appears to belong to the law of Gravity, and to the principle named ‘ The Conservation of Force.’ 4, As regards Logical Method, the general Uniformity of nature may be distributed under three branches, already expressed in the ultimate classification of Propositions— CO-EXISTENCE (as Co-inherence of Attributes), CAUSATION, and KqQuaLiry. The three great relationships found capable of embracing 240 THE GROUND OF INDUCTION. all propositions were stated to be (1) Co-existence, (2) Sequence, (8) Equality and Inequality (Number and Quan- tity). Under Co-existence was included Order in Plaee, and Co-INHERING ATTRIBUTES; the first—Order in Place, being resolvable into laws of Quantity. Under Sequeuce or Succes- sion was included Order in Time and Causation; the first-named being also a purely numerical relationship. The third rela tionship, Equality and Inequality, is the basis of Mathematics, the science of Quantity and Number. Thus the three distinct heads of scientific investigation, comprising all the uniformities or laws of nature, are Unifor- mities of Co-existence, Uniformities of Succession (Causation), Uniformities of Hquality and Inequality. These are the thiee cases that Induction has to deal with. é In the actual working of Induction, we find it to be almost entirely absorbed with the second head—CausaTIon. — Besides that there are very few general laws of pure Co- existence, Causation is singular in providing a comprehensive Uniformity, which may be appealed to deductively, for all cases. The uniformities of Co-existence (independent of Causation) can be proved only piece-meal; each stands on its own evidence of observation in the detail; no one assists us to prove another. There is thus a blankness of resources in regard to the proper laws of Co-existence ; their Logic is speedily exhausted. The same defect, strange as it may sound, attaches to the uniformities of Quantity—based on the relations of Kquality and Inequality. The certainty of the mathematical axioms is a certainty due to their easy and thorough verification one by one; not to their falling under any uniformity more compre- hensive than themselves. It is by ‘ Agreement through all Nature’ that we prove that ‘ Things equal to the same “thing are equal ;’ having found this fact always true, never false, we extend it, by the Inductive hazard, to all cases whatsoever. We repeat the operation upon the other. great axiom—‘ The sums of equals are equal.’ We must proceed, in the same method of detail, to all other axioms—as the dictum of the syllogism, the axiom a fortiori, &e. The extended machinery of Inductive research, constituting the Logic or Method of Induction, is thus nearly confined to Causation. The greatest resources for eliminating accidental accompaniments and for seizing the real concomitances of facts—the so-called ‘ Experimental Methods’—have their full application only to Cause and Effect. CHAPTER III. INDUCTION OF CO-EXISTENCE. 1. Of Uniformities of Co-existence, a very large num- ber may be traced to Causation. It remains to be seen whether there be any not so traceable. The numerous Co-existences of Order in Place, or the dis- tribution and arrangements of material objects throughout the Universe, are all the results of causation, starting from some prior arrangements. The distribution of sea and land, the stratification of the earth’s crust, the existence of an atmos- phere, the distribution of the materials of the globe generally, —are the result of natural agencies or forces, operating upon prior arrangements. Salt is found in the ocean, because the water has dissolved all accessible portions of it. The heavy metals are found in deep rocks in consequence of their weight ; the corrosible and combining metals occur in combination ; and those that are reluctant to combine, occur nearly pure, as Platinum and Gold. There are thus no independent laws of co-existence to be found among uniformities of Order in Place. We must seek for them, if there be any such, among Co-INHERING ATTRIBUTES. It is possible that attributes or properties not connected as cause and effect, may yet be conjoined uniformly through all nature, If so, they are likely to. be found among the natural kinds— Minerals, Plants, Animals. The conjunction of body and mind in man, and in the animals, is to all appearance such a case as we are in quest of. 2. It is the special peculiarity of the Natural Kinds to combine many attributes in unity of subject. In them we have the chief exemplification of co-inhering attributes ; and they seem to furnish uniformities of co-existence. Thus Gold unites a certain specific gravity (19.3), crystal- lization (cubical), tenacity, fusibility (melting point, 1200° C), colour and lustre (yellow), electrical conduction, atomic weight (196), combining properties (acted on by aqua regia). These are eight leading attributes that concur in every piece of gold; 242, INDUCTION OF CO-EXISTENCE. and unless we see our way to deriving some of them from others, we must pronounce them essentic, essential or defining attributes of gold. There is a co-existence, or co-inherence of these eight facts, with others, in the object named gold. To appearance there is here a uniformity of co-existence. No specimen of gold is devoid of any one of the eight proper- ties. Properly speaking, however, this is merely affirming an identical proposition. Should there occur a specimen wanting in one, two, or three of the eight, we should say not that a law of co-existence was infringed, but that a different substance was produced. If these be the essential attributes of gold—the meaning or connotation of the name, then, on the failure of any one or more, the name would cease to be applied, the substance would not be ranked as gold, it would be classed as a new and ~ distinct substance. Gold with the specific gravity of 9, or with a silvery colour, or with a lability to corrode, would not be gold, it would be treated as a different material, a distinct grouping or aggregate of powers and properties. If there be any one of the now enumerated properties of gold that we could see changed and yet keep up the designation gold, that property is declared not to be the essence, but a concomitant of gold. A proper inductive enquiry would hold in sucha case, 3. For a Law or Uniformity of Co-existence, properly so called, we must refer to examples, if such there be, where two or more independent properties are conjoined through all nature, or in all substances where one of them occurs. We must search among the properties of kinds—mineral, vegetable, and animal, for some that are coupled throughout every species, and under every variety of aggregation. For example, could we find a certain crystalline form regularly conjoined with certain chemical characters, not in one sub- stance only, but in all substances possessing that erystal- lization,—this would be a proper law or uniformity of co-exist- ence. There would still remain a question, often difficult to settle—whether, on the one hand, the two are mutually im- plicated properties, or, on the other hand, whether they are connected by cause and effect. To detect such uniformities of general co-existence, among the essential properties of mineral bodies, whether simple or compound, is a proper object of scientific enquiry. Nor has it been neglected by physical enquirers. The following are the leading examples obtained up to the present time, LAWS OF CO-EXISTENCE. 243 (1) A law has been discovered connecting Atomic Weight and Specific Heat by an inverse proportion. For equal weights of the simple bodies, the atomic weight, multiplied by a number expressing the specific heat, gives a nearly uniform product. Thus, for sulphur, the atomic weight (32), multi- plied by the specific heat (0.1776), gives 5.68; the atomic weight of platinum (197), multiplied by its specific heat, (0.0824), gives 6,88. The products for all the elements are near the constant number 6. (2) A law obtains between the Specific Gravity of substances in the gaseous state and the Atomic Weights. Thus, the specific gravity of oxygen is 16, its atomic weight 16; hydrogen, specific gravity 1, atomic weight 1; phosphorus, specific gravity 62, atomic weight 31 (the relation here is 2 to 1); steam, specific gravity 9, atomic weight 18 (relation of 1 to 2). The relationship of the two numbers is thus, in some instances, equality ; in other instances, the one is a multiple of the other. The law is one of importance in ascertaining atomic weights. With an exception to be noticed presently, these are perhaps the two most widely-operating laws, as yet discovered, whereby two distinct properties are conjoined throughout substances generally. There are various laws of narrower range, as, for example, Andrews’s laws of the heat of combination of the metals. 4, A peculiar importance belongs to the law of universal co-existence uniting the two properties — Inertia and Gravity. These properties are co-existent through all matter and proportionate in their amount. Inertia, the defining attribute of matter, means both resist- ance to moyement, and force when moyed. It is totally dis- tinct from gravity. A body rolled on a level surface shows its inertia; so also do two weights equipoised, as in the beautiful experiments of Attwood. Now, all inert matter gravitates ; and the force of gravitation is proportional to the inertia. Kqual weights, (which are the estimate of gravity), are equally resisting to a horizontal impulse (the measure of inertia) or to a vertical impulse in the balanced condition. It cannot be maintained that these properties are mutually implicated. We can easily suppose matter (considered as inert) without the property of distant mutual attraction, or gravitation ; this last property may be fairly viewed as added to, or superinduced upon mere inertia, Nor can we call the aS? ree 244 INDUCTION OF CO-EXISTENCE, two either cause and effect, or effects of a common cause ; our knowledge does not entitle us to make either supposition. We can prove cause and effect only by exhibiting first a cause, and then an effect flowing from it. Here the two facts or properties are inseparable. There is no other equally unambiguous instance of a law of universal co-existence. The examples above quoted with reference to three properties—specific gravity in the gaseous state, atomic weight, and specific heat—may, for anything we know, be mutually implicated, or related as cause and effect. If we understood more thoroughly the ultimate arrangement of the atoms of bodies, and their intestine motions, we might not improbably find that some one fundamental property was at the foundation of all the three ;—a real essence, of which these are but propria. As regards many of the minor laws, the existence of either implication or causation is more than a mere surmise. Under such circumstances we are entitled to conclude that uniformities of general co-existence are very rare. The pre- sumption or probability (although not the certainty) in every new case of uniformity is that it is a case of causation and not of co-existence. Thus, the conjunction of Mind and Body may be a co-existence independent of causation, like inertia and gravity ; but it may also follow the more prevailing type, and be a case of cause and effect. Which is cause and which effect, or whether they are effects of a common cause, a | be open to dispute. 5. The only proof of Uniformities of Co-existence not known to depend on causation, is uncontradicted Agree- ment through all nature. This is the proof of the Law of Causation itself. Now any uniformity not coming under causation must stand on its own independent evidence ; and this evidence is uniform agreement throughout the whole compass of observation. We must find it true in all times, all places, and all circum: stances ; and provided our search has been so extensive, that if there were any exceptions we should light upon them, and no exceptions have been found, we are entitled to declare it a law of all nature. The coincidence of gravity with inertia has been proved over the entire globe ; it applies undoubtedly to the solar system ; and by very strong analogy to the distant stars. This, there- fore, may be held to be an established uniformity of co-existence. CONCOMITANT PROPERTIES OF KINDS. 9A5 The alliance of mind with a bodily mechanism extends throughout the whole of animal life, past and present. The co-existences above mentioned regarding the properties of gaseous specific gravity, atomic weight, and specific heat, have to be verified by the method of Agreement throughout all bodies. We cannot, as in cause and effect, presume from a small number to all the rest. 6. The special coincidences making up the Natural Kinds must also be verified by Agreement over the whole field of instances. We have already remarked that an exception to a kind, arising from the failure of an essential property, would not be the infringement of a uniformity, but the setting up of a new kind. The only case for proving a co-existence would be the case of conconutant properties, or those not adopted into the essence or connotation of the kind. Of such a character is the blackness of the crow, the whiteness of the swan, and varia-. tions of colour generally ; a point seldom treated as essential, whether in minerals, plants, or animals. Now the sole proof that ‘every crow is black,’ is observation through all Nature ; so long as no other colour is seen, we affirm the general pro- position ; the occurrence of various albinos has disproved the generality, and reduced it to an approximate generalization, of a very high order of probability. CHAPTER IV. LAW OF CAUSATION. 1. The Uniformities of Succession presented in nature are subject to one great uniformity—the law of Causation. The law may be expressed thus :—In every change, there is a uniformity of connexion between the antecedents and the consequents. No single expression sums up all that is implied in Cause and Effect. When it is said, ‘Every effect has a cause, and every cause an effect, and that the sequence is regular, the same causes being always followed by the same effects,’ the — AY eo 246 LAW OF CAUSATION. proposition is an identical statement; the word ‘ Cause’ means what brings about an effect; and the word ‘ Effect,’ what follows from a cause. To avoid this objection, we may state the law as follows :—‘ Every event that happens is definitely and uniformly connected with some prior event, or events, which happening, it happens; and which failing, it fails’ The kindling of a fire follows regularly on the prior events of making a heap of combustibles and applying a light. A law is more sharply stated by help of its denials. Causa- tion denies two things. First, it denies pure spontaneity of commencement. If the law is true, no cuange arises out of vacuity or stillness ; there must be some prior event, change, or movement, as a sine gud non of the occurrence of any new event. A fire never bursts out without some commencing circumstance, in the shape of movement, change, or activity, Secondly. The law denies that events follow one another irregularly, indiscriminately, or capriciously. The same cir- cumstances that make a fire burst out to-day, will, if repeated, ‘make it burst out to-morrow, or at any future time. The same pain, in the same circumstances, does not at one time repel, and at another, attract and allure us. In short, the law is the statement of wnzformity in the Succession of events. 2. In Causation, the same cause always produces the same effect; but the converse does not hold; the same effect is not always produced by the same cause. There may be Plurality of Causes. . A severe blow on a man’s head will always cause death: but death is not always caused by a blow on the head. There are many causes of motion; and the presence of any one in — the proper circumstances, will always be followed by motion. — This is an important limitation of the law, and has to be kept in view in the investigation of causes. lH a change has occurred, there must have been a previous change, or ante- cedent fact, but not necessarily one particular antecedent. 3. The Plurality of Causes is subject to uniformity in two respects: (1) the number of causes is fixed ; (2) the character of each is as definite as if it were the sole cause. The causes of death may be numerous, but they are all fixed and knowable; and, when known, may be counted on with certainty and precision. The fact of plurality renders the causation of an event ambiguous; there may be several alternative antecalents. Yet, these antecedents being, once satel + PRACTICAL ASPECT OF CAUSATION, 247 for all, exhaustively known, we are sure that one of them is the operative circumstance in the case before us. It will be pointed out afterwards that plurality of causes is more an incident of our imperfect knowledge than a fact in the nature of things. As knowledge extends, we find less of plurality. The numerous apparent causes of motion are differ- ent only in superficial appearance ; they are all oue at bottom. 4, Causation may be viewed under three different aspects. (1) The first may be called the practical and popular aspect —a partial view suited to the ordinary emergencies of life. Under this aspect, the cause is some one circumstance or condition demanding our solicitude, as being precarious. Thus, when the soldier, on the eve of an engagement, is urged to keep his powder dry, this is not the whole cause of his hitting the enemy; itis the circumstance that happens to be an peril at the time. (2) The second aspect is the Scientific or complete view of Causation. Under this view, all the conditions or antecedent circumstances are fully enumerated. (3) A third aspect is Causation viewed as embracing the modern generalization, entitled the Conservation or Correlation of Force. CAUSATION PRACTICALLY VIEWED. 5. In common language, the Cause of an event is some one circumstance selected from the assemblage of condi- tions, as being practically the turning point at the moment. A man slips his foot on a ladder, falls, and is killed. The cause of the fatality is said to be the slipping ; for if this one circumstance had been prevented, the effect would not have happened. Yet, in order to the result, many other conditions were necessary :—the weight of the body (gravity), the height of the position (a certain collocation), the fragility of the human frame. Yet, for practical purposes, we leave out of sight at the moment all the elements that are independent of us and secure, taking notice only of what is in our power and needs our attention. By a common ellipsis, all arrangements that are fixed and settled, are passed over in silence. We presume on the forces of heat and gravity, and devote our care to the choice and shaping of the materials whereby these forces may be made to work out our ends. ~ When we speak of food as the cause of animal strength, we Fae sO ae ee ae MiG ets eo ‘ ' . 948 LAW OF CAUSATION. suppose a healthy constitution, able to digest and assimi- late it. But, in this particular case, mankind long erred in ignorantly suppressing a condition no less essential than food, namely, the oxygen of the atmosphere — the aerial element of our food.* Language is adapted principally to this mode of viewing causation. In the distinction of agent and thing acted on, which pervades the whole of grammar, and gives the character to the active verb, there is an arbitrary selection of one circum- stance as cause, other equally indispensable circumstances being overlooked. A prize ox is reared in a breed of cattle; the breeder is by courtesy styled the cause or agent; but his activity is only a single, although indispensable circumstance. A teacher instructs a pupil, and is credited as the cause or author of the pupil’s knowledge A still more glaring ellipsis is practised in attributing the issue of a war to the commander-in-chief ; as when we speak of the conquests of Alexander or Caesar. ‘The monk that shook the world’ is rhetoric for the agency of Luther. us The first attempt at a precise analysis of Causation was made by Aristotle. He enumerates four kinds of Causes, —the material, the formal, the efficient, and the final. The material cause is literally the matter used in any construction; marble or bronze is the material of a statue. The formal cause is the form, type, or pattern in the mind of the workman; as, the idea or design con- ceived by the statuary. The formal cause of a building is the architect’s plan. The efficient cause is the power acting to produce the work, the manual energy and skill of the workman, or the mechanical prime mover, whether human power, wind, water, or steam. The final cause is the end, or motive on whose account the work is produced —the subsistence, profit, or pleasure of the artificer. Pt Aristotle gives the instance of a physician curing himself, as combining all the four causes in one subject. * Whenever the existence or safety of anything depends upon a swum or system of contrivances adapted to a common end—which, together, are conditions necessary for its preservation —then the destruction, disturbance, or removal of one of these contrivances—the failure of any part of this composite system of safeguards—is considered as the cause of the ruin of the whole. For example, if the action of any one of the functions or organs necessary to human life is stopped, life is extinguished, and the circum. stance producing that effect is said to be the cause of death. So, if a ship springs a leak and sinks, or if an army is surprised through the absence of a sentinel from his post— the springing of the leak, and the absence of the sentinel, is said to be the cause of the loss of the ship and the surprise of the army. The language by which such an effect is commonly ascribed to a merely negative cause is elliptical. (G. C. Liuwis). t a 7 TEAR Fo SCIENTIFIC CAUSATION. DAD This analysis is obviously taken from humar industry, which contains the several circumstances mentioned. It throws no light upon causation in the order of nature; while the attempts to express natural phenomena according to such a scheme, have led to distortions and unmeaning conceptions, The first and second causes give the celebrated distinction of Matter and Form, which pervades the whole of Aristotle’s philo- sophy. The third, the Efficient, has continued in the language of science; a better designation for the meaning is Prime Mover, or Moving Power. The fourth, the Final cause, is more perspicu- ously expressed by Motive, End, Intention, Purpose, Object or Design ; it applies to nature only as personified, or as the work of @ personality. SCIENTIFIC CAUSATION, 6. In scientific investigations, the Cause must be regarded as the entire aggregate of conditions or circumstances re- quisite to the ettect. All the conditions suppressed by the practical man are brought back by the scientific man in a full statement of the cause. If any are omitted, it is because they are so obvious that no person could overlook them. There is a legitimate ellipsis of expression, even in the scientific enumeration of con- ditions. The cause of the inundations of the Nile would be described as (1) the fall of moisture as snow on the lofty mountains of Africa where the Nile has its source; (2) the melting of this snow by the summer heat. Gravity, the laws of heat, the con- stitution of water, are all a part of the cause, and if not men- tioned, are supposed to be fully present to the mind of the hearer. The growth of plants is a complicated causation. There must concur, the properties of the germ, the contact with the soil, air, water, saline bodies in the soil, heat, light, &e. The agriculturist thinks only of a select number of these—the seed, the quality of the soil, moisture, and heat; the vegetable physiologist brings into view the physical, chemical, and vital agencies, which are the causes of the phenomenon in the final analysis. The cause of vision is summarily given as light entering the lenses of the eye. The full enumeration of the circumstances would include the optical action of the lenses, the physiology of the coats of the eye, and of the nerves and brain; and finally, the link associating a certain activity of the brain with a feeling in the mind. 250 LAW OF CAUSATION. The cause of the Reformation was Luther’s preaching against the sale of indulgences, concurring with the administration of the church, and the state of men’s minds at the time. In speaking of antecedents of the French Revolution, it is customary to use the plural—Causes; signifying that a union of many circumstances or conditions was involved. In the enumeration of Alison, no less than stwfeen causes are given. Gibbon attributes the rapid growth of Christianity to one primary cause, namely, the convincing evidence of the doctrine, and of the ruling providence of its author; and to five aiding secondary causes, ‘ which assisted in prolucing the effect, viz.: 1, the inflexible zeal of the early Christians; 2, the doctrine of a future life, as held by the Christian Church; 3, the mira- culous powers ascribed to the primitive church; 4, the pure and austere morals of the Christians; 5, the union and discipline of the Christian republic.’ ; The conditions of phenomena include negative as well as positive circumstances; the absence of hindrances to the operation of the agents concerned. The sun is the cause of vision, provided he is not screened, provided the subject is not asleep or blind. It is usual to suppress the mention of all such hindrances, if they are really absent. 7. The suppressing of essential conditions is a common fallacy of Causation. When, in the statement of a cause, there is not merely an ellipsis of understood circumstances, but an omission of some ~ essential fact, the consequence is positive error. When the healthy effect of residence at a medicinal spa is attributed exclusively to the operation of the waters, there is a fallacy of causation; the whole circumstances and situation being the cause. This is a common form of Inductive fallacy, and prevails in all the complicated sciences, as Politics and Medicine. CAUSATION AS CONSERVATION OF FORCE OR ENERGY. 8. A great advance, in the mode of viewing Causation, is made by the modern discovery of the law named ‘ Cor- relation of Force,’ or ‘ Conservation of Energy.’ The great generalization of recent times, variously designated the Conservation, Persistence, Correlation, Convertibility, Equivalence, Indestructibility of Huergy, is the highest expres- sion of Cause and Effect. In every instance of causation, there LAW OF CONSERVATION. 951 is a putting forth of force in given circumstances, and the law in question states exactly what becomes of the force, and is often the sufficing explanation of the special phenomena, as well as the embodiment of nature’s uniformity in successions. Statement of the Law of Conservation. 9. Force, Energy, Moving Power, or Work Power, is embodied in various forms, all mutually convertible at a definite (fixed) rate. The extinction of energy in one form is accompanied by the creation of energy in another form: in the transmutation work is said to be done, and no force is absolutely lost. (1) Matter in motion is Force manifested as actual, apparent, or kmetic energy; but the modes of motion may be very various. We are most familiar with that of mechanical energy, as in the case of a flying-ball, a water stream, or the wind. There is, however, reason to believe that the forces named heat, light, and electricity, consist in minute move- ments of material particles. Matter in position corresponds to a possible production of power; or the configuration of a material system corresponds, in virtue of the mutual action of its parts, to a definite amount of possible or potential eneryy. A head of water represents a certain amount of moving power by is very position. This energy may not be evoked, and may exist for ever only as potential. Yet it is as really existing as when it is employed to turn a wheel. (2) The different forms of energy may, under certain ar- rangements, be transmuted one into the other. Mechanical force may pass into heat, and heat into mechanical force: an energy of motion may be exchanged for an energy of position and conversly. The rate of exchange is invariable. (3) In the interchange of energies nothing is lust. In every case where energy disappears by resistance, and is seemingly lost, a definite equivalent of heat is generated. If we suppose a portion of the universe isolated so that it neither gives nor receives energy from without, then the principle of the Conservation of Knergy asserts that the sum of the kinetic and potential energies within this material system is constant and unalterable. The actions and reactions of its parts can only vary the relative proportions of kinetic and potential energies, but not their amount. Of these three circumstances the first matter im motion or in position, is the definition or generalisation of force or energy ; MP 952 CAUSATION AS CONSERVATION OF FORCE, the second, transmutation of one form of power into another ; and the third, conservation of the sum of the energies of motion and position of any self-contained system, under all changes, are the properties or predicates, constituting the Law of Correlation or the Conservation of Energy. 10. In explaining the principle of Conservation as applied to the different forms of actual energy, we may rank them in two divisions, Moar and MoLecuLaR,— motion in mass and motion in molecule. The Molar Forces are the same as those termed Mechanical. The molar or mechanical forces are the motions of sensible masses, as a hammer, a waterfall, a locomotive, a planet. The science of Mechanics, or Molar Physics, is occupied with the computation of these forces, in their transfer and re-distribu- tion under all varieties of circumstances. The Persistence or Conservation of Force was first distinctly conceived with reference to these palpable motions. Newton’s First Law of Motion expresses the fact that a.massonce in ~ motion will, if unobstructed, always continue in motion at the same rate; which is the same as saying that force never decays. In free space, beyond the reach of molestation from — without, a moving body would preserve its motion for ever. This is the simplest aspect of Conservation. A moving body encountering a second body, whether at rest or already in motion—(1) if we suppose both bodies to be per-— fectly elastic—imparts its own motion, in whole or in part, to the body struck. This is a new situation. There is a loss of power on one side, and a gain on the other ; a redistribution of the movements of the two masses. Now, in this state of things, the Law of Conservation declares that in the inter- change nothing is wasted; whatever the striking body loses, the struck body gains. If the two masses are equal, there will be simply an in-— terchange of velocities, and of momenta ; and if they are not equal, still the impact will not alter either the total no or the moving energy of the whole. (2) When the bodies are inelastic, then the visible energy : will disappear in whole or in part. If a contemporary of Newton had been asked what becomes of the force of cannon shot arrested by a dead wall, he would probably have answered that an infinitesimally small movement was imparted to the me CONSERVATION OF MECHANICAL FORCE, 9538 mass of rock and its contiguous material. This would have ~ been regarded as a consistent following out of the theory of conservation in communicated momentum. The lost energy of the quick-moving ball would exist as energy in a huge mass very slowly moving. Had the farther question been asked—what becomes of the force of two opposing movements destroying one another— the above answer would not have served the purpose. No motion is created in any form; there is nothing to appearance but sheer waste on both sides. The new difficulty would in all likelihood have been met by a very plausible assumptiom. It might have been said that the conservation of force was to be interpreted as force operat- ing in the same direction ; all forces in the opposite direction being held as negative quantities, like debt to credit. It would be a sufficient account of any force that it had neutralized an equal and opposing motive force; as when a payment of a hundred pounds to any one’s credit extinguishes a hundred pounds of debt. Yet this explanation is fallacious as a principle, and in opposition to the facts of the case. Two bodies moving in opposing directions are not to be compared to positive and negative; each has a positive value, for any purpose whatso- ever. Two streams running in opposite directions, are as good for mill-power as two streams moving in the same direction. Hasy mechanical contrivances can, without loss, divert a moving power into any direction, The two opposing forces that by collision extinguish one another, could by a suitable arrangement, unite their power in the same course. The destruction, therefore, that ensues in a hostile collision, is (on the present assumption) pure destruction, unredeemed waste, annihilation. It is at variance with the Law of Con- servation, which would have to be restricted and qualified to moving bodies always following the same course. The principle of Conservation has been rescued from this perplexity by the discoveries of recent times. If two in- elastic bodies encounter and arrest one another’s movements, the mechanical or molar energy is indeed sunk ; but re-appears in an equivalent energy communicated to the molecules, and manifested as Heat. The molecular motion excited in the encountering masses is exactly equal to the molar energy consumed. This is an entirely new view of Force; and saves the principle of Conservation, by giving it an enlarged scope. It teaches us to take account of all the 254 CAUSATION AS CONSERVATION OF FORCE, protean transformations of energy, and prevents us from rashly declaring that force is destroyed when it has ceased to appear in the original shape. Mechanical force in some cir- cumstances, well understood, yields mechanical force ; in other circumstances, for example, hostile collision, it yields a mole- cular force, namely, Heat. Going back upon the first query propounded to a contem- porary of Newton,—the account to be given of a ball’s impinging on a dead rock,—we should now answer the ques- tion not by mechanical transference—a slow motion imparted to the rock—but by molecular transformation. The ball and the place where it struck would both be found to rise in tem- perature, and the more as the moving force of the ball was greater. All the energy would be accounted for in this way. Tn every case of collision, and even of impact without opposi- tion, something is lost by conversion into heat. The loss of power by friction is a generation of heat. 11. The MotecuLar Forces may be provisionally enu- merated as follows :—(1) Heat, (2) Chemical Force, (3) Electricity, (4) Nerve Force, (5) Light. This enumeration is to be held as provisional; it may not include all the species ; and it may represent, as distinct kinds, what are only slight modifications of one kind. (1) Heat.—Probably the best example for showing the mole- cular forces, in their contrast to the molar, or mechanical, is Heat. Our experience of this influence is abundant and various. Yet, only of late years have we been led to call it a form of moving matter, a species of molecular motion or vibration, which bursts forth on the shock tHat extinguishes a mechanical impetus. Such shocks of mechanical collision are the usual mode of transmuting mechanical energy into heat. Friction is only a more gradual and protracted collision. A familiar illustration is seen in hammering a piece of cold iron till it becomes red hot. The high temperature of the sun is hypo- thetically accounted for by collisions of enormous swift-moving masses, brought together by gravity. Such is the situation for converting mechanical motion into Heat. The transmutation of heat into Mechanical force, is effected through the expansion of bulk caused by raising the temperature of bodies. In solids, and in liquids, this expansion is small in range, but great in force; and is adapted only to special cases, as the splitting of rocks, where MOLECULAR FORCES. 255 there is need for a great power moving only a very little way. Through the medium of gases, the expansion can be converted into mechanical energy, in any form we please, as in the diversified performances of steam power. In generating mechanical power by heat, as in the steam engine, the source of heat must be of a higher temperature than the medium; the fire must be hotter than the water and the steam. The power is given forth by the descent of the heating body toa lower temperature. Between bodies equally hot, there is no development of mechanical power, no forcible expansion of any one body. There is a peculiar incontinence attaching to the Heat force. We usually find that some body possesses it in such superior degree as leads to radiation upon other bodies, with loss to the radiating body. This is the moment for obtaining a mechanical or other equivalent. It is also the moment of dissipation of energy without equivalent, if the opportunity is not turned to account. The solar heat falling on the planets gives an equivalent in raising their temperature, and in pro- _ ducing other forces; what is not intercepted is at once dissi- pated into empty space, without farther result than to elevate by a slight addition the general temperature of space; a real but unavailable equivalent of the heat lost to the sun. It is as regards Heat that the rate of exchange with mechanical force has been settled with the highest numerical precision. The assumed unit of mechanical energy is the foot-pound of England (and the metre-kilogramme of the Continent), meaning the force expended in raising one pound weight one foot. The unit of heat is defined as the amount that must pass to one pound of water in order to raise its temperature (or sensible heat motion) by one degree of the thermometer. The rate of exchange or equivalence 1s 772 foot-pounds to one pound of water raised 1° Fahrenheit; or 1390 foot-pounds to 1° Centigrade. In the Continental scale of weights and measures, the expression is 425 metre-kilogrammes to one kilogramme of water raised 1° Centigrade. By a perfect machinery of conversion of heat into mechanical power, the heat requisite to boil a gallon (ten pounds) of freezing water would lift 1889600 pounds one foot. i (2) Chemical Force.—Energy, in a form adapted to separate chemical compounds, and as it appears when bodies combine chemically, is chemical force. When water is decomposed into its Raman oxysen and hydrogen—a certain amount of force is a4 956 CAUSATION AS CONSERVATION OF FORCE. absorbed or used up in order to bring about the decomposi- tion ; and the same force reappears when the elements are re-combined. This chemical force is a very slight modification of Heat. In the case of combination, the force evolved appears as heat in it8 common form. Indeed, our artificial heat of combus- tion, is the chemical force liberated in the chemical combina- _ tion of oxygen and carbon (supposing coal or charcoal to be the fuel). By peculiar arrangements, this force of combination may be prevented from appearing as sensible heat, and may take other forms ; it may decompose other compounds (as in the double decomposition of salts); or it may pass into elec- tricity or into magnetism. Again, Heat may operate as a decomposing agent. Many compounds are decomposed at once by the application of heat, as the oxides of the noble metals. A familiar example is the decomposition of chalk or carbonate of lime, in a lime kiln; the heat drives off the carbonic acid, and what remains is burnt lime. Other compounds are decomposed by heat, when there is an arrangement for combining one of the de- composed elements with a third substance; as when water is decomposed in a red-hot iron tube, the oxygen combining with the iron. That heat, the result of combination, should be the means of decomposition, is the proper, the natural consequence of the Law of Conservation. Whatever is given out when ele- ments combine, must be restored when they separate again. — This is the exact relationship of heat to chemical action, which is disguised and apparently reversed by the familiar empley- ment of heat to make bodies combine, as in lighting a fire. The application of heat in such a case, however, is a mere incident; it seems to operate by disturbing the quies- cence of the elements. It no more renders heat a combining power, than the pailful of water thrown into a pump before pumping is the cause of the subsequent flow. The rate of commutation of Heat and Chemical Force, has to be given in the detail, inasmuch as different compounds give forth different quantities. I quote as examples a few oxygen compounds. One pound of hydrogen burnt (that is, combined with oxygen) would elevate, by 1° C., about thirty- four thousand pounds of water. This is the most heating of — all oxygen combinations ; we have long been familiar with the intense heat of the oxy-hydrogen blow-pipe. Of simple bodies burnt, or combined with oxygen, the next in rank, is — HEAT.— ELECTRICITY. 257 carbon, the chief ingredient of ordinary combustion, and also of animal combustion. The figure for carbon is less than one fourth the figure for hydrogen; a pound of carbon burnt elevates, by 1° C., about eight thousand pounds of water. Phosphorus ranks next among the simple bodies examined (5747 pounds); then sulphur (2307); the metals, zine, iron, and tin, are nearly equal (zinc, 1301, iron, 1576, tin, 1233). (3) Hlectricity—This variety of molecular force is distin- guished by two main peculiarities. The first is polarity, or the development of opposite forces at opposite points ; the magnet is the most familiar example of the power, operating in masses of matter. The second is named conduction, and means the rapid transmission of the force from one part of a body to another, along a wire, for example ; a process of conveyance quite different from any of the modes of the transmission of heat. An electrical charge passes almost instantaneously, and with little diminution of force, through miles of copper wire. The name ‘ Electricity’ now includes various phenomena marked by characters widely different. Three types or species may be indicated—Magnetism, Friction or Franklinic Elec- tricity, and Voltaic Electricity: all these have a molar as well as a purely molecular side; the last is in close relation to chemical force. Magnetism, as a member of the group of Correlated Forces, under the Law of Conservation, is best studied in the form called Electro-magnetism, or mag- netism generated from electricity ; for, while the magnetism, which is a mechanical attraction, can be estimated by its mechanical effects, the electricity can be estimated chemically by the amount of acid and zinc combined in the cells of the battery. Friction Hlectricity, in the common electrical machine, is generated by mechanical force (sometimes by heat, as in crystals); its discharge, being marked by vehemence, concentra- tion, or wtensity, is not measurable with accuracy ; the effects are seen in the rupture of atomic cohesions, in strong outbursts of heat and light, and other indications of concentrated force. Voltaic SLilectricity is the species most closely allied with Chemical Force; which force is its source, its measure, and one of its results. Through chemical force, as measured by the amount of material chemically combined in the voltaic cells, we can state the rate of exchange or commutation of Voltaic Electricity with Mechanical force, and with Heat, These three modes of Force—Heat, Chemical force, Elec- tricity—are the well-defined species of molecular activity; 258 CAUSATION AS CONSERVATION OF FORCE they can all be measured and put into strict equivalence with Mechanical Energy. ‘There siill remain, however, Light, and any modes of activity in living hodies, distinct from, and superadded to the forces of the inorganic world; the Nerve Force is one well-marked example. From the close analogies — between this last-named force and Electricity, we may take it next in order. R (4) Merve Force.—The Nerve Force is the special activity o the nerves and brain. Like Klectricity,itisacurrentforce. It differs from Electricity in moving at a comparatively slow rate; and also in depending for its maintenance upon chemical com- binations in the material of the nerves ; hence, while electricity decreases as it goes, the nerve force increases. Although this foree cannot be subjected to accurate measurement, we con- clude from analogy that there is an exact equivalence between it and the chemical transformations that are its source; part of the food of the body is expended in supplying it. It con- tributes to muscular power, in which case it has a mechanical equivalent; and to molecular changes, chemical or other, also on a definite rate. As the physical concomitant of mental states, we must still regard it as definitely related in quantity to these; a double amount of feeling, other things being the same, involves a double amount of nervous transformation. (5) Light.—The divorcing of Light from Heat, in the enu-— meration of the molecular forces, needs to be explicitly justified. The divorce is at best provisional and temporary ; the reasons ire such as the following. . Although Light is a distinct product of the other forces, more especially Heat, and is instrumental in causing at least one of them, Chemical force, yet hitherto nothing has been done towards establishing the rate of com- mutation or exchange between it and the others. Whena body is heated till it becomes luminous, there ought to bea definite loss of heat, equivalent, on a certain scale, to the light produced; at present, however, we have made no ap- proach to such an estimate. Moreover, although light is the instigator of chemical change, we cannot say that it oper- ates by supplying chemical power, as heat or as electricity does; the effect may be similar to the action of heat in lighting « fire, a mere disturbance sufficing to begin the chemical union of elements ready to combine. Chlorine and hydrogen, mixed together, will not combine chemically in the dark; the — combination begins under the light. It is to be remarked, — however, that decomposition is the direct test of chemical force. Now, light will not cause decomposition unlags in the presence ’ POTENTIAL ENERGY, 259 of a body, like hydrogen or chlorine, having a powerful tendency to combine; or, when, as in vegetation, light is accompanied by heat. We are, therefore, led to regard light chiefly as the prompter to a change otherwise maintained. And in this view there is a numerical proportion between the amount of light and the extent of the chemical action; as shown in the researches of Bunsen and Roscoe (Phil. Trans., 1857). When mechanical force operates against gravity, as when a projectile is thrown upwards, the force is at last spent ; the equivalent gained is a position of advantage, with respect to gravity ; for, by the continued operation of the gravitating energy, the whole of the impetus lost will be restored in the downward direction (the resistance of the air being left out of the account). We are familiar with this employment of gravity in clocks propelled by weights regularly wound up to a height. To this peculiar situation, Prof. Rankine has applied the name ‘potential energy,’ to distinguish it from the energy of a mass in actual motion. The placing asunder of the celestial bodies, all which gravitate towards each other, was the primeval situation of advantage, whence may have arisen (by collisions) the heat of our suns and planets, and by consequence all the other modes of force—mechanical, chemi- cal, and electrical. It is by this operation that the force of gravity is introduced into the circle of forces, and is counted as a cause or productive agent. Viewed in itself, it creates no force; what is gained in visible force is lost in position; to restore the position would require the power to be given back. It can, however, divert power; it can also store up and re-distribute it, as a banker does money. A similar position of advantage may be found in the mole- cular forces. Thus, the existence of two elementary bodies, able to combine, is a potential chemical energy, which, on the occurrence of the opportunity and the stimulus, is converted into actual molecular energy. Such is the potential force of our coal, and of all the uncombined and combinable elements of the globe,— as native sulphur, the native metals, and the lower compounds susceptible of entering into higher com- pounds. The molecular attractions of bodies (as cohesion) may oper: ate exactly in the manner of gravity. A spring is an obvious: example. The elasticity of compressed air may be turned to the same account, ca 260 CAUSATION AS CONSERVATION OF FORCE. 12. Causation, viewed as Conservation, is thus the trans- ferring or re-embodying of a definite amount of Force. When a ship is propelled by wind or by steam, the motion is said to be caused by those agents ; which expend themselves in producing the effect. The expansiveness of steam is due to heat operating through the medium of water. The heat arises from the combustion or chemical union of coal and oxygen. The coal was the carbon of plants of former ages, whose growth demanded an expenditure of solar heat. So, again, in the human body, mechanical force is obtained by mucsular exertion ; that exertion is owing to the oxidation of the materials found in the blood; these materials are either vegetable products, or the bodies of other animals fed on vegetables ; and, thus we come round again to the agency of the solar ray in vegetation. Transferred energy is thus the final and sufficing explanation of all change, and the only explanation in the highest sense of the word. Any ‘fact of causation not carried up into this supreme law, may be correctly stated, but it is not accounted for. . Whatever appearances militate against the principle of Con- servation are to be held as fallacious. The ‘ perpetual motion’ has long been rejected as incompatible with the mere mechani- cal phase of the principle. There still remain to be removed various errors against the more comprehensive view. For example, the incautious remark is frequently made that Light is the operative cause of vegetative growth, meaning light alone; but the large amount of chemical power required to decompose water into its elements (the bodies of all others most costly in their demands) could be furnished only by the heating rays of the sun; however much light may co-operate in giving stimulus or direction. 13. The Law of Conservation exhausts Causation, viewed as the transfer of Force or Moving Power, but leaves many complicated, and, as yet, unsolved questions of CoLLoca- TION. If we view causation as the transfer or re-distribution of a certain definite amount of moving power, nothing can be simpler than the statement of the principle; and, in many instances, we find it easy to make the exact calculation. But the circumstances attending the transfer, the situation or collocation of the materials engaged, may have all degrees of complexity. - + eaael Py Ae COLLOCATIONS, 261 The simplest situation is the transfer of mechanical power by impact, as when a golf ball is impelled by the momentum of 'the club, At least, we usually suppose this to be a simple case; we take no account of the internal agitations of the particles of the body struck, being content to assume that the momentum is transferred with inconsiderable loss. Here, then, the collocation is the easiest possible; it is the sensible contact of one moving body with another, either at rest or already in motion. Even when one moving body strikes another moving in a different direction, the difficulty of the collocation is not much increased ; the mechanical theorems of oblique forces will predict the new distribution, and assign the directions after the impact. When we pass from the interchange of mechanical forces, to the mutual interchange of mechanical and molecular, we en- counter situations or collocations of various degrees of com- plexity. Least difficult is the relation of mechanical energy to heat. When a moving body encounters a dead resistance, the whole of the energy is resolved into molecular motion of the encountering masses; if the body struck gives way in part, and takes on motion, the actual energy generated is so much deducted from the energy transformed into heat. The transfer of heat into mechanical force, as in the steam engine, is accomplished by the expansiveness of the heated matter. Starting from the fact of forcible expansion, the con- version is merely an instance of mechanical impact. The difficulties are postponed to the next stage. The interchange of Heat and Chemical Force, the production of each from the other, at will, is effected by an arrangement that can be expressed with considerable definiteness in the gross, although leaving the ultimate links of transition in deep obscurity. ‘The active combination of two combinable bodies, as carbon and oxygen, evolves heat ; but the minute circum- stances of the evolution can be only hypothetically surmised. The intestine heat motions of carbon and of oxygen, in their separation, when transferred to the joint carbonic acid mole- cules, are in excess, and the surplus gives elevation of tem- perature, or sensible heat, to the mass. The re-conversion of Heat into Chemical Force (potential), as in chemical decompositions, is somewhat more complicated, but an account can be given of the situation in gross. In the cases where decomposition is effected by heat alone, we have the simple restoring of the surplus heat of the combination, In the other cases, where a new combination must be formed, 262 CAUSATION AS CONSERVATION OF FORCE. we have an additional circumstance, still perfectly Seana and, in a rough manner, hypothetically conceivable. The difficulties of Collocation grow thick upon us when we grapple with the Electrical group of forces. The polarized state of matter, whether in mass, as the magnet and the Leyden jar, or in molecule, as in the decomposing cells of the voltaic battery, is a new and unique phenomenon; and its generation by mechanical force or by heat may be stated in the extreme terms, but without intermediate explanation, even by a plausible hypothesis. After many laborious tenta- tives, Faraday discovered the arrangement for directly convert- ing mechanical power into voltaic electricity (commonly called the magneto-electric machine), but the links of the transition or intermediate molecular changes are as yet unassignable. Yet worse perplexities surround the collocations for trans- ferring force in Living Bodies. Even the simplest case—the production of Animal Heat from chemical combination or combustion—is anomalous when compared with the same phenomenon out of the body. The general fact is oxidation, but the circumstances and arrangements are peculiar and unknown. Again, the production of Muscular Force from the process of oxidation is in accordance with the Law of Conserva- tion, while the transition links are hitherto inscrutable. Like- wise, the Nerve Force has the same common origin in chemical transformations (or closely allied molecular transformations) as the other forces, and follows a regular rule of exchange, while the mode of derivation is involved in obscurity. 14. Seeing that, in Causation, there must be provided, not merely a sufficient force, energy, or moving power, but also the suitable arrangement for making the transfer as required ; this completing arrangement, or collocation, is a part of the Cause, and (by ellipsis) is frequently spoken of and investigated as the Cause. A running stream is the proper source of the energy that — turns a mill. In order to the effect, however, the due colloca- tion or connexion must be made for bringing the water to bear upon the machinery. Hence, the stream being taken for granted, the cause of the grinding of the corn is the providing of machinery, and the regulation of the sluices ; which circum- stances are of the character, not of force, but of collocation. So, ina Voltaic Battery, intended to decompose water, or to excite an electro-magnet, the prime mover is chemical force arising in the cells of the battery; the completing * . ° _— EE . > ree i eB i eee UNKNOWN COLLOCATIONS. 263 arrangements include the whole apparatus of the battery, and the final act of closing the circuit. The combination of the food materials with the oxygen of the air, may be reckoned the source of all animal power; but so numerous are the conditions to be secured in the way of arrangement or due collocation, that we have often to think far more of these than of the propelling agency de- rived from the primal source of all moving power. We not unfrequently assign as the cause of a man’s bodily strength, a good digestion, healthy lungs, or a good constitution generally, and say nothing of the real derivation of the strength; the reason being that, without the complex group of arrangements implied in these facts, the power would not be transferred from the common fund and embodied in the man’s muscular and vervous energies. When a man properly supplied with food, goes through a day’s work, we recognize a transfer of moving power, under the Law of Conservation. When any, one prostrate with weakness is restored to strength by a few drops of laudanum, there is no proportion between the cause and the effect, con- sidered as moving power giving birth to equal, although different moving power. The salutary interference must be regarded, not as a communication of moving energy corres- ‘ponding to the access of energy that follows, but as the restor- ing of some arrangement or collocation, necessary to the conversion of the body’s nourishment into the various forces of animal life. | As our knowledge of the Law of Conservation is such as to account for the remote source of all power whatsoever, the enquiry usually presented for scientific investigation is by what arrangements a given effect has been secured, or through what media the bank of Nature’s Force has been drawn upon in the particular instance. Not many years ago the pheno- menon of volcanoes was regarded as wholly mysterious ; since the establishment of the Law of Conservation, all that part of the mystery connected with the source of the upheaving power has been removed. It is the internal heat of the earth con- verted at certain points into mechanical energy. What re- mains for scientificinvestigation is a pure question of collocation; we are still ignorant of the arrangements for effecting the transference of power in that particular manner. In the same way, all the great cosmical changes, marking the evolution of the solar system, and the geological history of the earth, are referable to the primal sources of energy; the 264 CAUSATION AS CONSERVATION OF FORCE. moving power at work is no longer a secret. Yet the circum- stances, arrangements, or collocations, whereby the ‘power operated to produce our existing mountain chains, the rise and fall of continents, the fluctuations of climate, and all the other phenomena revealed by a geological examination of the earth, are as yet in uncertainty. 15. The importance of Collocation appears in another aspect, as representing the modes of Potential Energy. Potential Energy is energy of situation, arrangement, or collocation. The Potential Energy, stored up when moving bodies work against gravity, till their force is exhausted, is described as a position of advantage, a collocation of power, with reference to a gravitating mass. Here we have the re- markable case of force embodied in absolute stillness or quies- cence. A mountain tarn is absolutely quiescent while its enclosure is perfect ; the immense impetus to be displayed in its descent to the plains is not at present represented even by molecular motion. A similar energy of collocation is created when bodies are distended in opposition tv their cohesive attractions, as in springs. Lastly, there is the energy of separation of Chemical ele- ments, as in coal, sulphur, metals, and other combinable sub-. stances, simple or compound. Gunpowder is a concentration of potential chemical energies, or of combinable elements in a situation of readiness to combine. It is in the case of these potential energies that we seem to create moving power, to bring forth force, without a prior equivalent force, to make small causes yield great effects. The apparent cause, or antecedent, of a great outburst of moving power, is something altogether trivial, as if force were evoked and absolutely created. Cause and Effect cannot, in such instances, be stated as one moving power transmuted into an equal moving power, molar or molecular. Human Society, with limitations easily divinable by any reflecting student. , In the situation of enquiring into the Cause of a given Effect, Experiment is for a moment unavailing. We can try the effect of a given cause, but we cannot try the cause of a given effect. Assuming heat as an agent, we can make experi- meats on its various powers or capabilities; but given the heat of a fermenting mass, as an effect, we cannot, by experiment, get out the cause. We must first conjecture a cause; experi- ments may then be instituted to find out the effects of that supposed cause; if these tally with the effect in question, — we have made out our point. The problem of Causation may thus be presented in both aspects—given a cause to find the effect, given an effect to find the cause—but the experimental solution is one; namely, to watch the effect of an assumed cause. The course of the phenomenon flows in one way; cause first, effect second. When we seem to be working backward, we are in reality working forward. REVIEW OF THE COMPLICATIONS OF CAUSE AND EFFECT, _ 4, The Inductive Elimination of Causes and Effects may be illustrated by a review of the various complications actually met with. We have already adduced examples of the complications that have to be unravelled, in order to assign the neat effects of a cause, or the causes of an effect. We are able to present a more comprehensive view of the actually occurring entangle- ments, COMPLICATIONS OF CAUSE AND EFFECT. 275 Those natural aggregates, termed Kinds by pre-eminence, are marked by the concurrence, in a single object, of many different properties. Oxygen, carbon, phosphorus, iron, mer- eury, platinum—have each a great number of distinct powers or activities ; hence, when the introduction of any one of them is followed by some change in the things they are brought into contact with, we are at first uncertain which of all the many properties of the substance is the operative circumstance. Carbon, for example, is found to absorb gases in large amount; which suggests the enquiry, which of the properties of carbon is this owing to:—its specific gravity, porosity, blackness, amorphous structure, or any other? Again, mercury has certain medicinal effects; and we desire to know which of its many properties is the causative circumstance. Platinum, in a finely divided or spongy state, brought into contact with a bie of hydrogen, makes it ignite. What does this depend upon So then, in the elementary bodies of Chemistry, the simplest substances known to us, there is a great concourse of anteced- ents present whenever any one is brought into play. But, in nature, these are usually found mixed together (I am not alluding to Chemical combination, which yields new substances) in great varieties of compounds. Thus, the Atmosphere is a mixture of two simple bodies—nitrogen and oxygen; various known chemical compounds—water, carbonic acid, and am- monia; and a great many other gaseous effluvia, together with solid particles, partly dust and partly ova of plants and animals. Moreover, it possesses at each moment a certain temperature, a certain electrical condition, and perhaps other peculiarities. Thus, when the atmospheric air is pre- sented to us as a cause or agency, the possible variety of antecedents is very great. Many researches have been occu- pied in eliminating the causal conditions in combustion, in vegetable and in animal life, in putrefaction, in spontaneous generation (so-called), &c. Again, the sea is not pure water, but a solution of numerous saline bodies. Most minerals are mixed substances. A geological stratum is highly compound; and when certain vegetables are found to grow in a particular soil, elimination must be applied to ascertain which are the needful constituents. In Vegetable and in Animal Kinds, the complication is still greater. The chemical constituents of plants and of ani- mals have very complex atoms, whose disintegration may yield 276 , WEAPONS OF ELIMINATION. a variety of different products. Hence, vegetable and animal — substances used as food, as medicines, as dyes, &c., have many & possible modes of operating. We must, however, ‘when living bodies are agents, farther take into account the organic or living structure; the poison of a living plant or animal has powers of derangement quite different from the chemical action of ite chemical constituents. The complication in the world of Mind is very great. ar human being is by nature many-sided, and by education still more so. Hence, when one person exercises an influence upon another, it is far from obvious, at first sight, by what peculiari- — ties the effect arises. So again, in the explanation of motives, a historian is often baffled to select the one that ates swayed a given effect. » The operations of Government are ramified in their conse- = quences. A single enactment—the imposition of a tax on windows or its removal, free-trade, or its opposite — Operates variously according to cir cumstances. te WEAPONS OF ELIMINATION, d 4 :aF 5. It is in the comprehensive Law of Causation itself, a once established by Induction, that we have the instru- ments for eliminating causes and effects in the detail, __ As already said, there is but one proper Inductive Method —Universal Agreement; there is, in the first instance, no shorter cut to an Inductive Generalization. We must go through the labour of a full examination of instances, until we feel assured that our search is complete, that if contrary cases — existed, they must have been met with. By such thorou oh-going examination, various inductive laws have been established, including that momentous truth called the Law of Causation. Now, in whichever of its two properly scientific aspects, we view this law—whether in the less sug- gestive but perfectly accurate form of Uniformity of Sequence, - or in the new and better form of Conservation accompanied with Collocation, we find in it a means of shortening the labour 4 of ascertaining specific causes and effects. By applying the — general law, in either form, there is often a possibility of ae a ing causation by a single instance. Thus, to take the first form of Causation— Every event uniformly followed by some other event; and every event is — i aniformly preceded by one or other of a definite number of” 4 events ’:—given an antecedent, one consequent succeeds; given _ CAUSATION THE BASIS OF ELIMINATION. OT a consequent, some one of a few definite antecedents has pre- ceded. Now from this it follows, that whenever an agent is introduced into a quiescent state of things, and when certain changes follow at once on that fact, the sequence happening once will happen always. Nothing springs out of nothing. Nature in the matter of sequences is uniform; and a single case, cleared of ambiguities, establishes a law. By the stroke of an axe, a block is cleft; the same effect will always follow the same cause. Hence, a single experiment in the laboratory may establish for ever a casual property. On the second or more precise form of Causation, there is a definite transfer of motive power under some given arrange- ment of things. We know, by this law, without any new observation, that a blow with a hammer will realize its equivalent, either in mechanical energy, or in some form of molecular force. If in a certain situation, it splinters a stone, it will always do the same thing, in the same situation. In a different arrangement, it raises the temperature of a surface ; and what it does once, it does always. All that we have to settle empirically in this form of the law, is the transfer attending each collocation, and the collocation attend- ing each transfer. By induction proper (universal agree- _ ment) we have already ascertained this to be uniform, and accordingly pronounce upon a single clear instance. There is thus only one Inductive Method at the foundation (Agreement), but there are several Deductive Methods, or methods depending upon the grand generalization of Cause. For instance, the method known as the ‘ Method of Differ- ence,’ is not an inductive but a deductive method; for, with- out the law of Causation, the method would be incompetent. Even the ‘ Method of Agreement’ as employed for the pur- pose of elimination, supposes the Law of Causation, and is to that extent a deductive method. 6. The Law of Causation involves the three following affirmations, each of which is the groundwork of a process of Elimination. (1) Whatever antecedent can be left out, without preju- dice to the effect, can be no part of the cause. A cause is what produces an effect. As the presence of the cause is the presence of the effect, so the absence of the cause is the absence of the effect. The absence of the cause, with the presence of the effect, would be a contradiction of the law. Weare sure, therefore, that whatever can be omitted 278 WEAPONS OF ELIMINATION. or withdrawn without making any difference to the effect in question, is not the cause, or any part of the cause. If we cut a string that we suppose to be the support of a weight, and the weight continues to be supported, the string is not the support. Upon the Law of Causation, viewed on this side, reposes Mr. Mill’s Method of elimination by Agreement. A certain effect remains after the successive withdrawal of all the ante- cedents except one; which leaves that one in sole and undis- puted possession, and therefore the cause. (2) When an antecedent cannot be left out without the consequent disappearing, such antecedent must be the cause or a part of the cause. ‘s+ This affirmation, likewise, is implied in the law. It presents the other side of the same linking of cause and effect; absence of the cause is absence of the effect. Whatever, by disappear- ing, makes the effect to disappear, is by that very fact an essential or causal condition. If the cutting of a string 7s the falling of a weight; the string is the support of the weight. This aspect of cause gives the decisive Method of Difference; the method whereby a single instance may be incontrovertible proof of a cause. (3) An antecedent and a consequent rising and falling together in numerical concomitance are to be held as Cause and Effect. This is Causation in the more special aspect of Conserva- tion, and is directly implicated in that principle. In the transfer of moving power, the quantity gained is the quantity lost ; and the tracing of quantitative concomitance is our very best clue to the force operative in a given effect. As the com- bustion of a locomotive is increased, so is the steam power. In those agencies that merely bring about a collocation, — there is no numerical ratio between the agent and the result. A slight touch is enough to complete the electric circuit, and a double vehemence adds nothing to the energy of the cirenit, The process now described is the Method of Concomitant Variations. These are the three chief methods of Eliminating the un- concerned circumstances present in cause and effect. After considerable progress has been made in the discovery of causes, recourse may be had to a farther proceeding, namely, to allow for the influence of all known causes, and to attribute ELIMINATION FOUNDED ON CAUSATION. 279 what remains of the effect to what remains of the cause. This also is a proper inference from the Law of Causation. It is termed the Method of Residues. The Method of Agreement may be employed negatively ; that is, cases may be found where cause and effect are uni- formly absent together. We may call it Agreement in Absence. When this circumstance can be conjoined with the positive _ method—Agreement in presence—an approach is made to the decisive cogency of the Method of Difference. Mr. Mill has given to this conjoint mode the designation—Joint-Method. The following chapter will exemplify the employment of these Five Methods of Inductive (or Deductive) Elimination in investigating Cause and Effect. It is not possible to separate from the thorough working of these instruments of Elimination the process of generalizing, or attaining to Inductive generalities. In carrying out the Method of Agreement, for example, the collation of a large number of instances where a cause or an effect. is present, cannot fail to suggest laws of causation of a higher generality than the enquirer sets out with. Nevertheless, it will not be expedient to dwell upon this generalizing operation while we are bent upon the eliminating process. Generalization belongs to Discovery ; Elimination is Proof; and Proof, more than ‘Discovery, is the end of Logic. Still, we shall have to make room for a consideration of the best modes of arriving at the higher generalities. CHAPTER VI. THE EXPERIMENTAL METHODS. 1. There are three chief methods of eliminating the — cause of a phenomenon from the neutral or indifferent accompaniments—Agreement, Difference, and Concomitant Variations. METHOD OF AGREEMENT, 2. The Method of Agreement is expressed thus :—If two or more instances of a phenomenon under investiga- 13 : 280 THE EXPERIMENTAL METHODS. tion have only one circumstance in common, that eireum- stance is the cause (or effect) of the phenomenon. The instances are studiously varied so as to leave out in turn all the circumstances attending the phenomenon. What- ever is left out, in any one instance, without detriment to the effect, cannot be the cause; the possibilities are gradually reduced in number; and, if the means of elimination are com- plete, the enquiry terminates in assigning one circumstance that has never been wanting where the phenomenon appears. | The method is illustrated symbolically thus :—Let A repre- sent a cause and aan effect. In nature we seldom have A followed by a alone; were such isolation the rule, the Experi- mental Methods would be unnecessary. What we find is A.in combination with other things as A B C, and a also in com- bination, asinabec. But, now, if these conjunctions were rigid and invariable, we should have no opening for the methocs. The real fact is, however, that though a cause may be always in combination with other agents, it is not always in the same combination ; at one time the union is A B C, at another time A B D, and again A C E; there being corres- _ ponding conjunctions in the effects—a b ¢,abd,ace, | If we suppose, then, the instances— ABC giving a be, ‘f ’ A BD giving a bd, Cee 4 ACE giving ace, pies we reason thus. So far as the first instance is concerned— ABC giving abc, the effect a may be produced by A, or by B, or by ©. In the second instance—A B D giving a 6 d, the cause C is absent, the effect a still remaining; hence C is not a cause of a. In the third instance—A C E giving ace, —B is absent, a remaining; hence B is not a cause of a. The only antecedent persisting through all the instances is A; when a is present as a consequent, A is always present as an antecedent. If, then, we are sure that every other antecedent circumstance has been removed in turn, the consequent a still surviving, we have conclusive evidence that A is a cause, condition, or invariable accompaniment of a. It matters not which is the form of the enquiry,—given an effect to find a cause, or given a cause to find an effect. The first is supposed to be the more frequent occurrence. Science, . from of old, was rerum cognoscere causas. If the problem be given in the first form, the proof is ali given in the second; we try a cause to see what effect — eee y METHOD OF AGREEMENT, 281 will follow, which proves at once that the consequent is the effect of the antecedent, and that the antecedent is the cause of the consequent ; the two affirmations being identical. Although our professed object now is to unfold the Induc- tive elimination of Cause and Effect, having already disposed of the case of Co-existence as Co-inhering Attributes, yet, in expounding the Methods, we must receive instances indis- criminately, as we do not at first know how they will turn ont. There are many connexions of Cause and Effect that appear as Co-existences, and there are instances that we must leave undecided, being unable to assign the ultimate nature of the union. The more obvious tests of Causation are these :— (1) sequence in time, as when innoculation is followed by the small-pox pustule; (2) expenditure of energy, as when a cannon ball shatters a fort. Where these tests are wanting, as in co-inhering powers of the same substance—for example, gravity and inertia—we are left to presume co-existence, there being, as alternative possibilities, mutual implication, and the co-existing effects of a common cause. This explanation is more especially called for in commenc- ing the Method of Agreement—the universal or fundamental mode of proof for all connexions whatever. Under this method in particular, we must be ready to admit all kinds of conjunctions; reducing them under Causation, when we are able, and indicating pure Co-existence when the presumption inclines to that mode. As a simple example, we may take the case of the conver- sion of solid bodies into liquids, and the farther conversion of liquids into gases. The bodies so converted are of every possible variety of properties ; the one circumstance common to all the instances of such conversion is the application of heat. ‘The elimination is complete as regards this antecedent, which is therefore correctly assigned as the essential condition or cause. We may apply in this example, the most decided test of Causation, the expenditure of energy or force; we should never regard the fact as a mere Co-existence. The next example is of a different character. The peculiar phenomenon known as the interference of polarized light—consisting in the exhibition of rings of alter- nating or ‘periodical’ colours, when a polarized beam of light passes through certain transparent substances—may be propounded for investigation. We may ask—is there any other property or phenomenon always present in the bodies that show this peculiar effect? Now, the bodies must, as a men Pes oe 4.44 \ ne , 7 Y82 THE EXPERIMENTAL METHODS. matter of course, be transparent; but all transparent bodies do not exhibit the polarized bands; hence, transparency is eliminated. By farther comparison of instances, we find that there is no constant mode of colour, of weight, of hardness, of form (crystalline), of composition (physical or chemical) ; ; so that no one of all these properties is concerned in ‘the phenomenon. There is, however, one property common to all the substances that furnish these coloured bands, they are — all doubly refracting substances, that is, present two images of things seen through them obliquely. By Agreement through all known substances, there is proof of the concurrence of these two properties, It is not ascertained, however, and cannot be ascertained by Agreement alone, whether the two facts are cause and effect, or whether they are a case of co-existence without causation. Agreement is the method of proof for all conjunctions what- soever—whether Causation or Co-existence. The enquiry belongs to a particular class—the conjoined Properties of Kinds, where there may be laws of co-existence without cau- sation. The decisive criteria of causation are wanting in the case. KL mit To take a third example. In flowers, there is a remark- able concurrence between the scarlet colour and the absence of fragrance. The following quotation gives a selection of instances. ‘Among all the colours that blooms assume, none are less associated with fragrance than scarlet. We cannot at present recollect a bright scarlet blossom that is sweet-scented—yet no other colour among flowers is more admired and sought ~ after. Scarlet prevails among Balsamina, Euphorbia, Pelar- — gonium, Poppy, Salvia, Bouvardia, and Verbena, yet none of — the scarlets are of sweet. perfumes. Some of the light-coloured i Balsams and Verbenas are sweet-scented, but none of the — scarlets are. The common Sage, with blue blooms, is odorifer- ous both in flower and foliage; but the scarlet Salvias are — devoid of smell. None of the sweet-scented-leaved Pelar- goniums have scarlet blooms, and none of the scarlet. bloomers have sweet scent of leaves nor of blooms. Some of the white- margined Poppies have pleasant odours; but the British scarlets are not sweet-scented. The British white-blooming — Hawthorn is of the most delightful fragrance; the scarlet- flowering has no smell. Some of the Honeysuckles _ are sweetly perfumed, but the Scarlet Trumpet is scentless’ (ELDER, American Gardener's Monthly). india cael EXAMPLES OF AGREEMENT. 283 Fourth Example. The North-Hast wind is known to be specially injurious to a great many persons. Let the enquiry be—what circumstance or quality is this owing to? By a mental analysis, we can distinguish various qualities in winds; —the degree of violence, the temperature, the humidity or dryness, the electricity, and the ozone. We then refer to the actual instances to see if some one mode of any of these qualities uniformly accompanies this particular wind. Now we find, that as regards violence, easterly winds are generally feeble and steady, but on particular occasions, they are stormy ; hence, we cannot attribute their noxiousness to the intensity of the current. Again, while often cold, they are sometimes comparatively warm; and although they are more disagree- able when cold, yet they do not lose their character by being raised in temperature ; so that the bad feature is not coldness. Neither is there one uniform degree of moisture; they are some- times wet and sometimes dry. Again, as to electricity, there is no constant electric charge connected with them, either positive or negative, feeble or intense; the electric tension of the atmosphere generally rises as the temperature falls. Farther, as respects ozone, they have undoubtedly less of this element than the South-West winds; yet an easterly wind at the sea shore has more ozone than a westerly wind in the heart of atown. It would thus appear that the depressing effect cannot be assigned to any one of these five circumstances. When, however, we investigate closely the conditions of the north easterly current, we find that it blows from the pole towards the equator, and is for several thousand miles close upon the surface of the ground ; whereas the south-west wind - coming from the equator descends upon us from a height. Now, in the course of this long contact with the ground, a great number of impure elements—gaseous effluvia, fine dust, microscopic germs—may be caught up and may remain sus- pended in the lower stratum breathed by us. On this point alone, so far as we can at present discover, the agreement is constant and uniform. _ What is the conclusion? As Agreement by itself does not decide that conjoined circumstances are cause and effect, we must find some mode of excluding Co-existence, and rendering the case one of succession. When the two circumstances are plainly in succession, as when a fracture follows a blow, uni- form agreement (with elimination) proves causation ; when they are not demonstrably successive; the agreement fails in this respect. -284 THE EXPERIMENTAL METHODS, Now, there is a general belief that the two events supposed —the east wind and the uncomfortable sensations—are not contemporaneous, but in succession; the wind first, the feel- ings afterwards. This belief is supported by the circumstance that a change of feelings, must have, according to the law of causation, an antecedent condition; and if all antecedents, besides the one above named, are eliminated, that one is the cause, or an essential part of the cause. ‘ The phenomenon to be explained is not a permanent fact or potentiality, like polarization or double refraction, it is a temporary manifestation, and requires some causal circum- stance to bring it forth. In this respect, it resembles the actual display of one of these optical properties; it cannot happen without a suitable agent and collocation, which is pro- perly a cause of the appearance. If then, the elimination be supposed complete, there is a proof by Agreement that the deleterious influence of the east wind is due to the circumstance named ; aud the case exempli- fies the eliminating efficacy of the method. | In the foregoing example, we cannot withhold from our mind a certain presumption in favour of the result, grounded on our knowledge of the deleterious tendency of atmosphere impurities caught up from the surface of the ground. This is a circumstance not properly belonging to the proof by — Agreement; it is a confirmation from deductive sources. The addition of such a presumption always operates strongly on our belief; the total absence of it leaves a considerable shade of uncertainty in all the methods, but most of all in Agree- ment. ‘The third example shows this deficiency ; we are not at present aware of any connexion of a causal kind between — the scarlet colour of flowers and the absence of fragrant odour; the proof of the law rests upon the Agreement alone. That method of proof is final, only when the elimination has been exhausted, by variation of circumstances, and when the coin- cidence has been shown through all nature, so as to establish a law of Universal Co-existence. Fifth Example. Let the phenomenon given be Crystallization, and let the thing sought be the antecedent circumstances, positive and negative, of the formation of crystals. This is a case of succession, and therefore of Causation. ‘ We must begin by collecting instances of the effect. In the following series, the circumstances are purposely varied with — @ view to elimination :— oad 1. Freezing of water. : ately EXAMPLES OF AGREEMENT, 285 . Cooling and solidifying of molten metals and minerals. Deposition cf salts from solutions. . Volatilizing of solutions. Deposition of solids from the gaseous state, as iodine. Pressure. . Slow internal change, as in rocks. . The transformation of metals from the tough to the brittle condition, by hammering, vibration, and re- peated heatings and coolings. Looking at the first and second instances—ice, and the solidifying of molten metal—we discover two antecedent cir- cumstances, namely, lowering of temperature, aud change from the liquid to the solid state. The third instance—deposition of salts from solution— agrees in the same two circumstances, there is a lowering of temperature, and also a change from liquid to solid. The fourth instance—the volatilizing of solutions, as in boiling down sea-water—appears to failin the matter of cool- ing, but still contains the circumstance of prior liquidity ; the prominent fact is that the solvent is driven off, and the dis- solved substance thereby compelled to resume the solid state. The fifth instance—the deposition of solids at once from the gaseous state, as in the case of iodine—seems to eliminate prior liquidity. We must then shift the ground, and, for liquidity, substitute one of the two higher states of matter. The sixth instance-is ‘ heavy and long continued pressure upon an amorphous substance ;’ principally shown in geology. This would eliminate the prior liquid or gaseous condition, and bring to view the forced approximation of the constituent particles of bodies. But the same circumstance accompanies all the previous cases, being merely a different expression of what is common to them. We know heat as forcibly enlarg- ing the bulk of bodies—making their particles mutually re- pellent ; the withdrawal of this force leaves the attractions of the particles free to operate. The seventh instance—slow geological transformation— unless viewed by the light of the circumstance just named, is difficult to interpret. It is not, however, incompatible with the predominance of the molecular attractive forces by the abatement of the repellent forces. The eighth instance—change of metals from the toagh to the brittle state—is a true case of crystallization ; brittle. ness is accompanied with an imperfect crystalline arrangement. The effect is produced by cooling after hammering ; by re- CO NI Or 09 BD 286 THE EXPERIMENTAL METHODS, peated heating and cooling; by long-continned vibration or concussion :—all which influences tend to expel the structural heat of the substance; the consequence being that the mole- cular attraction is more preponderant. We have thus eliminated Cooling, Deposition from Solution, and Prior Liquidity ; and have found but one uniform antece- dent—the increased scope and operation of the molecular or solid-forming cohesion; to which point, however, these other circumstances really tend ; they are all of them remoter ante- cedents of the one constant antecedent. The examination of the instances has enabled us to generalize the phenomenon, as well as to establish the generality upon evidence, namely, the evidence of Agreement. As we have stated this enquiry, it is a clear case of Cause and Hffect. We have sought the antecedent circumstances whereby a body in an amorphous or unerystallized state be- comes crystallized ; and we find that there is an expenditure and re-distribution of power or energy. The result of the ex- penditure is not an active manifestation, as when we produced mechanical force, or heat; it is an arrangement, or structural collocation ; a case already contemplated (p. 265) among the results of expended force. Sixth Example. Let us next apply the method to eliminate the cause, or the antecedent conditions essential to the pro- duction and maintenance, of Light. Now, the most constant circumstance is a high temperature ; solid bodies become luminous at a temperature of from 980° to 1000° Fahrenheit. So far, there is a remarkable unanimity. It is found, however, that gases do not always become lumin- ous at this temperature, nor at a much higher; a current of — gas may be raised to upwards of 2000° F. without being luminous; whence we conclude that the state of the body is also a condition. Again, the electric spark is a luminous effect, which would give the disturbance of the electric discharge as an antecedent. As there is a possibility, however, ihat the great violence of the discharge may be accompanied with sudden rise of temperature, this may be merely another form of heat. We should need to show, by varying the instances, that high temperature is not essential to the spark. _ In the next place, certain substances give light at common temperatures, to which fact has been given the name phosphor- escence. Some minerals, gently heated, emit a feeble light, which soon ceases, and cannot be renewed until the body hag been exposed to the sun or the electric spark. This.isstilla — COGENCY OF AGREEMENT. 287 form of heat, but not of the intense degree of ordinary light. More peculiar still is animal phosphorescence, as the glow- worm, fire-fly, and certain sea animalcules. Here the accom- paniment is a special mode of vitality hitherto uneliminated, and excluding the circumstance of high temperature (Mr. Herbert. Spencer suggests that it is an incident attending oxidation). Once more, a faint flash of light occurs with certain substances in the act of erystallizing. _ We may thus collect from Agreement, that ignited solids at the temperature of 1000° are luminous, and that an electric discharge is luminous; but we cannot at present lay down any wider generalization. Excepting the very general fact of molecular disturbance of some kind or other, which we are unable to qualify in the precise mode concerned in the effect, our comparison of instances does not point to a constant circumsta:ice. For the present, we regard Light as having a plurality of causes. As farther instances of Agreement, we may quote the proof of the coincidence of Sleep with low nervous action, which means a feeble cerebral circulation; also, the connexion of Memory with the intensity of Present Consciousness. The uniformity of these conjunctions under all varieties of other conditions is the evidence afforded by Agreement. The Rela- tivity of Knowledge is established partly by Agreement, partly by the method of Concomitant Variations, as will be shown. ‘The cogency of Agreement is manifestly in proportion to the thoroughness of the elimination. Whatever circumstance has never been eliminated is a possible cause. There are not a few instances, as in the action of drugs, where nature does not provide the variety requisite for a thorough elimination. The complicacy of the Natural Kinds passes our means of extrication by Agreement alone. METHOD OF DIFFERENCE, 3. Elimination by Difference is expressed in the follow- ing canon :—If an instance where a phenomenon occurs, and an instance where it does not occur, have every cir- cumstance in commen except one, that one occurring only, in the first ; the circumstance present in the first and absent in the second, is the cause, or a part of the cause, of the given phenomenon. We are supposed to have two instances and only two. Hach is a complex sequence, a group of antecedents followed by a 288 THE EXPERIMENTAL METHODS. group of consequents. The two complex sequences differ by only a single sequence, present in the one, and absent in the other. Thus the sequence A BC D gives a bed, and BC D gives bcd: the only difference being the presence of A in the antecedent, and of a in the consequent, of one sequence, aud the absence of these in the other sequence. Supposing A B C-D changed into B C D, by the loss of A; while at the mom- ent abcd is changed into b ¢ d by the loss of a; we have a proof of the connexion of A witha. Indeed, the assertions are identical; to say that the disappearance of one thing is followed by the disappearance of another thing, there being no other change, is merely a way of expressing causal connexion. Difference plays a great part in our everyday inferences. The usual form is the sudden introduction of some limited and — definite agency or change, followed by an equally definite con- sequence. When the drinking of water is followed at once by the cessation of thirst, we do not hesitate to pronounce the one fact the cause of the other. The human system is a great complication, but the only difference made upon it in two successive minutes is the sequence of drinking and the satisfy- ing of thirst; there has been, we presume, no time for any other change to manifest itself. So when we waken a sleeper by a noise, or strike a light by the friction of a match, we infer causation; the new agency being instantaneously fol- ~~ lowed by the new effect. The first example given, under Agreement, is also proved by Difference. That Heat is the cause of the melting of ice, of wax, or of lead, is proved by making, upon these substances, the one change of raising the temperature. Being quite sure that in the conversion of ice into water, no change has been made except this, we have a conclusive experiment of Differ- ence to show that heat is the cause. The same substance in two states, as solid and liquid, or as amorphous and crystallized, enables us to ascertain what effects are due to change of state. Thus charcoal, uncrystallized, is black, opaque, and a conductor of electricity ; as crystallized, in the Diamond, it is transparent and a non-conductor. A large part of our knowledge of nature and of living beings is gained by making experimental changes and watching the consequences. Our proof is the immediate result. An im- mediate response is satisfactory evidence in almost any de- partment. Thus, in medicine, there is little doubt as to the operative force of purgatives, emetics, sudorifics, diuretics, narcotics, stimulants, irritants; the uncertainty attaches to METHOD OF DIFFERENCE, 28% alteratives, tonics, and the protracted treatment of chronic cases. The effect of quinine, in ague, is established beyond dispute. _ Whether it be to add, or to withdraw, a definite agent, a change instantly following is proved to be an effect. Hvenin politics, we may have a proof from difference; as in the accession or resignation of a minister, like Chatham. No other circumstances arising in the ordinary course of a year would make that total change in the course of politics that followed on Chatham’s becoming minister. It could not be denied that he was the cause (in the practical sense of cause) of our successes in America, and on the continent of Europe. The consequences of his retirement were equally decided as proving, on the method of Difference, the vast superiority of his powers as an administrator. Wherever Difference can be resorted to, the knowledge of causes is gained at once. In ordinary cases, the method is so obvious in its application, so satisfactory and conclusive, as scarcely to need a master to explain or enforce it. The special discipline of Logic, so far as this method is concerned, lies in showing the precautions requisite in the more complicated cases. In Physiology, the functions of the nerves were ascertained by the experiment of, dividing each in turn, and watching the effect. Whatever function is immediately arrested on the division of a nerve, is shown to be due to that nerve, or to require that nerve in order to its performance. Such experi- ments, however, do not exhibit the entire circle of conditions involved in the function in question. We know that the integrity of the spinal cord is necessary to sensation and to movement in the trunk and in the extremities of the body; we do not exhaustively know what else is necessary. For this more extensive knowledge we should have to multiply experi- ments all through the brain. If the destruction of any part interferes with these functions, that part enters into the causal conditions; if otherwise, it does not enter into those conditions. The extension of this class of experiments to the brain exemplifies one situation where the method of Difference may be indecisive. Deep incisions in the brain, intended to affect one single organ, as the cerebellum, may injure adjoining organs; and may therefore be inconclusive as to the functions of the special organ in view. It is on this ground that Brown-Séquard objects to the views of Flourens regarding the 290 THE EXPERIMENTAL METHODS. function of the cerebellum. The one certain inference in such cases is, that whatever function survives, in its integrity, the destruction of an organ, cannot be exclusively due to that organ. The obverse inference is certain only on the supposi- tion that the injary has been confined to the part affected: With reference to the connexion of scarlet bloom with absence of odour, we have a seerming case of Difference in comparing such varieties as the white-flowering and the red- flowering hawthorn: the one fragrant, the other not. In the complicacy of Kinds, we can seldom be sure that a variation is rigidly confined to the circumstances that are apparent, Moreover, where there is not a clear case of Causation, Differ- ence is insufficient to prove a coincidence. Sir G. C. Lewis lays it down as essential to the validity of a proof by Difference, that we should know, by a previous induction, the general adequacy of the assigned cause to the production of the effect. When we infer that a man, shot through the heart, drops down dead, we need to know, he thinks, that, as a general rule, a gunshot wound in the heart, is a cause of death. ‘To this remark the reply is, that practi- cally we do make use of such previous knowledge, but itis not essential to the method of Difference. Provided we are quite sure that the new agent is the only change that has preceded the effect, the instance is conclusive, on the Law of Causation solely. The use of a more specific induction. is to supply the defect of certainty in the instance itself. There may be other unseen agencies at work, as well as the one supposed, and this is the only ground either for invoking a general presumption, or for multiplying instances of the phenomenon. In practice, we seek both for presumptions (from prior inductions) and for repetition of instances; but an ideally perfect instance of Difference, in a case of Causation, is conclusive in itself. Agreement and Difference can be easily compared as to their respective advantages and disadvantages. Agreement needs _a large number of instances, but their character is not re- stricted. Any instance that omits a single antecedent contri- butes to the result ; the repetition of the same instance is of use only as giving means of selection. Difference requires only one instance ; but that one is peculiar, and rarely to be found. A great extension is given to the power of Agreement, by, extending it to agreement im absence. When such cases are JOINT METHOD. 291 conjoined with those where the agreement is in presence, there is an approach to the conclusiveness of the method of Differ- ence. ‘I’his double employment of the method of Agreement is brought forward by Mr. Mill under the designations—the * Joint Method of Agreement and Difference,’ and the ‘ Indirect Method of Difference.’ It might also be called the ‘Method of Double Agreement.’ JOINT METHOD. 4. The canon of this Method is:—If two or more in- stances where the phenomenon occurs have only one cir- cumstance in common, while two or more instances where it does not ocenr have nothing in common save the absence of that one circumstance; the circumstance wherein alone the two-sets of: instances differ, is the effect, or the cause, ora necessary part of the cause of the phenomenon. If we require to ascertain, under this method, that A is the cause of a, or a the effect of A, we add, to the instances of uniform presence of A and a, other instances of uniform absence, as B F G followed by b fg, C H I followed by c h i, and so on. If we have never discovered A wanting as an antecedent without having a absent as a consequent, there is a strong additional presumption that A anda are united as cause and effect—a presumption that may approach to the certainty of the method of Difference. _ It is a confirmation of the cause, suggested by Agreement, of the noxiousness of the North-East wind, that the South- West wind, the genial and wholesome current, is wanting in the circumstance assigned. It descends upon us from the eleyated regions of the atmosphere, where impurities are highly diluted by dissemination. Again, to revert to the example of Crystallization. Let us review the non-crystallized solids, and note the mode of their formation. The amorphous stones and rocks, as sand- stone, chalk, &c., are known to be sedimentary deposits from water. Before being solidified, they existed as solid particles ; they were not dissolved in water, neither did they exist in a molten condition. This Agreement in absence would confirm the inference from Agreement in presence—that (so far as certain instances went) crystals existed in a previous higher condition. But the general inference, from the full compari- son of examples, was the superior play given to the molecular attraction by counterworking the molecular repulsion. Now, 992 THE EXPERIMENTAL METHODS, this general fact is absent from all mere sedimentary deposits; these bodies have no aid, in the shape of loss of heat or other cause, to their molecular attractions. ! The comparison of the amorphous rocks yields another circumstance, namely, the wregular mixture of different sub- stances. For, although in a mud sediment silica or alumina may prevail, neither is ever pure ; and the mixture of different elements is a bar to crystallization, unless they are of the kind called isomeric (from crystallizing alike). There is more to be got over in crystallizing compounds of unlike elements, and the crystals must be deficient in regularity. Another uncrystallized class comprizes the vegetable and — animal tissues. In their case, however, the antecedent circum- stances are too complicated and obscure to furnish insight; they rather stand in want of illustration by the parallel lights of more obvious eases. Besides, there is in them a method and order of aggregation more analogous to the crystallized, than to the amorphous solids. _ A third class includes the Colloids, or glue- bodies, of Graham (represented by gum, starch, gelatin, albumen, tannin, caramel). They are not confined to the viscid form of glue, but include compact solids, as flint. The points of contrast between these and crystallized bodies are numerous and ~ important. Their mode of formation is various; many of them are the products of living bodies, and therefore share in the complication of living growth. Flint is an aggregate of particles of silica, which particles were originally the shells of animals, and therefore also organic in their formation. In this case, the molecular attraction of silica, in its progress towards crystallization, is thwarted by the pre-existing forms of the silicious particles. It would require too long a discussion to show the bearing of the colloid peculiarities on the question as to the antece- dents of the crystalline formation, Enough has been given to show the working of the method of Obverse Agreement. — METHOD OF CONCOMITANT VARIATIONS, 5. Canon of the Method : — Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an — effect of that phenomenon, or is connected with it through — some bond of concomitance. The effects of Heat are known only through proportionate CONCOMITANT VARIATIONS. 293 variation. We cannot deprive a body of all its heat; the nature of the agency forbids us. But, by making changes in the amount, we ascertain concomitant changes in the accom- panyiug circumstances, and so can establish cause and effect. it is thus that we arrive at the law of the expansion of bodies by heat. In the same way, we prove the equivalence of Heat and Mechanical Force asa branch of the great law of Con- servation or Persistence of Force. The proof of the First Law of Motion, as given by Newton, assumed the form of Concomitant Variations. On the earth, there is no instance of motion persisting indefinitely. In proportion, however, as the known obstructions to motion— friction and resistance of the air—are abated, the motion of a body is prolonged. A wheel spinning in an exhausted receiver upon a smooth axle runsa very long time. In Borda’s experi- ment with the pendulum, the swing was prolonged to more than thirty hours, by diminishing friction and exhausting the air. Now, comparing the whole series of cases, from speedy exhaustion of movement to prolonged continuance, we find that there is a strict concomitance between the degree of obstruction and the arrest; we hence infer that if obstruction were entirely absent, motion would be-perpetual. The celebrated experiment of carrying the barometer to the top of Puy de Déme was a proof by variation of the connexion between the pressure of the air and the rise of the mercury. By Concomitant Variations, we derive one of the proofs of the connexion between the brain and the mind. In the same manner, we learn to associate health with the healthy agencies, and diseases with noxious agencies. The doctrine that change of impression is an essential con- dition of consciousness, from which proceeds the theory of Relativity as applied to feeling and to knowledge, is most strikingly attested by Concomitant Variations. The intensity of a mental impression notably varies according to the greatness of the transition from one state to another: witness the in- fluence of novelty, of all great changes of circumstances, of suddenness and surprise. The Statistics of Crime, reveal causes by the method of Variations. When we find crimes diminishing according as labour is abundant, according as habits of sobriety have in- creased, according to the multiplication of the means of detection, or according to the system of punishments, we may presume a causal connexion, in circumstances not admitting of the method of Difference. 994: : THE EXPERIMENTAL METHODS. The Concomitance may be inverse. Thus we find that the tendency to chemical action between two substances increases as their cohesion is diminished, being much greater between liquids than between solids. So, the greater the elevation of the land; the less the temperature, and the more scanty the vegetation. Parallel. Variation is sometimes interrupted by critical points, as in the expansion of bodies by heat, which suffers a reverse near the poimt of freezing. Again, the energy of a solu- tion does not always follow the strength ; very dilute solutions occasionally exercise a specific power, not possessed in any degree by stronger. So, in the animal body, food and stimu- lants operate proportionally up to a certain point, at’ which their farther operation is checked by the peculiarities in the structure of the living organs. The properties of highly rarefied gases do not exhibit an exact continuity of the phenomena that vary with density. In a perfect vacuum, there is no electrical discharge; but the variations of the discharge, in highly rarefied air, do not pro- ceed in exact accordance with the degree of rarefaction. We cannot always reason from a few steps in a series to the whole series, partly because of the occurrence of critical points, and partly from the development at the extremes of new and unsuspected powers. Sir John Herschel remarks, that until very recently ‘the formule empirically deduced for the elas- ticity of steam, those for the resistance of fluids, and on other similar subjects, have almost invariably failed to support the theoretical structures that have been erected upon them.’ The method of Concomitant Variations 1s powerful in suggesting, as well as efficacious in proving, causal connexions. The mind is apt to be aroused to the bond between two circumstances by encountering several conjunctions of the two in unequal degrees. Very often, we are not alive toa connexion of cause and effect till an unusual manifestation of the one is accompanied with an unusual manifestation of the other. We may be using some hurtful article of food for a length of time unknowingly ; the discovery is made by an accidental increase of quantity occurring with an ageravation of some painful sensation. This is one form of the efficacy of an Extreme Case; an efficacy felt both in science and in rhetoric. ? A remarkable case of Concomitant Variations is fornighed by the discovery of a connexion between the solar spots and the positions of the planets. Thus, as regards Venus, ‘spots are CONTINUOUS COMPARISON, 295 nearest to the solar equator when the heliographical latitude of Venus is 0°,’ and obversely. An important device for discovering, and also for proving, laws of causation, consists in arranging things possessing a common property in a serial order, according to the degree of the property. Thus, we may arrange bodies according to their Transparency or Opacity, according to Specific Gravity, to Conduction of Heat and Electricity, and so on. We are then in a position to detect any corresponding increase. in some accompanying property, and thereby to establish a law of concomitance or causation. This method is designated, by Mr. Mill, Classification by Series, and by Sir G. C. Lewis, the Method of Continuous Comparison. The progress of Life in the animal scale; the progress of mental development in human beings; the progress of civilized institutions, as Government, Judicature, the Representative System,—may be expressed in a series, so as to trace concomitant variations. It is greatly to be desired that, in Physical Science, all the substances in Nature should be set forth in distinct tabula- tions, according to the degree of every important property. It was when transparent bodies were arranged in the order of their refracting power, that the connexion was discovered between high refracting power and combustibility. METHOD OF RESIDUES. 6. The canon of Residues is :— Subduct from any phenomenon such part as previous induction has shown to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. After a certain progress is made in the inductive determina- tion of Causes, new problems are greatly simplified by sub- ducting from a complex sequence, the influence of known causes. Sometimes this of itself may amount to a complete elimination Such procedure is styled the Method of Residues. It is an instrument of Discovery as well as of Proof. The method is symbolically illustrated thus :—Suppose the antecedents A B C followed by the consequents abc; and that by previous inductions, we have ascertained, that B gives b, and C givese. Then by subtraction, we find. A to be the cause of a. The operation is substantially the method of Dif- ference, and has all the decisiveness belonging to that method. Sir John Herschel was the first to show the importance of studying residual phenomena. His examples are very. strik- 296 THE EXPERIMENTAL METHODS. ; ing (Introduction to Natural Philosophy, p. 156). Thus, the retardation of the comet of Encke has been the means of suggesting, and may ultimately suffice to prove, the existence of a resisting medium diffused throughout space. Again, the observation of Arago—that a magnetic needle, seta vibrating, is sooner brought to rest when suspended over a plate of copper —was the first clue to the discovery of Magneto-Hlectricity. The anomalies in the motion of Uranus led Adams and Le Verrier to the discovery of Neptune. 4 The study of the electrical odour was the first step to the discovery of the remarkable substance—Ozone. Sir G. C. Lewis remarks that ‘ the unforeseen effects of changes in legislation, or of improvements in the useful arts, may often be discerned by the Method of Residues. In comparing statistical accounts, for example, or other registers of facts, for a series of years, we perceive at a certain period an altered state of circumstances, which is unexplained by the __ ordinary course of events, but which must have some cause. __ For this residuary phenomenon, we seek an explanation untilit is furnished by the incidental operation of some collateral cause. For example, on comparing the accounts of live cattle _ ; and sheep annually sold in Smithfield market for some years past, it appears that there is a large increase in cattle, while i the sheep are nearly stationary. The consumption of meat in London may be presumed to have increased, at least in pro- portion to the increase of its population; and there is no reason for supposing that the consumption of beef has increased faster than that of mutton. There is, therefore, a residuary phenomenon, viz., the stationary numbers of the sheep sold in Smithfield—for which we have to find a cause. This cause is the increased transport of dead meat to the metropolis, owing to steam navigation and railways, and the greater convenience of sending mutton than beef in a slaughtered state.’ . The question as to the existence of a special force of Vitality— the vital force, or the vital principle—takes the form of an enquiry into aresiduum. We have first to make allowance for the operation of all the known forces of inorganic matter ; and when these have been exhaustively computed, the re- mainder may be set down to a special influence, or vital principle. For anything we know at present, the inoryanic forces, operating in the special collocations of organized bodies, may be competent to produce all the observed effects. The only proof of an exhaustive Analysis, whether in PROOF OF AN ANALYSIS BY RESIDUES, 297 material actions or in mental processes, is there being nothing left. Thus, in the Human Mind, it is disputed whether there be a separate and unique faculty, called the Moral Faculty, or the Moral Sense. Now, there can be no doubt as to the presence of common elements of Feeling, Will, and Thought, in our moral judgments and actions ; as, in the case of the vital principle, the question is, what remains, when these are all allowed for. ‘The same application of the Method of Residues occurs in the controversy as to Instincts, and Innate Ideas; does Experience, concurring with the usually admitted Intel- lectual Powers, account for the whole of the facts ? CHAPTER VII. EXAMPLES OF THE METHODS. The Experimental Methods have been regarded mainly as instruments of Elimination and Proof, or of separating irrele- vant accompaniments from causal accompaniments. In their working, however, they unavoidably lead to inductive generali- zations, in which aspect they are methods of Discovery. The same search for instances, the same comparison of them when found, both conduct us to new principles or laws, and prove them when once attained. Still, it was not desirable to keep up the double illustration throughout. In the miscellaneous examples that are to follow, occasional allusion will be made to the procedure suited to the discovery of generalities. The proofs adduced to show that the mode of action, in Smelling, is Oxidation, may be quoted in illustration of the Methods. The phenomenon is one of great interest, and of some perplexity. The following important facts were indicated by Graham. The sweet odours are due to hydro-carbons, as the ethers, alcohol, and the aromatic perfumes. Now, all these substances are highly oxidizable at common temperatures, being speedily decomposed in the air. Again, sulphuretted hydrogen, the most familiar of malodorous substances, is readily oxidized, and is destroyed in that manner. ‘These are instances of Agreement (in presence). 298 EXAMPLES OF THE EXPERIMENTAL METHODS. A farther instance of Agreement is shown in the decomposi- ‘tion of hydrogen compounds, in the act of causing smell. When a small quantity of seleniuretted hydrogen is inhaled by the nose, the metallic selenium is found reduced upon the lining membrane of the cavities. The sensation is an intensely bad smell. | _ A remarkable case of Agreement in Absence is furnished by the marsh gas—carburetted hydrogen. This gas has no smell. As the proof of the concurring absence of its oxidation at com- mon temperatures, Graham obtained it from the deep mines where it existed, for geological ages, in contact with oxygen. Again, hydrogen itself, if obtained in purity, has no smell ; and it does not combine with oxygen at the usual temperature of the air. An instance approaching to Difference is the following. If oxygen is excluded from the cavities of the nose, there is no smell. Also, a current of carbonic acid arrests the odour; an influence which may (although not with absolute certainty) be supposed hostile to oxidation. To make the evidence complete, it is requisite that all the instances of the effect should be of the same unvarying tenor, or that there should be no exceptions. Until every apparent dis- crepancy is reconciled, the facts are inconclusive. A seeming exception is the pungency of ozone, which is looked upon as a more active form of oxygen. Now wecan hardly suppose that ozone combines with oxygen; a more likely supposition is that, by its superior activity, it combines with the nasal mucus. The research into the cause of Dew has been used by Sir John Herschel, and again by Mr. Mill, as a happy example of experimental elimination involving nearly the whole of the methods. All the stages of this inductive determination are highly instructive. ! The first point is to settle precisely the phenomenon'to be explained. This is an exercise of Definition, and can never be too rigidly attended to. There is some danger, in the present case, of confounding the effect with certain other effects; and hence the expediency of defining by an exhaustive contrast. Well, Dew is moisture; but that moisture is not rain, and not fog or mist; it is moisture spontaneously appearing on the surface of bodies when there is no visible wetness in the air. — In a perfectly clear and cloudless night, there may be a copious moisture on the surface of the ground, and this moisture is the thing to be accounted for. FON RESEARCH ON DEW. 299 ~ Now, the problem being given as an effect, with the cause unknown, we cannot make experiments, until a cause is sug- gested. This is a pure effort of Discovery, preparatory to the application of the methods of inductive proof. On the various occasions when dew appears, we must look out for the atten- dant circumstances, with a view to their successive elimination. We know, for example, that dew appears chiefly at night, which would suggest some of the circumstances connected with night-fall, as darkness, cold, and any of the concomitants of these. That darkness is not the cause could be shown if either dew appears before sunset, or if it ever fails to appear at night. As the last alternative is very frequent, we must, so far as the Experimental Methods are concerned, pronounce ee darkness. There would then remain the agency of old. Farther, in this preliminary stage of looking out for a pos- sible cause, we need not confine ourselves to the actual pheno- menon. In the conduct of the research, as recorded, much ‘Stress was laid upon the reference to analogous effects, or to other cases where moisture spontaneously appears on surfaces, in the absence of visible wet. All such analogies are valuable for suggestion or discovery, in the first instance, and for proof afterwards. They are these :—(1) the moisture that gathers on cold stone cr metal when breathed upon ; (2) the moisture on the outside of a tumbler of spring water fresh from the well in hot weather; (3) the moisture that often appears on glasses when brought into a hot room full of people; (4) what appears on the inside of windows when a room is crowded, and during changes in the outside temperature ; (5) what runs down our walls, especially outer passages, when a warm moist thaw succeeds to frost. All these cases correspond to the definition; and their comparison is likely to indicate some circumstance to be subjected to experimental elimination. To take the first instance—the breath upon a cold metallic sur- face; the warmth of the air and the coldness of the surface are obvious accompaniments. Some of the others would sug- gest the same conjunction, while all are compatible with it. Now, this is the situation already suggested by the original phenomenon, the dew at night-fall. Consequently, we are in @ position to proceed experimentally ; we can try the cooling down of surfaces under variation of circumstances. An easy experiment will tell us whether the cooling of the surface be a uniform fact, in the production of dew. Lay a thermometer on the dewed grass, hanging another in the air; 300 EXAMPLES OF THE EXPERIMENTAL METHODS. and repeat this on many successive nights. The actual result is that whenever a surface is dewed, it is colder than the air around it. This is a proof from Agreement; but proofs from Agreement, unless they can be multiplied through all nature, in all climes, seasons, and situations, will not of themselves decide either causation, or universal coincidence. By varying the circumstances, we can bring to bear the other methods. We may, for example, try Agreement in Absence ; that is, make the same appeal to experiment in nights where there is no dew anywhere. The phenomenon, however, would be found to evade this test; there would be cases of actual cooling of surfaces below the temperature of the air, and yet without dew. Hence the necessity of a dif- ferent course of proceeding. Observation reveals to us the fact that on the same night, and in the same spot, some surfaces are dewed, and others not. ‘This holds out the prospect of an appeal to the Method of Difference. On the surface of a plate of glass, there may be dew, while on a polished metallic surface, there is none. Unfor- - tunately, however, such a couple is not suited to the canon of Difference. The points of diversity between glass and metal are too numerous to comply with the stringent requisite of that canon. We must, therefore, shift our ground once more. It being apparent that the nature of the material enters into the effect, let us expose a great variety of different materials—metals, glass, stone, wood, cloth, &c. We now find that there is a scale of degree ; between the extremes of no dew and copious dew, there is a gradation of amount. The enquiry then arises, is there any other property of these different materials varying in concomitance with their being dewed? Does their temperature (which is the clue that we are going upon) change in exact accordance with the amount of dew? There was here scope for a direct appeal to the thermometer. We have not, however, to record the issue of such an appeal; the history of the research pursues another and more circuitous route for arriving at the conclusion. It so happened, that the experiments, begun by Sir John Leslie, upon the conduction and the radiation of heat, came in to the aid of the present enquiry; and the use made of these is sufficiently illustrative of the canons of Elimination. It appeared, on the comparison of the various materials, that the rate of becoming dewed varies inversely with the conducting power of the substance; the good conductors—the metals— are not dewed, the bad conductors are dewed according to til Re RESEARCH ON DEW. 301 their badness as conductors. This is the method of Concomi- tant Variations ; what it points to will be seeg presently. It is next desired to ascertain how far difference of surface operates, material being the same. The comparison shows that rough surfaces are more dewed than smooth, and black more than white. Instead of the direct test of the thermo- meter, the appeal here also is to Leslie’s experiments on the radiation of heat from surfaces; those surfaces that are most dewed—rough and black—are the best radiators of heat. The interpretation of this will be taken with the foregoing. In the meantime, make another variation, namely, for tewture; comparethe compact textures of metal, stone, wood, velvet, eider- down, cotton, &c.; the compact bodies are little dewed, in the comparison, the loose bodies, much. Now, as regards heat, the loose bodies are very bad conductors ; they resist the passage of heat through them, and are therefore chosen as clothing. Let us now seek the interpretation of these three last re- sults of Concomitant Variations. The first and third relate to bad conduction of heat as a concomitant, the second to good surface-radiation. Now, both circumstances point to one re- sult, that is, swrface cooling, in a cold atmosphere. A surface is cooled down by a cool contact, but if heat is rapidly sup- plied from within (which is good conduction) the lost heat is ‘made good, and the fall of temperature is delayed, until the interior has cooled also. In bad conductors, the loss is not made good in the same way, and the surface temperature falls. Thus, bad conductors sooner become superficially cold, in a cold atmosphere. Next as to Radiation. The explanation here is still more easy. Good radiation is, by implication, sur- face cooling ; bad radiation, as from a polished metal surface, is retention of surface heat. We thus come round to the con- - clusion, which a series of trials by the thermometer would have given at once, namely, that surfaces become dewed exactly as they fall in temperature. To all appearance, therefore, we have established a link of connexion between cooling and dew. The appearance is not the reality. There is still outstand- ing the fact that the same fall of surface temperature will not always bring out dew. Neither the same absolute surface temperature, nor the same difference between the surface temperature and the air temperature, is constantly followed by a deposit of moisture. We have here obviously a residual circumstance, whose investigation should next follow. The instances where the same thermometric difference is unattended with dew need to be studied by exactly the same routine as = ge ee Sass a a Pen . 302 EXAMPLES OF THE EXPERIMENTAL METHODS. has now been followed. We must look out for the suggestion of a possible agency ; and next subject that to experimental trial, with a view to proof or disproof. This residuum would have given rise to a very arduous research if it had been left to experimental determination. The difficulty was conquered in another way. Already (1799) had Dalton published his theory of Aqueous Vapour, or the Atmosphere of Steam, which was the missing link in the explanation of Dew. His positions were— that the aqueous vapour contained in the atmosphere is vari- able in amount, according to cireumstances, and that the amount is limited by temperature. To each degree of temper- ature corresponds a certain amount, which is the saturation of the air at that temperature. An amount equal to one inch of mercury is sustained at 80°, half an inch, at 59°. Supposing the air saturated at any one moment, a fall of temperature will lead to precipitation as visible moisture ; but as the air is not always saturated, a fall of temperature will not bring dew or mist, unless the fall extends below the degree corres- ponding to saturation, called the temperature of the Dew- point. This is the residual circumstance, the thing wanted to complete the proof of the connexion of dew with surface cold- ness. The present instance is a case of Cause and Effect ; as may be shown in various ways. In the way that the case has been stated, there is not apparent any transfer of energy, which is the best criterion of causation ; but underneath the appearance, we find there is such a transfer. Heat is necessary to convert water into steam, and this conversion is an instance of the transmutation of power according to a definite rate of exchange. The withdrawal of the heat is followed by the re-collapse of the invisible vapour into water or visible moisture. So that the production of dew is clearly a sequence under the great law of transferred energy. Other proofs of causation are dis- pensed with by this decisive consideration. Mr. Mill, however, remarks, as a distinct criterion of cause and effect, as well as a means of settling which is cause, and which is effect, that cool- ing is a consequence of known and independent antecedents, — and therefore cannot be set down as consequent on the occur- rence of dew. The next example is of value as showing the Experimental Methods in their purity, or in the absence of all deductive applications of laws, such as completed the enquiry into the cause of Dew. = MUSCULAR IRRITABILITY AND PUTREFACTION, 303 On the 16th of May, 1861, Dr. Brown-Séquard delivered the Croonian Lecture before the Royal Society, and took for his subject the ‘ Relations between Muscular Irritability, Cada- veric Rigidity, and Putrefaction.’ In this he adduced facts to maintain the following position :— ‘The greater the degree of muscular irritability at the time of death, the later the cadaveric rigidity sets in and the longer it lasts, and the later also putrefuction appears and the slower tt progresses.” By muscular irritability is meant muscular power or apti- tude for contracting. A man fresh in the morning for his day’s work would be said to have a good store of muscular irritability: at the end of the day’s work, the stock is com- paratively exhausted. It would of course be still more ex- hausted after protracted fatigues continued through many days. The cadaveric rigidity is a stiffening of the muscles that occurs in all animals some time after death. The time when the stiffening begins, and the duration of it, are variable, and Dr. Brown Séquard tries to establish the law or cause or con- dition of this variation. This he does by a series of observa- tions, whose force will be appreciated by noting how far they comply with the exigencies of the experimental methods. First set of Experiments.—Paralyzed muscles. Here he has two connexions to establish, in order to the end in view. He first shows that the paralysis of a muscle leaves it for a time with more irritability than the unparalyzed or exerted muscles. He paralyzed the muscles of one leg in a dog, by section of the nerve. Five hours afterwards the dog is killed (by asphyxia). In the paralyzed muscles the irritability lasted ten hours; that is, it was possible to induce contrac- tions in them (by stimulants) up to that time. In the healthy leg, the irritability lasted only four hours; in other words was very much less. Now compare the results as regards Rigidity and the delay of Putrefaction— Duration of irrit. Duration of rigidity. a — Paralyzed M. 10 hours 18 days 17th day. Healthy ,, A Bren, 7th ,, Here then is an experiment clearly of the nature of Differ- ence; for two legs of the same animal were compared, and the only difference was the paralysis of one of them. It is true, as in all cases of vivisection, that an experiment of Dif- ference must always be received with caution, seeing that 14 304 EXAMPLES OF THE EXPERIMENTAL METHODS. other changes may be made by the means taken to produce the difference. Yet, at all events, here is a strong presumption. The doctrine is confirmed farther by another aspect of the paralysis. If an animal is allowed to live a month after paralysis of a member, the paralyzed muscles are then inferior in irritability, and when compared under those circumstances, they become rigid and putrefy sooner. | Second set of Experiments.—LHffects of diminution of tem- perature upon muscles.—Dr. Brown-Séquard had determined, by previous experiments, that cold increases the vital proper- ties of the nerves and muscles—a fact on which the stimulating power of cold upon the animal system depends. He now applies this fact to the enquiry in hand. Two kittens of the same litter were placed in different tem- peratures. After death, the following differences were discern- ible. The one, kept at « temperature of 98°.6, assumed the rigidity in 33 hours; this lasted three days, putrefaction commencing in the fourth. In the other, which had been kept so cool, that a thermometer inserted in the rectum stood at 77°, the rigidity was delayed till the 10th hour, and lasted nine days, putrefaction commencing on the tenth. This experi- ment was repeated with many animals, and is also an experi- ment according to the Method of Difference. This is the general principle of the fact known in hot climates, that the dead putrefy almost immediately after death, and must be interred without a moment’s delay. The relaxation of the vital powers in hot climates is only a part of the same fact. The full explanation of this point, or the resolution of the law into still higher jaws is not yet fully made out. Influence of death by lightning and galvanism.—It was — thought by John Hunter that animals killed by lightning did not stiffen. This has been found not the case. Still there are instances where the rigidity has either not set in, or been of so short duration, that its existence has not been traced. Lightning may kill in various ways :—1st, By fright; 2nd, By hemorrhage; 3rd, By concussion of the brain. In all these three modes, ‘there ought to be a manifestation of the rigidity. But there is a fourth mode, which is to convulse all the muscles so violently as utterly to exhaust their irratibility ; in which case the rigidity may fail to be noticed. This is the . way that galvinism acts upon animals. Experiments were accordingly tried by galvanizing the limbs of Rabbits; comparing the galvanized with the un- — galvanized limbs, with respect to the ‘time of rigidity. [i MUSCULAR IRRITABILITY AND PUTREFACTION. 305 Galvanized Limb. Not Galvanized, Duration of Irritability, 7 to 20 minutes. 120 to 400 min. a of Rigidity, 2 to 8 hours. 1 to 8 days. Putrefaction advanced, within a day. After several days. The experiments were repeated on dogs with the very same results. Also, guinea-pigs were subjected wholly to galvanism, but in different degrees. In those powerfully galvanized, the irritability lasted a short time, and the rigidity was correspond- ing rapid and brief. With a less degree of galvanism, the time of both phenomena was protracted. We have, therefore, an additional corroboration of the law, still by the powerful Method of Difference. Influence of prolonged muscular exercise. — This, of course, is a cause of diminished irritability. Now, there are well- ascertained facts that connect prolonged exertion with rapid putrefaction. Over-driven cattle and animals hunted to death putrify speedily. So in cocks killed after a fight. Soldiers killed in a very prolonged fight show the same phenomenon. The rigidity is quickly over, and the putrefaction rapid. These are instances of the Method of Agreement. Influence of nutrition on muscles.—Dr. Brown-Séquard here collects confirming instances, from the comparison of cases where death happens in a well nourished condition of the muscles, with cases where death had been preceded by inanition. Thus, when men strong and fresh have been killed suddenly, the rigidity and putrefaction have appeared very late. A case is recorded of muscular irritability continuing twenty-six hours in a decapitated man. Here is Agreement in presence. Compare those instances with others of persons dying of slow exhaustion, and the appearance is reversed. A man dying of prolonged typhoid fever, for example, was found to show no trace of rigidity, and putrefaction commenced in less than an hour. This is Agreement in Absence. Influence of Convulsions on rigidity and putrefaction.—It appears that muscles much attacked with cramps before death speedily give way to putrefaction. Certain poisons (as strychnine) sometimes produce con- vulsions before death, and in those cases the rigidity and putrefaction progress rapidly. Such is an ample body of evidence from observation and experiment to establish the position laid down. The Methods of Avreement, of Difference, the Joint Method, and the Method of Variations, have been all brought into play. And if there 306 FRUSTRATION OF THE EXPRIMENTAL METHODS. are any doubts about the decisiveness of the experiments on the Method of Difference, from the possibility of making other changes besides the one intended, these doubts are dispelled by the coincidence of results from so many distinct experi- ments. The research is purely Inductive. No consideration of a Deductive kind has been introduced; although there are general considerations that give great probability to the conclusion. Muscular irritability is the living condition of the muscle—its vitality—which may be greater or less; and the greater it is, the longer the muscle will retain its living characters, or the longer it will be in passing to the characters of death, which are rigidity and putrefaction. These, therefore, are delayed by fulness of vitality ; while loss of vitality hands the system over all the sooner to the destroyer. When we form conclusions, on an insufficient employment of the methods of elimination, we commit Fallacies of Induc- tion. Of these, numerous examples might be given, and the © proper place for them is in the course of the exposition of the Methods themselves. As it is still the custom, however, to retain, in works of Logic, a separate chapter or book on Fallacies, we shall reserve for that part of the subject, the instances of Inductive fallacy. CHAPTER VIII. FRUSTRATION OF THE METHODS, 1. In the Inductive Methods as hitherto contemplated, two conditions have been supposed; first, that an effect — has only one cause, or set of antecedents; secondly, that different effects are kept apart and distinguishable. Both conditions may be wanting. In the method of Agreement, for example, it is assumed, that the effect a has only the cause A; should A and C both be causes, the method would be defeated. The absence of A would not prove that it is not a cause; for the effect might still be due to C. The special difficulties attending this case must now be considered. " Aa Ue eet re PLURALITY OF CAUSES NOT FINAL. 307 Again, the effects a bc are supposed to stand out distin- guishable. They may, however, be fused or united in one simple effect 2ac, or 3a. This is the Intermixture of Effects ; and is still more baffling to the inductive methods, as hitherto given. PLURALITY OF CAUSES. 2. In many instances, the same effect is produced by a PLURALITY OF CAUSES : as Motion, Heat, Pleasure, Death. Bodies are put in motion by all the different agencies termed Prime Movers—animal strength, wind, water, steam, combus- tion (asin gunpowder), &c. Finding a body in motion, therefore, we cannot ascribe it to any special agent, merely from the fact that it is in motion: we see a wheel turning and doing work, but we may not be able to attribute its motion to one agent rather than another. In like manner, there are various sources of Heat; the solar ray and combustion are the most familiar ; but friction and electricity are also-sources. Hence the fact of the evolution of heat does not point out the cause ; as an example, uncertainty still attaches to the immedi- ate antecedent of animal heat. There are numerous causes of pleasure and of pain: nume- rous modes of stimulating the nervous system; numerous agencies of good health and of bad health; numerous ways of getting a livelihood ; numerous causes of death, It is to be noted, however, that the plurality in some of these instances is on the surface only. As regards Motion, the law of the Persistence of Force assigns a common origin to all the so-called prime movers; these, therefore, are prowimate, and not the ultimate sources. The same law covers the produc- tion of Heat, however various the apparent antecedents. The causes of Pleasure can be generalized into a small number of agencies, if not into one. Possibly all stimulants may, in the last analysis, be found to have a common effect on the sub- stance of the nerves. The ways to Wealth may be apparently many, but we can cover them all by one general expression,—- earning and saving. In Health and Sickness, there might possibly be generalized expressions of the many proximate causes. So with Death. Nevertheless, for practical purposes, we have to ascertain not simply the primal cause, but the special embodiment of that cause, on a certain occasion. It is not enough, when a man is found dead, to assign the. stoppage of the heart, or of 308 FRUSTRATION OF THE EXPERIMENTAL METHODS. the lungs, or the extinction of the vital forces; we desire to know in what form and circumstances these generalized causes were specialized ; whether by cold, by inanition, by poison, by mechanical violence, or otherwise. 3. The chief consequence of Plurality of Causes is to frustrate the Method of Agreement. The Method of Difference remains intact. Whatever be the plurality of causes of motion, if we observe the imtroduction of some one agent followed by the effect, we know the cause in that instance. There may be many ways of keeping up the animal heat, but the transition from the temperature of 60° to 30°, by causing an immediate sense of chilliness shows that the external temperature is essential to comfortable warmth on that particular occasion. | The operation of Plurality is to give uncertainty to the Method of Agreement. For example, we observe numerous cases of unhealthy human beings whose parents were un- healthy; this would be to a certain extent a proof from Agreement. On the other hand, many unhealthy persons are the children of perfectly healthy parents ; whence, concluding by the strict rule of Agreement, we should affirm that uuhealthiness in the parents is in no case a cause of unhealthi- ness in the children; that the two facts are not in any way connected as cause and effect. The conclusion is obviously wrong; it would be correct were there only one cause of ill health ; it is illegitimate if there be many causes. Plurality is illustrated by our English spelling. The method of Agreement is nullified in this instance. In certain words, the letters ough agree with a peeuliar sound, as in ‘rough.’ The same word occurs with other letters, as in ‘ruff,’ and the same letters occur with a different sound, as in ‘hough.’ Whence, by the Method of Agreement, we should infer that there was never any connexion between either sound and ‘ough.’ A similar illustration is afforded by ambiguous words. The word ‘air’ is spoken in company with a musical melody ; at other times it is spoken where there is no music; any one unprepared for plurality, and following out Agreement, would conclude that the connexion with music was purely casual; that there was no fixed bond of union between the two. We acquire the meanings of the vocables of our language chiefly by the method of Agreement. We gradually eliminate all accompaniments that may be absent consistently with the employment of each word. We find, after a number of FAILURE OF THE METHOD OF AGREEMENT 309 repetitions of the word ‘fire’ in various connexions, that the one fact common to all is blazing combustion with heat. We learn in course of time to extend the word to metaphorical significations. These being conjunctions of pure co-existence, without causation, they cannot be dealt with by any other method, while the occurrence of plurality, even when under- stood and allowed for, is a serious and painful distraction to the inductive process. Again, pressure on the brain is a cause of insensibility ; yet, as we find insensibility where there has been no pressure, we should say, according to Agreement, that pressure is not a cause. In the same way, every one of the causes might be _ proved not to be a cause—deficiency of blood, excess of dark unhealthy blood, rupture of the nervous continuity, &. Extraordinary facts have come to light showing the possi- bility of exerting the mental powers, under disease of very large portions of the brain. These facts would seem to prove that such parts have no share in the mental functions. The safer inference is that there is a plurality of nervous seats or tracks for the same functions. It has long been supposed that the two hemispheres have common functions. The discussion of the problem of Beauty is often rendered fruitless by the neglect of Plurality. The attempt is made to assign some one circumstance present in all beautiful things— as Colour, Harmony, Fitness, Unity, Suggestion of Mental qualities. Now, by the unqualified method of Agreement, every assignable circumstance could be disproved ; with refer- ence to each one in turn, would it be possible to find objects of unquestioned beauty where that one is not present. Jeffrey _ thinks it a sufficient refutation of the theories he opposes, to produce beautiful objects where the alleged source of beauty is absent. _ 4. The counteractives to the failure of Agreement, in the case of Plurality, are (1) great multiplication of in- stances, and (2) Agreement in absence, that is, the Joint Method. (1) One remedy for the failure of the Method of Agreement, under Plurality, is multiplication of instances. This will operate in various ways. It will tend to bring out all the causes; which is one desirable issue of Plurality. An ex- tended statistics of Crime or Pauperism will show us the pos- sible agencies, by giving a wide scope for elimination. The long experionce of medical practitioners has taught them 310 FRUSTRATION OF EXPERIMENTAL METHODS, nearly all the possible causes of the greater number of diseases. At this stage of exhausted plurality, the only point for enquiry, in the special instance, is—Which of the causes are present, and are these free to operate P Knowing, all the contributing causes of Pauperism, we ask which of these occur in England, in Ireland, or in Scotland, and are they free or uncounteracted P Being aware of the various antecedents of dyspepsia—bad food, too much food, too little food, hard labour, waut of exercise, intemperance, mental wear and tear, bad air, a hot climate, &c.—we can judge what brought on the disease in a given instance. If we do not know which causes are present on @ given occasion, and whether those actually present are counteracted, mere Agreement is wholly fallacious. The fallacy named post hoc, ergo propter hoc, is an abuse of Agreement, where elimina- tion is vitiated by Plurality, as in a great number of political inferences. It is remarked that Protestantism is accompanied with superior industry ; the instances attainable are insuffi- cient in number to eliminate other causes. (2) The other remedy is the Joint Method. We should seek out cases of Agreement in absence, which are of a very decisive nature. If in all cases where a particular effect fails, one par- ticular cause is absent, there is, in spite of possible plurality, a strong presumption that the two circumstances are cause and effect in those instances. The reason grows out of that close approach to the Method of Difference furnished by Agreement in absence. Although there are various causes of light, yet the union of agreement in presence with agreement in absence is sufficiently decisive of the connexion of light with a high temperature. The special connexions of light with low temperature are not denied; they are admitted as exceptions to agreement in absence, as a residwwm to be ac- counted for. We know one cause thoroughly; we find there are other causes, as yet imperfectly known, which have this uncertainty, namely, that a body at the common temperature of the air may possibly be luminous. THE INTERMIXTURE OF EFFECTS. 5. The Methods of Elimination suppose different effects to remain separate aud distinguishable ; whereas cases arise where the effects of different causes unite in a homo- geneous total. When, in an aggregate phenomenon, distinguishable ante- a ee ——— INTERMIXTURE OF EFFECTS. 311 cedents produce distinguishable consequents—A B C giving abc, and A D E giving a d e, the experimental methods operate to advantage. The combination of wind, rain, and increased temperature, produces a combination of distinguish- able effects—waves on the surface of water, flooding of streams, the sensation of warmth. In other cases, and these very numerous, the effect of the several causes is homogeneous, and is merely increased in amount by the concurrence. The sea is fed by innumerable rivulets. The wind often concurs with tidal agency, so as to produce a higher tide. A body propelled by several prime movers, as when a train is urged by three locomotive engines, shows only one effect, velocity of movement. The moon’s path is a resultant of the attractive forces of the sun and the earth combined with its projectile movement. The path of a comet is the resultant of many influences; it does not bear on the face of it the story of them all. An invalid repairs to some salubrious spot, and plies all the means of restoration to health; many influences combine to the result, but the effect is one and indivisible. A still more perplexing situation is the conflict of opposing agencies. In an equal balance nothing is seen, and yet great powers have been at work. In unequal contests there is an effect ; but that effect does not suggest the fact of conflict. A trader has a net profit at the end of the year; the statement of that profit, however, gives no information of his expenditure and receipts. The patient may be under various healthy stimulants, each working its proper effect; but some one noxious agency may counteract the whole. Natural agencies can never be suspended; they may be counteracted by opposite agents. The force of gravity is not interfered with when a balloon rises, it is merely opposed by a greater force ; it still operates butin a different form. Instead of causing the usual appearance, namely, the descent of bodies to the ground, it operates to diminish the effect of an upward force, the buoyancy of the air (itself an indirect consequence of gravity). A counteracted force is technically said to exist in tendency. There is a tendency in all bodies to descend to the ground; in water to find its level ; in the moon to move towards the earth, and towards the sun. Thereisatendency in human beings to seek their own interest; in despotic sovereigns to abuse their ower. The tendencies are not annihilated when they fail to be realized ; they are only counteracted by some opposing tendencies, 7 S| = @r.s.* aso cu6l ss : “ eee - - — 812 FRUSTRATION OF THE EXPERIMENTAL METHODS, A farther circumstance working to invalidate the operation of the methods is the mutuality of cause and effect. In political ciusation, this is illustrated by*Sir G. C. Lewis as follows :— ‘It happens sometimes that when a relation of causation is established between two facts, it is hard to decide which, im the given case, is the cause and which the effect, because they act and re-act upon each other, each phenomenon being in turn cause and effect. Thus, habits of industry may produce wealth ; while the acquisition of wealch may promote industry: — again, habits of study may sharpen the understanding, and the increased acuteness of the understanding may afterwards increase the appetite for study. So an excess of population may, by impoverishing the labouring classes, be the cause of their living in bad dwellings; and, again, bad dwellings, by deteriorating the moral habits of the poor, may stimulate population. The general intelligence and good sense of a people may promote its good government, and the goodness of the government may, in its turn, increase the intelligence of the people, and contribute to the formation of sound opinions among them. Drunkenness is in general the consequence of a low degree of intelligence, as may be observed both among savages and in civilized countries. But, in return, a habitof — drunkenness prevents the cultivation of the intellect, and strengthens the cause out of which it grows. As Plato remarks, education improves nature, and nature facilitates education. National character, again, is both effect and cause; it re-acts on the circumstances from which it arises. The national peculiarities of a people, its race, physical struec- ture, climate, territory, &c., form originally a certain character, which tends to create certain institutions, political and domes- tic, in harmony with that character. These institutions strengthen, perpetuate, and reproduce the character out of which they grew, aud so on in succession, each new effect becoming, in its turn, a new cause. Thus, a brave, energetic, restless nation, exposed to attack from neighbours, organizes military institutions ; these institutions promote and maintain a warlike spirit; this warlike spirit, again, assists the develop- ment of the military organization, and it is further promoted _ by territorial conquests and success in war, which may be its result—each successive effect thus adding to the cause out of which it sprung.’ (Methods of Politics, I. p. 375). | 6. The Intermixture of Effects is a bar to the Experi- — mental Methods, 73 5 s INTERMIXTURE OF EFFECTS. 313 If A B OC D conspire to yield, not abcd, but a; and if ABC F yield still a, nothing is eliminated, there is no pro- gress. If a were precisely measurable, and if its variations corresponded definitely to the removal of particular agents, the Method of Difference would cope with the case:. the omission of A followed by the reduction of a to 2 a, would be a proof that A produced ¢ a. But the Method of Agreement, in its proper character of varying the circumstance by ex- cluding some agents and including others, could not furnish a decisive proof, so long as a represented the sum of several effects. Now, as in many departments, effects are thus inextricably blended, we should be at a stand-still, were we not in posses- sion of some method more searching than Agreement. Even in the Inorganic Sciences, as Mechanics and Chemistry, we have this complication; in Biology, Mind, and Society, we have it still more. —, © = COMBINATION OF PROBABILITIES, 323 independent), the chance is # X 4 or $3; that is two for and seven against. . 10. If. The probability ofthe occurrence of one or other of two events that cannot concur is the sum of the separate probabilities. ‘If one man in ten is over six feet, and one in twelve under five; then in a large number, say 120,000, there will be about 12,000 over-six-feet men, and about 10,000 under-five-feet men ; the sum of the two 22,000, will represent the number of such as are one kind or the other.’ # 11. III. The rule for the cumulation of independent Testimonies in favour of a fact, is to multiply the numbers expressing the proportionate value of each Testimony. If a witness is correct six times out of seven, or speaks six truths for one error, his relative testimony is six for and one against, or $. Two witnesses of this character concurring would give a probability of 6 to 1 multiplied by 6 to 1, or 86 to 1, and so on. 12. IV. The rule for the deterioration of testimony in _ passing from one person to another, that is, for the weaken- ing of traditional evidence through lapse of time, is to multiply the fractions expressing the separate probabilities. If one witness speaks truth five times in six, the fraction is £; if another witness speaks truth nine times in ten, the value is 7%. Ifthe one repeats what he has heard from the other, the testimony is weakened by the transmission to 2 x fo = 63, or 3. Of facts attested by the second witness, de- riving from the first, three will be true and one false. A few such transitions bring the evidence below probability, and render it worthless. Four successive witnesses each valued #, would give 8, which would be a probability against their testimony. Now, there are many cases where a testimony is not put too low by the above fraction ; if a want of perfect veracity is joined with inadequate comprehension of the statement, weak memory, or other infirmity, a witness would not be correct three times in four. The application of the Theory of Probabilities to the induc- tive determination of Causes is given in the following theorem taken by Mill from Laplace. B24 CHANCE, AND ITS ELIMINATION. 13. ‘Given an effect to be accounted for, and there being a — several causes that might have produced it, but of whose presence in the particular case nothing is known; the probability that the effect was produced by any of these causes is as the antecedent probability of the cause, multiplied by the probability that the cause, if it existed, would have ri | duced the given effect. ; ‘Let M be the effect, and A, B, two causes, by either of a which the effect might have been produced. To find the pro- bability that it was produced by the one and not by the other, ascertain which of the two is most likely to have existed, and which of them, if it did exist, was most likely to produce the effect M; the probability sought is a compound of these two probabilities. ‘Case I. Let the causes A and B be both alike in the second respect : either A or B, when existing, being supposed equally _ likely (or equally certain) to produce M; but let A be itself twice as likely as B to exist, that is twice as frequent a pheno- menon. ‘Then it is twice as likely to have existed in thiscase, and to have been the producing cause of M. 4 ‘Case II, Reversing the last supposition, let us suppose that the causes are equally frequent, equally likely to have existed, — but not equally likely, if they did exist, to produce M; thatin — three times that A occurs, it produces that effect twice, while | B, in every three times produces it but once. Since the two ~ causes are equally frequent in their occurrence, in every six & times that either exists, A is three times and B three times, — But A in three occurrences produces M in two; while B in three occurrences produces M in one. Thus, in the whole six times, M is produced thrice, but twice by A and once by B. - So that the probability is in favour of A in the proportion of — two to one. ‘Case III. Let there be an inequality in both respects. Let A be twice as frequent as B; and let A produce the effect twice in four times; B thri ise in four times. Then the antecedent probability of A to B is 2 to 1: the probability of their producing M is as 2 to 3; the product is 4 to 3. In other words the probabilities in favour of A being the cause are as 4 to 8. And so on with any other combination.’ 4 The principle may be applied to distinguish casaal coin. a cidences from those that result from law. ‘The given fact may have originated either in a casual conjunction of ote . or in a law of nature. The probabilities, therefore, that the CHANCE APPLIED 10 CAUSATION. 325 fact originated in these two modes, are as their antecedent probability, multiplied by the probabilities that if they existed they would produce the effect. But the peculiar combination of chances, if it occurred, or the law of nature if real, would certainly produce the series of coincidences. The probabilities, therefore, are as the antecedent probabilities of the causes. One of these—the antecedent probability of the combination of mere chances that would produce the given result—is an appreciable quantity, on the principles already laid down. The antecedent probability of the other may be estimated more or less exactly, according to the nature of the case. CHAPTER X. INDUCTION AIDED BY DEDUCTION. 1, It is desirable at every stage to carry out Inductive Jaws into their Deductive applications. Now, Deductions cannot be made or verified without Observation of facts. Deduction or Ratiocination, in its purely formal aspect, is given in the Syllogism. In its material side, it involves the comparison of facts, and is akin to Induction. We have yet to view it as it plays a part in the Inductive Sciences. 2, The full scope of the Deductive Method comprises three operations. I, There must be certain pre-established INDUCTIONS. We must somehow arrive at Inductive Generalizations, and next prove them when arrived at. The Experimental Methods have in view these two ends, and especially the last, namely, Proof. Incidentally, the methods indicate the mode of Dis- covery, but they have not been expressly aimed with that view. It has been apparent, however, that the collection and study of instances, under the Method of Agreement, must suggest the points of Agreement, when we are ignorant of them, which is to suggest a general law. Our examination of the problem of Crystallization, and the enquiry into the cause of Dew, led first to the discovery, and next to the proof, of generalized coincidences. Still, it was not advisable to carry on a double 326 INDUCTION AIDED BY DEDUCTION. illustration, by means of the Experimental Methods, to eluci- date at once Discovery and Proof; of the two ends, the logician has most to do with the second; Proof is his main object, for which he can lay down definite laws; Discovery is a valuable end, likewise, but it is not equally amenable to prescribed rules. In the management of particular instances, with a view to the Discovery of generalities, assistance may be obtained in the three following ways :— . . (1) The number of instances should be as extensive as pos- sible. In the comparison of a large number the mind. will be struck with points of community, from the very fact of the recurrence; aS in the examples collected in the research on Dew. Moreover, there will start forth some one that contains the circumstance sought, in startling prominence; these are the glaring or suggestive instances. Such, in the case of Dew, was the example of the warm breath upon a cold iron surface, as a knife blade. ; (2) When out of mere number and variety of instances, ihe identity does not flash upon the mind, the next thing is to select a few for careful scrutiny. Each instance should be studied in isolation, should be gone over in every minute point, and examined from every side; the features being exhaustively set down in writing. After a few separate instances have been considered in this thorough way, the resemblances (unless at the time inscrutable for want of other lights) will become apparent to the view. Newton’s study of the phenomenon of the coloured rings of the soap-bubble, was an exercise of the severe mental concentration now described. \'¢ (3) The general laws of phenomena must be sought in the cases where they are least complicated or combined with other laws. This is an obvious precaution conducing to Discovery. The laws of motion are studied in simple cases, such as straight- lined movemenis, or wheel-movements, under a single impulse. Gravity is kest studied in bodies falling perpendicularly, where there is no other force operating. Neither the first law of motion, nor the law of gravity, could have been advantageously genera- lized, in the flow of rivers, or in the motions of the planets. These complications are not suited for inductive discovery, but for deductive application, as at present contemplated. The first principles of Optics are sought, not in the workings of the eye, nor in complicated lenses, but in the simple mirror for reflexion, and in the plane transparent surface for refraction. So the more transceudental powers of light, in causing moles eer et he SIMPLE DEDUCTION. 327 cular change, are not studied on the retina of the eye, but in the easier (although still obscure) cases—chemical action and photography. The osmotic action of cells is illustrated by Graham’s experiments on the passage of liquids through por- celain partitions. The capillary circulation of the blood is compared to the flow of liquids in capillary tubes. Salivation and digestion are examined by withdrawing saliva and gas- tric juice from the animal body, and subjecting different materials to their action apart. The laws of Mind, which are to be carried out deductively in resolving the complicated situations of human beings, as in Society, are to be generalized from observations of the individual man in favourable situa- tions. For the laws of mental growth, we have to begin at infancy ; for the germs of moral sentiment, we refer to the uncivilized races.* 3. Il. DeEpucTIoN proper involves two stages of com- plexity ; (1) The simple extension of an inductive law to anew case, and (2) the combination of several laws in a conjoint result, involving processes of Computation. (1) Simple Deduction is the extending of an inductive generalization to new cases. As in all enlargements of know- ledge, so in this, there is both discovery and proof. The cases have first to be suggested to the mind, and next to be rigor- ously verified by the procedure suited to the case. Without dwelling upon the means of suggesting new applications of laws, let us consider the mode of proving such applications. This resolves itself into a question of identity. Supposing that the inductive preposition ‘all matter gravi- tates’ has been formed upon solids and liquids, shall we apply it to gases? This depends upon whether gases are matter— whether any property of gases is identical with the defining property of matter. Now, the defining property of matter is inertia, and gases are proved to possess this property ; whence, the proposition ‘matter gravitates’ is extended to them. Again, Does Ether (the supposed medium of Light and Heat) also gravitate? As before, we must test its identity with the characteristic property of matter. Now, if, as seems to be implied in the retardation of Encke’s comet, the ether is a resisting substance, then it is matter, and accordingly gravitates. | * The Arts of Discovery, brought out by scattered allusions throughout the work, will be systematic |!) given in AppEnpix H. 15 328 INDUCTION AIDED BY DEDUCTION. | Questions of identity to establish a minor are necessarily part and parcel of inductive research ; but they must not be confounded, as they sometimes are, with the process of induc- tive generalization to establish a major or a general law. Thus, it is a moot point, whether any, and what alloys are chemical compounds; which must be settled by examining the characteristics of alloys, and comparing them with the essentials or characteristics of chemical combination. Yi We may instance important researches that have for their end the proof of an identity. Thus, Dr. Andrews imsti- tuted a series of experiments to identify Ozone (formed by | Electricity) with the atmospheric constituent that decomposes Iodide of Potassium. He selected three peculiarities of ‘i ozone ;~—(1) the power of oxidizing mercury, (2) the destruc- tion of ozone reactions by dry peroxide of manganese, (3) the: destruction of its reactions at a high rate of temperature (237° C}; and tried the element found in the atmosphere by these tests. It answered to them all. The first, however, (the oxidizing of mercury) is not conclusive, as other bodies, besides ozone, tarnish mercury. The last of the three tests: (high temperature), answers to no known substance, except ozone. The three tests conjoined furnish superabundant evidence of the identity of the so-called ozone of the air, with ozone as obtained by electrolysis, and by the electrical machine. Another remarkable discovery of Identity is seen in Graham’s experiments on the relations of Hydrogen to Palladium.’ There have always been chemical reasons for believing that hydrogen gas is the vapour of a highly volatile metal. Graham has contributed new evidence in favour of the identity. The metal palladium is capable of absorbing eight or nine hundred times its volume of hydrogen gas; and, when so charged, is found to undergo changes in Density, Tenacity, Electrical Conductivity, Magnetism, relations to Heat, and Chemical properties. On investigating these changes, Graham shows that they correspond to the alterations made on one metal when united in an alloy with another metal ; so that, as far as metallic properties can be shown in such a union, hydrogen is metallic. The metal ‘hydrogenium’ has a white aspect, is of sp. gr. 2, has a certain amount of tenacity, and is magnetic. The cumulation of proof is all but equivalent to the separate production of the solid metal. 7 Sir G. C. Lewis confounds the establishment of a minor, as — a part of Deduction, with the establishment of an Inductive major by the method of Difference. He considers that the COMBINATION. OF DEDUCTIONS. 329 Bost of a burglary in a Court of Law, or the proof that Sir hilip Francis wrote Junius, is an employment of the Experi- mental or Inductive method of Difference as one of the Inductive methods. In reality, all such cases are the making good of an identity to prove a minor. The kind of Difference employed consists in bringing out successive details or cir- cumstantials, to exclude by degrees every person but one; and thereby to complete the identity of that one person with the actor in the given case. (2) The more difficult employment of Deduction is in the concurrence of different agents to a combined result; as when we deduce the path of a projectile from gravity, the force of projection, and the resistance of the air; or the tides from the united action of the sun and the moon. This is the form of the Deductive Method, whereby we cope with the otherwise intractable situation called Intermixture of Effects. Physical Astronomy will ever remain the grand exemplar of Deductive Investigation, as the computation of joint causes producing an effect. The causes can be estimated with numeri- eal precision, and their combined operation can be calculated by the higher Mathematics. In other parts of Physics, there are instances of the Deductive Method. The calculations respecting Machinery, Fluid Pressures, Motions of Fluids, Gaseous Pressure and Movements, Sound, Light, Heat, Hlec- tricity,—proceed upon inductive laws, often united in their operation, and requiring to be computed in their joint effect. It has been seen, in the research on Dew, that Dalton’s generalization of the laws and constitution of the atmosphere of yapour, deductively applied, made up the wanting link in the experimental investigation. Equally telling examples of the Deductive Method may be culled from the recent applications of Chemistry to Animal Physiology. The laws of chemical combination enable us to trace the metamorphosis of tissue, by means of the products of waste. The single fact of oxidation is all-pervading in the animal system, and the deductions from it clear up at once many obscurities beyond the reach of experimental elimina- tion. The difficult question of Animal Heat is to a great extent solved already by this deductive application, and its complete solution will probably depend on the same method. We may quote farther the special applications of Chemistry, under the great law of Persistence, to the phenomenon of muscular power, of which no adequate account could be given by mere observation or experiment. We now know that 330 INDUCTION AIDED BY DEDUCTION, muscular expenditure represents a definite combustion of the material of the food, although we do not know the precise links of the transmutation. | When purely Inductive or Experimental proofs are sup- ported by reasons, or by a consideration of the nature of the case, the meaning is that Deduction is brought to the aid of Induction. The conclusion respecting the N. E. wind was confirmed by the general operation of atmospheric impurities. The result gained from the comparison of instances of Crystal- lization, is in accordance with the theoretical views of the two opposing molecular forces — attraction and repulsion. The experimental facts as to the exhaustion of the mind along with the body, are supported by what we know of the brain as the organ of the mind. Our inductions respecting despotic governments are aided by deductions from the laws of human nature. The applications to the Human Mind, to Character, and to Society, will be more fully exemplified afterwards, in the special chapters on the Methods of these Sciences. 4, III. The Deductive process is completed by VERIFI- CATION. This applies more particularly to the Computation of combined causes. The way to verify the deductive extension of a single law to @ new case, is actual observation of that case. We appl deductively the law of gravity to air, and verify the deduction by observing whether the air has weight. As, however, we may dispense with deduction when we have actual observation, — such an instance does not show the power of the Deductive Method. The thing meant is, that after verifying a deduction by one or more instances, we shall be able to apply it to other instances without farther verification; these last. instances depending for their proof solely on the deductive process, When an effect is the result of several conspiring causes, we may deduce it from a computation of the causes; as, for example, the lunar and planetary perturbations. To show — that we have taken account of all the causes, that we have obtained a proper estimate of each, and that we have correctly computed their conjoined action, we must compare the deduced effects with the observed effects in a variety of instances. If the two precisely tally, the deductive machinery is verified; — if not, not. A want of accordance points to a defect in one or — other of the circumstances quoted :—the causes or agents ara Bernd Kn — Vita oes ey a VERIFICATION OF DEDUCTIONS. 331 not fully taken account of; their exact amount is not precisely obtained; or the calculation of their united action is not perfect. Sometimes, the first point is defective, there being a residual agent. In other cases, we know the cause but not its exact numerical amount; thus, in Astronomy, we need to know the relative masses of the sun, moon, and planets, together with their mutual distances. Finally, it may happen that the calculations are impracticable. In Astronomy, where Deduction has gained its greatest triumphs, verification has also been most thoroughly worked. Upwards of fifty Observatories are incessantly engaged in watching celestial phenomena; the observations have been - the means of perfecting the deductive operation, and making good all its shortcomings. The deductive theory of projectiles combined gravity, pro- jectile force, and the air’s resistance; the experiments on gunnery are the verification. The laws of the strength of materials are deduced trom geometrical and mechanical laws, involving the size, shape, and position of beams, &c. ; but however certain the principles may appear, they cannot dispense with actual trials. We have supposed the verifying tests to consist of detached observations; they may be furnished by groups of observa- tions, summed up into what are termed Empirical Laws. Such was the verification of Newton’s planetary theory (founded on gravity) by Kepler’s Laws. So, any theory or generalization of the operation of refracting surfaces on light, must be in consistency with Snell’s law of the proportion of the sines of incidence and refraction. The formule of fluid motions are of themselves insufficient to predict the facts; experiments on the flow of rivers must be conjoined in a matter of so great complicacy. Newton calculated deductively the velocity of sound, and, on - comparing it with the observed velocity, found a difference of nearly twenty per cent. It is only of. late years, that the dis- crepancy has been got over, by a more complete view of the forces developed in the act of propagation. In sucha delicate question, one verifying instance is too little. Newton himself squared the results by arbitrary assumptions (as the thickness of the air particles), which would have required for their con- firmation an independent class of facts. Very confident predictions have been made to the intent that the Sun is cooling down in consequence of his enormous radiation ; and that the earth’s rotation must ultimately decay, 3382 INDUCTION AIDED BY DEDUCTION. through the friction of the Tides. The data and the calcula- tions seem very secure in both instances ; yet, in order that the deductions may be fully established, we need evidence of an actual change, in past time, as regards both these moment- ous facts. | Combined Induction and Deduction expresses the full force of scientific method for resolving the greatest complications. Induction alone, and Deduction alone, are equally incompetent to the great problems even of the Inorganic world; still more so with Life, Mind, and Society. Induction, exclusively relied on, is called ‘ empiricism;’ Deduction, without an adequate basis and an adequate check in the Inductive Methods, ex- presses the bad sense of ‘ theoretical,’ The two following chapters will continue the exemplification of the Deductive Method, of which they merely vary th aspect. | CHAPTER XI. SECONDARY LAWS—EMPIRICAL AND DERIVATIVE, 1. The importance of Secondary (as opposed to Ulti- mate) Laws, grows out of their close adaptation to concrete realities. , Speculation delights to attain ultimate generalities, which give the key to a vast department of nature; as Gravity, Conservation, and Relativity. These are highly satisfactory to the mind in its craving after unity, simplicity, ‘ the one in the many.’ A far more important use of these supreme generalities is to perfect the statement of the Secondary Laws, which are the more immediate guides of conduct, and the expression of the phenomena in their actual or concreie embodiment. The generalization of gravity did not supersede Kepler’s Laws of the Planetary Motions. So long as the concrete fact of planetary motion has an interest for us, so long are we concerned with the. secondary laws representing that fact. The use of the higher laws of Newton is to render these indispensable secondary laws more precise. The secondary laws are the ‘media axiomata’ of Bacon, They were viewed by him (too exclusively) as the steps for ascending to the supreme laws. Equally essential is the — IMPORTANCE OF SECONDARY LAWS, 333 descending movement from the higher to the middle generali- ties. No branch of knowledge is complete until it has assembled all the secondary laws that express the more usual configurations of actual phenomena, and until these secondary laws have attained all the precision that induction and deduc- tion can give them. : We formerly had occasion to remark (p. 79), with reference to Propositions, that, like the notion, they vary in regard to the reciprocal properties— Hxtension and Comprehension. As we increase the extension, we lose comprehension, and con- versely. Now, of the two attributes, the one most important for us practically is Comprehension. We have to deal with small classes, and with individuals, and our interest lies in knowing the whole of the specialities attaching to these. An English statesman needs to know the peculiarities of English- men. A physician has to deal with the diseases special to humanity, and still more those special to his own sphere; while even this degree of generality, is but to prepare him for mastering individual cases. Hence, the narrowing of a proposition, which may seem a defect to the theorizing or speculative intellect, is the highest merit in applications to practice: provided always that the limitation of extent is accompanied with a corresponding in- crease in amount of predication, that is, in meaning, connota- tion, orintent. The full enumeration of the properties special to iron, as it is found in a certain district, is essential to the working of that particular ore; the account of the properties common to all metals would be valuable merely as contributing a quota to the highly specialized and exhaustive knowledge telative to the particular substance. It was a frequent remark of Aristotle that the finishing stroke of knowledge is the tact that modifies all general pro- positions according to the individual case. This of course is in the more purely practical point of view. The secondary laws are either Emprrican or Dertvative. 2. An EMpiricAu Law is a uniformity supposed to be secondary, that is, resolvable into some more general uni- formities, but not yet resolved. That quinine cures a fit of ague is an Empirical Law. It is a uniformity established by experience; it is, however, a secondary uniformity; we have reason to believe that it is 334 SECONDARY LAWS. capable of being resolved into higher uniformities, The pre- sent inability to resolve it is a disadvantage, not merely in a theoretical or speculative point of view, but as regards the application of the law in practice. 3. When what was an Empirical Law has been resolved into more general uniformities, or into highest laws, it 1s termed a Derivative Law, The occurrence of snow on high mountains was at one time an empirical uniformity. It was established as an induction from experience, but was not susceptible of being referred to any higher generalizations, We can now resolve it into the laws connected with radiant heat passing through the atmos- phere. These may not themselves be the highest attainable generalities ; still they are much more general than the induc- tion connecting snow with height. The converting of an Empirical Law into a Derivative Law isa step gained both in scientific explanation, and in practical facilities. The defects inherent in an Empirical Law do not inhere to the same degree in a Derivative Law. 4, Empirical Laws are of various kinds. Their charac- ters are judged from their appearance after being resolved, that is, made derivative. L. Many are obviously made up of the combination of higher uniformities under definite arrangements or collo- cations. We see this class largely exemplified in the explained or derived laws. The law of a projectile, Kepler’s laws, the tides, the laws of wind and rain, the laws of geological action (igne- ous and sedimentary), combustion, the nourishment of living bodies—being formerly empirical laws, and now derived—we can, from them, presume the character of those that are still empirical. These combinations have been already discussed under the Deductive Method. They suppose certain ultimate laws, con- curring in their operation, and also a certain definite arrange- ment and amount of the concrete agencies or forces that the _ laws refer to, 5. II. Some secondary laws take the form of laws of succession between effects and remote causes; they still, however, possess the character last named. ee VARIOUS KINDS OF SECONDARY LAWS. 335 - When a sudden shower disperses a crowd, the shower is a very remote cause of the effect; a number of. intermediate links of causation are assignable. The taking of food is re- moved by a good many stages from the renewal of the muscu- lar strength. The sowing of a seed is followed at a long interval with the maturing of an oak. ‘This is merely a superficial variety of the first case—com- bination of agents, in definite collocation. Hach one of the links is a distinct law of causation or coincidence, requiring to be embodied in a definite collocation; and the combination of the whole, in a suitable arrangement, is necessary to the result. 6. ITI. Some are laws of Co-existence or of Succession between effects of the same cause. Such are the phases of the Tides, the flow of the Seasons, Day and Night. Here also there is the same constant circum- stance—a conjunction of agents and collocations. In every case of a secondary law, there is, from the nature of the case, more than one power at work. Only ultimate laws express agents in isolation, purity, or abstractness. In any complicated structure, a new agent produces a variety of changes. The taking of food leads to concurring alterations in almost every organ in the body. Every disease has concurring symptoms. A country engaging in war has its economy simultaneously disturbed in many different ways; hence there are numerous empirical statements applicable to the condition of war, which are co-effects of the one general situation. 7. The aggregation of properties in a natural kind—a mineral, plant, or animal—has something in common with Empirical Laws. As there may be uniformities of co-existence, not resolvable into cause and effect, such uniformities stand solely on their own inductive evidence, like empirical laws. They are proved by the method of Agreement alone, and the proof extends no farther than the cases observed. 8. The criteria of an Empirical Law are principally these :— If a uniformity is established only by Agreement, it is not shewn to be a law of causation; and (if not an ulti- mate law of co-existence) it is an empirical law. 336 SECONDARY LAWS. Agreement does not single out a cause when there is plurality. It is at fault, besides, in discriminating cause and effect from effects of the same cause. Moreover, unless the variation of the circumstances has been thorough and complete, there is an uncertainty even in cases where there is but a single cause, ‘and where the antecedents contain that cause. The Method of Difference does not at once lead to ultimate laws. The swallowing of alcohol is followed by a certain sensation; this is proved by the Method of Difference to be cause and effect, yet it is not an ultimate sequence; it is an empirical uniformity. 9. ‘The other criteria arise out of the characters already mentioned. Thus, when phenomena are obviously complicated, and when there are intermediate links of operation, the laws of such phenomena are not ultimate but secondary ; they are empirical, or, if resolved, derivative, The law that connects the fall of the barometer with wind or rain is plainly empirical. We can see that many different agencies enter into the sequence; and, also, that there are many intermediate steps between the antecedent and the consequent. We presume the action of a drug to be an empirical law, because we know, from the complication of the human body and the plurality of attributes of natural kinds, that there must be many concurring processes, each one governed by its own law or laws of causation. LIMITED APPLICATION OF DERIVATIVE AND EMPIRICAL LAWS. 10. A Derivative Law, and still more an Empirical Law must not be extended beyond narrow limits of ‘Time, Place ‘and Circumstance. | It being supposed that such laws are established by all th evidence that the case admits of, still they are applicable only a certain way beyond the narrow sphere where they have been observed to operate. The reasons are those already stated under the Deductive Method. A uniformity depending on several higher uniformi- ties, and on a definite collocation of agents, that is, on certain special co-efficients, must fail, first, if any of the concurring uniformities be counteracted, and secondly, if the proper ad- — justment of the agencies is departed from. The elliptic APPLICATION TO ADJACENT CASES. BOL motion of the planets would be defeated, if some great dis- turbing body were sufficiently near to counteract solar attraction, or if the tangential force were made different from what it is. Hence we cannot extend the law of the ellipse to ae body that may now or at any future time revolve about the sun. This limit to the extension of secondary laws—whether Empirical or Derivative—is the all-important fact respecting them, in the logical point of view. A large number of pre- - vailing errors might be described as the undue extension of Empirical Laws. We shall presenta few examples of secondary laws, calling attention to the difference of our position in regard to them, according as they are Empirical or Derivative. The rise of water in pumps was an empirical law, previous to the discovery of the pressure of the atmosphere. The application of the Method of Agreement in different countries, and with pumps of different bore, proved that no pumps could draw water beyond about 33 feet. The law could be relied on within the wide limits of place and circumstance where it had been tried. It could not have been extended to other planets ; but it might be extended, with apparent safety to any part of the earth. Since the law became derivative, the limits of its operation are precisely defined ; we can tell exactly where it would have failed. We know that on the tops of high mountains the maximum height would have been much below 33 feet; that the exact height would not be the same at all times; that other liquids, as alcohol, sulphuric acid, solutions of salts, mercury, vary in the height attained. Now, probably none of all these limitations had been actually discovered in the empirical stage ; they might have been obtained by sufficiently wide and careful experiments; the derivation superseded the laborious task, which was probably beyond the competence of an unscientific age. It is an empirical law that the temperature of the earth increases, as we descend, at a nearly uniform rate of 1° of Fahrenheit to 50 feet of descent. This law has been verified by observations down to almost amile. We might extend the law inferentially to the adjacent depths, as far perhaps as several miles; but we are not at liberty to extend it to the centre of the globe. We do not know that the requisite col- locations extend so far. Yet this law is not wholly empirical. It is a derivative uniformity. It is connected with the known facts—that the 838 SECONDARY LAWS, earth has a high temperature in the interior, and 1 is cooled at the surface by radiation in space. Knowing these, we are yet unable to deduce the law of decrease from the higher laws concerned, because we are ignorant of the degree of central heat, and imperfectly acquainted with the laws of its conduc- tion through the unknown materials of the globe. We under- stand the general situation, but do not possess the numerical and other data requisite for computing the effects. That air-breathing animals are hot-blooded, is a law formerly empirical, now derivative. It comes under the general law of the dependence of temperature on the oxygenation of the blood, and may be extended widely on the faith of that great generality. The Law of Continuity—‘ Natura non agit per saltum ’—is an Empirical Law. In the continuity of Vegetable and Animal Life, there would be, under the Doctrine of Development, a reason for the fact, and it would be in that case Derivative. Also, in the transition from one state of matter to another,—as in melting, boiling, and their opposites—there must be a ~ certain amount of continuity owing to the greatness of the — transition. But except where there is some presumption of this nature, the extension of the law is wholly unsafe; we are not to expect, for example, that the simple bodies of nature should be arranged in series with continuous or shading pro- perties. We find the greatest gaps in almost all the propertane _ of the elementary bodies. : In medical science, there is hardly such a thing as a single — effect produced by a simple cause. What is worse, there are scarcely any great inductive generalities relating to the cure of — disease, except through hygienic or constitutional treatment. Thus the use of drugs is almost exclusively empirical, — The limitation in this case operates variously. It forbids 4 our inferring that two medicines of close kindred will have — the same effect; thus bark and quinine are not interchange- able, although the one is the crude form and the other the essential extract. It also forbids our extending a mode of treatment to a closely allied ailment, as in reasoning from one species of fever to another. Lastly, it forbids the applica- — tion of the same treatment to the same disease, in different persons. Hence, medicine is of all sciences the one most completely tentative. Experience gives a probability to begin with; but until the effect is tried in the new case, we CON Oly as @ general rule, rely on it. | ling EMPIRICAL LAWS IN MEDICINE, 339 Until the day arrives when the operation of medicines is made derivative, the only progress possible is to obtain through multiplied experience, a more exact.statement of the conditions attending on the successful application of certain modes of treatment; as for example, the constitutional or other circum- stances in the patient favourable or unfavourable to special drugs. The treatment of tape worm by male fern is of old date in medicine. In the early period, the failures were frequent ; at present, the oil of the fern is extracted and given instead of the root, with an almost uniform success. This empirical unifor- mity is to a certain extent derived or explained ; the substance is a poison to the parasite. After such an explanation, there is afforded a clue to other remedies for the disease; previous to the explanation, the uniformity was confined to the one remedy. As an empirical law in Medicine, we may instance Bright’s discovery of the connexion between albuminous urine, and degeneration of the kidney. The law is as yet unresolved into any higher law of structure and function; the kidney degeneration is not associated with degeneration in any other tissues of the body ; and no account is given of the temporary production of albumen without the permanent disease. It is an empirical law that about 250 persons in a year commit suicide in London. This law may be extended a little way into the future, but it may not be extended into a remote time, when moral habits may be different, nor to other cities and populations. The Statistics of Mortality show a remarkable coincidence between the rate of mortality and the density of the popula- tion. A high degree of longevity is found in thinly peopled districts, notwithstanding even the poverty that sometimes occurs in sterile tracts; and mortality reaches its maximum in the most crowded parts of cities. If we knew nothing of the causes of this uniformity, if it were as empirical as the medicinal action of mercury on the system, we could not extend the law into other countries and other circumstances of the population. But it is a derivative law, and knowing what agents the effect depends on, and what circumstances would defeat their operation, we apply it without scruple to every portion of the human race. We should, however, refrain from applying it to animals very differently constituted from man as to the necessities of breathing pure air. All animals require oxygen, but some need it in smaller quantity, and are indif- 340 SECONDARY LAWS. for ‘ent to impure gases ; while warmth and the opportunities of better food might more than compensate for the close atmos- — phere of a confined habitation. et In regard to the Human Mind and character, we have uniformities that cannot be extended to the race generally. Thus, the universality of sympathy or fellow-feeling is liable to exceptions. Mr. Samuel Bailey, after quoting, from a travel- ler in Burmah, the incident of a drowning man being beheld by a crowd as an amusing spectacle, and being allowed to sink without an attempt at succour, makes the following remarks :— ‘Incidents of this kind (and the example might be easily ; parallelled from other nations) serve to show that when we ascribe certain sentiments to human nature or to men univers- ally on given occasions, because they exist amongst ourselves on those occasions, it is by no means a safe inference; we cannot safely ascribe them except to men under analogous circumstances of knowledge and civilization. ‘We may attribute with confidence to most men and to most races of men, the rudimentary feelings which I have shown to originate and to constitute moral sentiment; and some of them with equal confidence to all men: namely, sensibility to cor- poreal pleasure and pain; liking the causes of one and dis- liking the causes of the other; the propensity to reciprocate both good and evil; the expectation of the same reciprocation; and more or less sympathy with other sensitive beings; but the direction and intensity of these emotions respectively it is often difficult and even impossible to assign: there are so many causes at work to counteract, or modify, or cop y such of these common susceptibilities as can be counteracted, — or modified, or suppressed—to call them forth or to cea them in, that, unfurnished with precise knowledge of national — and social circumstances, we cannot predict with confidence — how they will manifest themselves on particular occasions. — Without specific information of this kind we cannot safely — pronounce that the people of rude or distant and imperfectly _ explored countries would, under given circumstances, share in those affections and moral sentiments which it seems contrary — to our own very nature, under such circumstances, not to have. That ‘ the mind of man is by nature conciliated and adapte¢ to his condition’ was formerly an empirical law. We may now consider it as a deduction or derivation from the law of — Universal Relativity. The principle has been greatly abused. — It has been loosely extended far beyond the limits where it is POLITICAL RULES, 341 observed to hold true ; indeed those limits were never correctly marked in its empirical state. As a derivative uniformity, we may assign its limits with tolerable precision. The laws of Political Society are all secondary laws, either empirical or derivative. Hence the necessity for limiting their application. The politician is, like the ancient sailors, obliged to sail close by the shore, rarely venturing out of sight of land. We are not at liberty to transfer to our own time the maxims suitable to the ancient world, supposing even that the ancients really attained any political rules highly salutary in their own case. ‘The distinction between ancient and modern history,’ says Mommsen, ‘ is no mere chronological convenience. Modern History is the entry on a new cycle of culture, connected at several epochs of its development with the perishing or perished civilization of the Mediterranean States, but destined to traverse an orbit of its own.’ It would be a vicious extension of secondary laws, to predict the extinction of modern nations, because the great ancient empires are perished. We cannot transfer at once the practice of one nation to another nation. Hardly any political device has been so much copied as the British constitution. Yet, its advantages being not purely empirical, but toa certain extent derivative, it may be extended to adjacent cases with some confidence. _ It is suitable to the complicacy of the political structure to make changes in the direction of existing institutions, and to confide in them only when introducing a state of things nearly adjacent to the present. After seeing the working of a ten- pound franchise in this country, the inference was fair that the lowering to eight, seven, or six pounds could not depart very far from actual experience. | The use of precedents in Law and in Politics exemplifies the rule of limitation. Bacon, remarking on legal precedents, lays it down that the more recent are the safer, although, on the other hand, they have a less weight of authority. ‘A prece- dent is at its maximum of proving force when it is sufficiently near our own time to ensure similarity of circumstances, and sufficiently distant to ensure the consolidation of practice, and the experimental exhibition of the practical result.’ (G. C. Lewis). 11. The rule may be farther illustrated under the second form of the Secondary Laws— Uniformities of remote connexion between cause and effect. 342 SECONDARY LAWS. Of these, the most prominent examples are the results of slow processes in the arts, protracted treatment in disease, the _ growth of plants, the development of animals, the formation of the human character. That all empiricisms of this class must _ be precarious and liable to frequent defeat is apparent. Hven when derivative to the full extent, they are rendered uncertain by the number and complication of the agencies. 1 hn. 12. Lastly, with reference to Uniformities suspected or — i known to be effects of a common cause. The principle of limitation is still the same. a As an example, the case is put—what reliance are we to — place on the sun’s rising to-morrow ? s Suppose, in the first place, that this were an empirical — generality, we being ignorant of its derivation. Suppose, — also, that we have authentic evidence that the sun has risen daily for the last five thousand years. How far intothe future — are we at liberty to extend the law; to what limits of time should we confine it? The answer is, we may count the con- — tinuance in the future, on the same scale as the continuance — in the past; we may fairly assume a period counted by © thousands of years; we may be tolerably certain for one ~ thousand years, and have a considerable probability, for three, four, or five thousand ; but we should not be safe in extending - the scale to tens of thousands, still less to hundreds of — thousands. For anything we should know, a catastrophe may - be preparing that will speedily interfere with the regularity of day and night; still, long continuance in the past reduces, — without annihilating the chances. «cn Let us next look at the case as a derivative uniformity. We know that the phenomenon will continue so long as these circumstances are conjoined, namely, (1) the luminosity of the sun, (2) the earth’s being within a proper distance of the sun, (3) the earth’s rotation, and (4) the negative condition of the absence of any intervening opaque body to act as a screen. Now, we know from past experience that all these conditions are likely to be perpetuated for a period of time, to be estimated by not less than hundreds of thousands of years. The sur may be cooling, but the rate, judging from the past, is extremely slow; the earth’s rotation is believed to be subject to decay, but the rate of decay is infinitesmally little; the removal of the earth out of the solar influence is in oppositio n to our very best guarantees ; and the permanent intervention of an eclipsing body is the most unlikely incident of all. Thus any eo at aa Fe INDUCTION OF CAUSE 343 then, while, as an empirical law, we cannot well extend the rising of the sun (or day and night as we now have it) beyond thousands of years at most, we may extend it, as a derivative law, to hundreds of thousands, if not to millions. EVIDENCE OF THE LAW OF CAUSATION, 13. It may be shown that the Law of Causation, the indi- spensable ground work of all Induction, itself reposes on the highest evidence suitable to the case—uncontradicted Agreement through all nature. We have hitherto taken for granted that sufficient evidence, of the only kind suited to the case, has been obtained in favour of the law of Universal Causation, on which law have been grounded all the processes of experimental elimination. A summary of this evidence will farther illustrate the logical processes detailed in the foregoing chapters. The uniformity of successions was first observed in easy instances, such as the more obvious mechanical effects. A body at rest was observed never to move from its place without the application of some force to move it; a body in motion was observed not to stop abruptly without interference and obstruction. The fact of the descent of unsupported bodies is invariable. So light and heat display obvious regularities that could be counted on. Even in the instability of the winds there would be discovered circumstances of constancy. The most complicated of all things, living bodies, were seen to have numerous points of striking uniformity. That change of every kind whatsoever follows on a definite prior change, could not be affirmed in early times, except by the mere instinct of generalization, which is no proof. Hence in ancient philosophy, there were alternative suppositions. Aristotle allowed an element of Chance, along with the reign of Law. Modern science has extended the search into natural se- quences, collecting new examples of uniformity, and removing exceptions and appareat contradictions. Investigations have been pushed into every department of nature; and had there been any decisive instances where change grew out of nothing, or where the same agent, in the same circumstances, was not followed by the same effect, such instances must have been — brought to light. 14. Inthe form of Persistence of Energy, under definite 344 EVIDENCE OF THE LAW OF CAUSATION. laws of Collocation, the Law of Cause and Effect has been subjected to the most delicate experimental tests. By irrefragable observations it was shown that Matter i is indestructible, which is one element of nature’s constancy. Farther observations have proved the numerical Persistence of Force throughout all its transformations, and also the unifor- mity of the collocations or arrangements for transferring it. The first contribution to this result was the proof of the Laws of Motion, as respects both the continuance of motion once begun, and the conservation of the total moving force in case of transfer by impact. These mechanical verities make up one department of uniform cause and effect, Next came the proof of the equivalence of mechanical force and heat— the constancy of the amount of one produced from a definite amount of the other. Joule’s mechanical equivalent of Heat testifies to nature’s constancy in a very wide department. Following on this is the mumerical estimate of the heat of Chemical combinations, also admitting of numerical statement, from which there is no deviation; a third great department of constancy is thereby established, If numerical equivalence has not been arrived at in Nerve Force, and in Light, the subtleties of the phenomena are sufficient to account for the deficiency. We have reasonable ground to presume that, according as these phenomena are fully understood, they will show the same constancy as all the rest; the burden of proof lies upon any one maintaining the contrary. The only exception usually claimed to the Law of Causation is the alleged Freedom of the Will. But whatever be the mode of dealing with this long-standing enigma, there is a statistical testimony in favour of the constancy of human motives. The actions of men have a degree of regularity compatible only with uniform causation. Mr. Mansel has characterised as a ‘paralogism’ the doc- trine that ‘the ground of all Induction is itself an Induction.’ He might have called it a paradow or an epigram, an apparent contradiction needing to be resolved: it is not a paralogism unless it can be made out a self-contradiction. If the account given above of the methods of Proof and Elimination is sufficiently intelligible and conclusive, nothing farther is necessary to resolve the paradox. There is one fun- damental mode of Proof—Agreement through all nature—by — which all ultimate laws are established, including Causation, — ee ee ee d -, CAUSATION RESTS ON AGREEMENT ALONE, d45 There are several derivative, deductive, or dependent methods of Proof, the special Methods of Elimination—Agreement (according to Mill’s Canon), Difference, and Variations ; these are called by courtesy Inductive Methods; they are more properly Deductive Methods, available in Inductive investiga- tions. The special form of Agreement described in the canon is not quite the same as the fundamental method of Agree- ment, on which alone repose all the ultimate generalizations. That canon, as supposing Causation, would be inapplicable to the proof of Causation. The method of Agreement that proves Causation is not a method of elimination. It does not proceed by varying the circumstances, and disproving successive antecedents ; it can only find A followed by a, wherever the two occur. Until the law is first proved, we cannot establish A as the cause of a, by omitting successively B, C, D, and all other accompanying circumstances, leaving nothing constantly joined save A and a; even if this were done, there must still be a search through all nature for A followed by a, when the ques- tion of causation itselfis atissue. Hence Agreement for estab- lishing an ultimate law is not the same as the Method of Agreement, in Mill’s canon, for establishing cases of causation, after the general law is sufficiently guaranteed. There is a certain propriety in comparing the establishment of the Law of Causation (or any other ultimate law), with the proof of an Empirical Uniformity, which has nothing but de- tailed Agreement to found upon. True, an Empirical Uni- formity is to be applied only a little way beyond the limits of time, place, and circumstances But, now, as Mr. Mill remarks, ‘if we suppose the subject matter of any generaliza- tion to be so widely diffused, that there is no time, no place, and no combination of circumstances, but must afford an example either of its truth or its falsity, and if it be never found otherwise than true, its truth cannot depend on any collocations unless such as exist at all times and places; nor can it be frustrated by any counteracting ageucies, unless by such as never actually occur. It is, therefore, an empirical law, co-extensive with all human experience; at which point the distinction between empirical laws and laws of nature vanishes, and the proposition takes its place among the most firmly established, as well as largest truths accessible to science.’ CHAPTER XIL EXPLANATION OF NATURE. 1. The laws arrived at by Induction and Deductiott are the proper EXPLANATION of natural phenomena, = Explanation has various meanings. ‘These all agree in affording us a certain satisfaction or relief when oppressed — with the difficulty, obscurity, perplexity, contradiction, mys- tery, of natural facts. But the human mind has at different — times been satisfied in different ways; and individuals still” vary as to the kind of explanation that satisfies them. . a When all Nature was peopled with deities, and the various phenomena partitioned among them, a sufficient explanation — of anything was that a certain god or goddess willed it. The — intervention of Neptune was a satisfying account of why a storm arose. The wrath of Apollo was the explanation of the — plague that broke out among the Greeks at the siege of Troy.* — oi There is a special and every-day form of explanation that — consists in assigning the agency in a particular occurrence; _— a as when we ask— what stops the way ? who wrote Junius ? who discovered gunpowder? These questions belong to our practical wants and urgencies, but the answer does not involve the provess of scientific explanation. If, however, we pro l from the ‘who’ or ‘what’ to the ‘ why: "why does A’s — carriage stop the way? why did the author of Junius write so bitterly ?—there is an opening for the higher scientific process. 2. The basis of all scientific explanation consists” in assimilating a fact to some other fact or facts, It identical with the generalizing DIOe that is, with il duction and Deduction. 185 Our only progress from the cinibitie to the plain, from the mysterious to the intelligible, is to find out resemblances among facts, to make different phenomena, as it were, fraterniz e. We cannot pass out of the phenomena themselves. We can explain a motion by comparing it with some other motion on * Bee Grore’s Plato (Phedon) tor the views of the ancient philosoph hers with ae to Explanation, or the Id.a of Cause. — * “« e ea EXPLANATION IS GENERALIZATION, 347 pleasure by reference to some other pleasure. We do not change the groundwork of our conception of things, we merely assimilate, classify, generalize, concentrate, or reduce to unity, a variety of seemingly different things. The phenomenon of combustion was considered to have been explained when Priestley showed it to be the combina- tion of oxygen with carbon or other substance ; in short, he assimilated the fact to cases of oxidation, as the formation of the red precipitate of mercury, the rusting of iron, &c. Lightning was explained by Franklin’s assimilating it with electricity. The polarity of the needle was explained by assimilating the entire globe to a magnet or loadstone. Explanation thus steadily proceeds side by side with assimilation, generalization. Combustion was explained by oxidation ; oxidation is explained by the higher generality— chemical combination ; chemical combination is swallowed up in the Conservation of Energy. 3. Mr. Mill distinguishes three forms of the explanation of facts and laws. I. Explaining a joint effect, by assigning the laws of the separate causes, as in the ordinary Deductive operation. The Deduction of a complex effect, by computing the sum of the separate elements, is also the explanation of that effect. By combining gravity with projectile impulse, we explain the motions of the planets. This deduction once verified, is offered as the explanation of the planetary motions. In other words, the showing that these motions are made up of the two causes—gravity and tangential force—is the explaining of their motions. In such cases, the explanation points out the simple causes concurring, in the shape of forces or agencies, and also indi- cates their amount and their due -concurrence. Jupiter's orbit depends on the mass of. the sun, on the tangential force of the planet, and on its mean distance from the sun. These are, in the Janguage of Astronomy, the coefficients, which must be given in order to our assigning the result of the operation of the laws. A mere law, such as the law of gravity, is not an explanation until it is clothed in the concrete statement of two or more gravitating masses, with a given amount anda given distance from each other. These numerical statements, the coefficients of Astronomy, are also said to determine the collocations of the agents concerned. 348 EXPLANATION OF NATURE, To explain the rise of a balloon, is to give the lawa: a gravity, of buoyancy, and of gaseous elasticity, and to steht 7 the exact weight and elasticity of our atmosphere, and the specific oravity of the mass of the balloon. ricer x ' To explain genius is to refer it to general laws of the mind, © or to certain elementary powers—intellectual and emotional— 5 ~ whose higher or lower degrees and modes of combination — produce the kind of intellectual superiority so named. v2 To explain the rise of free governments is to state the a general principles of human action, and the definite collocation of circumstances calculated to produce the effect. sole 4 The separate laws are obviously more general than the laws — of the conjoint effect. Gravity has a much wider sweep than planetary motions; the law of the perseverance of moving — bodies in a straight line-is far more comprehensive than tangential impulse. | 4, II. Explanation may assume the form of discovering an intermediate link, or links, between an antecedent and — a consequent. at Yous ¥ What seems at first sight the direct or immediate cause of a phenomenon may, by the progress of assimilation, turn out the remote antecedent. The drawing the trigger of a musket — is followed by the propulsion of a “ball. The why of that phenomenon is given by disclosing a series of intermediate — sequences, each of which is assimilated with some known — sequence. The trigger by concussion evolves heat; the heat — ignites the gunpowder; the gunpowder is a mass adapted for very rapid combustion ; the combustion evolve gases which, being confined in a small space, have a very high expanaiiay force ; the expansive force propels the ball. Again, the contact of sugar with the tongue is the precursor _ of a feeling of the mind, the sensation called sweetness. The explanation, so far as hithante attained, supplies the followi series of closer links. The sugar is absorbed by the mucus. membrane of the tongue, and comes in contact with the file . ments of the gustatory nerve; there ensues a chemical or some other molecular action on the nerve. This action | is of a kind that can be propagated along the course of the nervy: to the nerve centres, or the brain ; shania are diffused a multi tude of nervous currents er ding in muscular movements, y ) the cerebral agitation attaches the mental state called the § sel nsé — tion of swectness. ys INTERMEDIATE LINKS. 349 The unexplained phenomena connected with the Law of Conservation refer to the intermediate links, or transitions, in the interchange of the mechanical and the molecular forces, and of one molecular force with another. The molecular pro- cesses in the conversion of mechanical energy into heat, heat into electricity, chemical force into muscular power and nervous power,—are not accounted for: and we see only a beginning and an end where we have reason to believe that there must be various intermediate stages, each susceptible of being assigned and brought under some general law of causa- tion. The intermediate links, or sequences, are each one more general than the combined sequence. Take the case of a sweet taste. The absorptive power of the animal membranes for various substances (the crystalloids of Graham) is a general law, of which the action in tasting is merely one example or applica- tion. The molecular disturbance from the contact of nerve and sugar is but a case of chemical or molecular affinity. The current action of the nerve force is a limited instance of current actions; the electrical forces exhibit other cases, the whole being comprehensible under some higher law. Finally, the link that relates the physical actions of the brain with the mental effect belongs to some wider statement that relates mental states generally to their physical concomitants. As observed, in the previous chapter, it is incident to such many-linked sequences, to be more frequently frustrated than the simpler sequences that make them. A circumstance counteracting any one of the closer links counteracts the whole phenomenon. If the lock of the musket makes an in- sufficient concussion of the explosive substance; if the gun- powder is rendered incombustible by damp; if the expanding gases burst the piece :—in any one of these contingencies, the ball is not propelled. _ 5, Ill. The third mode of Explanation is termed the Subsumption of one law into another ; or the gathering up of several laws in one more general and all-comprehending law. This represents the upward march of generalization, pure and simple. We have attained a certain number of inferior generalities, by assimilating individual cases in ordinary in- duction. We have assimilated the kindling of fires for heat and for light and for the disintegration of compounds, under one head, called combustion ; we have assimilated the tarnish- 350. EXPLANATION OF NATURE. ing and corrosion of metallic surfaces under another head ; we subsume both under the higher law of oxidation, which both exemplify. We have also assimilated the action of acids” upon alkalies under a general head: we find that this case can fraternize with the foregoing and with many other phenomena, under a still higher, or more general aspect, signified by chemical combination. So, again, terrestrial gravity and celestial attraction, each the result of separate assimilations, being found to agree, are subsumed into the illustrious unity of Universal Gravitation. Magnetism, Common Hlectricity, Voltaic lHlectricity, Electro-Magnetism, &c., are all strung upon the common thread of Electrical Polarity. 3 Capillary attraction, solution, alloys (not chemical), cements, &c., are subsumed under the general law of molecular attrac- tion (not chemical) between different substances, named heterogeneous or alien attraction. Numerous laws of smaller compass are subsumed ence Relativity. The pleasures of variety and novelty, the neces- sity of contrast in works of art, antithesis in rhetoric, the statement of the obverse or counter proposition in science,—are minor laws generalized, but not superseded, by the tee law. When minor laws are thus merged in a greater law, the mind feels a peculiar and genuine satisfaction—the satisfaction of having burst a boundary to expatiate over a wider field. We rise from a statement bearing upon a-small group of facts” to a statement comprehending a much larger group; from a ten-fold condensation, we reach a thousand-fold condensation. The intellect, oppressed with the variety and multiplicity of facts, is joyfully relieved by the simplification and the unity of a great principle. The charm of resolving many facts into one fact was acutely felt by the speculative minds of antiquity. It took a power- ful hold of the earliest Greek philosophers; and made them almost unanimous in imagining that all phenomena whatso- ever are at bottom one, or are susceptible of being represented in some single expression, being merely the many-sidedness of. 3 some single central power, substance, agent, or cause. Such unity was, according to Thales, Water; according to Anaxi- mander, an Indeterminate Babetaies’! according to Anaxi- menes, Air; according to Pythagoras, Number, 1 1 3 4 ww Toe le ULIMATE PHENOMENA. . at LIMITS OF EXPLANATION. 6. Scientific explanation and inductive generalization being the same thing, the limits of Explanation are the limits of Induction. Wherever Induction (extended by Deduction) can go, there legitimate scientific Explanation can go, they being the same process differently named. 7. The limits to inductive generalization are the limits to the agreement or community of facts. Induction supposes similarity among phenomena, and when such similarity is discovered, it reduces the phenomena under acommon statement. The similarity of terrestrial gravity to celestial attraction enables the two to be expressed as one phenomenon. The similarity between capillary attraction, solution, the operation of cements, &c., leads to their being regarded not as a plurality, but as a unity, a single causative link, the operation of a single agency. So remarkable have been the achievements of modern times, in the direction of lofty generalities, that some countenance seems to be lent to the ancient dream of attaining an ultimate centralized unity in the midst of the seeming boundless diversity of nature. It depends purely on actual investigation, how far all phenomena are resolvable into one or into several ultimate laws ; whether inductive finality leaves us with one principle, with two, or with twenty principles. Thus, if it be asked whether we can merge gravity itself in some still higher law, the answer must depend upon the facts, Are there any other forces, at present held distinct from gravity, that we may hope to make fraternize with it, so as to join in constituting a higher unity? Gravity is an attractive force ; and another great attractive force is cohesion, or the force that binds together the atoms of solid matter. Might we then join these two ina still higher unity, expressed under a@ more comprehensive law? Certainly we might, but not to any advantage. The two kinds of force agree in the one point—attraction, but they agree in no other; indeed, in the manner of the attraction they differ widely; so widely that we should have to state totally distinct laws for each. Gravity is common to all matter, and equal in amount in equal masses of matter whatever be the kind; it follows the law of the 16 Ye ngs ay ea ae oe ae 352 EXPLANATION OF NATURE. diffusion of space from a point (the inverse square of the distance) ; it extends to distances unlimited ; it is indestruc- tible and invariable. Cohesion is special for each separate substance ; it decreases according to distance much more rapidly than the inverse square, vanishing entirely at very small distances. Two such forces have not sufficient kindred to be generalized into one force; the generalization is only illusory ; the statement of the difference would still make two forces ; while the consideration of one would not in any way simplify the phenomena of the other, as happened in the generalization of gravity itself. Again, gravity, considered as a power to put masses in motion, to generate visible or moving force, may be compared, by way of an attempt at assimilation, with the equally familiar mode of begetting motion by tpact, or the stroke of a mass already in motion ; as in propelling a ball by a mallet. Here too, however, we have, with similarity of result, a total contrast in the mode. Gravity draws bodies together from a distance ; impact must be supposed to urge them through their atomic repulsions. When the expanding gases of kindled gunpowder blow a bullet through the air, there is no actual contact of the parts; there is merely the operation of powerful forces of mutual repulsion, acting; however, at very short distances, like the cohesion of solidity. Now, there appears to be nothing in common to gravity and’ these atomic repulsions, except the result. We have, there- fore, no basis for assimilation or inductive generalization in such a comparison. The two modes of action must be allowed to lie apart in physical science; they must be em- bodied in different statements or laws, with no hope of being ever brought together. — rt It is because gravity does not assimilate with the propulsion of impact from a blow or a stroke that people have accounted it mysterious. In point of fact, there is no more mystery in the one than in the other. Attraction, from great distances, is one form of the production of force; Repulsion, at near i distances, is another form. The last of the two is, on the whole, most familiar to us; it is the genus that our own physical force belongs to; and we, by a mere whim, suppose’ it a simpler and more intelligible mode of exerting power; the truth being that, in all that regards simplicity and intel- legibility, gravity has the advantage. It is only by confining ourselves to the superficial glance of bodies coming into close: contact, thence giving and receiving momentum, that we = ———" — ULTIMATE FEELINGS OF THE MIND. 300 suppose this mode of exerting force a simple one; the inter- polated links of molecular repulsion are much more compli- cated than gravity. A similar line of remarks would apply to any endeavour to assimilate gravity with the Correlated Forces generally. These forces by their nature counteract gravity. The various move- ments in nature are explicable by the conflict and mutual action of two great Powers; Gravity, on the one hand, and the sum total of the Correlated Forces, molar and mole- cular on the other. The Correlated Forces mostly appear under the guise of repulsions, as, for example, heat ; so much so that this must be considered their typical manifestation ; the electrical and magnetic attractions are exceptional, and are probably mere superficial aspects of the deeper fact of repulsive separation. Three departments of Force thus stand out so distinct as to be incapable of assimilation :—Gravity, the Correlated Forces, and Molecular Adhesion. This last appears under two forms ;—the attraction between particles of the same sub: stance—iron for iron, water for water; and the attraction between two substances—as iron for lead, water for alcohol or for common salt. There may be a possibility of generalizing these two, or stating them as acommon force. Some approach has been made to this in the fact that the second kind of attraction holds between bodies nearly allied—as metals with metals, earths with earths. 8. The ultimate laws of Nature cannot be less numerous than the ultimate feelings of the human mind. This, as Mr. Mill pointed out, is the insurmountable barrier to generalization, and consequently to explanation. Whatever number of distinct states of consciousness, not mutually re- solvable, can be traced in the mind, there must be that number of ultimate fects or elements of knowledge, and of ultimate laws connecting those states with their causes or concomitants. If the sensation of colour be radically distinct from the feelings of resistance, of movement, of form, there must be a separate law with reference to colour. The phenomenon called white- ness cannot be resolved into the phenomenon of form, or of motion. Even if we found that the fact of whiteness is conditioned by a certain molecular structure, and certain molecular move- ments, we should not thereby resolve whiteness into movement; the facts would be distinct facts, although joined in nature. B54 . EXPLANATION OF NATURE. So, we are aware that the sensation of sound is conditioned by a vibratory movement of the particles of a sounding body ; but the vibration is not the sound; all we-can say is that a law of causation relates the vibration to the sound. Now there must always remain one law connecting the molecular movements of bodies with the sensation of whiteness, and another law connecting molecular movements with the sensa- tion of sound. In so far as all sensations are generalized into a common fact of sensation, having similarity with diversity, so far may we generalize the laws that connect sensation with corporeal activities. This is a real and important step of generalization. Yet it does not supersede the necessity of other laws for con- necting special and irresolvable modes of sensation with their special seats of corporeal activity. We may have a law of pleasure and pain generally ; yet we need laws for the distinct modes of pleasure and pain—the pleasures of light, of sound, &c.—inasmuch as these cannot be resolved into each other. The great generalities relating to Force all refer to one sensibility of our nature—the muscular, or the active side ; owing to which fact, they may admit of unity of law, or a common statement. Likewise, there may be unity of law as” regards Light and Colour, provided all the modes and varie- ties are resolvable into the variation in degree of some funda- mental mode of consciousness. If there be several fundamental modes, there must be a law for each; thus there may be wanted one law for white light, with its degrees, and one for each of the primary colours—four laws for the sense of sight. _ We may be able to discover how Heat causes Light to the extent of generalizing the molecular condition of luminosity, and connecting this with the molecular condition of high temperature ; but that such molecular condition and its ac- companiments—radiation, refraction, &c. — should yield the sensation of light, must always be expressed in a distinct law, a law uniting an objective with a subjective experience. Such — is the proper goal or end of our knowledge in regard to the phenomenon, a FALLACIOUS AND ILLUSORY EXPLANATIONS. 9. One form of illusory explanation is to repeat the fact — in different language, assigning no other distinct yet" | parallel fact. This is ridiculed in Moliere’s physician, who gives as eh reason why opium causes sleep, that it has a soporific virtue. — i Re i ss ay afd a z A ILLUSION OF FAMILIARITY. 355 Not much is done to explain the greenness of the leaf of lants by saying that it is due to a substance named ‘ chloro- phyll.’ The only step gained is the fact (if it be a fact) that greenness in all plants is due to the same substance. A simile is sometimes offered for an explanation. Black’s Latent Heat was merely a re-statement of the fact: he might have gone on to call it secret, concealed, embodied, shut-up Heat; all which expressions would merely iterate the circum- stance that a certain amount of heat no longer appeared as heat to the sense, or to the thermometer. It is with the great ultimate generalizations, such as the Uniformity of Nature, and the Axioms of Mathematics, that we are most prone to give as a reason, or proof, a mere various wording of the principle itself. ‘Why must the future resemble the past?’ ‘Because Nature is Uniform.’ The phenomenon, sleep, was referred by Whewell to a law of periodicity in the animal system. This, however, does nothing but repeat the fact to be explained ; there is no assimilation with another fact, so as to yield a higher gene- rality, which would be inductive explanation, and no reference to a higher generality already formed, which would be deduc- tive explanation. A step towards real explanation is made by comparing it with the repose or quiescence of the organs after any activity whatsoever. This is to assimilate the phenomenon with another distinct phenomenon ; the two taken together form a higher generality, which, so far as it goes, is an explanation. 10. Another illusion consists in regarding phenomena as simple because they are familiar. Very familiar facts seem to stand in no need of explanation _ themselves, and to be the means of explaining whatever can be assimilated to them. Thus, the boiling and evaporation of a liquid is supposed to be a very simple phenomenon requiring no explanation, and a satisfactory medium of the explanation of rarer phenomena. That water should dry up is, to the uninstructed mind, a thing wholly intelligible; whereas, to the man acquainted with Physical science, the liquid state is anomalous and inexplicable. The lighting of a fire, by contact with a flame, is a great scientific difficulty; yet few people think it so. A soap bubble is a conflux of unexplained phenomena Voluntary action, from familiarity, has long been reckoned so simple in 856 EXPLANATION OF NATURE. itself as to have provided a satisfactory explanation of all other modes of generating mechanical force. 11. The greatest fallacy of all is the supposition that something is to be desired beyond the most generalized conjunctions or sequences of phenomena. It is supposed by many that the possession of a supreme generality on any subject is insufficient; the mind, it is said, craves for something deeper, and this "craving (which can never be satisfied) is considered to be proper and legitimate. The generalization of Gravity leaves behind it a sense of mystery unsolved, as if there were something farther that we might arrive at if obstacles did not intervene. Newton seemed unable to acquiesce in gravity as an ulti- mate fact. It was inconceivable to him that matter should § act upon other matter at a distance, and he therefore desired a medium of operation, whereby gravity might be assimilated _ to Impact. But this assimilation has hitherto been impracti- cable ; if so, gravity is an ultimate fact, and its own sufficing and final explanation. The acceptance of the law of universal gravitation as a full and final solution of the problem of falling bodies, without hankering or reservation, is the proper scientific attitude of mind, There seems ne hope at present of making it fraternize with a second force, and there is no other legitimate outgoing of enquiry with reference to it. In the same way the niysteriousness often attributed to Heat, is partly resolved by the Theory of Correlated Forces, under which ‘heat is assimilated to movement. The subjec- tive fact of heat—the sensation of the mind so described, is a fact coming under the general relationship of body and mind. Light is still a mystery in the legitimate sense; it has been but imperfectly generalized as regards its physical workings. Every isolated phenomenon ‘is, in the proper acceptation, a mystery. 7 Apparent contradiction is something that demands to be explained ; investigation should never stop short of the attain- ment of consistency. Thus, the glacial period of the earth’s history, is at variance with the only hypothesis yet framed as — wy the solar agency—the slow but gradual cooling in the course of ages, The molecular aspect of the Correlated Forces is repulsion (as in Heat), yet in Magnetism and in Friction Electricity, it appears as attraction. — ' 4 =. wi LU naa * eed eda. 4 ; 4 ¥ 38 ee ar) 7 3 MYSTERY OF BODY AND MIND. 357 Free-will is often stated as a hopeless and insoluble contra- diction. To leave any problem in such a condition is un- scientific. The union of Body and Mind has long been considered the mystery by pre-eminence. The prevailing opinion has been that this connexion would for ever resist and paralyze explana- tion. Yet, the scientific mode of dealing with the case is clear. The material properties and the mental properties are each to be conceived according to their own nature—the one by the senses, the other by self-consciousness. We then en- deavour to assimilate and generalize to the utmost each class of properties ; we generalize material properties into inertia, gravity, molecular forces, &c.; we generalize mental proper- ties into pleasures, pains, volitions, and modes of intelligence. We next endeavour to rise to the most general laws of the union of the two classes of properties in the human and animal organization. When we succeed in carrying this generalizing operation to the utmost length that the case appears to admit of, we shall give a scientific explanation of the relationship of body and mind. Any farther explanation is as incompetent, as it is unnecessary and unmeaning. Such language as the following is unscientific :—‘ Conscious sensation is a fact, in the constitution of our corporeal and and mental nature, which is absolutely incapable of explana- tion.’ The only meaning attachable to this is, that bodily facts and mental facts are fundamentally distinct, yet in close alliance. So—‘To this day, we are utterly ignorant how matter and mind operate upon each other.’ Properly speak- ing there is nothing to be known but the fact, generalized to the utmost. ‘Is there’ says Hume ‘any principle in all nature more mysterious than the union of soul and body ; by which a supposed spiritual substance acquires such influence over a material one, that the most refined thought is able to actuate the grossest matter P’ 3 Again, ‘we know nothing of the objects themselves which compose the universe; our observation of external nature is limited to the mutual action of material objects on one another.’ What is the good of talking of a supposable, and yet impos- sible, knowledge ? * * See Fznnizr’s Remains (vol. II. p. 436), for some pertinent remarks on the nature of Explanation. ae ww o CHAPTER XTIL HYPOTHESES, 1. Various meanings belong to the word Hypothesis, I. It means the suppositions, suggestions, or guesses, as to any matter unknown, leading to ‘experimental or other operations, for proof or disproof. In the course of a research, many suppositions are made, and rejected or admitted according to the evidence. Kepler made an incredible number of guesses as to the planetary relations before he discovered the actual laws. Davy sup- posed the alkalies to be compounds before he established the fact by decomposing them. In the Inductive operation of arriving at general laws, the supposition made is some law that appears likely to explain the fact, as Kepler’s Third Law (of periodic times and mean dis- tances). Such suggested laws have to be duly verified according to the Experimental Methods. In the properly Deductive operation of carrying out a law by bringing cases under it, the supposition is an identity, as in the examples already giver under the Deductive Method. The hypothesis of a man’s being guilty of a certain crime is of this nature; the proof consists in the tallying or fitting of the circumstances of the accused with the circumstances of the crime (commonly called ‘circumstantial evidence’). Of the same nature is ‘the hypothesis of Wolfe with respect to the origin of the Homeric poems; the hypothesis of Niebuhr, with respect to the derivation of portions of the early Roman history from ballads or epic poems ; the hypotheses of Hich- horn, Marsh, and others, with respect to the origin of the text of the four gospels; the hypothesis of Horace Walpole, with respect to the character of Richard the Third, and various hypotheses with respect to the Man in the Iron Mask. So there are hypotheses, in literary history, as to the authorship of certain works, as the Aristotelian Gconomics, the treatise De Imitatione Christi, the Letters of Junius. In each of these - cases a supposition is made, the truth of which is tried by combining it with all the circumstances of the case.’ | A HYPOTHESIS DEFINED. 309 These cases contain no matters for logical discussion. They do not raise the questions that attach to the Undulatory Hypo- thesis of Light, the Development Hypothesis, the Atomic Theory, and other celebrated hypotheses. 2. The definition of a Hypothesis (according to Mill) is @ supposition made (without evidence, or with insufficient evidence of its own) in order to deduce conclusions in agreement with real facts ; the agreement being the proof of the hypothesis. Hypothesis, in this sense, is a defective kind of proof; there is some missing link; and the question is raised, how shall this be made good in other ways. For example, in the geological investigation concerning the transport of erratic boulders, there are various possible suppo- sitions—icebergs, glaciers, water currents. Now, we may be unable to get what we should desire, in accordance with the strict course of experimental elimination, namely, proof of the actual presence and operation of one or other of these agents. The only resource then, is to compare the appearances with what would result from the several modes of action. If these appearances are consistent with one mode only, there is a certain strong presumption in favour of that one. The pre- sumption would obviously amount to certainty, if we have had before us (what we cannot always be sure of having) all the possible or admissible agents. In the absence of proof as to a man’s real motives, on a given occasion, we often decide in favour of some one, because the man’s conduct is exactly what that motive would dictate. The soundness of the criterion depends upon there being no other motive or combination of motives that would have the same effects. 3. It is manifestly desirable, in assumptions relating to natural agencies, that these should be known to exist. The Hypothesis is then limited to such points as—their pre- sence, their amount, and the law of their operation. Such are the hypotheses as to the erratic boulders. So, we may ascribe an epidemic to excessive heat, to moisture, to electricity, to magnetism, to animalcules, to bad drainage, to crowded dwellings, or to some combination of these. The agencies ure real; every one of them is what Newton termed a vera causa, What is hypothetical is the actual presence of ie ; “i= 5 71, te 360 HYPOTHESES. one or other, the mode of operation, and the sufficiency to produce the effect. If all these could be established in favour of one, the point would be proved. If the presence cannot be proved (the difficulty in past effects), there must be shown an exclusive fitness in some one to account for the appearance. — The illustrious example of Gravity may be quoted in its bearing on Hypotheses. Newton’s suggestion was, that celes- tial attraction is the same force as terrestrial gravity. He thus proceeded upon a real or known cause ; the hypothetical element was the extension of gravity to the sun and planets. The preliminary difficulty to be got over was the rate of decrease of the force according to distance. From Kepler’s laws, it was proved that celestial attraction diminishes as the square of the distance increases. Was this true of the earth’s gravity ? The fall of the moon was the criterion, and exactl coincided with that supposition, Thus, then, the law of the sun’s attraction and the law of the earth’s attraction are the same. The earth’s attraction extends to the moon; may it not extend to the sun, and may not the sun reciprocate the very same attraction P The wonderful amount of tallying or coincidence in this case was sufficient in the minds of all men to justify the assumption that the two attractions are the same. The hypothesis was proved by its consequences. And, as no rival supposition has ever stood the same tests, the Newtonian theory is considered as beyond the reach of challenge. The rival hypothesis to gravity, in the explanation of the celestial motions, was the Cartesian vortices, or whirlpools of ether, which floated the planets round, as a chip revolves in an eddy of a stream. | The identity here assumed is between the circular motion of the planets, in what is commonly supposed to be empty space, and the circular motion of # whirlpool of water or of air, The first obvious disparity respects the fluid medium. In the whirlpool of water we have a liquid mass with density sufficient to buoy up wood, and mechanical momentum sufli- cient to propel it in the direction of the stream. No such fluid mass is known to be present in the celestial spaces; the very supposition is hostile to all familiar appearances. A fluid sufficient to move the planets at the rate they move in would have numerons other consequences that could not escape detection. It would mix with our atmosphere as an active element and produce disturbances on the earth’s surface. ee i el et i ~ ASSUMPTION OF A NEW AGENT, 361 In this vital circumstance, therefore, the comparison fails ; the assimilation is incompetent. A second disparity was brought to light in Newton’s criti- cism of the scheme. The laws of a whirlpool are not the laws of the p!anetary orbits; a whirlpool is incompatible with the laws of Kepler. Now, we cannot assimilate two mechanical phenomena, two attractions, for example, unless they follow ‘the same law of force. This is a vital point in a mechanical comparison. The following of the same dynamical law was the crowning circumstance of the likeness between gravity and solar force. It would be said, therefore, that the Cartesian scheme did not assign a vera causa. It assigned, no doubt, a mode of action quite familiar to us; whirlpools are a real fact. But it assumed a material substance unlike anything hitherto dis- covered ; water we know, and air we know, but the entity demanded for the vortices is eutirely foreign to all our experi- ence of material things, 4. As it would seem irrational to affirm that we already know all existing causes, permission must be given to assume, if need be, an entirely new agent. ‘The conditions of proof are, in this case, more stringent. The chief example of this kind of Hypothesis is the Undulatory Theory of Light. The supposition of an etherial substance pervading all space, and by its undulations propagating Light and Heat, as the air propagates sound, is in accordance with many of the facts of Light, more especially what is called the Interference of Light, a generalization of many distinct appearances. The hypothesis also served to discover new facts of luminous agency. Assuming what is not strictly accurate as yet, that the undulatory hypothesis accounts for all the facts, we are called on to decide whether the existence of an undulating ether is ehereby proved. We cannot positively affirm that no other supposition will explain the facts ; what we can say is, that of all the hypotheses hitherto suggested, this approaches the nearest to an exact explanation. Newton's corpuscular hypothesis is admitted to have broken down on Interference ; and there is at the present day, no rival. Still, it is extremely desirable in all such hypotheses, to find ' some collateral confirmation, some evidence aliwnde, of the supposed ether. This is supplied in part by the observations 362 HYPOTHESES. on the comet of Encke. If the retardation of that comet, and other observations of a like nature, establish the fact of a resisting or inert medium, there will remain, as hypothetical, the properties of that medium, namely, the peculiar mode of elasticity fitted for transmitting luminous and other emana- tions. There is farther to be urged, in support of the hypothesis, its constancy with the other hypothesis that regards Radiant Heat and Light as the propagation of molecular movements from hot and luminous bodies. The transmission of these influences through space, by the communication of molecular impulse, is in harmony with their character as motions in the molecules of the masses of ordinary matter. An additional confirmation is supplied in the remarkable fact that bodies, when cold, absorb the same rays (of the solar spectrum) that they give out when hot. This is precisely analogous to the law of musical strings, namely, that, of the notes sounded by another instrument in their neighbourhood, they assume each its own note. 5. Some Hypotheses consist of assumptions as to the minute structure and operations of bodies. From the nature of the case, these assumptions can never be proved by direct means. Their only merit is their suitability to express the phenomena. They are Representative Fictions. All assertions as to the ultimate structure of the particles of matter are, and ever must be, hypothetical. Yet we must not discard them because they cannot be proved; the proper cri- terion for judging of their value is their aptness to represent the phenomena. That Heat consists of motions of the atoms can never be directly shown; but if the supposition is in con- sistency with all the appearances, and if it helps us to connect the appearances together in a general statement, it serves an important intellectual function. The phenomena of the solid, liquid, and gaseous state of matter can be represented by the opposing play of two sets of forces—the attraction of cohesion inherent in the atoms of each substance, and the repulsive energy generated by the heat motions. Incrystals, the heat motions are at a minimum, — and in that case, the cohesion assumes a polar character, or 1s — concentrated at particular points, whose difference of relative situation makes difference of crystalline form. ; The Undulatory hypothesis of Light, even although it may — never be fully established as fact, will have a permanent yalue [are er, ct ae oy REPRESENTATIVE FICTIONS. 363 as a Representative summary of the facts of Light; and may be gradually carried to perfection in this character. In a paper by Graham, on the ‘ Molecular Mobility of Gases,’ published in the Transactions of the Royal Society, 1863, there is put forward a hypothesis of the Constitution of Matter. The assumptions are these :— (1) The various kinds of matter may consist of one species of Atom or molecule, having a different kind of movement in each substance. This is in harmony with the equal action of gravity upon all bodies. (2) The greater the energy or swing of the primordial and inalienable movements of the ultimate atoms, the lighter the mass. The leading fact named Density or specific gravity is represented by this assumption. (3) These ultimate molecules, whose primitive movement gives specific gravity, are supposed to be made up in groups, each group having a farther movement, vibratory or other; which second superinduced movement represents the gaseous molecule affected by Heat, and leading to gaseous expansion. This Graham also calls the diffusive molecule. (4) Equal volumes of two forms of gaseous matter, irre- spective of weight, have a facility of combining ; this is Chemical Combination. It is a hypothetical expression of the law connecting Atomic Weight with Gaseous Volume. The gaseous state is expressed by Graham as the typical state of matter; ‘the gas exhibits only a few grand and simple fea- tures.’ The special point of the hypothesis consists in assuming motions within motions, like primary and secondary planets, There is no limit to the successive groupings and their charac- teristic movements. For still more complex properties, new groupings may be assumed. A somewhat different hypotkesis of Molecular Motions has been given by Mr. Clark Maxwell (Phil. Trans. 1866). It might be superadded to Graham’s. _ Under the methods of Cnemisrry, we shall advert to the hypothesis named The Atomic Theory ; and under the methods of Bionoey, there will «ccur other examples of celebrated hypotheses. Also, in the Logic of Mepicinz, the representa- tive conceptions are brought under review. The political ficiion as to a Social Contract, determining the rights of sover:ignty, is not entitled to the dignity of a Hypothesis. It isa pure fabrication to serve a political, or 364 HYPOTHESES. even a party purpose; and ranks with the loge in the ee ancient Grecian states, relied on as giving validity to the title of a tribe to its territory, or of a family to the ens power. 6. It has been said (by Dugald Stewart and otbarts that the reasonings of Geometry are built upon hypotheses, The meaning is, that the figures assumed are abstractions, or ideals, and do not correspond to any real things. The word ‘hypothesis,’ is here employed in a somewhat peculiar sense. It is identical in meaning with ‘ Abstract,’ as opposed to actual or. ‘Concrete’ objects. The important truth intended to be conveyed would probably be given much better by avoiding the use of ‘ hypothesis.’ In Geometry, as in all Abstract Reasoning, the essence of the operation is to view the things in one exclusive aspect, or with reference to one single property, although, in point of fact, no object exists possessing that property in pure isola- tion. The geometrical Point is a mark of position; we reason upon it solely as marking position. Every real point, and even the point that we conceive in the mind, possesses at the same time a certain magnitude, a certain colour, and certain material substance. We, however, make abstraction of all — these features; we do not assume them in any degree ; we drop them entirely out of view; we consider ‘position,’ m so far as ‘ position,’ and make ‘affirmations on that” special assumption. When we come to deal practically with an actual point, we must re-admit all these properties belonging to it in its concreteness; we must allow for the fact that no — actual point can determine an abstract position ; it covers an i area, and therefore does not fix position except by an approxi- - mation. ‘2 In Mechanics, there are convenient fictions that subserve the abstract reasonings of the sciences; as, for example, the supposition that the whole mass of an irregular body is con- densed into its Centre of Gravity—an operation impossible in fact, but having a practical convenience in mechanical demon- — strations. It is desirable, for certain purposes, that we should | a make abstraction of the form and size of a mass, and view ; only its weight and its relative position to some other mass ; and one way of compassing the end is to imagine the form and fi the size non-existent, or that the mass exists in a m matical point. We say there is a certain definite position ix the Pe OF of the earth, wherein, if the whole mass vee are EXPERIMENTUM CRUCIS. 365 concentrated, the earth’s attraction for the sun and the moon would be the same as it actually is. This is merely a verbal aid to the process of reasoning in the Abstract. The remark is applicable to all the other abstract centres—oscillation, Suspension, gyration, de. 7. A fact that decides between two opposing Hypotheses was called by Bacon an experimentum crucis. The ‘Instantia Crucis’ of Bacon does not properly belong to the Experimental Methods of Induction. It is the decisive instance between two contending hypotheses. Thus, when the Copernican system was brought forward in opposition to the Ptolemaic, not only was there a necessity for showing that the new system corresponded with all the facts; there was farther required the production of some facts that it alone could conciliate. The first fact of this decisive character was the Aberration of Light, a fact incompatible with the earth’s being at rest. Another fact, equally decisive, is furnished by the recent pendulum experiments of Foucault with regard to the motion of the earth. Bacon himself, who never fully accepted the Copernican system, desiderated an ‘ experimen- tum crucis’ of this nature, namely, a fact to show that the velocities of bodies appearing to move round the earth are ir proportion to their distance; which, he says, would be a proof that the earth stands still, and that the apparent daily motion of the stars is real. The entire absence of mechanical energy in the rays of light is regarded as decisive against Newton’s Emission Hypothesis. The most delicate experiments fail to show any moving energy in the concentrated rays of the sun; which failure is inconsistent with a stream of particles of inert matter. CHAPTER XIV. APPROXIMATE GENERALIZATIONS AND PROBABLE EVIDENCE. 1. Probable Inference is inference from a proposition only approximately true. Every certain inference supposes that the major is a pro- position universally true, as ‘all men are mortal,’ ‘all matter 366 APPROXIMATE GENERALIZATIONS. gravitates.’ When a minor is supplied to such propositions, a Ss the conclusion is certainly true. 3 he From a proposition true only in the majority of instances, __ the inference drawn is not certain, but only probable. ‘Most (not all) phenogamous plants have green leaves; hence itis _— probable that any given class of these plants has green leaves. The word for such generalities is ‘most;’ the synonyms are ‘many,’ ‘usually,’ ‘commonly,’ ‘ generally,’ ‘ for the most — part,’ ‘in the majority of instances.’ 2. If we know the exact proportion of cases in an ap- proximate generalization, we can state numerically the degree of probability of an inference drawn from it. It being known that a certain thing happens in nine in- stances out of ten, the probability, in a particular case, is nine to one, or nine-tenths. All the metals, except copper and gold, are devoid of colour, (being either white or some shade of grey). The probability that a new metal is white or grey is as fifty-two to two. | On the supposition that the majority of drunkards are never ~ reformed, the probability is against the reform of any indivi- dual drunkard. The strength of the probability depends upon our estimate of the comparative numbers. If this estimate is vague and uncertain,—if we cannot say whether the reformed drunkards number one fiftieth, one twentieth, or one-fourth of the whole,—our estimate of the probability in the given in- stance is correspondingly vague. ohh What Hobbes says of Charles 1I— 59 Nam tunc adolescens : Credidit ille, quibus credidit ante Pater— is true of the vast majority of men even in the most enlightened _ countries. Hence a strong probability that any given indi- — vidual has never exercised any independent judgment in — politics or in religion. A hundred to one is a safe estimate of such a probability. ; - It is an approximate generalization that both intelligence and independent thought are most frequent in the middle — ranks of society. The generalization has in its favour deduc- tive as well as inductive evidence. We know the circum-— stances adverse to those qualities in the highest, and also in the lowest, ranks. Still, it is but approximate, and yields only probability in every given application. Like all proba- bilities, however, if applied to masses, it gives certainty, The PROBABLE INFERENCES. 367 collective action of a middle class body would be more intelli- gent and independent than the action of the other classes, The proposition is approximately true that the wealthy are more yirtuous than the indigent. There are numerous excep- tions, but the evidence is sufficient to prove the rule as an approximate generalization. The only dispute is as to the extent of it. Direct statistics on the great scale are wanting; and the deductive argument consists in comparing the tend- encies for and against virtue in the wealthy, as compared with the poorer class—a comparison where, from the vague nature of all estimates of human conduct, a certain latitude of expression must be allowed. The characters of men are described by such general terms as energetic, timid, tender-hearted, irascible, truthful, intel- Jectual, and so on. Even when most carefully generalized, these characters are only approximate; they represent prevail. ing tendencies, liable to be defeated in the complicacy of human motives, So with classes, professions, and nations. All the current generalities respecting the characteristics of sex and of age are mere approximations. Literary and Art criticism, as expressing the style and manner of authors or artists, is of a like nature. The operation of laws and institutions is at best but approximate. We cannot affirm that the general good con- sequences follow in every instance. The tendency of severe punishments is to deter from crime; they may do so in nine cases out of ten, or ninety-nine out ofa hundred. It is the duty of the state to seek out the mode that approximates most to the desired end. In such a case, statistics give a kind of numerical precision to the general tendency, and a corres- ponding exactness to the inference of probability. The very best institutions have to be defended on the ground of superior good, not of absolute or unexceptional good. This is all that can be said for liberty as against re- straints, for responsible government as agaihst despotism. Proverbial sayings are for the most part but rude approxi- mations to truth. Many of them can hardly be said to have a preponderance of cases on their side. ‘The more haste, the less speed’ is not true in the majority of instances; its merit is chiefly as an epigrammatic denial of the universality of the rule that activity succeeds in its object. We often take delight in parading the exceptions to approximate generalities ; and not a few of our proverbs are occupied with the representation of minorities. Tallyrand’s ‘No zeal’ is incorrect as a rule ; 368 APPROXIMATE GENERALIZATIONS. the rule that it crosses, however, is but approximate, and has exceptions ; the point of the saying lies in suggesting these. 3. It is a legitimate effort to endeavour to make the approximation of a rule as close as possible, before apply- ing it to cases. This can be done in various ways. (1) An approximate generalization is rendered absolutely certain in its scope, when all the exceptions can be enumer- ated; as in grammar rules, and in Acts of Parliament contain- ing schedules of exceptions. (2) A very near approximation can be made if we know the exact occasions and circumstances where the rule holds. Thus that ‘Honesty is the best policy’ is in the abstract only a rough generalization ; it is far from the exact truth. But we are able to assign the specific circumstances where it holds good more nearly. The ‘honesty’ should exactly correspond to the standard of the time, not rising above, and not falling below the established code. It should be apparent and not concealed from view. It should contribute something to the advantage of persons of weight and influence. Thus limited and qualified, the approximation is very near the truth; yet not altogether true. The dishonest successful men are still sufficiently numerous to constitute a standing exception to the maxim. The Proposition ‘ Knowledge is virtue ’ was maintained in the Socratic school. It is an appproximate generalization, giving a certain small probability in its applications. That it has the truth on its side is proved by the statistics of crime ; the majority of criminals coming from the least instructed part of the population. Still, the exceptions are numerous. We know from deductive considerations that virtue does not spring directly from the knowing faculties ; the filiation is in- direct or circuitous. The best application of so slight a pro- bability is to take it with concurring probabilities. The conditions of a virtuous character can be stated with consider- able precision, while intellectual culture also is an element whose value can be assigned. Hence, in applying the rule to a known case, we can infer with a far higher probability, than could be given by any one approximate generality, as to the virtuous tendencies of knowledge, of parentage, of occupation, and other circumstances. We can unite all the presumptions into one still stronger. 7 It is a usual defect of empirical generalities that the sub- ject of them is badly defined, or that the circumstances where mee INCREASED APPROXIMATIONS. 369 the predicate holds cannot be exactly specified. This is a common defect in the practice of medicine. A drug has a certain efficacy in the majority of instances, and is therefore only probable in its consequences. A higher knowledge would give the exact conditions wherein it succeeds, which would be to convert the approximation into certainty. Soin Politics. Certain institutions, as for example Tree Government, are good for nations generally. In some cases, they fail. It is for political science to specify accurately the circumstances where they are suitable, and those where they are unsuitable ; by which means we may attain to rules of a certain, or nearly certain character. It is commonly said that being educated at a public school developes particular manly virtues, as self-reliance, courage, &c. This is but an approximate generalization. If we had the comparative numbers of the successes and the failures, we could assign the probability in a given instance, Still better, however, would be the enquiry, what are the circumstances wherein the effect would arise ; what kind of youths would be operated on in the salutary way ? It is an approximate generalization that absolute sovereigns abuse their power ; it is true, in a large majority of instances, but not in all instances. It can be converted into a still closer approximation, if we can assign the particular situation of an _ individual sovereign—the motives operating upon him person- ally, either as encouraging or as checking the despotic vices. Hence, by a series of provisos (as Mr. Mill remarks) we may render an approximate rule, an almost certain rule :—An absolute monarch will abuse his power, wnless his position makes him dependent on the good opinion of his subjects, or unless he is a person of unusual rectitude and resolution, or unless he throws himself into the hands of a minister posses- sing these qualities.’ 4, Approximate generalizations give an opening to the bias of the feelings, and to the arts of a sophistical reasoner. It is impossible to deal fairly with an approximate genera- lization, except by forming some estimate, the best that can be had, of the instances on one side and on the other. This is often difficult even to the most candid and painstaking irnth-seeker. Nothing then is easier than to turn away the mind from a part of the instances, and to decide upon the remainder. Any strong feeling has this blinding efficacy. For example, our Patent Law has raised a certain number of 370 ANALOGY. persons to wealth; it has stimulated a certain number to. inventions, whether profitable or not to the inventors; it has induced a certain number to waste their lives in unproductive and hopeless enterprises : it has obstructed, in certain instances, the introduction of improvements. Whether the law has been good or evil on the whole, depends upon the relative number of these various instances. Now, it would be most © difficult to attain an exact comparative estimate in such a ques- tion. How easy then for any one to incline to the instances favouring a preconceived theory, and to pay no heed to the rest ? The arts of the pleader suit themselves to this situation. By dwelling upon and magnifying the instances in one side, by ignoring and explaining away those in the other, a skilled advocate reverses the state of the numbers in the approximate generalization, making the minority seem the majority. The reply needs to be conducted so as to redress the distorted estimate. (For the practical applications of Probability to Testimony and other Evidence, see Apprnpix I.). ? CHAPTER XV. ANALOGY. 1. The foundation and justification of all inference is Similarity. The similarity may exist in various forms and degrees, and the validity of, the inferences will be modified accordingly. When two situations are exactly the same, the uniformity of nature leads to the same consequences. Place equal weights in a balance so as to make an exact equipoise. Shift the — centre of motion to one end, and that end will rise and the — other fall, every time that the change is made. A great deal — of variety may be introduced into the experiment, with the same result. The rod may vary in length, and in material, and the weights may be small or great: so that we may have — sameness in the result without sameness of the antecedents, _ Again, having seen a great many animals die, we infer that — other animals living and to be born will die: the resemblance, — together with nature’s uniformity, being the justification, But there are often wide disparities between the instances observed and the instances inferred, Mads i INDUCTION IN DIFFERENCE OF SUBJECT, STi It was, however, the object of the experimental methods to eliminate the essential parts of a causal situation from the non-essential parts. In the midst of all the various forms of the experiment with the balance, we find, by the use of the methods, that the one circumstance that disturbs the equipoise is to remove the point of suspension from its central position in the beam ; that the size and material of the beam, the size and material of the weights, are unessential cireumstances. So with animal life ; the fact called organized life is the fact ac- companied with mortality; the forms and sizes of animals, their being vertebrate or invertebrate, are inductively elimin- ated as unessential. An inductive inference is thus an inference from sameness in certain particulars, shown by induction to be the particulars always present when some consequence or collateral is pre- sent. This is an inference by identity, a perfect induction. 2. ‘There may be a radical difference in the subjects of two compared phenomena with ut preventing a strict In- ductive inference. ‘The sole condition is that the same- ness apply to the attribute found by induction to bear the consequence assigned. To say ‘there is a tide in the affairs of men’ is to use a mere metaphor, the subjects compared being totally distinct. Now, to reason from one subject to another of a different kind, might be called reasoning by Analogy; yet, the inference might be such as to deserve the name of induction. Great as is the difference between the march of human history, and the flow of the tides, still, if the two phenomena exactly re- sembled in the single feature of ebbing and flowing, and if no inference were drawn, except what this feature involved, the _ argument would be a sound and strict induction. If human affairs in any way are truly describable as ebbing and flowing, we are entitled from one movement to predict the following. If periods of great public excitement in special topics as Liberty, Religion, aggressive War, are followed by periods of apathy, there is a species of tidal movement, and the laws of the tides may so far be applied to the case, by a legitimate induction, or else by a deduction founded on an induction. The Chinese profess to found their government on the paternal principle, and to justify their peculiar form of despot- ism on the similarity of the state to a family. The argument is not inductive; there is a failure in essential points. It is @ crude metaphor. There is a certain important similarity, 372 ANALOGY. namely, the fact of government, involving authority, superior- ity, and punishment; and any inferences drawn upon this single circumstance would be valid. Certain of the merits and of the demerits of government are identical in both instances; the graduation of punishment to offence, consist- ency and fairness on the part of the ruler to the ruled, are equally required in the family and in the state. But it is not an inductive inference to say that because the parent is despotical, so should the state. The two cases do not agree in the point whence the despotical relation flows; in the family, the subjects of government are children; in the state, the subjects are grown men, on a level with the rulers. The inference would require the case of a very ignorant and degraded community ruled by a wise and high-minded caste. To whatever degree a nation approximates to this state of things, there is an identity between it and the family relation- ship. Plato’s comparison of the state to an individual man is not an analogy in the proper sense of the term. It is one of those figurative resemblances where the points of agreement and of disagreement are perfectly ascertainable, and where there 1s noelement unknown. Any one can tell whether the inferences drawn from’ the comparison follow from the points of agree- ment. That there should be a three-fold classification of citizens in the state, cannot be inferred or confirmed by an analysis of the mind into three leading functions. The con- stitution of a state has nothing in common with the divisions of the mental powers of an individual man. . The same remark is applicable to another fayourite com- parison of Plato’s—virtue to health. The resemblance is exceedingly slight; yet, if nothing were inferred but what grew out of that resemblance, we could not object to the use of the comparison. But Plato’s theory of punishment derived. from it supposes. a likeness that does not hold; and the heen is refuted by exposing the dissimilarity. - The Ancient Philosophy was full of these misapplied com- parisons, improperly termed analogies. Speaking with reference to the early growth of Law, Mr. Mayne observes: — ‘ Analogy, the most valuable of instru- ments in the maturity of jurisprudence, is the most dangerous: of snares in its infancy. Prohibitions and ordinances, ori- ginally confined, for good reasons, to a single description of acts, are made to apply to all acts of the same class, because a man menaced with the anger of the gods for doing one ~ * J 3 77 PROPER MEANING OF ANALOGY. 373 thing, feels a natural terror in doing any other thing remotely connected withit. After one kind of food has been interdicted for sanitary reasons, the prohibition is extended to all food resembling it, though the resemblance occasionally depends on analogies the most fanciful. So, again, a wise provision for insuring general cleanliness dictates in time long routines of ceremonial ablution ; and that division into classes which ata particular crisis of social history is necessary for the main- tenance of national existence degenerates into tle most disas- trous and blighting of all human institutions—Caste.’ Analogy has been often defined ‘resemblance in relations :’ as when a wave of water is said to be analogous to an undu- lation of air, or of ether; or a magnet is compared to a charged Leyden jar because of the common polar condition. This definition is objectionable chiefly on the ground of vagueness. The word ‘relation’ is too general for a precise’ statement of the case. What truth or fitness there is in the expression can be given in other ways. 3 Analogy, as different from Induction, and as a dis- tinct form of inference, supposes that two things from resembling in a number of points, may resemble in some other point, which other point is not known to be con- nected with the agreeing points by a law of causation or of co-existence. If two substances agree in seven leading properties, and differ in three, the probability of their agreeing in some eleventh property (not known to be connected with any of the ten) is, with reference to the known properties, seven to three. But this rule would be modified by the consideration of the number of properties still remaining to be discovered, a cir- cumstance necessarily indefinite. If we had reason to suppose that a large number of properties still remained undiscovered, the probability could not be stated with the same fixity or confidence. 4. An argument from Analogy is only Probable. The probability is measured by comparing the number (and importance) of the points of agreement with the number and importance of the points of difference ; having respect also to the extent of the unknown properties as compared with the known. No Analogy can amount to full proof; very few give even a high probability. ‘It may afford,’ says Reid, ‘a greater or 374. ANALOGY. less degree of probability according as the things compared are more or less similar in their nature; but it can afford only probable evidence at the best.’ The natural Kinds afford the best examples of the typical case of Analogy. They have numerous properties, known and unknown; extensive agreements prevail among groups of them, together with differences’ more or less numerous. Thus, sodium and potassium have numerous points of agree- ment, and a few points of difference. There would, theretore, be a certain amount of probability that any effect due to sodium, or a given compound of sodium, might arise from potassium, or the same compound of potassium. | The celebrated guess of Newton, as to the Diamond, which was afterwards verified by experiment, was not an analogical inference in the strict sense. Had the inference been from, a single body, as an oil, to the diamond (the point of agreement between them being unusual refracting power), the resem- blance would have been too limited even fora gaess. The application to the Diamond was the carrying out of an Empirical Law, partially, if not wholly proved. The circum- stance that arrested Newton’s attention was that the refracting power of bodies is very nearly as their densities excepting that unctuous and sulphureous bodies refract more than others of the same density. Having obtained measures of the refractive powers of the densities of twenty-two substances, varying in density between air and diamond, he found that they fell into two classes. In one class, were topaz, selenite, rock-crystal, Iceland-spar, conmon glass, glass of antimony, common air: in all which, the refracting powers are almost exactly as the densities, excepting that the refraction of Iceland-spar is a little more than the proportion. In the second class were : camphor, olive oil, linseed oil, spirit of turpentine, amber, which are, ‘he said,’ ‘ fat, sulphureous, unctuous bodies,’ and diamond which ‘ probably is an unctuous substance coagulated ;’ all these, compared together, have their refractive powers almost exactly proportioned to their densities. But now, when the two classes are compared, the refractive powers of the second class (the unctuous substances) are twice or thrice as great, in proportion to their densities, as the refractive powers of the first class. Water has a middle position between the two classes ; salts of vitriol may stand between the earthy sub. stances and water ; and spirit of wine between water and the oils. The suggestion as to the diamond thus arose from its position among a number of highly refracting bodies that ~~ = ia EXAMPLES OF ANALOGY. 375 in being of an inflammable or combustible nature. The concurrence of high refracting power with inflammability was an empirical law ; and Newton perceiving the law, extended it to the adjacent case of the diamond. ‘I'he remark is made by Brewster that had Newton known the refractive powers of the minerals greenockite and octohedrite, he would have extended the inference to them, and would have been mistaken. As an example of Analogy proper let us suppose the Balsam of Peru to possess certain properties, medicinal or other. Suppose next, that the balsam of Tolu agrees in a great number of these, but differs in one or two important or unimportant properties. On this proposition, we should ground a very considerable presumption, that the one might replace the other in new and untried applications in Pharmacy. The illustration might be extended to Vegetable and to Animal species. A quadruped resembles a human being in. very many points of structure and function, but also differs in a considerable number; while there may be undiscovered properties in both. This reduces to a weak probability all inferences from one to the other as to the suitable kinds of food, liability to disease, or medical treatment. Hxperiments on animals may cast light on the human subject, provided we know that the particular organs are constructed nearly alike in both, as in the connexions of the nerves, the breathing, the digestion, &c. The function of the saliva and of the gastric juice has been studied by experiments on dogs and on horses. In a recent set of experiments on the action of mercury, dogs were operated on; care having been first taken to ascertain that they agree with human beings in the mercurial symptom of salivation. It is interesting to determine whether our inference from man to the lower animals as to the possession of conscious- ness, is an induction or only an analogy. We believe that, in human beings, consciousness is always associated with certain external manifestations, called the signs of feeling, and with an internal structure of brain, senses, and muscular organs. This we hold to be an inductive uniformity completely estab- lished as regards human beings. The induction extends to differences of degree; with fewer and feebler manifestations, and a smaller brain than usual, we couple a feebler degree of the mental functions. Now, the physical part is found in the brutes ; some approximating more, and some less, closely to the human type. It would seem, therefore, that by induction, 17 ; 376 ANALOGY. and not by analogy, we are to infer the existence of conscious ness in the animals, with modifications of degree only. Mind and Body are of opposite nature ; they are the greatest of all contrasts. Yet there are points of analogy that have been made use of to furnish language and illustration from the one to the other. As in material phenomena, we may have a plurality of forces conspiring or opposing each other, the resultant being arithmetically computable, soin mind we have motives uniting or opposing their strength, the effect being computable (although not with numerical exactness) by adding together those on each side, and noting which is the larger amount. Reid has objected to this comparison, re- marking that ‘the analogy between a balance and a man deliberating, though one of the strongest that can be found between matter and mind, is too weak to support any argu- ment.’ Yet, if the analogy is trusted only to the extent of the similarity, there is no good objection to making an inference from it. Now, the similarity is complete as far as regards the cumulative effect of concurring motives, and the neutralizing or frustrating effect of opposing motives. Whatever power a given motive adds to a man’s volition when it concurs, it must subtract or withdraw when it opposes. The intrusion, by Aristotle and by Kant, of phraseology derived from the intellect, into the domain of the feelings and the will, may be pronounced an improper identification, or an abuse of analogy. Aristotle’s syllogism of the Will, and Kant’s categorical Imperative, point to no real resemblance ; a syllogism expresses an argument conducted by the reason- ing faculty ;' it has no relevance or suitability to express the decisions of the will. Reflex Actions may be profitably compared with Voluntary Actions, if we confine ourselves to the points of similarity. The Reflex is the voluntary with consciousness suppressed or made unessential ; on the corporeal side, there is a considgr- able amount of resemblance, or still better, a gradation or — continuity. 2. Until recently, the sun was considered to be only analogi- 4 cally compared to terrestrial fires. The points of agreement, in giving forth radiant heat with light, are of the most essential — kind; but there was supposed to be a disparity also vital. It was conceived that the sun gave forth its vast flood. of radiance, with no diminution of intensity. Now, every hot body on the earth cools by radiation. Until this serious dis- parity was got over, scientific men felt that all inferences from ANALOGICAL HYPOTHESES. OTe terrestrial bodies to the composition of the sun were rash and unauthorized. Much speculation has been expended on the question—Are the planets inhabited? The argumentis at best analogical ; and there is not even the force of analogy except with refer- ence to a small number. Bodies, like the moon, possessing no water and no atmosphere, must be dismissed at once, The planets generally appear to possess atmospheres. We seem justified, however, in making a summary exclusion of the near and the remote planets, on the ground of temperature. All organized life known to us, is possible only within narrow limits of temperature ; no animal or plant can exist either in freezing water or in boiling water. Now, the temperature of Mercury must in all likelihood be above the boiling point, even at the poles, and the temperature of Uranus, and of Saturn, below freezing at the equator. The constituent ele- ments being now shown to be the same throughout the solar system—Carbon, Oxygen, Hydrogen, &c., we are not to pre- sume any such departure from our own type of organized life as would be implied by animals and plants subsisting in these extremes of temperature. On the supposition that the sun’s temperature has steadily decreased, and is still decreasing, by radiation, the day of living beings is past for Uranus and Saturn, and perhaps for Jupiter; it is not begun for Mercury. Confining ourselves, therefore, to the neighbouring planets, and referring to the others only for the periods, past or future, when the capital circumstance of temperature is suitable, we have an analogical argument as follows. Venus and Mars are gravitating masses like the earth, containing, we may now say with certainty, the same materials as this globe—solid, liquid, and gaseous. But we cannot tell the precise arrangement of the constituent substances ; and, seeing that with ourselves so much depends upon the mere collocation and amount of such elements as oxygen and carbon, we may consider that the un- known properties of the supposed planets are considerable in number, and serious in character. The probability arising out of the points of agreement, if not greatly affected by known dif- ferences, is reduced by this large element of the unknown. Many Hypotheses are of the nature of analogies or compari- sons, the degree and value of the resemblance being more or less uncertain, Thus, to refer to the undulatory hypothesis of Light. When Newton explained the waves of water, and the vibrations of the air in sound, by the:oscillations of a pendu- lum, he was assimilating phenomena of the same mechanical 378 CREDIBILITY AND INCREDIBILITY. character, and reasoning only from the points of similarity. But when we reason from the sonorous vibrations of the air to the vibrations of an ether assumed as occupying space, and conveying light and heat, we work by analogy. It would, therefore, not be irrelevant to apply the rule of analogy, and estimate the points of agreement, as compared with the points of disagreement, and conclude accordingly. On this view, the hypothesis would have but a small intrinsic probability ; it would be left in a great measure dependent on the kind of evidence already quoted in its favour, the tallying with the special facts of the operation of light. The first attempt to penetrate the mystery of nervous action was Hartley’s hypothesis of vibratory propagation, based on the analogy of sound. The comparison was crude and un- satisfactory ; but there was a certain amount of likeness, and the inferences founded on that were admissible. It realized the fact of influence conveyed inwards from the nerves to the brain, and outwards from the brain to the muscles, thus suggesting a circle of action, which circumstance alone is pregnant with valuable conclusions, as appeared after the discovery of Bell gave new vigour to the conception. The vibratory mode of communication had no relevance, and any conclusions drawn from it were unsound. Next came the analogy to the electric current, which was much-closer to the facts, more fertile in suggestions, and less charged with mis- leading circumstances. By taking liberties with current action, something like the liberties taken with the etber in adapting it for light, we are able to shape a view of nerve force that fits the actual phenomena with remarkable close- ness. A third mode of representing the action has been advanced by Mr. Herbert Spencer, which departs from electri- cal and chemical action and reposes upon the physical property called allotropisin. CHAPTER XVL CREDIBILITY AND INCREDIBILITY. 1. There are propositions supported by a certain amount of evidence, that are nevertheless disbelieved. From some en i 2s Pee CONSISTENCY WITH ESTABLISHED INDUCTIONS. 379 circumstance connected with them, they are pronounced INCREDIBLE. Irrespective of the evidence specifically adduced in favour of a certain fact, we often pronounce it credible or incredible ; in the one case we believe, and in the other disbelieve, under the same amount of positive testimony. We believe, ona slight report, that a fishing boat foundered in a heavy gale ; we do not believe, without much stronger testimony, that a fully equipped man-of-war was wrecked. It was lately rumoured that the Eddystone lighthouse was blown down; every one felt that the rumour required confirmation. 2. The circumstance that renders a fact Credible or Incredible is its being consistent or inconsistent with well-established inductions. In simple cases, this is apparent. That a child initiated in crime by its parents should become a criminal, is credible, be- cause it is highly probable, being the result of a well-grounded induction of the human mind. That sucha child should turn out a paragon of virtue, as is sometimes described in romance, we pronounce improbable and therefore incredible. In the one case we are satisfied with a small amount of testimony, in the other case, we demand very strong evidence. We are thus often led to reject evidence at once on the score of antecedent improbability. We may be in the posi- tion of refusing a large amount of positive evidence ; as when a number of respectable witnesses testify that a man after being immersed in the water for an hour has been resuscitated. It is to be remarked, however, that in all such cases the evi- dence tendered is only probable ; it may have a very high degree of probability, it may be 500 to 1, yet it does not amount to certainty. It fails once in five-hundred-and-one times, and is therefore, in certain circumstances, not safe from rejection. 3. Such well-established scientific inductions, as the Law of Gravity and the Law of Causation, render wholly in- credible any assertion that contradicts them. That Mahomet’s coffin hung suspended in middle air, that a table of its own accord mounted to the ceiling of a room, are facts to be wholly disbelieved. All the alleged discoveries of a perpetual motion, or the rise of force out of nothing, are incredible; they are opposed 350 CREDIBILITY AND INCREDIBILITY, to Causation as expressed under the Correlation or Persistence of Energy. All supposed modes of deriving motive power, otherwise than from solar heat past or present, are incredible. That any medium of force more economical than the combus- tion of coal remains to be discovered is all but incredible. If any one affirms that some change has happened without a cause, we refuse to listen to it. An exception to this rule is sometimes claimed in the case of the human will; but that exception has never yet been established upon evidence suffi- cient to cope with the evidence in favour of the law of causa- tion. The principle laid down by Hume, that nothing is credible that contradicts experience, or is at variance with the laws of nature, is strictly applicable to these completely proved induc- tions. We cannot receive any counter evidence in their case, unless of a kind so strong as to reverse our former judgment and make them out to be mistakes. No mere probability is - equal to this task in regard to the axioms of mathematics, the law of causation, the law of gravity, and many others. That every living thing proceeds from a previous living thing, or as expressed by Harvey—ommne vivum ew ovo, is an induction verified by simple agreement, through a very wide experience ; rendering spontaneous generation, for the present, incredible. It is an empirical law, true within all the limits of human observation hitherto, although we may not be able to extend it over an indefinite period of time. Among facts antecedently incredible, we must rank the spontaneous combustion of a human being, which is totally inconsistent with the constitution of the animal body. It has been alleged by witnesses that the mummy corn of the Egyptian pyramids has been sown and been productive. To a botanist, the assertion is wholly incredible. Seeds two centuries old are so completely changed as to lose their fertility. There appears to be unexceptionable testimony to the prac- tice of the Indian Fakeers, in allowing themselves to be buried for a number of days, after which they are dug out alive. This would be wholly incredible, but for the knowledge that we have of such states as trance, or lowered animation, which dispense with food altogether for a time, and require only the minimum of oxygen. It is alleged by travellers that certain tribes subsist upon earth as food. This is admissible, only on the supposition that the earth contains a quantity of organic products, such eats a wy? COMPARISON OF PROBABILITIES, 881 as starch, sugar, albumen, or their equivalents. That any human being or animal could live upon the purely inorganic matters of the soil is to be wholly disbelieved. The phenomena of clairvoyance are all in the position of antecedent incredibility. That any one should see with the eyes bandaged is at variance with the conditions of vision as established by all the authentic experience of the human race. Yet this has been affirmed by multitudes of witnesses. The testimony of witnesses, however, in such a matter cannot be received. The sole condition of admitting such a fact would be (what has never yet been attempted) a rigorous verifica- tion according to the methods of experimental science. So with the other facts of the same class—prophetic dreams, visions or intimations of events at a distance. These are all opposed to well-established inductions. 4, When a fact with a certain amount of evidence in its favour, is opposed, not to an established induction, but to an approximate generalization or probability, the case is one of computation of probabilities. What is only probable, or approximately true, has excep- tions; an opposite assertion, therefore, may be credited, if supported by a still higher probability, or by a generalization approximating still more to certainty. A fact true ninety- nine times in a hundred is not to be set aside by an opposing testimony correct only nine times in ten. In an age when physical laws were imperfectly understood, when the law of causation itself was not fully verified, the phenomenon of witchcraft stood between opposing probabili- ties. ‘There was no inductive certainty on the one hand, to controvert the mere probabilities of human testimony on the other. ‘The physical knowledge even of Bacon was not enough to render the testimonies in support of witchcraft wholly incredible, although it might have stamped these with inferior weight and cogency. 5. The allegations of travellers as to new species of plants, or of animals, are credible or incredible accord- ing as they affirm what contradicts, or what does not con- tradict, laws of causation or of co-existence. There are certain peculiarities of structure that are involved as cause and effect in the animal system. An animal species must have an organ for receiving aud digesting food, a respirae 882 CREDIBILITY AND INCREDIBILITY. tory organ, a means of reproduction. Any contradiction to these must be absolutely rejected. Next in point of evidentiary force are the typical peculiarities of the order, as the four limbs in the higher vertebrata. An animal of the higher tribes, with both wings and arms, would present an incredible combination ; there might not be absolute incompatibility, but there would be such a departure from the type as experienced, that it could not be received on less authority than ocular inspection fortified against every possi- bility of delusion. New combinations of compatible organs are improbable only in proportion as they have been hitherto undiscovered. Flying fish were improbable, but not to the degree of incredi- bility. The extension of our knowledge of kinds, by showing new variations, reduces the improbability in favour of other kinds, within the limits of compatibility. That a ruminant animal may be found without cloven hoofs is incredible, if these are cause and effect, or effects of a common cause, it is only improbable if they are co-existences without causation. Such a co-existence has been widely verified, but not as yet exhaustively. A late distinguished historian for a long time doubted the fact of persons having lived more than a hundred years. He did not regard the fact itself as absolutely incredible; but in the absence of authentic registrations, and the uncertainty of memory and tradition extending to events a century old, he considered that the improbability of so great an age had not been overcome by sufficient counter probabilities. At length he obtained what he deemed adequate evidence in favour of centenarians. 6. The assertion of a fact wholly beyond the reach of evidence, for or against, is to be held as untrue. We are not entitled to put the smallest stress upon a fact without evidence in its favour, because, from its being inacces- sible to observation, no evidence can be produced against it. To affirm that the centre of the earth is occupied by gold, is for all purposes, the same as a falsehood. On the Great Postulate of Experience, we are to believe that what has uniformly happened in the past will continue to happen in the future; we accept uncontradicted experience as true. But where there has been no experience, we can believe nothing. We are not obliged to show that a thing is not; the burden lies upon whoever maintains that the thing is, BOOK IV. DEFINITION. The processes having reference to the class, notion, or concept, have been already enumerated. The chief are, Classification, Abstraction, Naming eat a view to gener- ality), Definition. The class, notion, or concept as already explained, is a product of generalization. -.It-may be constituted by one common property, as resisting, moving, white, bitter; or by more than one, as house, mind, man. CLASSIFICATION, in its simplest form, follows the identifica- tion of like things; that is, a class is made up of things brought together by likeness. When the mind attends more particu- larly to the points of community, it is said to put forth the power of Ansrraction. A name applied to the class in virtue of the class likeness, is a GeneraL Name. ‘The precise delinea- tion of the likeness by a verbal statement is DEFINITION. The three processes—Classification, General Naming, and Definition—are what we are now to consider. The first- named process, Classification, has a larger meaning than the mere assemblage of things upon one or more points of likeness ; it includes the arts for systematically arranging vast multi- tudes of related objects, under higher and lower genera, as in what are called the three Kingdoms of Nature. With a view to this greater complication, we shall view the whole subject of Classification last of the three. As regards the generalization of the Class, or Notion, in all its aspects, the fundamental principle is stated as follows :— Of the various groupings of resembling things, prefer- ence is given to such as have in common the most numer- ous and the most important attributes. This is the basis of natural or philosophical classifications, 384 CANONS OF DEFINITION, in contrast to insignificant and unsuggestive classifications ; as in the distinction between the Natural and the Linnean systems of Botany. It may be termed the golden rule of classifying. We are often disposed to prefer classes on account of their extent, although the common attributes—the comprehension or connotation, may have dwindled down to a limited and unimportant resemblance. Thus, the class ‘land animals’ is very extensive, with little comprehension; and more insight is imparted by breaking it up into groups, as mammalia and birds, each having numerous and important points of com- munity. The class ‘adherents to a religious creed’ is so wide as to impart very little information respecting the indi- viduals ; the sub-classes Buddhists, Mahometans, Jews, Roman Catholics, Calvinists, each connote a large circle of peculiari- ties. “ CHAPTER L CANONS OF DEFINITION. _1. Definition consists in fixing by language the precise signification—the Connotation—of General Names. Defining does not apply to the unmeaning name. An arbi- trary name used for a particular object as ‘ Sirius’ for a star, ‘Snowdon’ for a mountain, ‘Samson’ for a locomotive, is ex- plained only by showing or indicating the thing.* Nevertheless, from the important consideration already stated (Introduction, p. 6), that even a singular is conceived by the mind as a conflux of generals, Definition becomes eventually applicable to individual things. A particular star, a mountain, a locomotive engine, may be represented and marked off from all other things by a «cries of descriptive names of general signification. For such an operation, how- ever, the name Description is more appropriate. It has been already explained (Part I, p. 71) that a perfect Definition is the whole connotation of the name. Somenotions have one point of community ; some two, three, or four; some @ great many, as the often-mentioned Kinds; the proper and * Hence the maxim of the old logicians, ‘Omnis intuitiva notitia est definitio’—‘ a view of the thing itself is its best definition,’ ris ali RR aca iE iy oad ty 1 aa" _? rd Ms a >” e+e. cya aay FUNDAMENTALS OF DEFINITION, 385 complete Definition must give an account of them all. The singling out of one or two properties, for the mere purpose of discrimination, is not a proper or perfect definition. 2. From the very nature of human knowledge, Defini- tion appeals to the two fundamental principles—Agreement and Difference, or Generality and Contrast. I, Every generality must relate to particulars. II To every real notion, as well as to every particular experience, there corresponds some opposite, also real. This is simply the Law of Relativity or Contrast. As the statement of what is common to a number of parti- cular things, Definition is essentially a process of generaliza- tion; while neither particular things, nor their agreements, have any distinct meaning, unless there be assignable a dis- tinct opposite. The act of Defining, therefore, consists of a generalizing operation, rendered precise at every step by explicit or implicit opposition, negation, or contrast. If, throughout the process of generalization, we avail ourselves of explicit contrast, to render precise both the particulars and the generalities, that one operation would be enough ; defining would be generalizing pure and simple, and nothing besides. But there is often a great advantage gained by viewing, in a separate and distinct operation, the opposite or contrast of the thing defined; and hence we may lay down two canons, or two stages of the process—the first the canon of Generalization, the second, the canon of Contrast or Relativity; or, as Gene- ralization must enter into both, we may call them the Positive and Negative Methods. Taken together they show that Defining is rendered thorough-going, first, by generalizing the Particulars of the Notion propounded, and secondly, by - generalizing the Particulars of its Negative. The method of Defining given in the ordinary works on Syllogistic Logic contains no reference to a generalizing opera- tion. The scholastic definition directs us to assign (1) a higher genus of the thing defined, and (2) the specific differ- ence, or the distinction between the thing and the other species of the same genus (per genus et differentiam). No mention is made of the way of obtaining either the characters of the genus, or the differential characters of the species, Suppose we were to define Chemistry in this way ; (genus) a Science, (differentia) having reference to a peculiar kind of Combination of Bodies, called chemical ;—it is obvious that 386 CANONS OF DEFINITION. to give such a definition we must scan the subjects ordinarily included in Chemistry, and, by generalizing them, find an expression suitable to them all, and to none besides. Hence, the direction to assign the genus and the difference, merely relates to the form of expressing the result of a generalizing operation. Allusion is made, by Mr. Mill, to a mode of defining by * Analysis,’ or by resolving a complex notion into its con- stituent elementary notions; as when we define Hloquence— ‘the power of influencing men’s conduct by means of speech.’ Here, Eloquence is a complex property, resolved into the two simpler properties, ‘exerting influence over men’s conduct,’ and ‘speech.’ If, however, the enquiry was made, how do we arrive at this definition, the only answer would be, by generalizing from the particular examples of eloquent address ; so that, in point of fact, this method, if it be a method, does not supersede the processes of generalization. The analytic statement could, if we please, be thrown into the scholastic form; we have merely to adopt one of the com- ponent notions as a ‘genus,’ and call the others ‘ differentia ;’ influencing of men’s conduct (genus), use of speech (differen- | tia). We might even reverse the notions; ‘speech’ (genus), ‘for influencing human conduct’ (differentia). Thus, neither of these two modes of defining can come into competition with the main circumstance insisted on, namely, that to define is to generalize. On what occasions, the generalizing process may be dispensed with, will be a matter of future consideration. Positive Method. 3. Canon. Assemble for comparison the Particulars coming under the Notion to be defined. By the Particulars are meant, not every individual instance, but representatwe instances sufficient to embrace the extreme varieties. To define a species of Plants, the botanist collects recognized examples of the species, including the widest extremes admitted into it. He compares the several specimens, noting their agreements, until he finds what characters pervade the whole ; these he expresses in suitable language, which language is henceforth the definition of the species. So, in dealing with the higher groupings —genera, orders, and classes—he follows pio ee a \~ a | “q GENERALIZATION OF POSITIVE PARTICULARS. 387 _ the same obvious plan. Likewise, the zoologist and mineralo- gist have, in the last resort, no other method. Further to elucidate defining by the generalization of the positive particulars, we will select examples such as to bring out the difficult situations, and will indicate, in the form of subordinate canons, the modes of overcoming the difficulties, Suppose we have to define a Monarchy. We must begin by assembling instances of every institution that has ever been called by the name: the kings of the heroic age in Greece ; the Spartan kings; the Roman kings; the Persian, Macedonian, Syrian, and Ezyptian kings; the Teutonic king; the kings of modern HKuropean nations; the kings of the negro tribes; the emperors; the reigning dukes, mar- graves, counts, bishops, &c. To these we should have to add the king-archon at Athens, and the king of the sacrifices at Rome—mere relics of the ancient kingly government (Sir G. C. Lewis, Methods of Politics, I. 86). Now, if we confined ourselves to a certain number of these, we should find the common fact of absolute or despotic government; this, how- ever, fails to apply to other instances, as our modern constitu- tional monarchies; and, if these are to be included, the common features are greatly reduced in significance, being, in fact, little more than (1) the highest dignity in the state, and (2) a participation, greater or less, in the sovereign authority. But again, if we look to the two last instances—the king- archon at Athens, and the king of the sacrifices at Rome—we shall not be able to apply to them even the attenuated com- munity just given; there would be required a still farther attenuation, reducing the points of agreement to utter insigni- cance. Now this is one of the most usual situations arising in the attempt to generalize a notion with a view to definition. We must be led in the first instance, by the popular denota- tion of the name; yet, if we abide by that, we fail to obtain any important community of meaning. It is in such a per- plexity, that the golden rule must be called to our aid; we must take some means to form a class upon a deep and wide agreement. If need be, we must depart from the received deno- - tation; leaving out some instances, and taking in others, until we form a class really possessing important class attributes, Thus, in the case of the monarch, we should cut off at once the mere relics of old kingly power. As regards the rest, we should divide the instances between the absolute and the limited monarchies ; there is a large and important community - a 388 CANONS OF DEFINITION. of meaning in the class termed ‘absolute monarchies,’ and — this class should be isolated, and should make a distinct notion in political science. The remaining individuals should be dealt with apart; they (as shown by Sir G. C. Lewis) are far better excluded from Monarchies, and classed with Republics, ‘By including in monarchies, and excluding from republics, every government of which a king is the head, we make every true general proposition respecting monarchies and republics wmpossible.’ In this state of things an operation of re-classing is the indispensable scientific corrective of the popular and received generalities. . . The definition of a Colony would afford a case exactly parallel. Taking together all the things that have ever borne this name in ancient or in modern times —the colonies of the Phenicians, Greeks, Romans, Italians, Spaniards, Portugese, Dutch, French, English—we should find these facts in common, namely, emigrating from the mother country, settling in some new spot, and displacing the previous government, if not also the population, of the place occupied. With this small amount of agreement, there are very wide disparities, and until we narrow the instances, we do not arrive at a large and im- portant connotation or meaning. If, however, discarding the ancient colonies, we make the comparison among the modern instances, we find the important circumstance of a sustained political relationship with the mother country ; which is better expressed by the word dependency. And by sub-divid- ing the class, we can obtain inferior classes, with still more numerous important points of agreement; as, for example, the Canadian and Australian colonies of this country, which exercise the powers of independent legislation, under the least possible control by the home government. | Let us next endeavour to define Food. According to the canon, we assemble representative examples of all the sub- stances ever recognized under thisname. We have before us, the flesh of animals, the esculent roots, fruits, leaves, &ec. We have also a number of substances of purely mineral origin, as water and common salt. Our work lies in generalizing - these, in detecting community in the midst of much difference. _ Were man a purely carnivorous feeder, his food might be generalized as the flesh of animals taken into the mouth, and passed into the stomach, to be there digested and thence to be applied to the nutrition and support of the system. But when we include vegetable and mineral bodies, we must leave out ‘flesh,’ and substitute ‘animal, vegetable, and mineral %y Wi bl ti, veel a aN arate a RULE OF IMPORTANT COMMUNITY. 3889 substances ;’ the other part of the statement being applicable. Even as amended, however, the definition is still tentative, and needs to be verified by comparison in detail with everything that has ever been put forward as food. We must challenge all informed critics to say where the definition fails. Thus, nourishment is afforded by substances absorbed through the skin, which would exclude the medium of the mouth and stomach, and narrow the definition to nourishing or supporting the system. . Again, it is doubted, whether alcohol, tea, tobacco (chewed) really nourish the system. This is a far more serious objection; and the manner of dealing with it will illustrate the principles of defining. In the first place, there may be a contest as to the matter of fact. Could it be shown that these substances do give nourish- ment, support, or strength to the system, the difficulty is at once overcome ; in that case, they fall under the definition. On the contrary supposition—that they do not nourish the the system,—two courses are open. First, we may exclude them from the class ‘ Food,’ and retain the definition. Or secondly, we may include them, and alter the definition. As modified to suit the extension, the definition would be ‘ sub- stances that either nourish or stimulate the system.’ To de- cide between those two courses, we must, as before, refer to the golden rule of classification, which recommends the adherence to a smaller class founded on a great and important community, rather than to a larger where the community of meaning is attenuated to comparative insignificance. Better, therefore, to retain two groups—Foods and Stimulants,— each with its own definition. In that way, we should derive much more information respecting any individual thing de- _signated either ‘ Food’ or ‘Stimulant,’ than if the word ‘food’ covered both. It may be that some substances combine both functions; which would entitle them to be named in both classes. We may notice the definition formerly given of ‘ Axiom’ by way of remarking that a definition is obviously spurious that does not distinguish the given notion from notions already settled. Thus, unless an Axiom bea real proposi- tion, it is not divided from Definitions; and unless it is fundamental within the science, it does not difter from the great body of Propositions so far as employed to prove other pro- positions. ‘The characters proposed are alone sufficient to constitute a separate notion bearing the name. These cases sufficiently exemplify the situation where a 390 CANONS OF DEFINITION. word is extended to denote things that have few or no im- portant points of community. The next example will bring to view a perplexity of another kind. Suppose we seek to define a Solid. Summoning to view, if not all the solids in nature, sufficient representatives of all the varieties compatible with the name—metals, rocks, woods, bones, and all the products of vegetable and animal life denominated solid—we set to work to compare them, and note their agreement. There is little apparent difficulty in this instance. We see that, however various these bodies may be, they agree in resisting force applied to change their form ; so readily does this strike us at first sight, that the case seems scarcely worth producing to exemplify a logical formula, Let us, however, apply the Socratic test—exposing the defini- tion to the cavil of every objector,—and we shall probably soon be told of a grave difficulty. The quality, so very decided in the great mass of instances, is found to have degrees, to shade insensibly into the state called ‘liquid,’ where solidity terminates. Now, at what point does solidity end, and the opposite state begin? Is a paste, a glue, a jelly, solid or not? Is Hamlet right in talking of ‘this too, too solid flesh ? We have here not a mere cavil, but a frequent and serious per- plexity. Many couples of qualities, unmistakeably contrasted in the greater number of instances of them, pass into one another by insensible gradations, rendering impossible the drawing of a hard and fast line. Whoshall say at what moment day ends and night begins? So, there has always been a doubt as to the exact individual that ends the animal series, and is neigh- bour to the beginning of the plant series. Sleeping and waking may have an intermediate state, with difficulty as- signed to either, The great chemical sub-division into metals — and non-metals has an ambiguous border in the substances arsenic and tellurium. In the animal system, the voluntary shades insensib!y into the involuntary. The Greek philosophers displayed to the utmost the in- genuity that lights upon difficulties; and this example did not escape them. They grounded upon it a puzzle named the Soriies, or heap. A certain heap was presented, which was fairly designated small ; it was then increased by very gradual additions; and the spectator was challenged to declare at what point it ceased to be small, and deserved to be accounted large. There is but one solution of the riddle. A certain margin MARGIN OF TRANSITION. 391 must be allowed as indeterinined, and as open to difference of opinion ; and such a margin of ambiguity is not to be held as invalidating the radical contrast of qualities on either side. No one would enter into a dispute as to the moment when day passed into night; nor would the uncertainty as to this moment be admitted as a reason for confounding day and night. We must agree to differ upon the instants of transi- tion in allsuch cases. While the great body of the non-metals can be distinctly marked off from the metals, we refrain from positively maintaining arsenic and tellurium to be of either class ; they are transition individuals, the ‘ frontier’ instances of Bacon ; in that position we leave them. There is a margin of transition in the ethical distinction of Reward and Punishment. ° In the great part of their extent, these two motives are amply contrasted; to bestow a reward for performance, is a different thing from inflicting punish- ment for non-performance ; and the withholding of a reward is not confounded with punishment Yet circumstances arise when the one merges into the other. ae 4° yee whe. 452 LOGIC OF PHYSICS. MOLAR PHYSICS. Divisions of the Subject. 2. The Abstract Branches, comprising Motion and Force in general, and susceptible of Deductive and Matha, matical treatment are these :— Mathematics of Motion —Kinematics. Forces (1) in Equilibrio —WStaties. Forces (2) causing Motion—Dynamies. The Concrete Branches are— Mechanic Powers and Solid Machinery. Hydrostatics and Hydro-dynamices. Aerostatics and Pneumatics. Acoustics. Astronomy. Notions of Molar Physics, 3. In Physics, are pre-supposed the Notions (as well as the Propositions) of Mathematics. Only those special to the science are here reviewed. Motion—fest.—This antithetic couple is the fundamental conception of Physics, and is probably an ultimate experience of the human mind. We obtain the idea of Movement by a peculiar employment of our active energies, assisted by sen- sation. We also obtain a knowledge of the varieties of move- ment—quick, slow, uniform, varying, straight, curved, con- tinuons, reciprocating, pendulous, wave-like, &e. The modes that depend upon degree, or Velocity, are part of the ultimate experience of motion as such ; those characterized by shape or Form have a property common to mere extension. Force.—-This is without doubt the most fundamental notion of the human mind; in the order of evolution, it concurs with, if it is not prior to, both motion and extension. It cannot be defined except in the mode peculiar to ultimate notions. The feeling that we have when we expend muscular energy, in resisting or in causing movement, is unique and irresolvable. Inertia, Resistance, Momentum.—These names designate our experience of force from the objective side, or as embodied in the things of the object world. The occasion of calling forth our feeling of energy when referred to an external factis Re- sistance, Inertness, Momentum, or External Force—all signi- ‘ oe Bt NOTIONS OF MOLAR PHYSICS, 453 fying the same thing. This great fact must be learnt, in the first instance, by each one’s separate experience ; the best mode of scientifically expressing it is a matter for discussion. Matter is Hxtension, coupled with Force or Inertia. Any- thing extended and at the same time possessing force, either to resist or to impart motion is Material. Mass, Density, Solidity, are derived notions; they are ob- tained by putting together Force and Extension or Volume. The Mass is the collective Force of a body, shown by its degree of Resistance, and also by the amount of Lesistance it can overcome when moving at a given rate. The Density is the degree of space concentration; a given power of resistance, _with a smaller bulk or volume, is a greater Density. Solidity, when not signifying the solid state of matter generally, as opposed to liquid or gas, is another name for Density. Impact is a phenomenon expressed by means of Space or Extension, Motion, and Force. It is one mode of imparting visible or kinetic energy, and is a test or measure of Force. Attraction is definable by Extension, Motion, and Force. It is a mode of communicating Force, distinct from Impact, and in some respects simpler. Among its specific examples are Gravity, Cohesion, Adhesion, Magnetism, Electrical Attrac- tion, (Chemical Attraction). ftepulsion is definable by reference to the same fundamental notions. It also is a mode of imparting or redistributing force, and differs from Attraction only in the way that it changes the relative situation of the masses concerned. It is exemplified in the Expansive energy of Gases in their ordinary state, in the Expansion of Liquids and Solids from rise of temperature and after compression (called Elasticity). The Polar Forces—Magnetism, Hlectricity, &c., exercise, along with Attraction, a counterpart Repulsion. By still farther combining these primary notions, we obtain —Hquilibrium, Composition and Resolution, Resultant, Virtual Velocity, Centripetal, Centrifugal, Tangential force, Projectile. To Mechanics belong Specitic Gravity, Centre of Gravity, Stability, Oscillation, Rotation, Percussion, Friction, Mechanic Power, Machine, Work. In Hydrostatics, occur Liquid, Liquid Pressure, Liquid Level, Displacement, Flotation, Column of liquid. In Hydro-dynamics, Liquid Motions, Efflux, Discharge, Liquid Waves. In Aerostatics and Pneumatics, Air, Atmosphere, Expansion of Gases, Flow of Gases, Undulations, Atmospheric pres- sure. 454 LOGIC OF PHYSICS. In Acoustics, Sound, Pitch, Timber, Vibrations, Noise; Note, Echo, Harmony. In Astronomy, Sun, Planet, Satellite, Comet, Aerolite, Bolid, Star, Nebula, Orbit, Ecliptic, Year, Month, Day, Eclipse, Pranait, Parallax, Aberration, Right Anpeniiolig Declination, Eccentricity, Node, Apside, Per ihelion, Perturbation, Libration, Precession, N atadioin Tides. Propositions of Molar Phystes. 4. These are of the following classes :—(1) The Indue- tions of Force and Motion; (2) ‘Vhe Deductive Propria asserting the quantitative relationships of Motion and Force; (3) Empirical laws of the concrete phenomena. (1) The great Inductions, commonly called the Laws of Motion, are the axioms of the science. These will be con- sidered afterwards. They are all quantitative in their expres- sion. Another fundamental Induction is the Law of Gravity. (2) The science being pre-eminently Deductive, its proposi- tions are for the most part deductions from the axioms. Such are—the propositions of the Composition and Resolution of — Motions and Forces; the proposition called the ‘law of Areas;’ the principle of the Mechanic Powers; the principles of the pendulum ; the law of liquid pressure ; the principle that con- nects fluid motion with fluid support; the laws of the propa- gation and the reflection of sound. All these matters are stated in the form of real propositions, which, however, may be deduce from the axioms or induc- tions of the science applied to the particular cases as scientifi- cally defined. For example, the law of fluid pressure is a proposition to this effect. ‘At any point in a fluid at rest, the pressure is equal in all directions ;’ the subject of the proposi- tion supposes a fluid at rest, a point taken in it, and considera- tion given. to the pressure; the predicate is ‘ equality in all directions.’ The proof is deductive, and ultimately rests on the axioms of motion and force, together with the definition of fluidity, although the proximate majors are the propositions of the Composition of Forces. Subsidiary to the working out of the science are the propo- sitions «xpressing the quantities of motion, force, &ec., existing in actual things. Thus, besides the Law of Gravity, we have a statement of the numerical amount of gravity at the earth’s surface ; also the relative gravities of different solids and fluids. These numerical propositions are called the “aa ‘DEFINITION OF MOTION. A455 cons‘ants, or co-efficients of the science, and are ascertained by observation and experiment. (3) There are certain empirical laws obtained by observa- tion or experiment. Such are the laws of the Strength of Materials (to some extent Deductive), the laws of Friction, the Motion of Projectiles (partly Deductive), the Flow of Rivers, the Spouting of Liquids, the Compression of Liquids and of Gases, the Diffusion of Sound, the action of Vibrating Strings, &c. These are all real propositions ; they are in their nature propria, or deducible from ultimate principles ; but, in the present state of knowledge, they must be gained by direct experiment. Definitions of Molar Physics. d. As in Mathematics, so in Physics, there are certain properties that are ultimate, and incommunicable by lan- guage ; being known by each one’s independent experi- ence. Nevertheless, it is open to us to consider the best mode of generalizing and stating this experience. The facts named Motion, Force, Matter, are understood only by our concrete experience of the things denoted by the names. But our crude observations may be rectified by more careful comparisons, and may be reduced under precise general state- ments. Moreover, as in Mathematics, we may select the aspect most suitable as a point of departure for our deductive reasonings. Definition of Motion.—Of the fact of motion no knowledge can be imparted; there is nothing simpler to express it by: ‘change of place’ is not more intelligible than ‘ motion.’ We must assume that each one understands motion both generically, and in its degrees (capable of numerical statement); and also in such simpler modes as straight or divergent. The more complex movements are then definable. Velocity means degree of motion. The only thing needing to be expressed formally is the measure of Motion or Velocity with reference to Space and to Time; these last-named elements being presupposed as themselves intelligible. Matter, Force, Inertia. These are three names for substan- tially the same fact. At the bottom, there is but one experi- ence, although varied in the circumstances, namely, the experience of putting forth muscular energy in causing or in resisting movement. To this experience we give the names Force and Matter, which are not two things but one thing; 456 | LOGIC OF PHYSICS, of which Inertia is merely another expression. It is pure tautology to define one of these terms by the others ; matter is nothing except as giving the experience called also force; force is only revealed by matter moving, or obstructing movement. Matter, however, affects us in other ways than by the mus- cular feeling of resistance or of expended energy. It is always extended, and in most cases visible, and also tangible. Are we not, then, to include these facts in the definition? No, and for these reasons:—(1) Extension is not confined to matter; it belongs also to empty space; therefore, though a predicate of all matter, extension is not the exclusive charac- teristic of matter. (2) Visibility and Tangibility belong to many kinds of matter, but not to all matter; hence, these properties cannot be the defining characters of matter in general, or of all matter; they are to be reserved as properties of the kinds of matter wherein they occur; solids and liquids, for example. Accordingly, the only fact occurring in all matter is the fact expressed by resistance, force, or inertia ; all which are names for a single phenomenon. This phenome- non, when fully examined, and generalized to the utmost, has two different aspects, which we may separate in expression, but cannot separate in nature ; the one is the resistance to move- ment by bodies, whether at rest or in motion, and the other, the imparting of movement or momentum by being in motion, The first aspect of resistance is the more popular meaning of inertia ; the second aspect, the imparting of movement, is the popular view of force; but in the scientific consideration of the subject, these are but one property. The definition of Matter and of Inertia, or Inert substance, is, therefore, but one. It generalizes our familiar experiences of resisting motion and of communicating motion, which always concur in the same thing. Fully expressed, it amounts to the statement given in the First Law of Motion. We are entitled to lay down as the fundamental or defining attribute of matter, in whose absence matter is not, that if once at rest it remains at rest, and if once in motion, it continues moving in a straight line. To put it from rest to motion, moving power must be employed; to arrest its course, matter, either in motion or at rest, must be opposed to it. All this is involved in the very meaning of matter, We cannot divide these expressions, and assign one as the defining mark of matter, and the other as a predicate distinct from the defini- tion. No one has ever succeeded in constituting a REAL proposition out of these properties. The appearance of a real a: - se DEFINITION OF MATTER, 457 3 proposition could be given only by assuming as the meaning of matter the imperfect view entertained by the unenlightened mind (which, owing to adverse appearances and imperfect knowledge, does not fully recognize the persistence of moving matter), and giving as the predicate the scientifically recti- fied generalization of matter; but when this generalization is attained, it is wholly embodied in the definition of matter; it cannot furnish one fact as a defining property and reserve another as a predicate. There is a definition of Inertia; there is no law. Thus, then, the persistence in a state of rest or in a state of uniform rectilineal motion, is the meaning of Inertia, and of Matter in general; in which meaning there is an unavoidable implication of active resistance, and active communication of motion. The difficulty is to find an expression to comprehend all these aspects of one indivisible property. Matter at rest operates at one time in dead resistance, at another time in using up force by itself passing into motion ; matter in motion may resist movement, or it may generate movement; but, these are not a plurality of properties ; we cannot suppose one of them separated from the others. The definition employs - plurality of phrases in order to encompass a unity. Matter and Inertia being thus defined by one stroke, Force is merely another reference to the same fact. Inert Matter in motion is the most characteristic expression or aspect of Force, and is adopted as its numerical measure; but we cannot ex- clude from the idea the consideration of matter at rest. In measuring force by moving matter, we mean matter transferred from rest to motion, or from one rate of motion to a quicker ; this is force as generated. Again, the force is manifested in the abatement of the motion, in reducing bodies to the state of rest; this is force as expended. As there is but one fact underlying Matter, Inertia, Force, so there is but one measure. A larger quantity of matter, or inertia, is the same as a larger expenditure of force to change the matter from rest to a given pace of motion. The ultimate measure is the human consciousness of expended. energy. There is a palpable impropriety in the expression, given as a law,—‘ The amount of inertia increases with the quantity of matter ;’ the two properties stated are but one fact. To sum up. Hach person by their own experience must become acquainted with the concrete examples of matter and force. A comparison of all varieties of the phenomenon re- veals the presence of a common feature, at bottom one and 458: LOGIC OF PHYSICS. indivisible, but variously manifested as resistance, as a source of movement—as persistence in rest or in uniform rectilineal movement. To this many-sided unity, we give the names Matter, Inertia, Force, which have a commen definition and a common estimate: The word Matter is the concrete name, while Inertia and Force are the asbtractions for what is com- mon to all matter. Mass, Density.—Mass is the quantity of matter, measured in the mode already described, namely, by the expenditure re- quisite to change the body’s state by a given amount. When the Mass is given, and also the volume, or bulk, we obtain the Density. Volume and Mass rightly precede Density, in order of definition. Messrs Thomson and Tait make Density pre- cede Mass. Momentum means quantity of motion; its measure is the mass multiplied by the velocity. The unit quantity of motion is some unit of mass, multiplied by a unit of velo- city. Mass is usually estimated by weight, but this is to anticipate the consideration of gravity, which should be ex- cluded from the elementary definitions of motion, matter, and - force. The defining of the notions following on these—Impact, Attraction, Repulsion, Gravity, Cohesion, &c.—presents no logical difficulties. They are all derivative notions, their elements being the above named primary notions coupled with those of mathematics ; and they are defined as such, although concrete examples may be given to aid the understanding of the more difficult abstractions. Thus, Impact is the transfer of force from one body to another by momentary concourse; the direction communicated being the direction possessed. Attraction is the continued gene- ration of moving force shown in the mutual appreach of two bodies ; Repulsion is the generation of force leading to the mutual recess of bodies. Gravity is the attraction inherent, persistent, and unchangeable in all matter, being proportioned to the mass, and extending to all distances, at a uniform rate of decrease. Axioms of Molar Physics. | 6. The chief axioms of the science are usually stated under the titleh—Laws of Motion. } In the statement of these laws verbal and real proposi- tions are confounded. | NEWTON'S LAWS. OF MOTION. 459 - Newton’s First Law—‘ Every body perseveres in its state of rest or of uniform rectilineal motion, unless compelled to change that state by impressed forces ’—is merely the full expansion of the definition of matter, inertia, or body. It no doubt expresses more than the vague unscientific notion of matter, but no more than is absolutely inseparable from matter. It isa verbal and not a real proposition—a definition disguised as a proposition. ‘Body’ means what Newton pre- . dicates of it; withdraw from ‘body’ all that the law affirms and implies, and there would be nothing left. If a body did not persevere in its state of rest or motion, until disturbed by another force, it would not possess the most elementary con- ception that we can form of body, the property of resistance, Of the various modes of exhausting the aspects of body, matter, inertia, force, it may be doubted whether Newton’s is the most felicitous. At all events, the attempt would succeed better, if the statement were in the only legitimate guise—a Definition. Newton’s Second Law is—‘ Change of Motion is proportional to the impressed force, and takes place in the direction of that force.’ This law assumes the fact of the communication or transfer of motion, and affirms, although not in the best manner, the quantitative equivalence of the motion given with that received. The Third Law is—‘To every action there is always an equal and contrary re-action; or the mutaal actions of any two bodies are always equal and oppositely directed.’ More shortly expressed thus—‘ Action and Reaction are equal and contrary.’ Objections have often been taken to the word * Re-action’ in thislaw. The meaning put upon it by Newton is gathered from his own illustrations. His examples are of two classes. The first puts the case of impact, as in pressing a body, or in drawing it by some solid medium as a cord or a rod. There is, to say the least, great awkwardness in repre- senting the communication of force by impact, in these terms : —‘ when we push a stone with the hand, the hand is pushed back by the same force as the stone is moved forward ;’ or ‘a horse towing a boat is dragged backwards by the same force as the boat is dragged forwards.” The more natural expres- sion is that when one moving body gives motion to another, it loses exactly the energy that it communicates; or that on the re-distribution of force or moving power nothing is lost. Now, if there be any real affirmation in the Second Law, it is this and nothing else. 460 LOGIC OF PHYSICS, _ The other class of examples given by Newton comprises a distinct case, and the only case that gives the appearance of propriety to the word ‘ re-action.’ It is the communication of movement by distinct attraction (or repulsion). When one body attracts a second, the second equally attracts the first ; the attractions are mutual and equal; the momenta produced are exactly the same in each. This is a fact of great import- ance in nature and deserves to be singled out; indeed, it is the only case of communicated momentum where the result is _ unaffected by disturbances that interfere with exact calcula- tions. Now this is to be regarded as a separate induction. It is fully consistent with the principle of the conservation of energy, under re-distribution, as represented by impact, and has some inherent probability in its favour, but still requires the confirmation of experience. Ingenious reasons might be given, why no other result should arise, but there is no infallible deductive cogency in applying the Law of Conser- vation, founded on impact, to the equality of mutual attrac tions. Searching thus through the three Laws of Motion, we encounter only one principle—the principle of Conservation of Force under re-distribution. The second law has no mean- ing but this. That ‘change of motion is proportional to the impressed force’ with difficulty escapes from being a verbal proposition, for there is no other measure of force but ‘ change of motion,’ imparted, or impartible movement. The assertion would have no reality but for the circumstance that a moving body encounters another body and changes the state of that other body—urging it to move or arresting its movement. This is a supposition not made in the bare definition of force; and, therefore, we do something more than repeat the defini- tion, when we affirm that the force imparted to the second body is lost to the first. Now, this is all thav the Third Law contains; only that law brings into prominence the distinct case of force arising by attraction or repulsion at a distance. Discarding, therefore, the present First Law, as being but the definition of Inertia, we may condense the second and third into a single statement declaring the Conservation motive Energy, under re-distribution, whether by impact, or by attraction or repulsion. This is the one axiom of the Science; its foundations are inductive. It is a partial statement, applicable to molar forces, of the all-comprehending law of the Conservation of Force. Indeed in the limitation to molar ONLY ONE LAW OF MOTION. 461 force, the principle is not strictly true; it is true with regard to attractions and repulsions, and hence in Astronomy no error is committed in applying it; it is not true of impacts ; there is always force lost in a mechanical collision, or in the transfer by machinery ; the lost mechanical energy re-appear- ing as molecular vibration or heat. Newton’s second law has been considered as a way of pro- viding for the case of the communication of movement to a body already moving in some other direction. A force impel- ling in any direction will accomplish its full effect in that direction, even although the body should be already in motion in some different direction ; as when a ship sailing in a westerly current is propelled by a north wind. This is the foundation of the law of composition of Motion and Force, but it is still only an application of the principle of Conservation of Energy under re-distribution. Direction as well as amount _are included in the principle; a body moving in a certain direction and imparting motion, imparts it in its own direc- tion, and in no other. Before affirming the Law of Conser- vation in its full generality, we are bound to verify it for this case as well as for mutual attraction; it has been verified, and is affirmed accordingly. The so-called ‘Principle of Virtual Velocities’ is a hypo- thetical expression of the Law of Conservation suited to various mechanical applications, such as the demonstration of the mechanic powers. We cannot prove the statical proposi- tion of the lever, without supposing it to move. Dynamically the law of the mechanical powers is the only one consistent with the Conservation of Force; and the dynamical proof is given as the statical by the supposition of a very small motion. 7. The second great Induction of Molar Physics is the Law of Gravity. The Law of Gravity associates the two distinct properties— Inertia and Gravity, and declares the one to be proportioned to the other, throughout all varieties of matter. The Law is sufficiently expressed thus :—LEvery portion of matter attracts every other portion, the attraction in each being in proportion to the mass (or inertia), and inversely as the square of the _ distance. This Law has been frequently referred to, in previous parts of this work, as the one unequivocal case of two co-extensive properties, constitut'ng a proposition fully reciprocating, and convertible by simple conversion. ee wee ae 462 LOGIC OF PHYSICS. Our unit of force (so much inerta acting through so much space) is thus the unit of weight, say a pound, moved against gravity through the unit of space, say a foot. Concatenation and Method of Molar Physics. 8. The branches of Molar Physics follow a Deductive arrangement. The Abstract departments are purely deduc- tive ; the Concrete unite Deduction with Experimental determinations. | The great division into Statics and Dynamics—Kquilibrium and Movement—exhausts the abstract portion of the subject. These are thoroughly mathematical in their structure; the propositions and demonstrations are worked out according to Geometry, Algebra, or the higher Calculus, respectively. A preliminary mathematical department is constituted, which has been termed ‘ Kinematics,’ containing propositions that assume only the fact of Motion, together with mathematical elements. The Composition and Resolution of Motions, under every possible variety of complication, are mathematically de- veloped under this branch ; it being also applicable to Optics. The theorems are then found to be transferable to Statical and to Dynamical Problems, which regard Motion as the result and the essential fact of Force, whose full expression includes as factors the Velocity and Mass. The Concrete Branches are :—I, The Mechanic Powers, and Machinery generally (fluid action not included). Here there is an application of the deductive laws, but these have to be modified by the molecular structure of bodies; and the modifi- cations are ascertained experimentally. The laws of friction, of stress and strain, of molecular transfer in impacts, &e., are the subject of experiment almost exclusively. Where deduc- tion is applied, it must be submitted at every step to experi- mental confirmation. . IL. Aydrostatics and Hydro-Dynamics, or abstract Statics and Dynamics applied to Liquids. There is here also the employ- ment of experiment to find ont the modifications of dynamical _ laws due to the molecular structure of liquids. There is a farther use of experiment, in aid of the deductive process itself, which is apt to be foiled by the complications of fluid mobility. III. Aerostatics and Pneumatics comprise the treatment of gaseous bodies, to which the foregoing remarks also apply, IV. Acoustics treats of vibrations of the air and other bodies, - CONCRETE DEPARTMENTS OF MOLAR PHYSICS. 463 constituting the agency of Sound. Here we have the transition from the molar to the molecular; but the mode of dealing - with the phenomenon (through the similitude of pendulous and wave motions) has close alliances with the preceding molar branches. In this department, however, j OmPAEIOS predominates over deduction. VY. Astronomy might be taken either first or last among the Concrete branches. It departs the least from abstract Statics and Dynamics; which is owing to the purity of the gravitating force ; there being no friction and, in the celestial region, no resistance. It is deductive throughout; yet, owing to the great mathematical difficulties, the deductions must be checked by continual observation; while to observation alone we owe the knowledge of the co-efficients or constants, In Astronomy, there are various problems that draw upon the other concrete branches of molar physics, and even upon molecular physics ; so that the position of priority among the concrete branches has to be qualified. The tides, the physical constitution of the sun and the planets, the theory of solar and planetary heat and light—are examples of these far-branching portions of the subject. MOLECULAR PHYSICS. 9. In Molecular Physics, the phenomena have reference to the action of the component molecules of matter. The chief subjects are— Molecular Attractions—Cohesion, §e., Heat, Tight, Hlectricity. The primary assumption, axiom, or induction of Molecular Physics is to the effect that the masses of matter are composed of small particles, atoms, or molecules, attracting or repelling each other in various modes, and possessing intestine motions. This is a real proposition respecting matter, and not a mere repetition of its defining property—Inertia. It is pre-emi- nently hypothetical in its character ; that is, the evidence for it is only the suitability to express the phenomena open to the senses ; as, for example, the solid, liquid, and gaseous forms of bodies, the heat or temperature of bodies, luminous and electrical effects. tt se Aa St ee ae 464 LOGIC OF PHYSICS, Notions of Molecular Physics, Molecule, Atom.— It is known asa fact that every kind of | matter is made up of very minute portions, called atoms or. molecules; the limit of minuteness being hitherto unascer- tained. By supposing attractions and repulsions between the atoms, we can represent the varieties of solid, liquid, and gas, as well as the imponderable forces—heat, &c. The phenomena, however, require that there should be different orders of atoms or molecules; the ultimate atoms being grouped into complex atoms, and those again, perhaps, into still higher com- pounds. Thus, the Cohesion atom, the Heat atom, the Chemical atoms, the Solution or Diffusion atom, are all hypothetically distinct, the assumptions being varied to suit the appearances, The definition of the atom or molecule,* therefore, is hypo- thetical and fluctuating ; the only constant assumption is a very minute element gifted with attractions and repulsions, by which is brought about the aggregation into masses. Motecunar Arrractions—Propertizs OF Marrer. Nume- rous important notions arise out of this department of Physics, — which discusses the various modes of aggregation of material masses, and their causes, real or hypothetical. Solid, Liquid, Gas.—These names for the three states of matter, have already occurred under Molar Physics, and must there have been defined up to a certain point. The exhaustive definition of the various forms of solidity falls under Molecular { Physics. I shall indicate, for ulterior ends, what seems the best arrangement or succession of the properties of Solids, Crystal.—Antithesis of amorphous. The crystal is not difficult to define. The common fact is a regular and constant geo- metric form as determined by the angles of the faces or boundary planes. A substance, for example, always found in cubes, or with right-angled solid angles, is a crystal; a sub- stance that has no regular or constant form is amorphous; such isa cinder. Subsidiary to the main idea, are the notions —face, axis, nucleus, cleavage, fracture—and the several systems * Although the adjective ‘ molecular’ is usedin the broad contrast with the molar, while the substantive ‘molecule’ also conforms to the usage, a more specific meaning has lately been attached to the mole. ule, in con- tradistinction to the ‘atom.’ An atom is supposed to be chemically indi- visible ; a molecule is the smallest combination believed to exist separately. There is a hydrogen atom represented by H; but the hydrogen molecule is HH, or Hy. The molecule of Phosphorus and of Arsenic is each composed of four atoms. All this belongs .v the hypothetical part of Chemical Combination. a MOLECULAR ATTRACTIONS. 465 of crystals—Tesseral, Tetragonal, &c.; also Isomorphism, Dimorphism, Allotropy. Hard, Hlastic, Tenacious, Ductile, Malleable. These are names for a series of important attributes of solid bodies, to which there is a corresponding series of contrasting properties —soft or flexible, inelastic, brittle, inflexible, inductile or wnmal- leable. They are mostly distinct properties, althongh to some extent related. They are all strictly definable, and measurable in amount or degree by given tests. Hardness is the resistance to change of form, as by scratching or dinting; Elasticity is the rebound from compression. Tenacity is opposed to being pulled asunder. JDnuctility is tenacity under the process of being drawn out into wire; if the hammer is employed, the substance is called Malleable. Viscosity is a softness approaching to liquidity. ‘ All bodies capable of having their form indefinitely altered, and resisting the change with a force proportioned to the alteration, are called Viscous Bodies.’ (J. Clerk Maxwell). Cohesion (Homogeneous attraction). Definable as the mutual attraction of particles of the same substauce, as iron, flint, or ice. The crystalline structure, hardness, and other qualities in the previous enumeration, may be expressed as different degrees and modes of cohesive energy. Cohesion is therefore the hypothetical summary of the properties just named; and its modes are to be accommodated to represent these with accuracy. A crystal must have one mode of cohesion, a lump of clay, a different mode. The limits of cohesion are small; two pieces of plate glass will adhere strongly if in close contact, but will not attract one another through a sensible distance. Adhesion (Heterogeneous attraction). A wide-ranging phe- nomenon. It is defined — the attraction of particles of one substance for particles of a different substance, as when glue sticks to wood, mortar to stone, water to wood, &c. Cements, Capillary action, Solution, Absorption of Gases, Alloys—all suppose this mode of action. To express the full details— which substances attract which, and with what degrees of foree—requires a great many propositional statements, mest conveniently given in the mineral or the chemical description of each substance. Under the present head, the general results should be presented. Diffusion, Osmose.—These are properties extending beyond what is implied in solution, and even anticipating Chemical processes. Still, they are the immediate sequel to the preced- 466 LOGIC OF PHYSICS, ing group of phenomena. Their definition is a generaliza- tion of the phenomena brought to light by the researches of Graham. Crystalloid, Colloid, Dialysis.—By extending the application of Osmose, Graham arrived at a distinction among bodies, expressed by the antithesis—Crystalloid and Colloid, whose definition is in the highest degree pregnant with important attributes. (1) The colloid state is a mode of the anti-crystal- line or amorphous modification of matter. (2) The colloids are inert chemically, they are not powerful as acids or bases. (3) In their own form, they have peculiar powers; as soft and semi-liquid they allow other substances to diffuse in them. (4) Still more important is their instability, their readiness to pass into change, and gradually to sink down towards the deadness and fixity of the crystal ; during which process they are sources of molecular power. These two last peculiarities fit them to play a part in living structures, into which they enter largely as constituents (albumen, fibrine, starch, &., are colloids). (5) Colloids, while permeable by bodies of the erystalloid class, as salt and sugar, are impermeable to each other; a most important law, on which Graham has founded his method of Dialysis, and which is the explanation of many interesting phenomena. LH ffusion, Diffusion, and Transpiration (of gases).—These are the phenomena parallel to the foregoing as manifested in gases ; they have a modified definition accordingly. Such is an orderly statement of the great leading notions of the initial branch of Molecular Physics. They all demand strict definition, and a separation of defining properties from predicated properties, according to the best logical method. Descending into the very depths of molecular action, they un- avoidably anticipate other parts of molecular physics, and even of Chemistry ; but this is not avoidable by any arrangement. The priority of position is justified by the circumstance that Cohesive Force is the inalienable attribute of all kinds of matter, and is the counter-force to the great total of Huergy expressed by the Correlated Forces- Heat, &c. Matter is what we find it, on the one hand, through the opposing play of internal cohesions, and on the other hand through the repulsion derived from the transferable energy of the universe. It is as Heat, Electricity, and Chemical Force, that this energy ab extra counter-works internal cohesion; just as, in the capacity of mechanical energy, it counter-works Gravity on the great scale of molar movements, . DEFINITION AND PROPOSITIONS OF HEAT. 467 -Heat.—The next department in order is the primary and the typical form of molecular energy, in the great circle of Conserved or Persistent Forces. The leading notion—Heat itself is the only one attended with logical difficulties of defi- nition. Properly speaking it is an ultimate, indefinable, in- communicable notion, and its essential character is subjective. Hach of us must be referred to our own sensations of heat and cold in their different degrees, which sensations are unique and not to be confounded with any uvthers. Nor is there any perplexity in generalizing the particulars, with a view to a comprehensive definition, as there is with matter and inertia ; he that has one or a few experiences of change of temperature knows all. The physical or objective counterparts of this unmistakeable subjective experience are numerous and various, and Lelong to strictly physical investigation. The most obvious are the increase of bulk by warmth, and the so called destruction, (more properly re-construction) of material masses. A great and protracted effort of generalization has been requisite to encompass all the manifestations of this physical correlate of a familiar feeling, and to embrace the whole in a unity of expression. Hven at the present moment, the generalized unity rests upon a hypothetical assumption, true in the main fact, but uncertain in the shaping, and as yet imperfectly adap- ted to the multiplicity of the thermal phenomena. Heat, physically, is a mode of molecular motion, exchanging at a definite rate with mechanical movement, as well as with the other molecular modes termed Electricity and Chemical force. If we define Heat by its subjective phase, the great physical generalization is a predicate of concomitance, constituting a real proposition. If we use the subjective fact merely as a clue to the objective, and insist on making the definition ob- jective, this property is then the defining property, from which would flow innumerable deductive attributes (propria); while there would be propositions (either propria or concomitants) affirming the relationships of heat to other forces, and also the material collocations or arrangements connected with the transmutation. The notions involved in the various phenomena of Heat, give the heads of the science ; they are all definable by generaliza- tion, and their elucidation needs abundant reference to facts in the concrete :—Conduction, Convection, Radiation, Reflexion, Absorption, Diathermacy, Refraction, Specific Heat, Latent - Heat, Melting, Freezing, Evaporation, Condensation, Kbull- 468. LOGIC OF PHYSICS. tion, Boiling Point, Distillation, Tension of Vapour, Dew Point, Heat of Combination, Calorific equivalents. Licut.—The exact position of this subject in a athiot hy studied arrangement of topics is somewhat dubious. In some important points, it has a close alliance to Heat; its manifesta- tion in a body is almost always dependent on a certain temperature. Moreover, as an influence radiating through space, it has not only great similarity to heat, but also is singularly open to mathematical treatment. Still, being as — yet imperfectly understood in its reciprocation with the cor- related forces, it does not stand to heat on the same footing as electrical and chemical force. But for the close and easy transition from Electricity to Chemistry, we might put Light at the end of Molecular Physics. Or, as haying abstruse chemical relationships, it might succeed to Chemistry. Thus, the position actually accorded is owing to a seeming prepon- derance in favour of one out of several alternatives. Light, lke heat, must have a subjective definition to start with ; and, in this view, it has the same freedom from ambi- guity. But as Sight isa highly objective sense, we can incor- porate with the subjective property the objective particulars —radiation and transmission in space—which are revealed at once to the luminous sensibility. We may give the definition thus :—Light expresses a dis- tinct state of mind known only to individual self-consciousness, to which state is added the ‘objective experience of an emana- tion from a material body to the eye, whereby we become cognizant of the characteristic properties of matter named visible. The subsidiary notions are the main topics of the science :— Transparent, opaque, translucent, shadow ; Incidence, Refrac- tion, Index of Refraction, Tisai) Image, Reflexion, Mirror, Caustic, Focus, Colour, Spectrum, Complementary Colours, Dispersion, Chromatic Aberration, Diffraction, Rainbow, Double Refraction, Polarization, Interference, Undulatory Theory. So far as these topics are concerned, the science of optics depends upon no extraneous source beyond Mathematics, and might have precedence of all the other subjects of molecular physics. The connexion of Light with Heat, with Electricity, and with Chemistry, would then fall under these peneae departments. Brecrrictry.—As the denotation of Electricity takes in— Magnetism Voltaic Electricity Magneto-Electricity Friction Electricity Electro-Maenetism Thermo- Electricity— aya eae CHARACTERS OF ELECTRIC FORCE, 469 it is no easy matter to find an exact connotation for the general name. Two properties may be put forward: (1) Polarity, and (2) Current action. As regards the first, Polarity, there is uniform agreement in all the modes; and, moreover, the polar attribute is prominent and pervading, and imparts a destinctive character to all the phenomena. Still, in carrying out the idea, we are met by the ambiguous phe- nomenon, named by Faraday, Diamagnetism, a force mani- fested by the magnet upon heavy glass and certain. other substances, but without polarity, being equal repulsion by both poles. This phenomenon, however, must be held in suspense in the meantime, and not allowed to interfere with the defini- tion on so vital a point. The second characteristic of the Electric Forces, is their being carried to any distance, through solid conductors, so as to discharge themselves at any point. In ordinary chemical action, as in the double decomposition of two salts, the sub- stances must be in contact ; but by an electrical arrangement, the oxidation of zinc in one vessel, may lead to the decompo- sition of water in another. This important point of commu- nity makes a strong alliance, although with differences, between the electric forces. These two leading features, coupled with subjection to the great Law of Conservation, are all that can be at present brought under the connotation of Electricity asa whole. The different branches have each their special definition, attainable by the same generalizing process. Definitions are also to be provided for the subsidiary notions—Magnetic Poles, Meri- dian, Declination, Inclination ; Electrics, Non-Electrics, Con- duction, Insulation, Circuit, Induction, Charge, Discharge, Electrica] tension ; Electrolysis, Electrodes. Propositions of Molecular Physics, Axiom of Conservation of Force.—At the threshold of mole- cular physics, there must be provided a staterhent of the Law of Conservation, in all its compass, or as embracing alike the molar and the molecular forces. Although the law cannot be fully comprehended at this stage, yet some attempt should be made to exemplify its workings as Heat, as Hlectricity, and as Chemical force, and also to point out the mutual conversion of all the modes—molecular and molar. The law is the pre- siding axiom of molecular Physics, and of Chemistry, and through them reaches the domain of Physiology. It is every- where the sufficing explanation of the origin of Force ; leaving 470 LOGIC OF PHYSICS. to be investigated, the arrangements, situations, or circum. stances, attending on the manifestation of force in each par- ticular case. Other propositions of Molecular Physics.—The various notions or defining properties being clearly characterized, we may readily ascertain what class of predicates usually go with them so as to constitute the real propositions of the science. Thus, with reference to the first department—Molecular Attrac- tions, or the Properties of Matter, from which are excluded whatever comes under Heat, Electricity, and Chemistry—the atom or molecule being defined, we have, as real propositions, the following: ‘ Matter is composed of atoms,’ ‘ the atoms of matter attract each other.’ This last proposition being one of wide generality, there fall under it many special propositions, or modes of attraction, for different kinds.of matter ; but, in this department, we are perpetually disposed to palm off verbal propositions for real—as in affirming that hard bodies have a powerful atomic cohesion. Hxamples of strictly real propositions are these :—crystals are hard bodies, that is, the cohesion of crystallization is intense in degree; crystals are usually brittle, or the cohesion of crystals is of a short range. Again, with regard to Adhesion, there is an import- ant inductive generalization, that bodies of a nearly sumilar nature are those possessing mutual adhesion; thus metals adhere in solders and in alloys, earthy bodies, in cements and in cohesive mixtures, and so on. Farther, the Diffusive volume of a gas is inversely as the square root of its density. These are propositions of co-inhering attributes, verified only by wide and exhaustive agreement through the whole sphere of the things concerned. | Another large class of propositions under the same depart- ment includes the numerical expressions of the degrees of the | different attributes. These are the constants of the department, and need no farther remark. The propositions of Heat have the reality -arising in the concomitance of subject and object facts. Apart from this, they may be classified under the following heads. The first class takes in the deductions from the law of Conservation, confirmed by observation and induction :—such are the facts of the dilatation of bodies by heat, of which fusion and eva- poration are special manifestations. There is herein comprised a wide field of natural phenomena; and many specific state- ments are needed to cover the variety of modes in different substances. Another class of propositions affirm, in their a ee et PROPOSITIONS OF HEAT. 471 several modes, the great molecular property named Conduction, _@ property with numerical degrees ; while important laws of dependence or concomitance connect this property with the molecular properties of bodies. Radiation next demands to be considered, a fact with geometrical aspects and correspond- ing predicates ; this part of the subject haviug a considerable parallelism to the leading facts of Optics. The specific rates of radiation of different bodies may be numerically ascertained, and laws enounced, whose character is jointly deductive and inductive. Absorption is another predicate, and similar remarks apply to it. The exhaustion of the consequences of the Law of Conserva- ° tion, would require a statement of the mode of deriving heat from Mechanical force (crushing, collision, or friction), and from the other ‘molecular forces; and also the situations or arrangements whereby it returns to these again; the case of producing mechanical force having been given under the great fact of Dilatation. On the whole, propositions of heat are (1) Derivatives from Conservation ; (2) Constants, or numerical measures of the various phenomena for different bodies; (3) Laws connecting manifestations of heat with molecular structure; (4) Laws of situation, or conditions of the transmutation cf Heat, to and from, the other energies, with the constants, expressing the rates of equivalence. The foregoing account may suffice to exemplify the propo- sitions of molecular physics. Were we to proceed to Liaur, we should find a statement of definite phenomena—called radiation, refraction, reflexion, dispersion, colour—all expressed under numerical and geometrical relations. We should also find some cases of concomitance of attributes, as Double Re- fraction and Polarization. The connections of Light with Heat and with Chemical Force, being underivable i om the great Law of Conservation, must be given as empiiical induce tions of co-inhering attributes, some of them of considerable generality, as the connexion of light with temperature; others narrow and special, as in the chemical relations. Execrricity has the advantage of being fully correlated with the other forces. It involves, however, great complexity of arrangements, as conditions of its manifestation in the various species ; whence the propositions are greatly occupied in stating these arrangements or collocations ; many of them being hidden in the molecular depths of bodies, and rendered in hypothetical language. 21 e ees 472 LOGIC OF CHEMISTRY. Predominant Methods of Physics. | 10. Physics has been seen to be partly Deductive, and partly Inductive. The Inductions principally relate to Cause and Effect ; while, in Molecular Physics, there are inductions of Co-inhering Attributes. The principles of Definition are appealed to, and more especially for the primary notions ; but there is scarcely any opening for Classification. As a Deductive Science, Molar Physics is a branch of applied Mathematics, checked and controlled by the perpetual reference to facts. As an Inductive Science, Physics makes an unsurpassed display of the machinery and resources of Observation and Experiment. It also shows to advantage all the Methods of Experimental Elimination. The facts being subject to the great law of Conservation, the deeper experimental problems consist in ascertaining the collocations or arrangements for transmuting or evolving the different modes of force. The researches and discoveries relating to Heat, Electricity, and Light have this character to a very large degree. The Hypotheses of Physics exemplify all the forms of Hy it thesis formerly laid down. The chief instances—the Dynamical Theory of Heat, the Undulatory Theory of Light—have already been adduced in expounding the general subject. Another hypothesis of inferior weight and character is the two Hlec- trical Fluids, for representing the polar phenomena of Eleo- tricity. \ CHAPTER IIL LOGIC OF CHEMISTRY. — 1. The relationships of Chemistry to all the departments of Molecular Physics are intimate and sustained. The special fact of the science is given in the name Chemical Attraction. Chemistry deals with the union and the separation of ae ments ; it regards all the substances of nature as either simples REAL PREDICATIONS OF CHEMISTRY. 473 or compounds; the manner of union or composition being special to the science. There are unions not chemical; as when bodies are pulverized and mixed together without farther intimacy. There is a still more intimate union in solution, which, however, also comes short of chemical union. 2. Chemical Attraction, or Union, involves these facts : (1) The Properties are definite. (2) In the act of union, there is Heat evolved. (3) The chief properties of the elements disappear. A fourth mark, which may either enter into the definition, or be reserved as a predicate, is that chemical union takes place between dissimilar substances, while solution or adhesion is between similars. If reserved as a predicate, this property will be one of the properties forming real propositions, as ex- emplified in next section. It is not necessary here to exemplify these defining proper- ties. Ina work on chemistry, it would be advisable to offer in advance a few illustrative cases, as a preparation for enter- ing on the systematic detail. This disposes of the leading notion of Chemistry, being the essence or connotation of the name, the Definition of the Science. A mistake in Logic is made when these properties are stated as real propositions; they are not predicated of a subject called Chemical Attraction, they constitute or make up that subject. 3. The Propositions, or real predications, of Chemistry relate (1) to the circumstances, or conditions of Chemical change, (2) to the substances that undergo the change. (1) When we have defined the fact of Chemical union, (with its correlative and implicated facts, Decomposition, Simple Body, Compound Body), we have to state the various circumstances, conditions, or modifying influences of Chemical change. This constitutes numerous real predications, of great theoretical and practical moment. (2) The enumeration of substances that combine together chemically, or that bring about chemical decompositions yields _@ large mass of real propositions, under the general predicate of Co-existence, or Co-inhering attributes. Oxygen com- bines with hydrogen, and forms water; sulphuric acid decom- poses chalk, common salt, &c. The expressions for the definite combining numbers are real propositions, corresponding to the ‘constants’ of Physics. 4°74. LOGIC OF CHEMISTRY. The relation of Chemical Force to the other Correlated Forces may be re-iterated at the commencement of the subject ; although, as with the other preliminary statements, the under- standing of it will grow with the unfolding of the future details. Arrangement and Methods of Chemastry. 4. The division of Chemistry is into [NorRGANIC and ORGANIC. Inorganic Chemistry is laid out under the succession of the Simple Bodies. The distinction of Inorganic and Organic would exemplify definition with a broad doubtful margin. The basis of the distinction is the circumstance that a large class of highly important substances can be obtained only from living bodies ; such are starch, sugar, albumen. This peculiarity of origin is associated with two other peculiarities, namely, the limited number of elements in organic bodies, and the great complexity of the chemical constitution. There would be a.convenience in adopting all the three facts as a complex definition of Organic bodies, from which, by antithesis or negation, we have the definition of the Inorganic. The Chemistry of the Inorganic or Mineral world comes first ; and its method of arrangement is to adopt some succes- sion of the Simple Bodies, and under them, to distribute the various Compounds, Classification of the Simple Bodies or Elements. 5. The Simple Bodies, or Elements, are divided, in the first instance, into Metals and Non-Metals. Although there are transition elements, as Tellurium and Arsenic, the distinction is founded on important differences. , The Metals have certain prevailing characteristics, but yet in a varying degree, and with occasional exceptions. (1) Most striking are the visible properties— Opacity, Lustre, and Colour. Metals are opaque; they have thepeculiar lustre termed metallic; and their colour is white or grey, with the exceptions —Gold, Copper, and Titanium P which are yellow. (2) They are solid, Mercury and Hydrogeff being notable exceptions. The solidity is usually joined with compactness of structure, as shown in the properties—hardness and tenacity. (3) They are com- paratively good conductors of Heat. (4) They are conductors — 4 of Hlectricity. (5) They are Ei ectro-positive. (6) They com- wa METALS AND NON-METALS CLASSIFIED. 475 bine chemically with the Non-Metals. (7) Their compounds with Oxygen are for the most part Buses, and not Acids. The question is not here raised how far some of these pro- perties are implicated in others. Since the implication is not obvious, the properties are provisionally given as distinct. A more important remark, from the logical point of view, is the occurrence of exceptions to almost all the properties. In the complex defining of natural objects, we must be prepared for this circumstance, which does not render the classification vain or nugatory. Although mercury is a liquid we neither sur- render the property of solidity, nor exclude it from the class. Solidity is wanting only in two; and mercury has all the other six properties. This is probably one of the cases where Whewell would desiderate a type, or average representative Specimen, some metal possessing in fair measure all the prevailing characters. The Non- Metals are defined by the antithesis of the above group of properties. As regards Light they are not uniformly opaque, and when opaque, they are, except selenium, wanting in lustre. There is only one Gaseous metal, there are four gaseous non-metals. They are non-conductors of Electricity, and Hlectro-negative. Their compounds with oxygen (one of their number) tend to Acids, and not to Bases. _ Whenever aclassification is possible, there must be common properties, and these are possible to be stated. Still, in the usage of Chemical writers, the statement of the generic pro- perties of the classes ‘metal’ and ‘ non-metal,’ does not dis- pense with the repetition of these in the detail of the species. The Natural History methods, not being susceptible of exten- sive application in Chemistry, are hardly attended to, even where admissible. Nevertheless, as the situations arising in the classification of the Simple Bodies are highly illustrative of situations in Botany and in Zoology, we may follow out the present case a little farther. 6. Both Metals and Non-Metals are sub-divisible into smaller classes or groups. In the Metals, there are certain groups that have important affinities—such are the Alkali-Metals (Sodium, é&c.), the _Alkaline-Earth Metals (Barium, é&c.), the Earth-Metals (Aluminium, &ec.), the Noble Metals (Mercury, Silver, Gold, &c.)remarkable for refusing combination. sy : 480 LOGIC OF CHEMISTRY. about one twentieth to one thirtieth of its bulk (.04114 at 32° F.; .02989 at 59° F.), (+) Relations to Heat.—Rate of Dilatation not stated. As regards the temperatures of Liquefaction and Freezing, has never been liquified, although condensed to z}q of its bulk. Specific Heat, about one fourth of water (.24.05). (5) Relations to Hlectricity.—Is a magnet at common tem- peratures. In the Voltaic series, it is at the head of electro- negative elements. (6) Chemical relations.—Speaking generally, it is the most widely-combining element in nature. With a doubtful excep- tion (fluorine), it combines with every known element; not merely its natural opposites, the metals, but non-metals like- wise. Classes of leading importance in chemistry are com- pounds of oxygen with the other elements ; the oxides of the metals are what are termed bases; the oxides of the non- metallic elements are generally acids. With Hydrogen, it yields water. The act of combining with Carbon, either alone, or along with hydrogen, is the most familiar example of violent and rapid chemical union, with evolution of heat and of light, and is termed ‘ combustion.’ The peculiar circumstances attending the combinations of oxygen vary with the character of the second element. Thus,- in the leading fact—Heat of combination—the maximum evolved is with Hydrogen; Carbon yields one fourth of that amount; Phosphorus, about a sixth; Sulphur, about a fifteenth ; Zinc, Iron, Tin, about a twenty-sixta. Atomic number, 16. . As regards the conditions of entering into combination, there is great variety, from the extreme of readiness at the ordinary temperature of the atmosphere, to the extreme of indifference, conquered only by the aids to combination, namely, artificial condensation, heat, the electric spark, the contiguity of chemical action already begun, &c. Part ofthe — peculiarity is due to the state of oxygen itself:—which may be either in the ordinary atmospheric dilution; or prepared apart free from any other gas (whereby all combinations are acclerated) ; or, lastly, in combination with other bodies as in water (a powerful oxidizer); in the nitrates, in chlorate of potash—which salts permit of the liberation of their contained oxygen in a highly concentrated form. Local spread of Oxygen.—Need not be here detailed. Modes of obtaining Oxygen. I doubt the propriety of including, under Oxygen, any more OXYGEN DESCRIBED. 481 detailed account of the oxygen compounds. There are better opportunities afterwards, under the several elements that form the other members of the compounds,—carbon, hydrogen, the metals, &c. Nor is it necessary to bring forward Combustion, of which a sensational use is commonly made, in the descrip- tion of oxygen. A disproportionate prominence is thereby given to what is, strictly speaking, incidental only to some of the modes of oxidation, and is found in other chemical com- binations if they happen to be rapid and energetic. Combustion is a special thesis under the general head— Chemical Union, its conditions, and circumstances—and is of great importance both theoretically and practically, but it need not be appended to Oxygen. If involving too much anticipation of details to be given in the preparatory view of Chemical Combination (where, however, it might be briefly indicated), it might be brought in at some convenient point, by way of digression, as for example, at the end of Carbon, the chief element in ordinary combustion. Ozons.—A supposed allotropic form of Oxygen, under which the oxygen is rendered more active in entering into its various combinations. The specific gravity of ozone is greater than of oxygen. Adhesion.—It is not soluble in water, nor in acids or in alkalies; but it is soluble in iodide of potassium. - Relations to Heat.—Its active character is destroyed by a temperature not much above boiling water. Relations to Hlectricity.—The transmission of a series of electric sparks through dry oxygen is one of the modes of producing it. Odour.—It has a characteristic odour, whence its name.* Chemical properties —While it does not combine with any substance but those that oxygen combines with, it combines at temperatures, and under circumstances where oxygen does not combine. Hence it is a powerful oxidizing agent—ain oxi- dizing metals, in destroying vegetable and animal compounds, in bleaching, in purifying the air from miasmata, in stimulating the respiratory organs. Modes of preparing Ozone. Remarks on Ozone.t—lt is interesting to note the power of electricity to give a new combining aptitude to oxygen. * Taste and Odour may provisionally be given after Electricity, and before Chemical properties. They are doubtless a consequence of Chemi- cal re-actions. 4 The heading ‘ Remarks’ is intended, among other uses, to avoid the A o eg egrey Se 482 LOGIC OF CHEMISTRY. Nirrogey.—A gas. , As regards Light, transparent, colourless; Refracting In- dex, 1.0093. Specific gravity.—.9713. Atmosphere 1. Adhesion.— Water dissolves about a thirtieth of its bulk at ordinary temperatures. Relations to Heat. —Dilatation not stated. Never been liquefied. Specific Heat, slightly less than Oxygen, .2368. Relations to Llectricity—Next to oxygen in the EHlectro- negative series. Chemical relations. —Nitrogen enters into a very limited number of compounds. Where it does combine, it is sin- gularly inert, or indisposed to enter into combination; de- manding to be placed in the most stimulating conditions. Many interesting consequences in vegetable and in animal life are traceable to this peculiarity. Compounds with Oxygen.—Recited in so far as illustrating Nitrogen. Compounds with Hydrogen.— Ammonia, &e. Compounds with Carbon.—Cyanides. | Spread of Nitrogen.—Modes of obtaining it. Remarks :— bearings upon Chemical theory. The next example is a solid element. Carpon.—A solid, in two states—crystallized Diamond, and amorphous Graphite. These occur in such a degree of purity that they may be taken as typical of the element. (Diamond).—The Crystallization, Optical Properties, Speci- fic Gravity, need not be here recited. Cohesion.—The hardest body known; hence at the top of the scale of mineral hardness. . Adhesion. —A very important circumstance as regards other . forms of carbon, but not ascertainable in the diamond itself. j Relations to Heat.—Is not fused or volatilized by the highest | known heat; is not known to exist'either as liquid or as vapour. An intense heat merely reduces it to a black opaque mass. Relations to Hlectricity.—A non-conductor. Carbon has a high relative place in the Electro-negative series (place given), Before stating the chemical relations, a similar recital should be given for the other form, Graphite. Chemical relations. The range of elements combining with carbon comprises—Oxygen, Nitrogen, Hydrogen, Phosphorus, Sulphur, and many Metals, especially Iron. It does not enter confusion and perplexity of introducing speculative considerations inte the methodical description, . ee DESCRIPTIVE METHOD. 483, into combination unless at high temperatures, and then com- bines with rapidity and copious evolution of heat. Compounds with Oxygen.—Carbonic Acid, Carbonic Oxide (described at full length). With Nitrogen.—Cyanogen ; alluded to. The other compounds may be postponed. Spread and Sources of Carbon.—Impure Forms. Remarks on Carbon.—Combustion. These examples are suflicient for the purpose of indicating a systematic mode of describing the elementary bodies. They would apply equally to compounds. In them, however, the chemical relations involve another circumstance, namely, the modes of decomposition. In certain of the elements, the chief practical interest is found in impure forms—alloys, or mixtures with other in- gredients; for example, Iron. Still, itis desirable, for theo- retical completeness and consistency, to advert, in the first instance, to a pure or typical form, in order to know what the substance is in itself, both physically and chemically. The alloys or mixtures may then be given; but before their practical bearings are touched upon, their properties are to be recited as illustrating the changes brought about by mixture, thereby contributing facts to the inductive laws of Adhesion. 8. In Descriptive Method, it is of importance not to mix explanations and theorizings with the description. In deseribing a quality, the first thing is to state precisely whatit consists in, or how it is discriminated. Moreover, the whole series of qualities should be gone through, in the first instance, and no attempt made to connect them with one another, or with other properties, in general laws. This last operation should always be kept distinct. The remark applies to every science where description enters. 9. When bodies are closely allied in their nature, and are in consequence grouped as genera, their differences should be exhibited in marked contrast. The Halogens among the non-metals, the Metals of the Alkalies, &c., make groups or genera, with agreeing peculiari- ties. These points of agreement are stated at the outset, so as to abbreviate the details of the species. Attention should next be given to contrasting pointedly the agreeing members among themselves. Thus Sodium and Potassium agree to a Veer , 484 LOGIC OF CHEMISTRY. very large extent; and after the agreements, the differences should be given in a tabular antithesis. epttiel 10. The generalities of Chemistry are H’mpirical Laws. The Atomic Theory is commonly said to be the highest generalization of Chemistry. This, however, must) be guardedly stated so as not to confound definition with pro- positions. The nature of Chemical Attraction is expressed in a complex definition (Definite numbers, Production of Heat, Merging of elements). There may be real predication in declaring these three facts to be conjoined; and their con-— junction may be resolved into higher laws, or converted from an empirical to a derivative conjunction. The propositions, in connexion with Chemical action, that have in the highest degree the character of real concomitance, are those that affirm the conditions, arrangements, or situa- tions attendant on combination and on decomposition. For example, Combination requires proximity of the ele- ments, and is favoured by all the circumstances that aid proximity, as liquefaction ; it is resisted by strong cohesive or adhesive forces, and proceeds as these are released. It is brought on by elevation of temperature in numerous instances. It is induced by the electric spark; which may operate by mere rise of temperature, but more probably by polarizing the atoms. Itis promoted by concurring combinations ; it accom- panies decompositions. These are all empirical laws. They are, moreover, statements as to general tendency, and need to be accompanied, each with a schedule, stating the individual substances and situations of their applicability. Many other laws might be cited:—The celebrated law of Berthollet, regarding the double decomposition of salts; the laws that simple substances exhibit the strongest affinities,— that compounds are more fusible than their elements,—that combination tends to a lower state of matter—from gas down to solid. | As Empirical laws, these have no other verification but Agreement ; they are only surmised to be laws of causation ; they are limited to adjacent cases. | 11. The ultimate generalizations of Chemistry must fall under the Law of Conservation of Force, and must express the most generalized conditions of the re-distribution of Chemical Force. | The Law of Persistence over-rides every phenomenon of — 1 ] ‘ ‘ : ' HYPOTHESES IN CHEMISTRY. 485 change, but it must be accompanied in each case with laws of Collocation. In Chemistry, there must be indicated the pre- cise conditions of chemical re-distribution, whether in com- bination or in decomposition. It is necessary to find out, in the most general form, the situation or situations that bring about chemical change, in either direction. If this can be comprehended in one law, that will be the highest, the ulti- mate law of Chemistry, the Chemical appendage of the Law of Conservation. The Empirical laws above quoted will then have the improved character attaching to Derivative laws. 12. Chemistry contains, as a part of its nature, nume- rous Hypotheses. These are mainly of the class named Representative Fictions. To express in the most general terms the numerous pheno- mena of combination and decomposition, certain arrangements of the component elements of the compounds are assumed hypothetically. It is a fact that sulphate of potash contains certain proportions, by weight, of sulphur, oxygen, and potas- sium; it is a hypothesis that the salt is made up in the particular way shown by the formula KO,SO;, being a binary compound of two other compounds. The Atomic Theory of Dalton contained a generalization of facts embedded in Hypothesis. The facts were the fixed pro- portions of bodies combining chemically; the hypothesis, that each substance is composed of atoms, and that, in chemical union, an atom of one substance joins with one, or with two, or with more atoms of another; there being always a neat numerical relation without remainder. No one now regards this as more than a representative fiction, unsusceptible of any other proof than its facility in expressing the facts. The Constitution of Salts is the great battle ground of chemical hypotheses, being the key to the entire structure of chemical representation. There is, however, a perfect under- standing as to the nature of the proof to be offered for the rival hypotheses, namely, the suitability to comprehend the greatest number of chemical re-actions, or combinations and decompositions. It is a question purely chemical, and not in anywise logical in the sense of demanding attention to be re- elled to neglected logical principles. As examples of the subordinate hypothetical points, we may quote the singular idea of supposing an element to combine with itself—hydrogen with hydrogen, chlorine with chlorine, and so on; a very great stretch, seeing that opposition of ele- ‘ as a. : e 486 LOGIC OF CHEMISTRY. ments is a predicate of chemical union. A better example of a likely hypothesis is the proposal to assign to bodies of dif- ferent properties, having the same ultimate constitution, a dif- ferent proximate constitution; as formic ether and acetate of methyl. The bold hypothesis of Gerhardt and Griffin—to re- gard as two substances, iron when entering into proto salts, and when entering into sesqui-salts, and the same with all other elements producing sesquioxides—was considered as a relief from otherwise inextricable difficulties. The hypothesis of the Atom, or lowest chemical constituent is now coupled with another hypothetical entity—the molecule representing the smallest number of atoms of each substance supposed to possess separate action. Thus the molecule - of nitrogen is said to be made up of 2 atoms; the phosphorus and arsenicum molecules, 4 atoms, and so on. When a number of different salts are in the same solution, as in a mineral water, it is a matter of hypothesis which acid is attached to which base. (Miller’s Chemistry, II. 824.) The class of Scientific Hypothesis consisting of unverified theories, does not require special mention in Chemistry, Apart from the representative fictions, essential and permanent in the science, there are no hypothetic forces or agents. The great prevailing agent or cause of chemical change is, and can only - be, a molecular aspect of the great primeval force named under the Law of Conservation. Until the supplement of this law, as regards chemical transformation—the universal conditions or collocations—be worked out, there will be many hypotheti- cal collocations, which will be susceptible of final proof or disproof. Nomenclature and Classification of Chemistry. 13. The Nomenclature and the Classification of Chemi- stry involve these points :—(1) The use of a symbol for each elementary substance; (2) ‘lhe expression of the ultimate constitution of compounds; (3) an expression of the supposed proximate constitution of each compound in a manner suited to its re-actions with other bodies. (1) The symbolical notation has the advantage of affording a brief and yet full expression to the most complicated com- pounds, rivalling, in this respect, the notation of Mathematics. It also enables bodies of like composition to be readily classed, and their class indicated to the eye. The nomenclature for expressing in terms the various bodies a CHEMICAL NOTATION, 487 is made up of the names of the elements—Oxygen, Carbon, Tron, Silver—and of a systematic mode of uniting these in compounds—carbonic acid, carburet of iron, &e. Only binary compounds are stateable in this way ; a higher combination is expressed in some supposed binary resolution—sulphuric acid, acetate of potash, chloride of formyl. Substances like sugar, starch, albumen, are given in their familiar names. Hence double naming is, in Chemistry, a special and limited process ; and has no analogy to the names of species in Botany and Zoology. (2) The notation exhibits the ultimate constitution of all compound bodies, by stating their constituents and the pro- portions of each ; H, O is the analysis of water; F O, protoxide of iron; F, O;, peroxide or sesquioxide. (3) The symbols are farther accommodated to give the hypothetical upbuilding of the elements in complicated com- pounds ; as in the theory of Salts. The ultimate analysis gives the amount of oxygen in a compound, and the formula states in what ways the oxygen is supposed to be distributed; an oxygen salt, in the old theory was a binary compound of two oxidized radicles, the oxide of a non-metal (as sulphur) and ofa metal (as iron); sulphate of iron (proto=ide) S O; Fe O. The analytical (or Empirical) formula of acetic acid is C, H, 0,4; of the rational or hypothetical formula, there are no less than seven renderings (Miller’s Chemistry, vol. TLL o. OL 14. A desideratum in Chemical Nomenclature is the statement of the structural Heat of the bodies. The formula H, O is given indifferently for steam, water, and ice; although the exact difference of structural heat in the three admits of numerical statement. Calling ice H, O; - we may call water H,O + 180°; steam H, O + 1180", on the usual reckoning of the heat of boiling and of evaporation. Farther, when Hydrogen and Oxygen combine, there is a great evolution of structural heat, which is lost to the com- pound; a provision might be made for indicating the exact figure, which has been found out by experiment; a certain minute quantity would be attached to H, O, on this account, _ and about one fourth of that quantity to © O; LOGIC OF BIOLOGY. 1. Biology is the Science of Living Bodies—Plants and — Animals ; its exact definition is the definition of Life. - Definition of Life. 2, Life is to be defined by a generalization of what is common to Living Bodies. The Denotation of the term Living Body is well fixed ; there is scarcely even a debateable margin between the Organic and the Inorganic worlds. Choosing Assimilation as a characteristic fact of bodily life, and Reasoning, as an example of mental life, and contrasting both with the characters of dead matter, Mr. Herbert Spencer arrives at the following highly complex definition :— 1. Life contains a process or processes of change. 2. The change is not a simple or individual act, but a series or succession of changes. 8. Life involves a plurality of simultaneous, as well as suc- cessive changes. 4, The changes are heterogeneous, or various in character. — 5. The various changes all conbine to a definite result. . 6. Finally, the changes are in correspondence with earternal _ co-existences and sequences. In sum :—Life is a set of changes, simultaneous and succes- sive, combined toa definite result, and in correspondence witb external circumstances. Or, in a briefer form, Life is the continuous adjustment of internal relations to external rela- tions. So carefully has the comparison been conducted, that no exception could be taken to any part of this definition. Hvery one of the particulars occurs in all living bodies, and in no kind of dead matter. The apparent defect of the definition is omission ; it does not express or seem to suggest points that strike the ordinary observer. For example, there is no allusion ~ to the organized structure, at the foundation of which is the — peculiar constituent known as the cell, or nucleated corpuscle. Again, there is no mention of the individual and independent SO ee Jere hen ELEMENTS OF LIVING BODIES. _ 489 existence of living bodies; with which is also associated the cycle of birth, growth, and death. These omissions, real or apparent, might be defended or explained on one of three different grounds. First, it might be said, that the facts mentioned, although present and conspicaous in many or in most living bodies, are not found in all, and therefore cannot be adopted into the general definition, They can be taken notice of only in defining the classes or subdivisions of the whole kingdom of animated nature. This remark would be a sufficient justifica- tion, if it were true; but it is not true, at least to the extent of excluding the mention of the circumstances from the definition. Secondly, it might be said, that the definition does not aim at being e:haustive, but only at being discriminative ; while it is based on essential characters, it does not profess to give all the essential characters. Enough is given to prevent us from ever confounding a plant or an animal with a stone; but there is no intention of stating every feature that separates living bodies from the inanimate world. To this the obvious reply would be, why should all the essential characters not be given? There is no apparent reason for omitting in the statement whatever can be dis- covered as common to the whole department of animated nature. Thirdly, it might be alleged, that the aspects in question although not appearing on the surface of the definition, are yet implicated on it, and are unfolded in the due course of the exposition. The definition, it may be said, goes to the root of the matter; while all else branches out from that, and is duly unfolded in the subsequent exposition of the science. Tn order, however, to bring forward at once whatever can be assigned as general characters of living bodies, whether primary or derived, we shall re-cast the definition, and dis- tribute it under the heads—Constituent Elements, Structure, and Functions. 3. I. Living bodies are constituted from elements com- mon to them with the inorganic world. The chief constituents of Living bodies are these four— Carbon, Hydrogen, Oxygen, Nitrogen ; the last, Nitrogen, being most abundant in animals. To these are added, in smaller proportions, Phosphorous, Calcium, Sulphur, Chlorine, Fluorine, Sodium, Potassium, Iron, Magnesium, Silicon. 490 LOGIC OF BIOLOGY, The various properties, Physical and Chemical, belonging to the several elements are found operative in their organized form. All the mechanical and molecular laws are traceable in living bodies. Chemically considered, organic bodies, are exceedingly complee compounds. The department of Organic Chemistry is devoted expressly to these compounds. According to the chemical reckoning, a single atom of an organic substance, as sugar, starch, albumen, contains hundreds of simple chemical atoms; the atom of albumen is said to be made up of 880 atoms of the four chief organic elements. Il. With reference to STRUCTURE. (1) Living bodies possess a peculiar structural complexity, commonly called the Organized Structure. Associated with our notions of life is a certain mechanism, or machinery, very various in its extent and complication in individuals; attain- ing in the higher animals a degree of complicated adjustment unequalled in any other department of nature. Such strne- tures as the eye, the ear, the brain, of human beings are, in our conceptions, the very acme of structural mechanism. It is now known that the ultimate constituent of all the variety of structures is a microscope element called a cell, or nucleated corpuscle ; by whose aggregations and transforma- tions, tissues are formed, which tissues make up the organs. It is true that in certain low forms, both plants and animals, the cellular structure is not apparent, and therefore its visible peculiarities — namely, the bounding pellicle and internal 3 nucleus—are not absolutely essential; still, we cannot omit q from the definition an arrangement so completely bound up with all living nature, the few apparent exceptions being equivocal. (2) Another prominent feature of the living structure is Indwwiduality, or individuation. Living matter instead of exist- ing in vast continuous masses, like rock, is separated into distinct individuals. As with other peculiarities, however, there is an ambiguous margin here also. In animal life gene- rally, and in plant life generally, we have no misgiving as to individual existence ; men, sheep, forest oaks, are all distinet and separate. Still, a scientific definition must grapple with the whole field of cases, having merely the requisite latitude of a small doubtful margin. Mr. Spencer defines the indi- vidual, with reference to his definition of Life, as any concrete whole performing within itself, all the adjustments of internal LIVING STRUCTURE AND FUNCTIONS. 491 to external relations, so as to maintain its own existence. This definition, to a certain extent anticipates Function, but so does :.ny adequate statement of Structure; the separation of Structure and Function is one of great logical convenience, but, in nature, the two things are inseparable. With Individuality there is closely associated, in our con- ceptions of living beings, the Cycle of existence, the derivation of one living being from others, and the necessary termination of each individual’s existence, after a definite career. Here, too, we may seem to anticipate what belongs to Function. (3) We may not improperly state in connexion with struc- ture, and as following on Individuality, a circumstance so notorious, that to omit it from the comprehensive statement of hfe would appear inexplicable, namely, the vast Variety of Forms and Structures. Uniformity, comparatively speaking, pervades dead matter; variety is the characteristic of living substances. The different forms of Plants and of Animals count by thousands; there are upwards of one hundred thousand species of Plants, and a still greater number of Animal Species; while of every one of these distinct species, there is an indefinite unceasing multiplication of individuals, nearly, although not absolutely alike. One of the chief demands of Biological science is to find an orderly arrangement for such a host of various forms. This makes Biology, inter alia, a science of Classification. III. As to FUNCTIONS. The living structure is naturally active, changing, produc- tive, and its most characteristic points must have reference to these activities. Here we may embrace the substance of Mr. Speneer’s definition, in two principal heads—Change, and Adjustment to external circumstances. (1) A definite combination of changes, simultaneous and successive. (2) An adjustment to external circumstances. (3) It must seem unpardonable, however, not to bring out into prominent statement at the outset, that very remarkable phenomenon of living bodies, to which there is no exception, namely, Assimilation, or the, power of an existing organized - particle, to impart its own organization to an adjoining particle having the proper chemical constitution. This magic touch of vitality, has only a faint parallel among inanimate bodies ; combustion, and chemical combinations generally, make but a small approach to it. Its lesser manifestations are in the A9Q LOGIC OF BIOLOGY. renewal, by nutrition, of the living tissues; its culmination is in the throwing off of the germ, or seed, apparently homo- geneous and structureless, but possessed of interior markings that decide whether its future is to be a man or an oak; a white man, or a negro; a flat nosed or an aqulline-nosed man or woman. We may not be able to consider whether this great property be essential and fundamental, or whether it be derived from other properties, already given in the defini- tion. ney te We may repeat under this head, the peculiarity abov adverted to, under individuality of structure—the Cycle of existence, or birth, growth, and death. . (4) It cannot be irrelevant to the comprehensive definition to advert to the connexion of Mind with Living Bodies. True, this is not a concomitant of all living bodies, yet it appears only in connexion with the living form. When we make the first great division of life, into Plants and Animals, we obtain the more precise boundary of the mental manifesta- tions. Still, at the very outset, we are interested to know that this characteristic manifestation appears only in the department of living structures. . The foregoing definition professes to leave out no fact that can be found inhering in all living bodies. The first requisite in defining is to be exhaustive; it is an after operation, of _ great scientific interest, to trace the dependence of one or more properties upon the others, and to assign what appears to be the ultimate and underivable properties. At present, however, all such derivation is but tentative and hypothetical, and therefore, is not suitable to be brought forward at the commencement of the subject. Provisionally, these various peculiarities are to be held as distinct; no one being assign- able as a derivative of another. é Divisions of Biology. 4. The Divisions of Biology are in conformity with the Definition. | The first part of the Definition refers to the Organic Chemi- stry of Life. This subject is partly given under Chemistry, and partly as the Introduction to Biology. | The two other parts of the definition suppose a separate consideration of Structure and of Function. We should fully — understand the reasons and the limits of this separation. STRUCTURE AND FUNCTION VIEWED SEPARATELY. 493 _ These two facts are inseparable in the reality. But as, in less complicated subjects than Life, we have often to make _ abstraction of some qualities to the exclusion of others where there is no actual separation possible, so in the present case we find it advisable to consider Structure by itself, before * viewing it as connected with Function. Yet this separation may be carried to an unjustifiable extreme. As soon as the mind has perfectly comprehended a structural arrangement, we are prepared to enter upon the uses or functions of that arrangement. Indeed, while the know- ledge of the structure is still fresh, the knowledge of function should be imparted. Function completes and fixes the idea of structure, in so far as the two are manifestly connected. The only reason for not following up the account of structure, _ with the account of function, for every distinct living organ, would be the necessity of viewing Function as a connected whole, and therefore not to be entered on unless it could be given as a whole. For example, the Function of Digestion could not be entered on till the entire group of alimentary organs were structurally described. The separation of the two subjects is carried to a question- able extreme in the special Biology of man; Anatomy and Physiology being, by present convention, treated in distinct works, and taught by distinct teachers in the schools. The just middle plan would be to include both in one work, and to append to the Anatomy of each organ—Bones, Muscles, Heart, &c.—the Physiology or function. In the usual treatment of Plant Biology, Structural Botany is given first, Physiological Botany next (in the same treat- ise); the student being made to wait for the account of Function in any organ until Structure has been gone through in every organ. The justifying reasons are probably these :— (1) It is possible to carry provisionally the whole structure in the mind, without the assistance that function would give ; and (2) there is a convenience in treating function as an un- broken whole. In Animal Biology, the branch called Comparative Anatomy takes each organ apart, giving both structure and function, and exhausting the varieties of each through the animal series. Structure has to be viewed, in its successive moditications, through the cycle of the individual life. This is called Embryology. A still more extended view is the considera- tion of successive structures in the hereditary line, where there may occur changes requiring to be taken account of, 494. ; LOGIC OF BIOLOGY. being the initial step of the new biological department called Evolution. It is proper to generalize to the utmost the wide variety of structures, and to exhibit all the generalities apart as giving a mental command of the entire field. Such generalities would be cclled General Morphology, and General Embryology. Function, or Physiology, is an account of all the living pro- cesses, in the most convenient order; all those changes con- stituting Life—changes simultaneous and successive, contri- buting to a definite result, and adapting each organism to the environment. Here there isan unlimited scope for inductions, and for deductions, confronting and correcting one another. The high generalities of Function comprehending all Life, if such there be, would form a General Physiology. The subject of Evolution involves the mutual actions and modifications of Structure and Function. It deals with the general truth that when external circumstances demand and prompt an increase of function (as when an animal is called to exert unusual muscular energy) the structure is liable to be increased, and thus to increase the function apart from stimu- ’ lation. This is one way of the supposed re-action of Structure and Function. Another way is by Mr. Darwin’s Natural Selection, or Survival of the Fittest. The carrying out of these principles is the substance of the great Biological Hypothesis of Development or Evolution. Biology can to a certain extent be treated as a whole, there being certain things common to living beings—Conistituents, Structure, Function and Evolution; it would then have to be divided, as has always been usual, into Plant Life and Animal Life ; each of these subjects being subdivided according to the plan above laid down for the whole. Remaining Notions of Biology. The general definition of Life has been seen to carry with it the definitions of Organization, Cell, Protoplasm, Assimi- lation, Individual, Germ, Reproduction, Growth, Death. The specializing of the structures and functions introduces many other Notions. Plant—Animal.—The greatest line of demarcation in living ; bodies is between Plants and Animals; these are the two » highest genera of living bodies, a perfect dichotomy of the __ whole. Allowing for a doubtful margin, the distinctive characters are numerous and important. As in all dichoto- mies, we have the advantages of a definition by Antithesis. PARTS AND PROCESSES OF PLANTS, 495 The leading characters may be stated in contrast thus :— PLANT. ANIMAL. Number and complewity of Tissues, Organs, and Functions. Small Great . Local habitation. Fixed Moveable (Locomotion) Food matervals. Inorganic Organic Mode of reception of Food. Absorption Reception into a mouth and stomach Process of nutrition. | Deoxidation Oxidation, Tissue. Organ. Vessel.—These are comprehensive parts or constituents of the organized structure, as made up of cells; they are common to all living bodies, and admit of exact definition. There is a difference between the Tissue and the Organ; one Organ, as the stomach, may contain several tissues. Hach Tissue is analyzed into a distinct cell structure, which is its defining peculiarity as regards structure, to which there also corresponds a certain kind of activity or function. Thus, the nervous tissue is made up of nerve fibres and nerve cells, in a special aggregation; these are connected with the peculiar activity or function called nerve function, or the manifestation of nerve force. The view of Plant Life contains the definitions of the structural parts of the plant. Cellular Tissue Integument (Stomata, Hairs, Glands) Vessels Root Vascular Tissue Stem . Leaves Inflorescence (Flower, Fruit, Germ). From the enormous number and variety of plants, a great effort is needed to present these parts in their widest gener- ality; while the general idea must be accompanied with a classified detail of modifications. ann must also be given of the processes of Plant e. Osmose Flowering Exhalation Vigils of Plants Transpiration Sexual union Secretion Impregnation Irritability and Contractility Fecundation Defoliation Germination Circulation, sap, capillarity Propagation, ane yes et" 496 LOGIC OF BIOLOGY. A set of notions, parallel but more numerous and compli- cated, belong to the description of Animal Life as a whole. The modifications of the ultimate materials are described as blustema or matrix, crystals, protoplasm, granules, homogeneous membrane, vesicles, nuclei, nucleated cells, simple fibres, nucleated fibres, compound fibres, and tubes. These are compounded into the characteristic Tissups—Cellular, Adipose, Vascular, Carti- laginous, Osseous, Muscular, Hlastic, Epithelial, Nervous. The OrcGans are Bones, Muscles, Alimentary Canal, Respiratory Organs, Heart and Blood Vessels, Sympathetics, Skin, Brain, Senses, Reproductive Organs. The Functions follow the Organs; and in several instances, give these their distinctive names. The Classification of Plants and of Animals gives scope for Definition as applied to the several grades. 5. In these detailed Notions, we have the analysis of the Living Organism—Plant or Animal. An organism is by its very nature a complexity. Ina scientific consideration this complexity has to be resolved into the related parts—organs, tissues, constituents: The laws of structure are laws of relations of the parts to each other; and if our analysis has hit the natural partition, it is the basis of our subsequent statements, in propositions, of the natural relations. If the analysis is inexact, no exacé propositions can be grounded on it. Propositions of Biology 6. The Laws and Propositions of Biology differ in their logical character, according as they relate to Structure or to Function. First, as to STRUCTURE. ‘y The propositions or laws of Structure, affirm co-existence, as order in place, between the different parts of living bodies. Human Anatomy is a vast congeries of such propositions. How far the co-existences are ultimately dependent on Causa- tion, rests with the theory of Evolution. In the meantime; they are to be regarded mainly as Co-existence without Causa- tion. . These propositions may be special to individuals and limited groups of individuals ; or they may be generalized over very wide areas. The narrow class is exemplified in human Ana- tomy, and in all specific descriptions whether of plants or of © a a a 4 cr . a : " PROPOSITIONS OF ANIMAL STRUCTURE, 497 animals. High generalities, realizing the scientific ideal of Biology, are not wanting. For example, in Plants—all the parts are homogeneous in structure; or, as otherwise expressed, the flowers are modified leaves; the monocotyledonous mode of germination co-exists with the endogenous mode of growth ; flowering plants are generally multiaxial ; complexity of struc- ture is accompanied with permanence of form. In Animals, we have the anciently observed coincidence of ruminant sto- mach, cloven hoof, and horns; the grouping of mammalian characteristics—mamme, non-nucleated red blood-corpuscles, two occipital condyles, with a well-ossified basi-occipital, each ramus of the mandible composed of a single piece of bone and articulated with the squamosal element of the skull. Viewed, in the first instance at least, as co-existences with- out causal connexion, these propositions must be verified by agreement through all nature, and held as true only to the extent observed. There are numerous and striking co-existences between Structure and External circumstances, the so-called Adapta- tions of one to the other; but in these there is a great pre- sumption of cause and effect; they furnish the best support to the doctrine of Evolution. There are likewise laws of causation, more or less traceable, in the operation of all the outward agents. Thus, Heat, Light, Air, and Moisture, are essential or causal conditions of the growth of plants. Light is necessary to the colour of the leaves. The oxygen of the air is an indispensable condition of all animal life. Many other laws of causation are occupied in expressing the agency of different kinds of food, of medi- cines, &c. There are laws of cause and effect, in the mutual actions of different organs, in each individual plant or animal. Thus, in animals, the digestive organs affect, and are affected by the circulation, the muscles, and the brain. 7. Next as to Function, or Physiology. The propositions here affirm Cause and Effect. The process of Digestion, for example, is an effect of the contact of food material with the complicated alimentary organs. In like manner, every organ of every living being has a function, more or less assignable. It is a deduction from the permanence of Matter, established since the researches of Lavoisier as a law of nature, that what- ever materials exist in plants and in animals, must be sup- 498 LOGIC OF BIOLOGY. plied asa condition of their growth. Plants being constituted from Carbon, Oxygen, Hydrogen, Nitrogen (in small portions), and Saline bodies,—must find all these elements in the earth or in the air. The animal tissues being highly nitrogenous, animals must have nitrogenous food. The gastric juice con- tains hydrochloric acid, whence the necessity of salt as an article of food. 8. The law of the Conservation of Force, and all the subordinate generalizations of Molecular Physics and Chemistry, are carried up into Biology. The law of Conservation holds true in organic changes, and is a deductive key to the phenomena, Every manifestation of force in a living body—mechanical energy, heat, decom- position of compounds,—is derivable from some prior force of exactly equivalent amount. The laws of Cohesion, Adhesion (in all the forms—Solution, Capillary Attraction, Diffusion, Osmose, Transpiration), Heat, Light, Electricity, and the laws of Chemical combination and decomposition, are carried up into organic bodies. In the present advanced state of knowledge respecting these laws, there are many deductive applications of them to the pheno- mena of life. The complications of Biology are thus, in part, susceptivle of being unravelled by pure deduction. So far as concerns Force, or energy, in any shape, there is nothing special to living bodies. As regards Collocation, there is the peculiarity of the organized structure. It is not correct to speak of Vital Force in any other sense than the molecular and chemical forces, operating in a new situation. It would be strictly proper to speak of a Vital Collocation of elements, under which the molecular forces put on new aspects, although never inconsistent with the primary law of Conservation. Thus the nerve force is something new, not as regards its derivation from an antecedent equivalent of force, but as regards the singularity of the nerve structure, which leads to a new mode in the manifestation of the force. 9. In the department of Function, there are necessarily many Empirical Inductions. Excepting the deductions from Physics and Chemistry, every law of Biology must be considered as empirical. There are, however, some empirical laws established by an agree- ment so wide and sustained that they are considered, for the present, as laws of nature. Still, no such laws can be held as oe eee peer PROPOSITIONS OF FUNCTION. 499 absolutely certain. Notwithstanding the agreement in favour of the derivation of living beings from germs or seed, there is yet a possibility of spontaneous generation. The following are examples in Plants. Vegetable cells absorb fiuids, elaborate secretions, and form new cells; they also unite to form vessels. Roots absorb material from the soil, in part by osmotic action. The sap circulates under the influences of heat and light, and the actions going on at the surfaces of the leaves and of the roots. In flowering plants, reproduction is performed by the access of the pollen to the ovules. Fruit succeeds to fecundation. Seeds germinate in the presence of heat, moisture, and air, with absence of light. _ There is something very unsatisfactory in the inductions of Vegetable Physiology. Some of them are now obvious results of the law of Conservation; as for example, the influence of Heat at all stages of vegetable growth. The great lack is in the intermediate steps of the process ; what happens in the interval between the incidence of heat and air in the leaves, and the elaboration of the sap, the setting free of oxygen, &e. But this is the defective part of our knowledge of all the organic processes. In the functions of Animals, there are numerous empirical inductions. Thus the conditions of Muscular contractions are well known by experimental research; they are the presence of blood, and the stimulus of the nerves. That blood should be necessary is a consequence of the law of conservation; muscular force must be derived from some prior force. That non-azotized materials are sufficient for causing muscular energy could be known only by experiment. Again, the circumstances affecting the heart’s action, are empirical inductions ; so is the fact that the red corpuscles of the blood carry the oxygen for the tissues. The processes of Digestion are stated in the form of empirical inductions, The same holds of Urination and Re- spiration. Farther, the multiplied actions concerned in Impregnation, Germination, and Growth, are ascertainable only as empirical laws. All the functions of the Brain and the Senses are given in propositions of the same character. That exercise (within limits) strengthens all the animal organs has long been established as an Empirical Law. Mr. Darwin is dissatisfied with the physiological reason or deriva- tion of the law; to him, therefore, it remains empirical. These empirical inductions are to a certain small extent controlled by high generalities, and are in so far derivative. The law of Conservation is a check upon many of them; and 500 LOGIC OF BIOLOGY. the special laws of Molecular Physics and of Chemistry are seen at work in some. But in such a process as Digestion, the recognized physical and chemical actions are thwarted by deeper forces, of which we have only an empirical statement. The most potent instrumentality of deductive explanations at present known is that furnished by the researches of Graham on Transpiration, Diffusion, Osmose, and Capillarity. Animal Mechanics, and the propulsion of the fluids by the heart’s action, are susceptible of a complete deductive treat- ment, through the applications of Mechanics and Hydrostatics. This is well exemplified by Dr. Arnott, in his ‘ Elements of Physics.’ Logical Methods of Biology. 10. In Biology, the facts are open to Observation and to Experiment ; although with some limitation owing to the peculiarities of the living structure. The difficulties attending the observation of living beings are greatly overcome by such instruments as the microscope, stethoscope, laryngoscope, ophthalmoscope, &c., and by the chemical examinations of the various products. Accident sometimes lays open the interior, as in the case of Alexis St. Martin, through whom was obtained invaluable results as to digestion. 11. Through the variety of the cases presented by Biology, there is great scope for elimination by the methods of Agreement and Concomitant Variations. The means of varying the circumstances by the comparison of instances, agreeing and yet disagreeing, is very extensive. From the number of different vegetable and animal species, each structural peculiarity is presented under the greatest possible variety of accompaniments. And this is only one part of the case. In every individual there is scope for additional comparisons in the different stages of its existence, the method of Embryology. Lastly, the occurrence of monstrosities still farther contributes to the desired variation of circumstances. In these three ways, the opportunities of plying the Methods of Agreement and Concomitant Variations are exceedingly multiplied. Thus, an examination of the structure of the eyes, in their oa ae rudimentary types in the lowest animals, and in their succes- sive phases of growth in the higher, has both suggested and Re CHANCE AND PROBABILITY. ; 501 proved (as some believe) that an eye is a modified portion of the skin, Mr. Owen enumerates seven different modes of carrying out comparisons of the animal structures (Vertebrate Animals, Vol. I. Preface). The use and limits of the Deductive Method in Biology have been sufficiently adverted to in previous remarks. Some notice may be taken of the applications of Chance and Proba- ‘bility. 12. There are many biological conjunctions of wide, but not of uniform concurrence. Such cases must be dealt ‘with according to the rules for the Elimination of Chance. When a concurrence, although not universal, is, neverthe- less, more frequent than chance would account for, we are bound to recognize a natural tendency, or some law of nature liable to be defeated by other laws. [or example, the con- currence of superiority of mental power with superior size of brain, although liable to exceptions, is yet very general, and far more than chance can account for. Hence we must regard this as an established law, with occasional liability to be defeated. Weare not at liberty to predict it of every instance, but only with a probability proportioned to the observed fre- quency as compared with the failures. 13. It is a result of the great complicacy of vital pro- cesses, that many inductions are but approximately true ; and, therefore, are to be reasoned on according to the principles of Probable Evidence. The prevalence of approximate generalizations is a mark of the increased complicacy of the Biological processes, as com- pared with the processes in Physics and in Chemistry. The best that can be done, in this state of things, is to ob- tain statistics of the actual occurrence of certain conjunctions. There is a large department, of modern creation, termed Vital Statistics, which enables us to reason on vital phenomena with the degree of probability belonging to each case. It is thus that we can infer the proportions of mortality at different ages, _ and the proportion of male to female births. When Agricul- tural Statistics shall have been continued for a sufficient time, the recurrence of good and bad harvests will be capable of being stated with numerical probability. 14. Many of the propositions of Biology are defective in numerical precision. 502 LOGIC OF BIOLOGY. In Physical and Chemical facts, it is usually possible to measure numerically the degree of the qualities. Thus most of the properties of a mineral can be stated with numerical precision ; others, as colour, and fracture, can be referred to a known type. But when we say a certain amount of exercise streagthens the organs, while a greater amount weakens them, we leave the estimate very vague. Change of air is said to invigorate the powers, but there are no precise reckonings, either in the general or in particular cases, of how much invi- goration may be expected from a definite change. So, the influence of altered circumstances on breeds and on races is given in vague indeterminate language, and must be taken with great latitude. , Hypotheses of Biology. 15. The character of the science requires the utmost aids that can be afforded by well-contrived Hypotheses. Biology has all the difficulties of Molecular Physics and Chemistry as regards the impalpable nature of the constituent parts in living bodies, and its own additional complications from the organized structure. The hypotheses of Biology are of all the varieties enu- merated in the general chapter on the subject (Inpuction, chap. XIII.). Some assume a real cause, as the Development Hypothesis ; others assume unreal or unknown agencies, as the supposed adherence to ly pe or plan; a third class would claim to be Representative assumptions. Of the first class, we may cite, as instances involving the smallest amount of peril in the assumption, the unverified deductions from general laws of the inorganic world, such as the molecular and chemical laws. These powers of cohesion, adhesion, solution, osmose, &c., are assumed as operating in the living body, but the deduction from them is not sufficiently exact to be fully verified. Hence there is much that is hypo- thetical in the theories of oxidation, of animal heat, of secre- tion, &c. From the known chemical inertness of Nitrogen, Mr. Herbert Spencer draws some remarkable inferences in explanation of the vegetable and animal processes (Biology, I. 8). Development Hypothesis—This renowned speculation, with all its boldness, has the characters of a legitimate hypothesis ; it assumes a real agency, a vera causa; its difficulties lie in showing that the supposed agent is equal to the vastness of the results. HYPOTHESES. 503 . _ Properly speaking there is no rival hypothesis. The Special- Creation view is a phrase that merely expresses our ignorance. Its power of explanation is confined to making a comparison ; it assigns to the living species that have successively appeared - in the course of ages the same mode of origin as the earliest species of all, and asthe whole framework of the universe ; an origin that must for ever be inconceivable to the human mind. As the physical theorists who speculate upon cosmical develop- ment—the formation of suns and planets—start with the assumption of matter spread out over a great amplitude of space, and coming together by gravity, so the biological theo- rists assume a primeval start, either of living broods, or of matter ready to become organized under particular circum- stances. Now the value of any scientific explanation of life is measured by its capability of tracing the whole of organized nature to the fewest primitive assumptions. The modification of plants and animals in the course of generations is a fact. It happens even in the same external circumstances ; while under alteration of circumstances, the changes become vastly greater. Now, if any means can be assigned whereby some of the modified forms are kept alive while all the others perish, the deviations are rendered per- manent. Mr. Darwin provides an instrumentality of this nature in what he calls Natural Selection, or the preservation of the fittest in the struggle of life. It has been his endeavour to accumulate a vast multitude of facts showing the principle in operation, many of them inexplicable on any other supposi- tion. Herbert Spencer, Huxley, Hooker, Wallace, and others, have contributed to the support and elucidation of the hypo- thesis. The occurrence of allied species in the same geographical area, and the wide differences in character of the species in localities widely apart, are adapted to the doctrine of deve- lopment and not to any other view as yet provided. Again, says Mr. Darwin—‘ How inexplicable is the similar pattern of the hand of a man, the foot of a dog, the wing of a bat, the flipper of a seal, in the doctrine of independent acts of creation ! how simply explained on the principle of the natural selection of successive slight variations in the diverging descendants from a single progenitor!’ In the course of time and change, certain parts originally useful have become superfiuous ; and their retention in the useless condition is intelligible only on « hypothesis of descent. So long as the Development Hypothesis tallies with a very 504 LOGIC OF BIOLOGY. large number of facts, and is not incompatible with any, itis - a legitimate and tenable hypothesis; and its worth is propor- tioned to the extent of the phenomena that it explains, com- pared with those that it fails to explain. Hypothesis of Iteproduction.—The reproduction of each living being from one or from two others, through the medium of a small globule which contains in itself the future of a definite species, is the greatest marvel in the whole of the physical world ; it is the acme of organic complication. Mr. Herbert Spencer and Mr. Darwin have recently pro- mulgated hypotheses to represent this process. (Spencer, Biology, L, 253; Darwin, Domestication, II., 357). The two views have a good deal in common, and might be taken together. Mr. Darwin’s, however, ventures farthest, and may be here quoted ag exemplifying a biological hypothesis. He prepares the way by generalizing all the different modes of reproduction—whether unsexual or sexual. The unsexual modes, as buds and fissure, are to be held as identical with the processes for maintaining each organ in its integrity, for the growth or development of the structure, and for the restoration of injured parts. And it seems to be a tenable supposition that the sexual mode of reproduction is a mere modification of the same general fact. The hypothesis then is that each egg, or seed (of the female) and each spermatozoon, or pollen grain (of the male) is already a vast aggregation, a world in itself. It is made up of a host of smaller bodies, which may be called gemmules, with all the properties of growth or reproduction commonly attributed to cells in general ; this host is different in each species. For every separate part of the animal or plant to be formed; down to a feather, there are distinct gemmules of the type of that part, and unfolding to produce it by ordinary growth. Hvery animal contains circulating through it the undeveloped gem- — mules of all its organs, and parts of organs; a complete set is bound up in the ovum of the animal (or plant), and by due expansion reproduces the new individual complete at all points. Something must be assumed as determining them to fall into their places ; but that there is no absolute fixity in this respect, Mr. Darwin shows by the frequent occurrence of misplaced organs; this, he thinks, favours the view of the multitudinous gemmules, and refutes any hypothesis of a formed microcosm — existing in the seed, to which supposition there are many other hostile facts. To grasp, reconcile, and generalize the facts, is an ample HYPOTHESES, 505 justification of this bold venture; by the nature of the case, we can never hope to penetrate the precise operation, nor yet to arrive at a supposition that shall exclude every other. It is, however, an important appendage to whatever hypothesis may be formed of the great vital fact named Assimilation. CHAPTER V. LOGIC OF PSYCHOLOGY. 1. Psychology, or the Science of Mind, comprises both Mind proper, and its alliance with Matter, in the animal y- Definition of Mind. 2. The ultimate antithesis of all knowledge is called the antithesis of Object and Subject. The object world coincides with the property called Exten- sion ; whence the Subject, or Mind, is definable by antithesis asthe Unextended. A tree is extended ; a pleasure, a thought, a desire, have nothing in common with extended things. 3. By the method of Particulars, Mind is definable as possessing the three attributes named Feeling, Volition, and Intellect. _ Feeling is exemplified by pleasures and pains; Volition is action prompted by Feelings ; Thought, or Intellect, contains the processes known as Memory, Reason, Imagination, &c. All our emotions are included under Feeling; our sensa- tions are partly Feelings and partly Intellectual states. The positive definition of the Mind is also a Division, and must conform to the laws of Logical Division. | Concomitance of Mind and Body. 4, To the Definition of Mind, we must add the Con- comitance of the Body. The concomitance of Mind and Body is a conjunction alto- gether unique. The extreme facts of human experience—the subject and the object, mind and extended matter—are found in union. We cannot say with certainty whether the unionis Yn ee 506 LOGIC OF PSYCHOLOGY. @ case of causation, or a case of co-inhering attributes. It stands apart. 5. The union of Mind and Body must hold throughout, While many, from Aristotle downwards, have held that portions of the mind are unconnected with bodily processes, no one denies that mind is to some extent dependent on the body. But all have failed in every attempt to draw a line between the functions that are dependent, and those that are supposed independent of bodily organs. 6. The concomitance of the two radically distinct phenomena gives the peculiar characteristic of the science. Every fact of mind has two sides. Every feeling has its mental side known to each one’s own consciousness, and its physical side, consisting of a series of physical effects, some superficial and apparent, others deep and intricate. It depends upon circumstances whether, and how far, these physical adjuncts should be brought forwaed in the scientific exposition of the mind. On the one hand, if they are unvarying in their concomitance, they can hardly be excluded without impairing our knowledge of the mental part. On the other hand, it is a bare possibility that the mental pheno- mena, being radically distinct and unique, may be studied better by making entire abstraction of the physical accompani- ments. Moreover, much depends upon the degree of insight actually possessed respecting the nervous system and the various organs related to the mind. It might be expedient at one stage of knowledge to drop these from the view, and at another stage to take them up, In point of fact, until the present century, only a very small number of philosophers gave systematic attention to the physical implications of mind ; the chief being Plato, Aristotle, Hobbes, and Hartley. In spite of the crndity of their know- ledge of physiology, they all (with perhaps the exception ot Plato) gained most valuable psychological hints by means of that knowledge. The physiology of the present century — having placed the whole subject on a new vantage ground, - the attention to the physical side may be expected to be much more rewarding. ' Thus, on one side, Psychology is a department of Animal Biology, and subject to biological laws. The all-pervading — law of Persistence of Force extends to the physical concomi- ‘ Roe is. = DEFINITION OF MENTAL PROPERTIES. 507 fents of mind, and is pregnant with consequences of the utmost practical value. On the other side, Psychology presents a unique phenome- non—individual self-consciousness—to which there is no forerunner in any of the previously enumerated sciences. Still, the methods and spirit of scientific enquiry, as exhibited in these other sciences, are of value in the study of mind in its psychical side. States of consciousness have degrees of intensity and duration; they are single or compound; they aid or thwart one another ; they have their laws of emergence, increase, decline; in all which particulars they observe analogies to physical forces; so that the intellectual habits of accurately estimating physical agencies may, with due allow- ances, be of service in dealing with the complications of mind. The two-sidedness of the phenomena appears in language. The terms of mind had all an objective origin; and, while some of them have now an almost exclusively subjective meaning—as pleasure, pain, feeling, thought, sweetness, fear, conscience, remorse,—others have also an objective reference, as shock, emotion, excitement, avidity, irritation. Jn these last, the language is ambiguous; we cannot always tell whether the physical or the mental is aimed at. There is, morover, a liability to represent the mental fact as a physical fact. Other Notions of Psychology. Consciousness.—The most difficult word in the human voca- bulary. It concentrates in itself all the puzzles of metaphysics. If it were strictly synonymous with Mind, it would be defined accordingly. But the object, or extended world, is inseparable from our cognitive faculties; so that a word that expresses every conscious state whatever is wider than mind, strictly so called; it comprises both matter and mind. Hence, if ‘ con- sciousness” be the name for all sentient states, it is the widest word that we can employ, in fact, there is no meaning corre- sponding to it; like Existence, it is a fictitious addition of the two highest genera. To state these separately, we must have the double epithets Subject-consciousness and Object-con- ‘sciousness; which, however, give only the meanings—Object and Subject, ; Sensation.—A word with several distinct meanings. In the first place, it may either cover the physical operations con- nected with the exercise of our senses, or it may be restricted to the purely mental state arising therefrom. In the next 508 LOGIC OF PSYCHOLOGY. place, inasmuch as the senses give us feelings in the purest form (pleasures and pains) and also intellectual discrimina- tions, the ground work of our ideas,—sensation may be used for either class. In the third place, there is a contrast of Sensation with Perception, or between the immediate effect on the mind, and the associated effects; colour and visible magnitude are sensations, distance and true magnitude are perceptions. The special modes of sensation, together with muscular feeling, are ultimate states of the mind, to be defined solely by individual reference. Resistance, Motion, Warmth, Diges- tive Sensibility, Taste, Smell, Touch, Hearing, Sight,—as states of feeling, must be known by independent experience. Emotion.—The emotions are a department of the feelings, formed by the intervention of intellectual processes. Several of them are so characteristic that they can be known only by individual experience ; as Wonder, Fear, Love, Anger. These stand very near the ultimate elements of human feeling. Many, however, are evidently derived; such are, in an emi- nent degree, the Aisthetic and the Ethical emotions. Phases of Volition.—The definition of the Will, or Volition, is a part of the definition of mind as a whole. Will, as con- trasted with Feeling, is a unity, indivisible. Yet, there are various aspects or modifications of it, that receive names. Motive is the feeling that prompts the will in any one case; the motive to eat is the pain of hunger, or the pleasure of eat- __ ing, or the pain of defective nutrition. Deliberation supposes conflicting motives. Resolution is a volition with the action adjourned. Desire is ideal volition, either as preparatory to the actual, or in lieu of it. Belief is preparedness to act, for a given end, in a given way. | Intellectual States.—In the Intellect, we have three fun- damental processes—Discrimination, Similarity, Retentiveness or Revivability ; all requiring actual experience in order to be understood. Discriminationis another word for the fundamental fact called Relativity and also Contrast. Similarity, or agree- ment in difference, is a distinct fact of the mind; the sensi- bility corresponding to it is unique; and it is one of the most iterated of human experiences. Retentiveness and Revivability describe a great characteristic of our mental nature, for which we have other designations, as Idea, Memory, Recollection ; it ean be defined only by reference to actual experience ; al- though the figurative words—retention, revival, resuscitation, — seem to be a definition by the medium of other notions. - ——— ESSENTIAL AND REAL PREDICATION. 509 The complex intellectual faculties—Reason, Imagination, &c., are defined each by its proper department of exercise ; thus, Reason is the power of drawing conclusions from pre- mises, or the scientific faculty. To this definition may be appended, as a real predicate, the derivation from the ultimate intellectual elements just named. Psychology contains scope for Classification, both according to Logical Division, and according to Ramification or Compo- sition. The ultimate sensibilities—namely, the Senses, the elements of Intellect, and the Simple Hmotions—are classiied as genera and species, and according to Logical Division. The compound faculties and sensibilities, as the popularly named Intellectual Powers, and the Complex Emotions, are classified solely by Ramification; their classes do not comply with Logical Division. Propositions of Mind. 7. The complexity of many of the Notions of Mind gives rise to Essential Predications. Mind itself being defined (positively) by the union of three distinct and irresolvable characteristics, there may be proposi- tions affirming the concomitance of these three facts; as Feeling is accompanied with Volition and with Intelligence. When we say that Mind (as a whole) feels, wills, remembers, we give a verbal or essential predication. So with many other notions. Such simple feelings as fear, love, anger, if defined, would have a plurality of circumstances. That such circumstances are united, may be a real predica- tion ; but when any one of them is predicated of the name, the proposition is essential. ‘Anger makes one delight in retaliation ’ is a purely verbal predication. Our common talk on mind is full of Essential propositions. His vices were condemned, his virtues praised. Prudence keeps a man out of difficulties. The strongest motive deter- mines action. 8. The conjunction of Mind and Body is a real predi- cation ; it being understood that the definition of Mind is restricted to subjective facts. This holds throughout the detail of feelings, volitions, and thoughts. When the name for an emotion is the subject of a proposition, and the physical accompaniments are affirmed, the predication is real :—‘ Fear depresses the vital organs’ is 510 PSYCHOLOGY OF LOGIC, an affirmation of concomitance. ‘The hope of the reward quickened his speed.’ conjoins a motive to the will (a feeling) with the bodily part of a voluntary act. 9. The three leading functions, given as the Definition of Intellect (Discrimination, Agreement, Retentiveness), are unfolded in predications. That Mind discriminates is an Essential proposition ; yet the full account of the fact of Discrimination, Relativity, or Con- trast, demands numerous propositional statements, many of them real. Not to re-iterate the double-sidedness of every mental fact, the conditions, circumstances, and limitations of each of these leading properties are enounced in propositions that are in no sense verbal. (1) Thus, we speak of the law of Ielativity, expressed as the concomitance of consciousness with change of impression, This is the general statement ; and constitutes a real predication by virtue of the distinctness of the two facts—change of im- pression (physical, in great part), and consciousness (strictly mental). (2) Retentiveness, Revivubility, Contiguous Association, are names for a fundamental property of mind, which in its expo- sition takes the form of a law. A certain condition or situa- tion has to be assigned (the reception of present impressions), and to this is attached as a real predicate, the property of being retained, revived, remembered. The various modifying circumstances (engagement of attention, physical vigour, &.) are real propositions in subordination to the main principle: It is a grand generalization, resuming, explaining, and ren- dering precise the media axiomata of acquisition, as regards intellectual growths, emotional growths, and volitional growths, — Under it are given numerous affirmations as to the derivation of complex phenomena from simpler, the unfolding of thoughts _ and emotions, and the evolution of the mature mind from its primary elements. This is commonly called the Analysis of the Mind. The proof of such assertions rests partly on the consciousness of the hearer, and partly on indirect reasonings. Thus, the proof that Beauty is a compound, and not a simple Emotion, is that we can consciously identify its constituents. The same with the Moral Sense. ‘The indirect prodfs are, the absence of the Feeling prior to certain opportunities of mental association. (See § 12.) (3) The Law of Similarity, or Agreement in Difference, is, — for the same reasons, an inductive generalization of real LAWS OF MIND. SEE concomitance. ‘ Present states of feeling, &c., tend to revive their like among former states, notwithstanding a certain amount of difference.’ As before, there are required many subsidiary propositions to express all the qualifying circum- stances of this wide generality. Another important law of the mind is sometimes described as the law of the Fixed Idea, namely, that ideas tend to act themselves out ; as when the sight of yawning makes us yawn, merely by giving us the idea of the act. 10. There may be laws of the rise, continuance, and subsidence of Feelings. The connotation of each distinct mode of feeling, whether sensation or emotion, indicates both its character as feeling, and its mental antecedent. The laws connecting mind and body, predicate its physical side; the laws of Relativity and of Retentiveness contain additional predicates. ‘To all these may be added inductions as so the rise, continuance, and sub- sidence of Feeling ; which laws, like every other, have a physical side, and may possibly, on that side, be generalized into still higher laws. Like all sciences where simple elements contribute to form compounds, Psychology contains affirmations respecting the composition of feelings and other states. The assertion is made, for example, that Beauty, Conscience, Imagination, are not simple facts, but are compounded of certain assignable elements. Among the ordinary predications respecting living beings, we may mention the passing of the various capabilities into action. Thisextendstomind. I walk, speak, reason, wonder, desire, &c., are examples; to all such belongs the reality of predication. Logical Methods of Psychology. 11. In Psychology, special importance attaches_to the ultimate Analysis of the phenomena. In all sciences, we desiderate an accurate and thorough- going analysis of the phenomena. It is only an ultimato analysis that can be the groundwork of the most general pre- positions respecting them. In proportion to the difficulty of ascertaining and proving the facts in detail, is the valne of an ultimate analysis, whereby we can reduce to a minimum the number of independent 512 LOGIC OF PSYCHOLOGY, assertions. When we know the component parts of an Emo- tion, for example, Beauty, the Moral Sentiment, or Veneration, we can apply our experience of the parts to correct and con- firm our experience of the totals. 12. The proof of a Psychological Analysis is (1) the feeling of identity between the compound and the parts. This must be a matter of individual self-consciousness. _ That the Moral Sentiment contains a feeling of obedience to authority, under dread of punishment, is proved by each one’s being conscious of the presence, in the compound, of that special element. 13. An Analysis is proved (2) by the identity of the consequences and collaterals of a feeling. ‘This will afford an Objective proof. That the Religious Sentiment contains an element of Fear, _ is proved by identity in the eRe and the Actions | dictated by the state. 14, The greatest difficulty is felt in establishing the sufficiency of an Analysis. This is a difficulty in all cases where there is great com- plexity in the phenomena. We may identify the presence of certain elements, without being able to show that these are the whole. Where the quantity of the elements can be measured, as in Chemistry, we can prove the analysis by casting up their sum. Where quantity is not exactly esti- mable, as in many biological facts, and in nearly all psycho- logical facts, this check is indecisive. For example, some have maintained that Benevolence is exclusively made up of self-regarding elements. Others, while admitting the presence of these elements, deny that they account for the whole. Owing to the vagueness of our estimates of quantity in mind, the dispute cannot be decided ~ by a process of summation in ordinary cases. We must — proceed by varying the circumstances, and by finding — Instances where self-regarding elements are either wanting, or so small in amount, as to be obviously unequal to the effect produced. Such an instance is found in the pity called forth by the punishment of great criminals. 15. The Inductions of Mind bring into play the Experts mental Methods. LOGICAL METHODS IN MIND, 513 The great Law of Concomitance of Mind and Body must be proved by the Method of Agreement. We must show that the whole of the facts of mind—Feelings, Volitions, Thoughts, are at alletimes accompanied by bodily processes. The case has something of the peculiarities of the Law of Causation. We can prove the concomitance in a vast number of cases ; while in many mental exercises, as in meditative reflection, the physical processes almost escape detection from their subtlety. These instances, however, although unable to confirm the proposition, are not opposed to it; and they do nothing to invalidate the force of the unequivocal in- stances. We can do more than establish a law of concomitance of mind and body generally. We can, by the methods of Elimi- nation, ascertain the exact bodily processes connected with mental processes. On this determination, we can bring to bear all the Hxperimental Methods. The Law of Relativity is established by Agreement, and, in a remarkable manner, by Concomitant Variations. The Intellectual Laws, called Retentiveness and Similarity, are established, both in general terms, and as respects their peculiar conditions, by all the methods. 16. From the circumstance that, in Psychology, we have attained to laws of high generality, there is great scope for the Deductive Method. While every one of the great laws above enumerated is fruitful in deductive applications, the instance that perhaps best exemplifies the Deductive Method of enquiry, considered as a Supplement to Induction, is the Law of Conservation or Correlation, applied to Mind, through the physical supports. By this law, every mental act represents a definite, although not numerically expressible, physical expenditure, which must be borne by the physical resources of the system. The deduc- tive consequences of this fact are innumerable. 13. From the circumstance of passing through the Linnean classification, so well adapted to the ready deter- mination of plants, Botany affords the best example of an Index Classification. ie z We may retain for se purpose the Linnean system in qo literal form ; or we may have recourse to the modified schemes ~ of recent Botanical writers. The principle is the same. We - commence with certain characters, having alternative modes ; 17 and the key or index informs us what classes each mode points 7 to. A second character is then examined, its alternatives — found, and the corresponding classes discovered. (See tote ley’s Vegetable Kingdom, Bentham’s British Flora, &c.) _ LOGIC OF ZOOLOGY. ' oe a 14. The difficulties of Zoological Classification rolatal to the multitude and the complication of the Animal King dom. The multitude of the objects to be arranged, and the com- plication of even the lowest forms, distinguish Zoology from all other classificatory sciences. There are certain partial s compensations. As compared with Minerals, the organs of Animals present numerous relations of concomitance ; and as compared with Plants, the Animal Kingdom falls ina ‘remark= ; able degree, under a lineal series, or consecutive development. I. Characters of Animals. he a ui 15. We must look for the characters of Animals in the division of the animal system into constituent Organs. - - The Animal, like the Plant, is made up of Tissues and ‘ Organs, which have a certain amount of sameness, with variety, throughout the entire Animal Kingdom. The enu- meration of these belongs to Biology ; Connective tissue, Elastic tissue, Adipose tissue, Cartilage, Bone, Muscle, Nerve, Vascular tissue, Blood corpuscles, &c. In Zoology, howe the Tissues are viewed mainly in the Organs; and Zoolog characters are characters of organs. There is not the san use made of distinction of Tissue, as we have seen in B The basis of Zoological Classification is the division 9 ie oe ae | A Whites in: ; P COMPARATIVE ANATOMY AND ZOOLOGY. 5389 Animal system into Organs. These, with their functions, may be variously arranged, there being two natural groups; (1) the Vegetative Organs and Functions (Nutritive and Repro- ductive) — Digestion, Absorption, Circulation, Nutrition, Secretion, Excretion, Respiration, Generation, Development ; i (2) the higher Animal Organs — Locomotion, the Senses, the Brain. In all these various organs, characters may be sought; there being none but what are subject to variation throughout the Animal series. The Anatomy of Vertebrates comprises the following parts:—Skeleton, Muscles, Brain and Senses, Teeth, Alimentary Canal and Appendages, Absorbents, Circu- lation, Respiration, Urinary organs, Skin, Generative Organs. The Blood is also a source of distinction in the larger divisions— as between Vertebrate and Invertebrate, Warm-blooded (Birds and Mammals) and Cold-blooded (Fishes and Reptiles). The grand separation, common to all classificatory sciences, between the General and the Special Departments, in the Animal Kingdom, gives birth to the two subjects,—Compara- tive Anatomy and Zoology. As in Mineralogy, and in Botany, these should repeat and support one another, giving the same information in two different forms. The Comparative Anatomy arrangement, besides settling the selection and the order of Zoological characters, is a most powerful instrument of generalization. The exhibition of each successive organ in.all varieties and modifications, discloses many aspects otherwise hidden; and places the more general and fundamental peculiarities in a strong. light. Much of the insight that we at present possess regarding the brain ‘is due to Comparative Anatomy. Too great pains cannot be * given to the perfecting of the Comparative Method; and the grand secret is the lucid presentation of agreements and of dif- ferences. 16. There being, in Animals, a number of distinct _ organs, a search is made for Laws of Concomitance be- tween them. It is a part of Biology, and an indispensable aid to Zoology, to find out the correspondences or laws of concomitance between the different organs—Moving Organs, Nervous System, Digestion, Reproduction, &e. These laws occur under various aspects. Some are empiri- cal generalizations, such as the coincidence of the ruminant characteristic with the cloven foot and horns on the frontal 540 - LOGIC OF ZOOLOGY. bone. Other coincidences are mutually related, and are and parcel of the development of the species; as the adv: of the brain with the muscular system, the reproductive organs, and the organs generally. The fact of increase of — : organization as a whole implies laws of concomitant ae ment of all the leading organs. The connexion between an animal’s organs and its circumstances or conditions of life is not a law of co-existence, but of mutual implication; it does not — ¢ give us two independent facts, but the same fact on two sides, — All references to the element of each species—water, air, earth, the body of another animal—are to be held as not G illustrating the nature of the organs. 63 > The best established laws of concomitance in the asia s organs, on which depends the existence of a science of Zoo- — logy, as distinguished from a Comparative Anatomy of ani- — mals, are liable to exceptions. Sometimes a single species — will mar the unanimity of an entire Division, like Amphioxus | ‘ among fishes. It is clear, however, that such exceptions are — to be mentioned, and then disregarded. They do not even — prevent us from supposing that the characters whose con- a junction they violate are united by cause and effect; for although causation permits no exceptions, it may be ocasionally counteracted. The more we can exhaust the relations of conespoactil or concomitance, and the more precisely we can express them, the better are we prepared for the great classifying operation | that makes up Zoology. The full import of the remark will appear under the next head. (hae It might seem superfluous to insist on preserving a regular order in the statement of Characters throughout the whole scheme—whether in the Comparative Anatomy or in the > Zoology,—seeing no one ean follow out comparisons that ¢ are not uniformly expressed. 4 im ' TI. The Maximum of Affinity as gwing the Classes. — ng a 17. The choice of Classes follows the maximum of ag 2. ments in the several organs. The existence of Laws of Concomitance indicates “he “possi more organs, or important modifications of organs. zoologist grasps at this circumstance, in order 0 forn leading classes. In appearance, but only in appearance, there i is. ay BASIS OF CLASSIFICATION. 541 principle of grouping. Some one organ is chosen as the basis of classification ; for example, the Reproductive system, which gives the name to Mammalia. In reality, however, such choice is made not on account of the organ by itself, but on account of the number of its alliances. An extreme supposition will place this fact in a clearer | light. Let us imagine that every one of the leading organs, or systems,—Nervous, Reproductive, &c.—was wholly uncon- nected in its modifications with every other organ; that the nervous system might vary through all possible modes without any corresponding variation in anything else. Under such circumstances, we might have a comparative anatomy of each organ, but no concurrence of organs. Zoology would be incompetent and non-existent. The only possible classifi- cation would be according to the Comparative Anatomy of the several organs. We might assign a superior dignity to same one organ, as the Brain, and give it a priority in arrange- ment, and a preference in study; but after the entire animal kingdom had been exhaustively arranged under thecomparative anatomy of the Nervous System, the same operation would have to be repeated under the other systems ; the work would then be finished ; being substantially the present science of Comparative Anatomy, without the relief that is at present afforded, to the overwhelming mass of details, by laws of Concomitance. Accordingly, the justification of preferring one organ as the classifying basis, is avowedly its alliances. The taxonomic value of the ‘ placenta’ in Mammalia is the number of charac- ters that it carries along with it. ‘Man, the Apes, the Insec- tivora, the Cheiroptera, the Rodentia,—are all as closely con- nected by their placental structure as they are by their general afjinities’ (Huxley). The real motive to the grouping is not the placental structure, but the general affinities. We may make another illustrative supposition. If all the organs were strictly co-equal in development and in modifica- tions; if the Nervous System, the Muscular System, the Reproductive System, &c., were all modified in strict concomi- _ tance, there would be no such thing as a preference organ whereupon to base classification; the Reproductive organs could be no more a clue to the ‘ general affinities’ than the digestion, or the respiration. There would be no mention of a special basis ; general affinity would alone be prominent. It would appear, however, that the constituent systems of the animal organization are not co-equal and concomitant in 549 LOGIC OF ZOOLOGY. their changes; some carry with them more, and some less, me 3 general affinity or concomitance. Taking the whole Animal — Kingdom, we find that the Nervous System is by far the most _ important basis of classification; the reason being that the organs generally cannot advance without a corresponding rise ‘in the regulating and co-ordinating organ. There cannot be an extension of the muscular apparatus without an extension of the brain; while the muscular apparatus itself implicates many other parts of the system. , Next to the Nervous System is that part of Reproduction, embracing the mode of Development of the animal from the germ upwards. We have already seen how far this governs the divisions and sub-divisions of the Mammalia; their very name is founded on it. Y If, for the sake of illustration, it were asked what would be the worst organ for classifying upon—the one that undergoes the greatest degree of unconnected or isolated variation,—the — answer would probably be the Heart. IIL. Classification by Grades.—Spectes. 18. It being assumed that each class is formed on the — maximum of affinities, the number of grades is regulated — by the occurrence of a succession of suitable groupings. The grades, or halting-places, are a relief to the burden of numerous common characters; but there is no need tocon- stitute them where the amount of resemblance is inconsider- __ able. 5 In the higher Vertebrates, a succession of six, seven, ormore grades is admissible and advisable; while the attempt to con- stitute Natural Orders, Genera and Species, in the Protozoa, — is misplaced and savours of pedantry. - In Mammalia, the distinctions of Species may be numerous — and important; profound differences separate the Lion and — the Tiger, the Horse and the Ass. In Birds, on the other hand, the species often turn upon small and nice peculiarities. - Of the three hundred species of Parrots, it is impossible that — there can be specific differences either numerous or important; _ the Psittacos erithacus, for example, is distinguished as grey, — with tail red! The domesticated varieties of the horse, dog, — and cat, have wider differences than many species, or even — genera, of the lower animal tribes. The differences between a Negro and a Caucasian (varieties of the Species—Man) pro AGREEMENT AND DIFFERENCE, 543 bably surpass in number the distinctions between two Natural Orders of Infusoria. Iu some cases, there occurs a single character so bold and remarkable as to satisfy our utmost demands for a specific distinction. Such is the extraordinary electrical organ in cer- tain fishes. The species of the Gymnotus named eleciricus, is sufficingly marked by this single feature, in whose presence the describer abstains from all further specification. IV. Marking of Agreement and Difference. 19. Zoology depends greatly on the rule of parallel array for Agreements, and of pointed contrast for Differ- ences. The characters of classes, high or low, should be thrown into the form most advantageous to the reader, that is, the tabular arrangement, with appended remarks and comment- aries in ordinary typography. For example, the characters of Aves (reckoned sufficient for discrimination, although inadequate asinformation) are these:— Reproduction :—oviparous Respiration :— air-breathing Heart :—four cavities, as in the Mammalia Integument :—feathers Teeth :—wanting ; substitute horny jaws Locomotive Organs :—the anterior limbs are wings. Besides these characters much is to be said as to the points of community, in the Nervous System, the Digestive System, and other parts. For the statement of Difference we may select Mr. Huxley’s primary division of Birds into three classes ; an instance where the pointed contrast may be extended to three members :—- SAURURE RATITA CARINATS Metacarpal Bones Not ankylosed §Ankylosed Ankylosed Caudal Vertebree and Tail Longer than body Shorter Shorter Crest of Sternum None Present Barbs of the Feathers Disconnected Connected. There are several other characters of the second and third classes, and no more of the first. Hence, we might have put the first against the two others as a whole, and then worked out the present contrast upon these two. Ov ann 3} Lye , or “Pn te A a 544 LOGIC OF ZOOLOGY. oa. te Not merely in the formal exhibition of generic and specific characters, but in every incidental comparison of one class with another, the statement of Agreements and of Differences should always be clear, emphatic, and ostentatious. V. Index Classification. 20. An Index Classification for Zoology might choose between the two alternatives—-the tabular and the dichotom- OUS The Tabular method has already been suggested for Mine- ralogy, and will again be brought up for Diseases, The Dichotomous method is carried to perfection in Botany. a A tabular plan could be based upon Comparative Anatomy ; there being given, under every peculiar mode of each organ, a complete list of all, animals possessing that mode. Thus, there would be a table of the species conforming to each grouping of the Teeth, so that the discovery of such grouping in any given specimen would decide the animal as one of the — list. A second character being noted as present in the speci- __ men would direct to a second list, where the animal must — appear; the choice is now narrowed to such as are common to both lists. A third, and a fourth character, being followed — out in the same way, would reduce the choice to still smaller limits ; and eventually the enquirer would be guided to the proper Species. pong The dichotomous method of Botany, if fully adapted to — Zoology, as it might obviously be, would be still better, = The want of an Index is less felt in Zoology because of the — better marked specific distinctions, at least until we descend — to the inferior tribes, where there are numerous species, — slightly marked. It would be pre-eminently necessary for Birds, among Vertebrate animals, and for the Invertebrate — Orders generally. It is less necessary for Mammalia, except , in a collection of unusually vast extent, ei CHAPTER VIL LOGIC OF PRACTICE. 1. The Practical Sciences are defined by their several ENDs. Medicine is the practical science having for its end Health. Grammar and Rhetoric have for ends the perfection of the instrument of Language. 2. There is one crowning end, the sum of all other ends, namely, Happiness or Well-being, People desire Health in order to be happy. There can be no end beyond human enjoyment—the gaining of pleasure and the averting of pain. 3. ‘The final end of all pursuit must be assumed or granted ; it cannot be proved. No proof can be offered of the position that Happiness is the supreme end of human conduct. We must be satisfied with the fact that mankind make it the end. As all proof consists in referring the point in question to something more fundamental, there must be at last something taken for * granted on its own account. Such is Happiness, the highest crowning end. Men desire Happiness, either for themselves or for others, as the goal of all endeavour. 4. There is, however, a want of perfect unanimity as to the final end. Some even deny that Happiness is the end; while there may be great difference of opinion as to the nature of the happiness to be sought. The end set up by some, as the final end of all, is Virtue. To those that embrace this view consistently, there is no reply; there is no possible appeal from a fundamental end. We may, however, enquire whether any class of persons do consistently and thoroughly maintain virtue, and not happi- ness, to be the sole end of all endeavours. Wherever there is inconsistency, an argument is possible. Now, in reply to the setting up of Virtue, or mere self- denial, as an end, we may urge, first, that the conduct of man- kind shows that, in the great mass of cases, they regard virtue 546 LOGIC OF PRACTICE. asa means to happiness. The virtue of Howard consisted not in the fatigues and privations suffered from his journeys, and from visiting squalid dungeons ; it was in the amount of human misery that he relieved. Secondly, the position that Virtue is an end is almost uniformly coupled with the assertion that, in the long run, Virtue is Happiness; which is merely another way of assign- ing Happiness as the end. Thirdly, the thorough carrying out of the position that Virtue, in the form of ascetic self-denial, which is Virtue dissociated from Happiness, is the ethical end, would be tanta- mount to abolishing the difference between good and evil, with which virtue itself is identified. Virtue, in the sense sup- posed, flourishes in misery ; the more miserable we are, the greater scope we have for virtue; the more miserable we make other people, the more scope we give them for virtue. Again, Happiness may be allowed as the end, and yet there may be wide differences of view in the interpretation of the end. The partizans of virtue may re-appear on this ground, affirming that Happiness is only to be found in Virtue or Duty, not in enjoyment and in the absence of pains. The reply proceeds as before; are these reasoners thoroughly consistent with themselves? If they are, they cannot be refuted; if they are not, they may. Great variety of opinion may be held as to the beings whose happiness is to be sought. Are we to seek our own happiness solely, or the happiness of others solely, or partly the one and partly the other? How far are we to extend our regards— to our own kinsmen, to our fellow citizens, to humanity in general, to the lower animals? In none of these points is argument possible, unless where people are inconsistent, which they need not be. We cannot reason a person into the adop- tion of other people’s happiness as an end, unless such person has already of his own accord embraced some doctrine that involves this, as for example, the profession of Christianity. Neither can we offer any reason for extending sympathy to the lower animals. An education of the feelings is the only — mode of enlarging people’s sympathies. Noman can be argued — out of a consistent selfishness. CHAPTER VIII LOGIC OF POLITICS. 1. Politics, in the largest sense, refers to the action of human beings in Society. The notion of Society can be gained only by each one’s individual experience. The first example of it is the Family, which contains a plurality of persons in mutual co-operation, withcommand andobedience. The earliest notions of authority, law, command, obedience, punishment, superior, inferior, ruler, subject,—are gained from the various aspects of the small domestic circle. The larger aggregations of the school, village, parish, town- ship, church, &., repeat all those aspects of the family, while dropping the incidents special to the family. 2. Thescience of Politics, as a whole, is either Thanraan cal or Practical. Under the Theoretical Science of Politics must be described the structure or organization of Political Society ; this being equally essential as a preparation for the Practical Science. All the leading terms of Politics must be defined ; all the parts of the Political system explained. To this preliminary branch, Sir G. C. Lewis applies the designation ‘ Positive Politics,’ In the second place, the Theoretical Science traces cause and effect in political institutions, as facts of the order of nature; in the same way as Physics and Chemistry describe cause and effect in inorganic bodies, and Biology in living bodies. The theoretical department of Society would state, upon evidence of fact, conjoined with reasonings from human nature, what are the consequences of given institutions. To quote from Sir George Lewis :— ‘It assumes that we know what astate is ; what are its functions ; what are the conditions necessary for its existence; by what in- struments it acts; what are its possible relations with other states. Starting from this point, it inquires how certain forms of govern- ment, and certain laws and political institutions, operate; it seeks. from observed facts and from known principles of human nature, to determine their character and tendency; it attempts to frame propositions respecting their probable consequences, either uni- * 548 -- LOGIC OF POLITICS. | a versally, or in some hyyothetical state of circumstances, Thus it may undertake to determine the respective characters of monarchy, aristocracy, and democracy ; it may show how each of these forms of government promotes the happiness of the community, and which of them is preferable to the other two, It may inquire into the operation of certain modes of preventing crimes—as police,—of criminal procedure, and of legal punishment, such as death, trans- portation, imprisonment, pecuniary fines,—and it may seek to determine the characteristic advantages and disadvantages of each, in certain assumed conditions. It may inquire into the operation of different systems of taxation—of laws respecting trade and- industry—of modes of regulating the currency—of laws regulating the distribution of property with or without will—and other economical relations. It may lay down the conditions which render it expedient to govern a territory as a dependency; or q which tend to promote the prosperity of a new colony. It may define the circumstances which ensure the permanence of national confederacies, and it may inquire what are the rules of interna- tional law which would tend to promote the uninterrupted main. tenance of peace. ‘It seeks to lay down general theorems respecting the operation and consequences of political institutions, and measures them b their utility or their capacity for promoting the welfare of the national community to which they are applicable. Propositions of this sort may lead (though not by so direct a road as is often supposed) to preceptive maxims ; but they are themselves merely general expressions of fact, and they neither prescribe any course of conduct, nor do they predict any specific occurrence; though, from the generality of their form, they may relate as much to the future as to the past.’ The Theoretical Science of Society is sometimes expressed as the ‘ Philosophy of History,’ or the accounting upon general principles of cause and effect for the actual course of political events, the growth of institutions, the progress and decay of nations. History, in the ordinary signification, recounts these things in the detail; the Philosophy of History generalizes the agencies at work, and endeavours to present the whole as fol- lowing out certain great leading ideas. A few writers have aimed at establishing such generalities—Vico, Montesquieu, Millar, Condorcet, Auguste Comte, &c. Practical Politics consists of maxims of political practice. Here we have to suppose an end,—the welfare of the com- munity, or any other mode of stating the political end. This necessarily appears with more or less prominence in all political treatises. Aristotle’s work is a search after the best — government. Machiavel’s treatises are preceptive or practical. — Locke does not formally enquire after the best constitution, SCIENCES COMPRISED IN POLITICS, — 549 but under the guise of what is necessary to a state, he insinuates certain political forms, and certain legislative principles. Sound method requires that a writer should, in the first instance, separate the Theoretical from the Practical. 3. The entire department of Political Science at the pre- sent day comprises several sciences. It has been found practicable and convenient to withdraw from the wide region of human society, certain subjects that can with advantage be cultivated apart, and thus to reduce the complication of political enquiries. (1) The first of these is Jurisprudence. This is a distinct branch bearing on the form of Law, as apart from its substance. It teaches how laws should be expressed, with a view to their satisfactory interpretation by the Courts ; it embraces evidence, * and the principles and procedure for the just administration of the laws. It does not consider the choice and gradation of punishments, but explains how they should be legally defined, so as to be applied in the manner intended by the legislator. (2) International law is the body of rules agreed upon by independent nations for regulating their dealings with each other, both in peace and in war. It includes, for example, questions as to the Extradition of Criminals, and the right of Blockade at Sea. (3) Political Economy, or the science of the production and distribution of Wealth, relieves the political philosopher of a_ considerable part of his load. The legislation regarding Pro- perty in Land, Trade, Manufactures, Currency, Taxation, &c., is guided by the enquiries of Political Eeomony. Within its own sphere, this science has the same logical character as the mother science. It has its definitions, its principles or laws, partly inductive and deductive, and its methods, which are the ordinary logical methods. (4) Statistics is a branch of the Science of Society, admit- ting of being cultivated separately. It furnishes the facts and data of political reasoning in the most complete and authentic form. 4, The subjects remaining to Political Science, are (1) the Form of Government, and (2) Legislation on all topics not otherwise embraced. The different Forms of Government, their precise defini- tion, and their several tendencies, constitute the foremost preblem of the political science. The discussion of Monarchy, 550 LOGIC OF POLITICS. Aristocracy, Democracy, enters into every treatise called political. In immediate connexion with this subject, if not a part of it, is the distribution of the functions of government, into Legislative, Administrative and Judicial; the delegation of the powers of government to subordinate authorities, as in provincial, local, or municipal government. These subjects are sometimes considered as exhausting the sphere of Politics; but ina very narrow, although distinct signification of that sphere. Thus, Mr Mill remarks,—‘ To attempt to investigate what kind of government is suited to every known state of society, would be to compose a treatise on political science at large.’ It must, however, be matter of enquiry how a government, when constituted, is to discharge its functions. This supposes that the functions are classified and defined; an operation involving one very important enquiry in Politics, namely, the proper Province of Government. There are certain things that Government must undertake, in order to fulfil its primary ends; such are Defence, and the Preservation of Life and Property. There are other things that government may or may not undertake—as the Support of Religion, Education, Postal com-— munication, the maintenance of Roads, main Drainage, aiidi other works of general utility. 5. The curtailment of Individual Liberty is a necessary effect of government ; and the degree of this curtailment is a vital consideration i in Political theory. In order that men may act together in society, each must in part subordinate their own actions and wishes to the general scheme. Obviously, however, individual liberty, which is in itself a chief element of well-being, should be restricted in the least possible degree; and the burden ei proof must always lie upon the proposer of restraint. The Structure of Political Society. 6. The preliminary branch of the Social Science, con- 4 tains the Definition of Political Society, and of all the — Relationships and Institutions implied therein. r This is the part of the subject entitled by Sir G. C. Lane Positive or Descriptive Politics. It teaches what is essentially ' involved in the idea of political government. It an the — THE POLITICAL STRUCTURE, 551 necessary instruments of government; as a law, rights and obligations, sanctions, executive commands, and the like. It neitlier enquires into the operation and tendency of institutions (which is Theoretical Politics), nor urges the preference of one to others (Practical Politics). It explains the meaning of monarchy, aristocracy, democracy, but does not teach which is the best form. It shows what is the nature of punishment, bust does not say which punishments are the most efficacious. It expounds the relations of master and free servant, and of master and slave, but does not trace their bearings on the welfare of the parties concerned. It explains the nature of a dependency, without arguing the question—Should colonies have a separate government. It shows what are the acts constituting an exchange, and the difference between barter and a money equivalent, but does not dwell upon the advan- tages of exchange in facilitating trade. (Methods of Reasoning in Politics, vol. I., p. 54). The fundamental notions of Political Society—Sovereignty, Law, Command, Duty, Sanction, Obligation—are treated of by John Austin as a part of the special science of Jurispru- dence. That these notions are at the basis of Jurisprudence is beyond doubt. Still, in a completely formed Political Science, they would be given once for all at the outset, under the head of the Structure of Political Society, and would need only to be referred to by the Jurist. 7. The very fact of Political Society involves a series of primary notions, forming a mutually implicated, or corre- lative group. Government.—This is the essential fact of political society ; to define it, or any one of its numerous synonyms—NSovereignty, Authority, Ruler, Political Superior—is to define political society. The definition must be gathered from the Particulars common to Political Societies. It is given by Sir G. C. Lewis, as follows :—‘“ When a body of persons, yielding obedience to no superior, issue their commands to certain other persons to do or to forbear doing certain acts, and threaten to punish the _ disobedience of their commands by the infliction of pain, they are said to establish political or civil governinent.”” Closely examined, this definition contains the very terms to be defined—for example, superior and command—so that it is not a definition suited to inform the ignorant. It is rather of the nature of the first definitions of geometry (Line, Angle, &c.) which do not communicate notions, but employ terms to 552 LOGIC OF POLITICS, fix with more precision the boundaries of notions already gained from experience. We should require, in the first place, to know political societies, in concrete instances; and the definition would teach us the corresponding abstraction or generality. Austin (Province of Jurisprudence Examined) endeavours to build up the definition from its simplest assignable elements. Starting with Command, he defiues this as ‘ the expression or intimation of a wish, to be followed with some evil, if not complied with.’ This involves only such facts of human nature as wish, expression, non-compliance, infliction of evil. In the notion of Command, as thus defined we have nearly all that is signified by Government, Sovereign, Superior, Authority. We have only to specify the persons intimating the wish (to some other persons) and following up the non-compliance with the infliction of pain. The supposed command is a Law. The evil to be inflicted is a Sanction, Penalty, or Punishment. 'The persons addressed are Subjecis, Inferiors ; they are placed under Obedience, Duty, Obligation. The aggregate of persons comprised within the scope of the same commands, is a Political Socvety, a Community, a People. They are in the Social state, as opposed to the state of nature. Moral Right and Wrong must be referred to the same com- plex fact. 8. Government is usually said to have three distinct functions—Legislative, Executive, and Judicial ; each one giving birth to a numerous class of notions. iad od ie coe Sa hea Legislature-—The power of making general commands uni- versally applicable, under given circumstances, is called Legislation ; it is the most extensive and characteristic func- — tion of government. The process is very different under — different forms of government. In every shape, there are — implied as subsidiary notions—statute, and its synonyms, pub- lication or proclamation, enactment and repeal, &c. ~ Huxecutive, Adminisiration.—Implies performance of the speci- — fic acts occurring from day to day, in the exigencies of society — —organizing and directing the military force, negotiating with foreign governments, appointing the officials of government, erecting public works, &c. In this function, the government is said to use ministers, to issue orders, to receive and i issu despatches, reports, to suwpermtend all functionaries. i Judicial,—A distinct function of government, delle en- a as -* Rie THE POLITICAL STRUCTURE 553 trusted to a separate class of persons. It supposes impedi- ments to the commands and operations of government, either in the way of misunderstanding, or of disobedience. These are removed by Judicial Institutions, called Courts of Law, presided over by Judges, said to administer Justice, according to a definite Procedure, and rules of Hvidence. The ramified arrangements belonging to these several heads are detailed and defined by the special science of Jurisprudence. With all varieties of government there must exist these three functions ; in rude governments, they are exercised by the same persons ; in civilized governments, they are more or less divided between different persons. 9. Under ‘ Form of Government,’ there is a number of structural modes, for which there are specific designations. The Form of Government brings out the designations Monarchy, Aristocracy, Democracy, Republic, Mixed Govern- ment, Balance of Power, Constitution. The logical division of Forms of Government is into the government of one person (Absolute Monarchy) and the govern- ment of more than one (Republic or Commonwealth). If, in the second alternative, the governing body is small, the government is an Aristocracy ; if the power is lodged in the majority of adult citizens, the gorenment is a Democracy. Such names as Limited Monarchy, Constitutional Monarchy, mean either Aristocracy or Democracy; they indicate the form of monarchy, but the reality of another power. A Mixed Government is a mere semblance; some one of the con- stituents is in point of fact the sovereign. Aristocracy, where it prevails, makes a division of the people into Nobility and Commonality. Often the governing body is a hereditary nobility. Representative Government, the growth of modern Democracy, is a leading notion of Political Science. The meaning is that the whole people, or a large portion, exercise the ultimate controlling power, through the deputies periodically elected by themselves. In the ancient republics, the corporate or col- legiate action lay with an assembly of all the citizens, or of as many as could be got together. The operations of corporate government give birth to the political elements expressed by assembly, deliberation and debate, decision by a majority, chairman, election, suffrage. 10. The Functions or Business of government introduce many structural elements. 554 LOGIC OF POLITICS. ou aN The first function of a political society being defence, there is a large institution corresponding, called the War eget tion—Army and Navy. “ The protection of the members of the society from one another is either by an application of the War force, that is the soldiery, or by a separate force called Police. = These two leading institutions involve many others. An official machinery, or bureaucracy, is interposed between the sovereign power and the actual instruments. For paying the cost, there must be a levy of Taxes, with a bureaucracy corresponding. If the government undertakes public works—roads, bridges, public buildings, means of communication—it becomes a sort of industrial management on the large scale. The coining of money is a proper function of government. The regulation of bargains and contracts of every description, as well as the enforcing of them, is a matter for the state. The marriage contract, in particular, the relations and rights of the different members of the family, are under state control. A Church Establishment, whether incorporated with the civil government, as is most usual, or existing apart, is a vast social machinery with elements and terms corresponding, all admitting of definition. - 11. In a society spread over a wide territory, there must be a division into local governments, duly subordinated to the chief or Central Authority. This originates the terms Central, Centralization, and Local, _ Provincial, or Municipal government and institutions. Asmall locality may represent in miniature nearly all the features of — the entire society. The delegation of power to the loc . may be small or may be great. Moreover, the Form of - Government of the entire society repeats itself in the localities. — If the sovereign is an absolute monarch, the local authority is. absolute in the local sphere; such is the oriental satrap, an the viceroy of the absolute European monarch. 12. The Province of Government marks the line between Public and Private management. | eke The habitual industry or every day avocations of the mass of the people must be left to themselves. Their manner bo subsistence, their recreations and amusements, are also their — own choice ; although governments have often anne es to regulate all such matters. ORDER AND PROGRESS. 55D 13. The mutual bearings of Public and Private Institu- tions are so numerous, that a statement of the Political structure is incomplete without the Private Institutions. The Industry of the People is an important element of the state politically. So are their Recreations, Tastes, Opinions, Literature, and Science. However much the government ab- stains from control in these matters, its operations in its proper sphere are influenced by every one of them. An agricultural community gives a peculiar character to the entire action of its government. A community largely occupied in foreign trade involyes the government in relations with foreign coun- tries. 14. The good or ill working of the Political system leads to a variety of situations, requiring the consideration of the political reasoner. When the government fails to accomplish its main functions —defence, protection, justice, &c.- -it receives the designations, ‘bad government,’ ‘mis-government.’ Its badness may con- sist in partiality to individuals, which is injustice; in not adhering to its own published regulations; in the capricious. introduction of changes ; in preying upon the community by exactions, or by affronts, . When the government is excessive in its restraints on indi- vidual movements, it is called despotical, tyrannical, oppressive ; and the re-action or. revolt is Political Liberty. When it meddles with what might be left to private management, it is said to over-govern ; the euphuistic phrase is a paternal govern- ment. The emphatic expression Social Order means, in the first place, that the government, whether good or bad, is obeyed ; the opposite state is Anarchy, Revolt. Order is also contrasted with Progress, Improvement, or Owwilization. .Those things that maintain the existing structure in its integrity are said to minister to Order; while the agen- cies that raise the society to a higher pitch of improvement, are said to minister to Progress. In point of fact, the opposi- tion between the two is very slight; what is good for one is, with very trifliug allowances, good for the other (Mill’s Re- presentative Government, chap. II). +556 LOGIC OF POLITICS, | he THEORETICAL POLITICS. er “a 15. The Laws, Principles, or Propositions, of political 4 society, together with the Methods of invesiaaae consti- | a tute Theoretical Politics. ‘ite i The foregoing head, including the Analysis of the Social ; Structure, the meaning of State of Society, the Notions of — Politics—is preparatory to the enunciation of the Laws of — Society, so far as known. These Laws are best discussed in | the theoretical form; they may afterwards be changed into the practical or preceptive form, that is, nto maxims of the a Political Art. 7 4 16. The Laws of Society may be either Laws of Co- | existence, or Laws of Succession, of the different parts of a the Social Structure. In both cases, they are laws of Cause and Effect. a The complex structure of Political Society involyes many relationships of Co-existence and of non-coexistence. Soned arrangements always carry with them some other ane a ments ; some things are repugnant to other things. Ther mark was made by Volney that the ‘plains are the seat c indolence and slavery, the mountains of energy and ooo But whatever co-existences and repugnances can be predicna generally are dependent on causation. 4 Again, we may take any one part of the social structure a8 a cause, and lay down the laws of its effects; as when w describe the consequences arising in a given state of = from an absolute monarchy or from a state church. We may even take up an entire state of society, with all's it os mutual actions, and endeavour to trace its future destiny. . This is the large problem of the Philosophy of History. But for devices of simplification, such problems would be wholly unworkable ; the complication of elements could be embraced by the human mind. We should need to fas upon some single agency, either comprehending, or outwei ing the others, whose solitary operation will give the ke. the entire problem. The state of opinion and enlightenm of a community is an example of those over-masterin cumstances. fi re ‘ie Human Character as a Political Element. 17. As the subject-matter of Political Science is humar a es * "vid oye An aaa ae a ¥, i oils POLITICAL ETHOLOGY. ‘ 557 beings, the characteristics of humanity must enter as a primary element. If all human beings were alike, either wholly or in those points concerned in political action, the construction of a political society, whether easy or not, would be but one pro- blem. But there are wide differences as regards peculiarities of character essential to the working of the political scheme. The differences between an American Indian, a Hindoo, a Chinaman, a Russian, an Englishman, an Irishman, an Italian, taken on the average, are such as to affect seriously the struc- ture and the workings of political institutions. Given a certain Form of Government, or a certain constitution of Landed Property, the tendencies would alter greatly under these various types of character. The theory of Society consists in stating how human beings will act under a given social arrangement; it is, therefore, essentially a special application of the laws of mind and char- acter. Hence a thorough knowledge of whatever Psychology can teach would be a preparation for this study. Yet, all parts of human nature are not equally concerned in political action; the ethical qualities of Honesty, Industry, Steadiness of Purpose, are more vital than the Artistic sensi- bilities. Moreover, Politics is concerned only with the characteristics that appear in collective bodies. The politician leaves out of account all those individualities that are merged when men act together in a body; that is, the qualities occuring merely in scattered individuals and in minorities. Whence, national character is a much simpler phenomenon than individual character ; as the flow of a river in mass is a simpler physical problem than the molecular adjustments of the liquid state. 18. A Political Ethology would be a modified science of character, consisting (1) of a selection of the qualities that appear in national character, and (2) of the laws of their operation, (1) Following the divisions and subdivisions of character, as formerly sketched (p. 518), we should have to bring out into prominence all that arise in human beings when working collectively. Thus, to commence with Action, in the form of Spontaneous Energy. Prior to an account of the various motives that induce men to activity, there is a notable peculiarity of cha- 558 ' LOGIC OF POLITICS. racter in the degree of the energetic disposition itself. this shows itself, as high or as low, in whole nations, na s importance as respects both the Form of Government many other political arrangements. The inhabitants of tempe rate climates are superior in natural energy, irrespective of al all modes of stimulation. to the dwellers either in the roma r in the arctic circles. The English and Anglo- -Americ peoples are probably at the top of ‘the scale. Now this attribute has numerous social bearings. It iansieeh private industry and the accumulation of wealth, an effect leading to many other effects. It is both directly and indirectly ee hostile to monarchical or despotical rule, and is, therefore, the ‘ parent and the guardian of liberty. 3 In like manner, we might survey in detail the FEELING < Sensibilities, or Emotions of the mind, and mark those that have social significance, and those that appear in men eae = lectively. Thus, the Tender Sentiments, or the Sociability of re the Mind, when strong, draw human beings together in society, — and favour the cohesion of states as well as of families. Again, a the strength and the mode of the Sentiment of Power may be — a collective peculiarity, with national consequences. The fig conjunction of tender feeling, as patriotism within our own nation, with the love of domination beyond, is a pecntay by often repeated. aa The InrELLEcTUAL qualities that stand out in national pr O- minence are too numerous to be touched upon. It was an intellectually minded people, the Greeks, that began all the civilization flowing from science or philosophy, “There is a certain depth of ignorance and incapacity that renders th higher modes of Political society impossible. A signal fail e in either of the intellectual virtues—prudence and sympath > is incompatible with political union. "i (2) The next part of Political Ethology is an account of tendencies of these various characteristics, and of the me whereby they themselves are modified. The general scie of character embraces this investigation on the wide scale, : the present department is a special application of the panei Ss. Propositions of Theoretical Politics. 19. The Political Structure, or Organism, being defi net the Laws of Theoretical Politics are the laws of Causi Effect, traceable in the working of the several Instit What are the consequences of Absolute Monarchy ~~ iyo. : CAUSE AND EFFECT. 559 Democracy ; of Castes; of Hntails; of Free Trade; of Poor Laws; of Indissoluble Marriage ; of State Churches? These are a few of the enquiries of Political Science ; they are strictly enquiries of Cause and Effect. Given any of these institutions as causes, the effects may be sought. Again, given certain effects, as the repression of agrarian crimes, the impartial administra- tion of justice, the encouragement of trade,—we may seek for causes. This is really the same problem in a. different form. To all intents and purposes, the one enquiry is—Given a cause, required the effect ? t is not uncommon for political philosophers to entertain such problems, as What are the effects of Monarchy, Aristoc- racy, Democracy, in general; what are the effects of Slavery in general, that is, under all circumstances, under every possible variety of human character. Now, with such strongly-acting causes as Absolute Monarchy, there may be assigned certain universal tendencies so decided as to be seldom wholly defeated. There are points in common to the despotism of a single person in all countries and times. The possession of power, whether _ on the great scale or on the small, operates with remarkable uniformity. This is a psychological tendency whose free course is best seen in politics; where, by the necessities of the case, individuals have to be entrusted with power in a large amount. The same consideration renders the workings of slavery uniform to a high degree. 20. The Propositions of Political Science range between two extremes; on the one extreme are propositions affir- ming vniversal tendency, and, on the other, propositions affirming specific effects in limited cases. (1) The propositions affirming a universal tendency are exemplified above. Similar propositions may be found respect- ing every institution of human society. In many institutions, however, the tendencies are difficult to find out, and are so liable to be defeated by other causes, that their enunciation has scarcely any value. For example, the operation of guilds, or privileged corporations, admits of no definite statement with reference to all possible circumstances. The division of land into large or small properties may have opposite effects in different social states. Nevertheless, the attempt should be made to generalize the tendencies both of the Forms of Government, in their detailed varieties, and of all the leading Institutions growing out of legislative action. It is equally indispensable to estimate the 560 LOGIC OF POLITICS. precise worth of this class of propositions, to be aware of the infirmities, and of the cautions needed in applying them. ~ There are prevailing tendencies of every important Institution —of the Succession of Land, of Direct or Indirect Taxation, — of Religious Endowments, and the rest. The affirmations re-— specting these are only probable; they afford a certain Pe sumption of what will actually happen in individual cases. The special departments—Political Economy and Jurisprae dence—share the burden of these difficult problems. == a (2) Propositions confined in their range to limited cireum- _ stances, to a narrow field of observation, may be so qualified — as to state the causation with almost perfect exactness. Thus if we confine our views to communities in similar climates, of the same race, of nearly the same advancement in general — intelligence, we can formulate with comparative precision the tendencies of a given institution, whether the Form of Govern- — ment, or any of the other leading social elements. These — Limited or Partial Theories are the really valuable parts '€: Political Science ; they afford the guidance in the art or pre tice of Politics. With a view to these propositions, there must be a aiviieal and subdivisions of communities into classes. An example of — such a classification is given by Sir G. C. Lewis, as follows:— _ ‘One large classification of communities for the purpose of a common predication is—1, those communities which are in a wild and unsettled state, ‘such as the African and Indian savages, the Bedouin Arabs, the Nomad Tartars; 2, those Oriental communities white live under a regular polit al government, but whose social state is nevertheless fixed and unprogressive, such as the Turks, the Persians, the Hindt / the Chinese, the Japanese; 3, Christian communities partaki of the modern European civilization.’ i Setting aside the first class, as affording too een a fi for political data, Sir G. C. Lewis institutes a comparison ¢ contrast between Oriental and European communities, show each of the two classes as a whole. The following are sc leading points of the contrast. | ORIENTAL. EUROPEAN. Government. Despotical Free oe By Delegation _ Direct from the centr re International Law. ? Rude Intricate, forming : i LIMITED OR PARTIAL THEORIES, 561 Laws—Civil and Religious codes, Interwoven Distinct Marriage. Polygamy Monogamy Women. Secluded At large Status of the Labourer. Slavery Civil Freedom Punishments. Cruel Mild Dress. Loose Closely fitting Alphabet. _ Intricate Simple Form of Interature. Poetry and mystical prose Argumentative prose. Numerous propositions of Cause and Hffect could be laid down respecting these peculiarities, connecting them with one another, and with the Climate and Physical Situation, the Physical and Mental Constitution, and the Historical Ante- cedents of the oriental races. Methods of Theoretical Politics. 21. As in all other sciences, there must be Observation of Facts. In Political Observation, there are special peculiarities amenable to logical canons. The education of a political observer is scarcely in any degree, as in the physical sciences, an education of the senses; it consists mainly of intellectual habits. 22. The Facts of Politics coincide with authentic His- tory or Narrative. The individual occurrences that, when generalized, make up political principles, have to be correctly recorded, with all the circumstances essential to the link of causation. The sequence of events in a revolution must be stated exactly as they occurred, and in sufficient fulness to give the conditions of canse and effect. The rules of historical evidence are a branch of Inductive Logic, and as such they are given elsewhere (Appendix, I). They have in view principally the number and the nature of the testimonies needed to establish the truth of a past event. 562 LOGIC OF POLITICS. A farther exercise of discrimination is requisite in the polit ti historian, namely, to include all the circumstances enter into the chain of causes, and to separate accompaniments — that have only a poetic interest. To do this, the his-— torian must be himself a_ political philosopher ; he must know that the dazzling glitter of spears in the sun has nothing | to do with the fighting strength of an army, that the stature, — complexion, voice, or dress of Charles I. had no bearing upon — his quarrel with his parliament. In short, as regards the — relevance of facts and circumstances, the narrater must under- — stand what it is to trace cause and effect in history. Tn ; order to frame a coherent narrative, some theory of causation > is necessary ’ (Lewis). 23. In Politics was first developed the reducing es observations to the form called Statistics ; definable as the observation, registration, and arrangement of such facts as | can be given in numbers. i The cultivation of statistics was first owing to the impeltatl given to political economy by the French economists ; it being | possible to state in numbers the most material facts regarding — trade, currency, taxation, production, population, &c. The — subject now comprises matters relating to all branches o} f political observation ; Population, Births, Marriages, Deaths ~ Occupations, Diseases, Crimes, Pauperism, Education. : Statistics gives an entirely new precision both to Theoretical AG or Speculative Politics, and to the operations of government. The increase or diminution of pauperism or of crime, in a la country, could be judged only in the vaguest manner with statistical returns from the officials concerned. The govert ment would be at the mercy of accidental displays, and of circumstances where the impressions are exaggerated. — bread riot in a particular locality, an outrage of appal accompaniments, would distort the judgment of the nation, as to the general state of destitution or of crime. 24. The causes of erroneous observation in Politics, partly common to the sciences generally, and para arg to the political science. 7 Indolence and inattention, the love of the marvello esthetic likings and dislikings, the support of a fay theory, are operative in politics as elsewhere. The special sources of bias in the political department are admira tion of individual actors, party feeling, and, where practice i r feos POLITICAL EXPERIMENTS. . 563 concerned, direct personal interest. As a matter of course, these corrupting motives extend their influence to the general- izing no less than to the observing of facts. Politics deals with human beings, whose springs of action are in the mind; while observation relates only to outward appearances, from which the mental states are obtained by inference. The right performance of this process of inference is an operation based on Psychology, and guided by the rules of Inductive Logic. That Charles I. was executed is a fact ; the motives of Cromwell and the Puritans in executing him are a matter of difficult inference ; requiring us to apply laws of human nature (veracity, bias, &c.), to what the actors said and did in connexion with the fact. The secrecy of motives is the characteristic of many ethical maxims. Eaperiment in Politics, 25. Experiment, in the strict scientific meaning, is usu- ally regarded‘as inadmissible in Politics. The substitutes are (1) the sudden introduction of extraordinary influences, and (2) the practical operations of government. It is not possible to submit a society to the process em- ployed in studying a metal, or in detecting the laws of Heat or Magnetism. A political community cannot be manipulated with a view to excluding artificially this or that agency, iso- lating it from all but known circumstances. (1) Some of the advantages of experiment are derivable through the introduction of a new and extraordinary influence into the society—such as a famine, a commercial crisis, an insurrection, an epidemic, an invasion, a new invention, as the steam engine, a religiousrevolution. The Irish potato famine of 1845, is adduced by Lewis as a casein point. The influence of this terrible calamity laid bare the evils in the state of the Irish poor, and disclosed the secret springs in the social economy of the people, as effectually as could have been done by an artificial experiment contrived for that purpose. (2) It is the very nature of government, especially an im- proving government, to be trying experiments. Every new law is an experiment.. There being an object to be achieved by the law, the public is supposed to be interested in watching the effects of the measure. A Police is organized, and the effects upon crime observed. A Poor Law is introduced, and the consequences traced. So every great innovation is a new agent in society, which is followed by definite effects. The 564. LOGIC OF POLITICS. Bae experiments are not always free from ambient thesed be concurring agencies either defeating or exaggerating the results; hence a demand for the precautions of the various — Inductive Methods, Sau a Causation in Politics, Wee 26. In Political Causation, the predominating fact is” Collocation ; there is seldom, yet occasionally, an eee to Conservation, 7S aa tee A political sequence is always immersed in a host of arranger ments, positive or negative; and although impelling forces | must always be present, the result is dependent in a pre-emi- nent degree upon the direction given to these forces. Thus, a political rising depends less upon the greatness of an impel-_ ling force, than upon the direction given to forces always present. The demand for thirty shillings of ship money from — John Hampden was the turning point of the English Revell 4 tion. . Yet in dealing with human nature, whether as individuals or political masses, any omission to allow for the principle of Conservation, in the form of Limitation of Human Energy, will lead to mistakes. Thus, a politician that would expe ct an Art-loving people like the Italians, Germans, or French, to’ take on the energy of the English in business and in politics, without becoming less artistic, would be guilty of overlooki ng the law of Limitation. x : a (Oo 27. In Political Causation, it is especially necessary keep in view the entire aggregate of conditions, positiv re and negative, entering into the cause. ; ff When Luther preached against Indulgences, and when Hampden refused to pay ship money, these were merely a sin condition out of a large assemblage concerned in bring about the great events that ensued. Hence, the histo considers it requisite to describe the whole of the surroundi in the state of society at the time, but for which the conse quences would not have arisen. ae To seek the cause of a political event in a single cir cumstance is a perversion of the political problem. The most enlightened reasoners and historians are accustomed t state the case as an enquiry into the causes of a phenom The phrase is not strictly correct; the entire aggre antecedents is properly the cause; but as bringing forw o ae =| CF wae i DEFECTS OF THE METHOD OF AGREEMENT. 565 idea of plurality of circumstances, conditions, or collocations, the mistake is on the right side. The causation of the French Revolntion was a vast aggregate of prior arrangements in the state of the French nation, together with numerous circum- stances in the world at large. The Method of Agreement in Politics, 28. The Method of Agreement enters into political investigation, but not without shortcomings. Like every other inductive enquirer, the political reasoner first collects his facts; then compares them with a view to attaining laws of concomitance, which he farther verifies by _Agreement, as a method of Elimination. This has always seemed the obvious course. When Aris- totle enquires into the effects of Despotical or of Democratical _ government, he collects examples of each, and looks out for the attendent peculiarities. By an inductive determination, founded on Agreement, we are accustomed to connect differ- ent forms of government with lower or with higher stages of civilization. The first peculiarity of the inductive problem of society, as affecting the sufficiency of the Method of Agreement, is the mere number of concomitant circumstances in a state of society. The cause A, say Despotism, works in conjunction with such a large variety of other circumstances,—climate, race, history, institutions in detaili—B C DE F, &c.,—that we can hardly find in the whole area of our experience a sufficiently diversified series of instances to eliminate them all, and find A followed in every instance by a. Worse than the mere number of accompaniments is plurality of causes with intermixture of effects. _ Whatever results might really flow from Despotism—whether discontent and insurree- tions, or the repression of men’s energies and the arrest of prosperity and progress—could flow from other social agencies; . the effect a, an actual effect of A, might also be an effect of C, F, H. This would not prevent a Honk being always present with A; it would rather in some instances make it supera- bundantly present ; yet, as proving too much, it would be fatal to the evidence. An apparently more paralyzing instance would be, when the effect a, properly belonging to A, is neutralised by some accompanying agent D; one of the commonest of all occurrences in politics. Hardly any effect of absolute monarchy is better substantiated than the discouragement of intellectaal 566 LOGIC OF POLITICS. activity generally; yet this did not follow at once on the — imperial despotism of the Roman Empire; the prior impeti acquired under free institutions was for a long time unspent. So, a law designed to produce a certain effect, may really be acting as intended; but the effect may be frustrated by evasions, or by passive resistance to its enactments. Restric- tions on trade are adverse to commercial prosperity ; yet the effect may happen to be counteracted by other circumstances. The United States of America, in the abundance of land to be occupied, can prosper under many arrangements that would be ruinous to Great Britain. The other Experimental Methods, 29. The Method of Difference may be exemplified in Political Cause and Effect. j The introduction or withdrawal of a single agent, followed at — once by a definite change in other respects, is our most cogent, — as wellas our shortest proof of causation. In the complications — of Political Society, we cannot always be sure that only the one innovating circumstance is present; so many unseen — operations being always at work. ‘This source of ambiguity is practically overcome when an agent suddenly introduced, is _ almost instantaneously followed by some other change; as when the announcement of a diplomatic rupture between twonations — is followed the same day with a derangement of the money 4 market. According as the supposed change is more gradual in i introduction, and the consequences slower in their deen ment, the instance is less and less a decisive example of differ ‘4 ence. The deterioration of value is saved only when we are a sure that every other thing has remained the same. A new religion introduced into a nation, remarkably stationary in its” other institutions, would be held as the cause of all the oe a quent changes. ; 30. Agreement in Absence may be advantageously re ; sorted to in Politics, tions ; and if any circumstances uniformly present in the are uniformly absent in the other, the force of proof is” gre atl augmented. DEDUCTION IN POLITICS, 567 30. Concomitant Variations is employed in tracing political causation. There is a marked concomitance, in the History of England, between the growth of Free Institutions, and the progress of the nation, both materially and intellectually. This may be compared with the inverse instances of Greece and Rome, where, by a gradual process, the extinction of liberty was ultimately followed by intellectual and social decay. Even all these instances, in the complications of Politics, may not be final ; yet they afford a very high presumption of cause and effect The Deductive Method. 31. The Deductive Method, in conjunction with the Inductive or Experimental Methods, must be regarded as the mainstay of political investigation. Neither the Deductive Method alone, nor the Inductive Methods alone, can be trusted in the complications of the social science. Their mutual consilience or confirmation, is requisite in order yield trustworthy conclusions. Pure Deduction appears to most advantage in following out the tendencies of separate agents. This is the motive for subdividing the Social Science into branches, as Political Economy, &c. The tendency of the single motive of the desire of wealth can be studied apart from other tendencies. An essential part of political deduction consists in tracing the wide operation of the Sentiment of Power, in the various degrees of its development among human beings, and under all circumstances. The deduction should comprise a wider area than mere political situations. The Sociability of mankind, their Sympathies, the grades of Intelligence, have consequences traceable by a purely deduc- tive operation. We might even venture a certain way in the second deduc- tive process—Calculation or computation of concurring agen- cies; as Wealth, Power, Sociability, Sympathy, with Habits, Customs, &c. Here, however, we become aware of the help- lessness of the deductive method by itself. Having no correct quantitative estimate of the separate agents, onr attempt to combine them in a quantitative sum, isentirely hopeless. The errors of calculation may be so wide as radically to vitiate the conclusions. It is the third step of Deduction—Verification—that gives 25 568 LOGIC OF POLITICS. the method all its weight, by joining it with Inductions, In point of fact, politicians in applying the conjoint methods usually have an inductive or empirical generality presented in the first instance ; which induction they compare with the deduced tendencies of the agents concerned. ‘Thus the work- ing of despotism is first given as an empirical generalization from history ; we then compare these alleged results with the deductive consequences of the love of power, and all other human motives, both of the ruler and the ruled, entering into the situation. Such maxims as the following require, for — their verification, the consilience of induction and deduction.— __ ‘The possessors of supreme power, whether One, Few, or Many, have no need of the arms of reason; they can make ~ will prevail.’ ‘The governments most distinguished for sustained vigour and ability have generally been aristocracies.’ The deductive reasons in favour of this last position are founded on the consequences of devoting a small number of men exclusively to public business. Thus, the usual course of the Deductive Method is to lay hold of a number of empiricisms, derived from history and political experience, and to subject them to the test of deduction, thereby converting them into derivative laws. Considered as inductive generalities, everything should be done for them that can be done by strict compliance with the Inductive Methods; after which they are to come into comparison with the deductive results of the tendencies concerned. Among Empiricisms demanding to be confronted ith deductive conclusions, we may instance thefollowing—‘*modern civilization tends to collective mediocrity,’ (J. S. Mill); ‘unity — in religion is unfavourable to civil interests’ (G. C. Lewis); — ‘there is no necessary connexion between hereditary royalty — and hereditary nobility > (ib); ‘the human race is on the > whole progressive’; ‘ there is a constant relation between the — state of society and the state of intellectual per i —_ (Comte). Deductive confirmation is especially needed in oscenieainallll causes of some one historical event. Unless there happen to — be other events closely analogous, our inductive basis is of the - slenderest kind ; succession may be taken for causation with-— out any check. Thus, the account of the rise of free institu: | tions, in modern Hurope, must be far more deductive than inductive. Si: The introduction of Christianity into Europe co-existed ie so many other changes, that its consequences cannot easily be EMPIRICAL AND DERIVATIVE LAWS, 569 eliminated. Our only means of varying the instances is to take the separate nations apart; but in none of them was this one cause introduced singly. Hence any inference as to the political and other results of Christianity would want much deductive confirmation; and we find that this method is largely appealed to. The tendencies of the Christian religion __ are laid out deductively, and the attempt is made to show their _ coincidence with the facts. To be properly checked, a similar deduction should be made of all other tendencies—as Greek and Roman influences, and the mental endowments of the European races ; which subtracted from the total would give a case of the Method of Residues. In the foregoing brief allusion to the Deductive Method is included a reference both to Empirical and to Derivative Laws. The subject of Politics furnishes pertinent examples of the limitation of Empirical Laws, and ina less degree of Derivative Laws, to adjacent cases. There is safety in extending an em- pirical law only to the same territory, the same time, and similar circumstances. Whena ten pound suffrage had sub- sisted in Britain for thirty years, with good effects, it was a small matter to risk the extension to a seven pound or a six pound franchise, on the mere faith of the empirical coincidence ; whereas, the sudden transition to universal suffrage, could not be relied on from the same empiricism. The consequences of such a step, if computable at all, could be computed only by the aid of deductive reasoning—by the establishment of a deri- vative law. A well-informed, sagacious, and unbiassed reasoner, might be trusted to predict, within certain limits of error, the probable issue of such an extension of the franchise; but only by a superior handling of the deductive method. The Method of Residues being properly a Deductive Method, is occasionally valuable. It takes the problem ona varied aspect; as in the case of Christianity already referred to. In applying the methods of Agreement and of Difference, to single out a cause, our prior knowledge of the general adequacy of the cause, prepares us to receive the inductive evidence, without the misgivings that we must feel when we know nothing on this head. Hypotheses tn Politics, 32. In Politics, we are seldom under the necessity of assuming an unknown agency ; the known forces of human nature are the sufficing causes. Our assumptions refer to 570 | LOGIC OF POLITICS. the presence, and the amount, of the supposed agent ; and these may be proved by their exactly tallying with the facts, pe Assumptions are perpetually made regarding the conduct of human beings under all circumstances, The passions of Power, Pride, Fear, the Self-interest of men, their Sympathies, - are all real or genuine causes, ‘There may be doubts which of them produced a certain line of conduct ; and we may apply the logical conditions of hypotheses to solve the doubt. If any one’s actions tally precisely with the consequences of Love of Power, we receive this coincidence as so far a proof of the hypothesis. But the proof is completed only by showing that the action does not tally with any other motive ; a thing that we cannot always be certain of. The execution of Charles I. might have - resulted from the fears of the Puritans, from their revenge, from their ideas of justice, from their interpretation of the designs of providence. Definition of specific Diseases—The very general states above quoted exemplify definition under the greatest simplicity, as respects the number of characters, although not as respects the generalizing and seizing of the true characters. When we proceed to the more concrete forms of disease, Typhus, Gout, Pleurisy, Neuralgia, Jaundice, &c., we have the general processes, Fever and the rest, with many various accessories, constituting the specific characters of the individual affections, Consequently, the definitions are apt to be voluminous in their statement; and there is still more need of method. Examples have now been given of the two different modes of medical definition; the one corresponding to Diagnosis, and framed with a view to identify a disease by such signs as are best accessible ; the other, the most complete generalization of the essential fact or facts of the disease, which facts may or may not lie upon the surface. The first is requisite for distinguishing diseases ; the second, for understanding them. Let us take an example. Gout is defined by Dr. Garrod— ~ ‘A specific form of articular inflammation, invariably accom- — panied with uric acid in the blood, and the deposition of urate of soda in the affected tissues.’ The positions given to — the words ‘specific’ and ‘accompanied’ suggest what was probably not in the author’s mind, Strictly interpreted, the er DEFINITION OF SPECIFIC DISEASES. 587 language means—Gout is articular inflammation of a specifie character (not described); it has, for concomitants, uric acid in the blood, and deposits of urate of soda. The real mean- ing must be presumed to be—Gout is articular inflammation, specifically marked by uric acid, &c. This definition is one of those advanced generalizations, attained in some diseases, which penetrate to the essential features of the disease, without fully expressing the symptoms. A detailed account of the symptoms is therefore added, first under the title ‘ Description of an attack of Gout, and of the progress of the disease’ (a sort of popular history of a case), and secondly, under ‘ Phenomena occurring during an acute Gouty Attack,’ where there is a more rigid and systematic analysis into (1) Febrile Disturbance, and (2) Local Appear- ances. Again, Small-Pox is thus defined (Dr. Aitken). ‘The pro- duct of a specific and palpable morbid poison, which is reproduced and multiplied during the course of the malady. (1). After a definite period of incubation a remittent fever is established and followed by an eruption on the skin, and sometimes on the mucous surfaces, with other concomitant and occasionally succeeding affections (2). The eruption on the skin passes through the stages of pimple, vesicle, pustule, scab ; and leaves marks or cicatrices on its site (3). The disease runs a definite course, and, as a rule, exhausts the suscepti- bility of the constitution to another attack (4).’ Here we have, in sentences (2) and (3), the leading symp- toms of the disease, which, when elucidated at full, make up, as far as book description can go, the characters whereby the disease is known and discriminated. Sentence (1) does not properly belong to the definition, but to the predication ; the cause of a disease must always be accounted a predicate. Sentence (4) contains two statements, first, ‘the disease runs a definite course,’ which surely is true of many other diseases, if not of nearly all; second, ‘it exhausts the susceptibility of the constitution to another attack,’ a most pertinent circum- stance, but still better reserved for a predicate or concomitant, than mixed up with the defining marks. Influenza is thus defined by Dr. Parkes :—‘ An epidemic specific fever, with special and early implication of the naso- laryngo-bronchial mucous membrane ; duration definite of from four to eight days; one attack not preservative in future epidemics.’ The transposition of the epithet ‘ specific’ is desirable :—* An epidemic fever, specially characterized by 588 LOGIC OF MEDICINE. early implication, &c.’ This definition also isa summary of symptoms, and nothing more. The author proceeds, under the head ‘Symptoms’ to describe the general course’of the — 2 : disease, and under ‘ Consideration of the Special Symptoms’ ‘to analyze them in the detail; Temperature, Condition of the _ Skin, Nervous and Muscular ‘Symptoms, ee System, a Circulation, Digestion, &c. aa All the facts stated in the Definition may be fairly allowed as defining circumstances, with the exception perhaps of the last ‘ one attack not preservative in future epidemics,’ which might be reserved for predication. Doubtless, if we hada — generalization of the central or fundamental fact of the disease, this would take place among deductive consequences, or propria. But we do not need it in a definition consisting of a summary of the symptoms. The following sentence commences Dr. Buzzard’s definition of Scurvy : tt A peculiar state of mal-nutrition, supervening gradually upon the continued use of a dietary deficient in fresh vegetable material, and tending to death, after a longer or shorter interval, if the circumstances under which it arose remain unaltered.’ Here we have first a theory or hypothesis _ of the essence of the disease (a state of mal-nutrition), secondly, _ its cause, and thirdly, an announcement of its dangerous character. All this is extraneous to the definition, whichis given unexceptionably (as a summary of symptoms) in what succeeds to the above quotation. Propositions of Medicine. 10. The Real Predications of Medicine, as ‘sonhanteeet 2 guished from the Essential or Defining Propositions, fall | under distinct heads. ; The coupling of the Essential characters, even atchodge a numerous, is Definition, and not Real Predication. Nay farther ; the modified characters shown in different constitu- — tions dnd different circumstances, should be held as a part, or. as an appendage, of the Definition. Real propositions may — arise in connexion with these modifications when certain cir- ¥ cumstances are alleged to intensify or to resist the diseased 4 action. Ls. ease. ‘m+ BCC PROPOSITIONS IN MEDICINE. 589 Having given the defining marks, in their ultimate state- ment, together with the important moditications and varieties, we can by the help of general principles—Physical, Chemical, Biological, or Pathological—draw many conclusions bearing on the treatment of the disease. It would be easy, for ex- ample, to unfold a great many facts respecting Fever, from the Law of Conservation, the laws and facts of Organic Che- mistry, &c. The maintenance of an excessive temperature, with less than the ordinary nourishment, involves waste or inanition of the organs, and the formation of special products of wasted tissue; with many other consequences under given situations. This deductive process, when based on well ascertained generalities, affords propositions capable of great precision and certainty. 12. The second class of Real Predications consists of the Causes of Disease. A Disease is one thing, its cause is another thing; proposi- tions of Causation, are, therefore, in their nature, strictly real. Their importance demands a distinct and separate enunciation. Implicated with the great subject of Hygiéne, or Health preservation, there is a body of information respecting the General Causes of Disease. It is all one thing to know what are the means to keep the body in health, and what will cause loss of health. Many forms of disease are due at once to the disproportion between the expenditure and the nutrition of the system. The diseases of exhausted organs—functional weakness and degeneration of the muscles, the brain, the stomach, the lungs, the heart, the kidney—are of this class. To the same general head should be referred nearly every- thing meant by Predisposing Causes of Disease. There are many diseases that do not spring up unless by poison or infec- tion from without; called Zymotic Diseases. As the poison of many (but not of all) such diseases may be resisted by a healthy system, any circumstances that destroy general vigour, or weaken particular organs, are called predisposing causes; as when cholera attacks constitutions exhausted by _ intemperance, or by insufficient food, or by ill-ventilated dwellings. Tt is less easy to generalize the various influences expressed as Infection, Epidemic poison, Miasmata, &c. This is one great field for Representative Hypotheses in Medicine. Under each separate Disease, an account is given of the 590 LOGIC OF MEDICINE. Cause, as far as known, whether general or special. Where- ever there is a loss of power from the predominance of waste over supply, Causation in Disease appears as ‘ Conservation ; ” it, however, still more largely implicates Collocations. 13. There may be a distinct class of Real Propositions, expressing the effects of Disease. The full definition of each disease comprises its whole history to the termination; the temporary prostration of Typhus is not an effect of the disease, it is the disease itself. When, however, a disease, besides accomplishing its course, makes permanent changes in the organs or constitution of the patient, this is a distinct fact, and may be enrolled under the head of Causation. Such are the after effects of Small Pox, Measles, Scarlet Fever, and Syphilis. While a few diseases have a wholesome efficacy, the greater number weaken the system at some point, and are therefore predisposing causes of future disease. 14, The Remedies of Disease constitute Real Propositions. All the previous classes of assertions prepare the way for the present. ‘The remedy of a disease may be suggested by its Characters, whether primary (Definition), or inferred from the primary (Propria) ; ; or by its Causation, on the principle of ‘remove the cause.’ Diseases of functional degeneration, or premature decay of organs, involve in their cure ‘repaying the debt to nature’—the restoration of the balance of nourish- ment and waste. In many instances, the remedy consists in something differ- ent from either treating the symptoms, or removing the cause. The Specifics that have been discovered for particular diseases, as quinine, colchicum, lime juice, cod liver oil, are affirmed as independent facts, resting on no deductive inferences from Cause and Effect in Disease, but on the experience of their efficacy. | | The Experimental Methods in Medicine, 15. All the Experimental Methods are applicable to Medicine, with certain cautions and qualifications. The ultimate problem of Medicine is to find a remedy for every remediable disease ; and the apparently direct solution is to try various remedies upon actual cases. If by Agreement, under a wide variation of circumstances, a certain remota ik THE EXPERIMENTAL METHODS. 591 found to succeed uniformly, or in a great proportion of instances, there is proof that it is the remedy. Still, we cannot but remark the very serious difficulties that weset all the Experimental Methods in thisattempt. Plurality of Causes and Intermixture of Effects occur in the most aggra- vated shape. Moreover, drugs, being natural Kinds, have so many possible ways of acting, that the elimination of the precise property that affects the system is all but hopeless. Without, therefore, abandoning the tentative process, as applied to actual disease, modern medicine has advanta- geously approached the problem in circuitous ways; and has instituted researches where the experimental methods are less likely to be defeated. Thus—to take the example that departs least from the empirical method—the mode of action of medicines and of remedies is studied by experiments, not re- stricted to special diseases, but applied to the system in health and in disease alike, under every variety of conditions. This is a far more thorough and searching procedure; and the Method of Agreement will, of itself, give trustworthy results under so great an extension of instances; while by superad- ding Difference, Inverse Agreement, and Variations, there may accrue results of the highest certainty. I may cite, among this class of Researches, the Report of Dr. Bennet on the Action of Mercury on the Biliary Secretion, and Dr. Harley’s work on the Old Neurotics. By such researches is built up that part of Materia Medica relating to the Therapeutic action of medicines. Again, the Pathology of Disease, the concurrence and se- quence of symptoms, studied, in the first instance, apart from modes of treatment, is open to experimental enquiry, and may lead to results having ali the precision attainable in the science of Medicine. For such enquiries, the Kxperimental Methods are suitable; the endeavour being made to bring each one of them into play, by searching for the approp- riate class of instances. Mere Agreement is usually what suggests itself to the untutored mind; the force of Agreement in Absence and of Variations is apparent only to such minds as have reflected largely on the conduct of scientific researches. The influences commonly called Hygienic, and the simpler Therapeutic agencies, as cold and heat, change, exercise and rest, stimulants, &c., not only present fewer difficulties to ex- periment, but are also within the scope of the Deductive method. In like manner, the proof of noxious agencies—as impure water, and the efiluvia of decay —is easy and complete. > 26 592 LOGIC OF MEDECINE. 16. The Elimination of Chance is of great value in - Medicine. Its groundwork is Medical Statistics. th Nowhere more than in Medicine may laws of Causation be defeated ; there is rarely such a thing as a simple cause yield- ing a simple effect. Hence, the necessity of ascertaining = whether a coincidence is more frequent than would be ac- ; counted for by chance. Thecinchona bark sometimes fails to cure ague, yet its general efficacy is satisfactorily established. To prove the efficacy of medicines as a whole, in opposition : to some speculators that ascribe all cures to nature (aided by repose and regimen) the physicians of a French hospital made the experiment of withholding drugs from all the patients for a certain time. ‘The conclusion seemed to be that the mortality was not increased, but the recoveries were more protracted. This was a competent inference from statistics. The difficulties in obtaining a statistical proof of the action of a remedy in a given disease are exactly those already mentioned respecting the use of Agreement in the same determination.* A large hospital statistics is better than the inferences of a single physician in private practice, and yet may come short of the proof. There should always be obtained, if possible, a parallel statistics—cases with, and cases without, the treatment in question. The statistics of cholera treatment may be alleged in favour of many modes; but none appear 19 be decisively established. Statistics, as applied to Scarlet Fever, has shown that a second attack is extremely rare; that the ages of two and three are most susceptible to the disease; and that the maxi- mum of prevalence is in October, November, and December, and the minimum in April, May, and June. I The Deductive Method. 17. The scope of the Deductive Method in Medicine is co-extensive with the number of well-established generali- ties than can be appealed to. The sciences applicable to Medicine—Physics, Chemistry, and Biology—yield a considerable number of these fertile generalities. The science itself contains few of a very com-- manding character, but a considerable number that have a sufficient range for deductive operation, and for converting. empirical into derivative laws. All the propositions of general * See an estimate of these difficulties in Dr. Barclay’s work on Medidél! , Erro1s, p. 35. y ough / OO ee SS ee ee eee ee ee HYPOTHESES. 5938 cansation in medicine, the laws of general Therapeutics, the laws of the action of drugs on the system generally, have sufficient breadth to control and correct empirical practice ; and the mastery of these, as well as of the more commanding principles of the preparatory sciences, increases the power of the physician. The physiology of Food as regards the various forces of the system, muscular, heat-giving, nervous, &c., and the products of elimination,—is pregnant with deductive consequences, both in warding off and in curing disease. The experimental methods are greatly at fault with slow- acting causes; and hence deduction is pre-eminently desirable in such points as the influence of alterative medicines, stimu- lants, climatic influences, and modes of life. Only a thorough- going statistics, or a deduction from general principles, can dispose of the doubts that arise on such points. Hypotheses in Medicine. 18. Medical Science is largely dependent on Hypotheses. As a department of applied Biology, Medicine needs all the aids rendered by hypotheses in the mother science, and some special to itself. The great biological fact—Assimilation— takes on a new aspect in the production and spread of Disease. The first and simplest case of Hypothesis, the assuming of an agent known to exist, but not known as present in ade- quate amount in the given case, is abundantly exemplified. Thus, the origin of contagious disease is ascribed hypotheti- cally to various real agents, and among others, to actual living organisms. The effects tally in a general way with such an agency. What remains is to find whether they tally closely at all points. The hypothesis, however, receives a powerful support from individual cases where the presence of ~ an animalcule, or living germ, appears to be actually estab- lished. The alternative, and older, hypothesis is that organic particles, in a state of change or activity, are thrown off from one living body and infect another, such particles not being complete organisms or the germs of organisms. This bhypo- thesis may seem to assume less than the other, but in reality it assumes a class of particles not distinctly proved to exist. A strong analogy may be pleaded for them, in the supposed communication of morbid action within the system; the action of the poison of small pox must be the same on the blood of the innoculated patient as on the original patient. Yet the aerial effluvia of typhus may consist of something more 594 ; LOGIC OF MEDICINE, definitely organized than the supposed active particles. Fer- mentation by yeast is found to be due to an animalcule. The Representative Fiction is indispensable in Medicine, and its rules and properties need to be well understood. Diseased appearances, like all manifestations of living bodies, are the superficial outcome of a vast concatenation of hidden changes. These intermediate links are in great part unknow- able; yet, by following the clue of what we know, we may so conceive or imagine them, as thereby to unite the appearances in a consistent whole. When an organ is liable to derange- ment from slight causes, we prononnce it weak, which is merely to express the fact in another word; when, however, we assign such circumstances as that its tissue has degenerated or changed, that it has very little tendency to assimilate nutri. ment from the blood, or that the superior exercise of all the other organs of the body withholds from it the fair amount of blood and nerve force,—we employ convenient hypotheses, which are more or less in keeping with the facts, As regards the two leading diseased processes—F'ever, and Inflammation—probably no hypothesis yet framed adds any- thing to the facility of conceiving or of generalizing the facts. Supposing the different fevers generated each by a specific virus, or animated body, we cannot even in imagination sup- pose a connexion between the structure of the infecting element, and the specific characteristics of the fever; as in the difference between typhus, scarlet fever, or intermittent fever. Indeed, we cannot form a plausible supposition as to the intermediate link that connects a certain infecting substance with the febrile state generally. The difficulty here is exactly the difficulty in representing the facts of living action, Hypothesis appears to more advantage in connexion with what is termed Functional Degeneration, Functional weakness, — strength and weakness of parts. Great convenience attaches to the use of such phrases as healthiness, robustness, vigour, constitutional foree—which are modes of stating the absence of disease under circumstances that usually provoke it. We may increase the value of this class of terms, by pak Seigers +r interpolations, to the following effect :— Assuming an average healthy system to begin with, we know by reasonable inferences, (1) that every one of the organs needs an equable supply of blood, with more or less aid from. the nervous centres, and (2) that each organ is capable of a cer- tain amount of exertion. Suppose now, that by any cause, either the nutrition is below the mark, or the exertion above i el HYPOTHESIS OF DEGENERATION, 595 it, or both. It is the nature of the system not to show im- mediately the effects of such a mal-proportion, yet there must be an immediate effect ; the overwork, or the defective nutri- tion, of asingle day does not leave the organ exactly asit was; we are entitled to assume that there is superinduced a minute structural change, or degeneration, perceptible only after many repetitions, but actually realized. Suppose the disproportion of expenditure and supply to continue for a length of time; the first outward symptoms will probably be, that the organ is enfeebled in some duty that is required of it, and becomes positively disordered under influences that, in its regular con- dition, it would have successfully resisted. At this point, degeneration or structural change has made a decided ad- vance ; another equal advance would bring down the organ to the bare performance of its functions; a third would be utter suspension and death. Now, we have here scope for a great variety of suppositions, as to the relative condition of all the organs in the body. We can represent the constitu- tioual peculiarities at birth, by the proportionate dispositions of the several organs—nerves, muscles, lungs, digestion—to appropriate nutriment, and to become vigorous or the oppo- site ; we can state to ourselves the practical mode of redressing the inequality, namely, by restraining the vigorous organs from their tendency to impoverish the rest, and by giving greater opportunity to the nourishment of the weak. We can also state the rationale of the constitutional treatment of diseases, viz., the placing of the weakened organs in such a position as to increase their nutriment and abate their over-exertion. We can give a hypothetical account of the degeneration of or- gans such as the heart and kidney, which often show no signs until the structure has reached a mortal disease. We should, moreover, feel no surprise at the sudden breaking down of constitutions reputed strong ; the popular eye sees only the prosperity of those organs that cast a dash and a glare—the muscles, the stomach, and the brain. The deeper glance dis- closes the degeneracy of the heart, the lungs, the kidney, following on the very strength of these ostentatious members of the system. Classification of Diseases. _19. There being upwards of one thousand recognized Diseases, they may, like other great aggregates, come under a regular Classification. 596 LOGIC OF MEDICINE. Diseases may fall under a classified arrangement, like Minerals, Plants, or Animals, attention being given to the peculiarities of the department. , I. Order of Characters.—In Mineralogy, and in Botany, a strict order of characters is observed. This is disregarded in Zoology, and also in Medicine, from difficulties that can be readily assigned. There is every likelihood, however, that both sciences would gain by a systematic arrangement of char- acters, avoiding the sacrifice of the spirit to the letter. In a work to be afterwards referred to (p. 597), the remark is made ‘ that the labour of analyzing and comparing clinical observations would be greatly lightened, and the precision of the observations themselves increased, if the records of these were in every instance arranged on an uniforny plan.’ One obvious precaution is to make the outward symptoms precede the subjective. Thus, of the usual marks of inflam- mation, the pain should come last. In nervous diseases, the physical symptoms should be fully enumerated before entering upon the mental symptoms ; the two classes are then viewed in such a way as to check and confirm each other. Il. Maximum of Affinities. — The propriety of classing Diseases by their closest resemblances is sufficiently allowed in the abstract ; the difficulties in execution are not logical, but pathological. icity III. Arrangement by Grades.—The formality of Grades is observed in the classification of Diseases, but without the full carrying out of what it involves. There is something of lax- ness attending the use of the method even in Chemistry, the statement of the points of community of the higher grades — being sometimes given, and sometimes not, without any apparent reason. . Occasionally there is vacillation as to whether diseases ar different in species, or mere varieties. Little importance attaches to the question; and the workable criterion is the comparative number and persistence of the distinctive marks. IV. Statement by Agreement and Difference.—Hverything already said on this head applies to the exposition of Diseases. The systematic and orderly stating of Agreements, and the pointed contrast in Difference, have the same efficacy here as elsewhere. Under the heading ‘ Diagnosis,’ it is usual to mention the closely resembling diseases, and to indicate the diagnostic marks. For example, Roseola is distinguished from Scarlet Fever, thus :—the eruption in Roseola is gene- rally confined to the chest. When the diagnostic points are Pi a i nel a | aS il) INDEX CLASSIFICATION, bOY two or more, they might be set forth in the formal manner already exemplified. 20. V. Index Classification.—For Medicine, an Index Classification might be provided on the tabular plan. This aid to the discrimination of Disease is still wanting. Probably, it would be best attempted, in the first instance, on the tabular plan. A basis is afforded in a small work, pub- ‘lished by the Medical Society of Observation, with the title ‘* What to Observe in Medical Cases.’ - The work professes to lay out in order an exhaustive state- ment of all the appearances connected with each bodily organ, besides adverting to the external circumstances of the patient. The enumeration commences with the Skin, which is followed by the organs of Locomotion, Digestion, Respiration, Circula- tion, Lymphatics, Urinary Organs, Organs of Generation, Brain and Nerves, Vascular Glands. As an example, I quote the varieties of the Pulse :—‘ Radial Pulse :—number ;—size and force; large, small, thready, equal, ‘unequal, strong, feeble ;—resistance; soft, compressible, hard, -incompressible ;—rhythm; regular, irregular, intermittent ;— time as compared with that of heart’s impulse ;—artery tortuous, rigid.—Special characters of pulse; jerking, bounding, undula- tory, continuous (one pulse appearing to run into the following), ‘vibrating, quick, tardy, vermicular, tremulous, reduplicate.— Effects of posture on pulse (its number and other characters).— Phenomena of pulse in one arm as compared with the other.’ The authors have evidently studied exhaustiveness to, begin with. It is possible, however, to be too minute; distinctions that are not marks of anything else are worthless and may be an encumbranee. ‘The next step, therefore, should be to abridge and group the symptoms with a view to the maximum of significance. There being obtained a methodical array of symptoms under each organ, the mode of proceeding with a view to an Index is to append to each symptom a list of the diseases where it occurs. Should a symptom appear in only one disease (as urate of soda in gout) the occurrence of the symp- tom would decide the disease at once. Should a symptom appear in three diseases, its occurrence points to one of those three diseases. By appending, to every symptom of value in diagnosis, a complete list of diseases, there is provided a means of deter- mining every disease according to the knowledge of the time. One symptom refers us to one list, containing two, three, or 598 LOGIC OF MEDICINE, four diseases ; a second symptom leads to another list. [fon comparison, there is found only one disease common to the two lists, the diagnosis is complete. Ifthere are two or three © common to both lists, a third symptom must be sought out with its corresponding entries, by which the alternations are again reduced ; and so on, till the concurrence of symptoms points toa single disease. Suppose, for illustr ation, that ‘Irrecularity of the Pulse’ appears as symptom. According to Dr. Watson, this may attend (1) disease within the head ; (2) organic disease of the heart ; (3) simple disorder of the stomach ; (4) debility, and a pr elude to stoppage of the heart’s action from asthenia, Now supposing the tabulation of symptoms and of diseases complete upon this plan, and supposing a second symptom in the case under enquiry had opposite to it a list, agreeing with the first only in the entry ‘simple disorder of the stomach,’ the diagnosis is made out by two easy references. Owing to obvious causes—the great number of diseases accompanying particular symptoms, the occasional ambiguity of actual diseases by the failure of some of their usual symp- toms, and the imperfection of the terminology of symptoms,— the best scheme that could be given would be imperfect. This would not, however, prevent it from being a boon to the student, and an occasional aid to the experienced practitioner. It does not supersede, but indicates, the reference to the systematic works on Medicine and Pathology, which arethe authorities in the last resort ciate eae BOOK VI. FALLACIES. CHAPTER I. MILU’S CLASSIFICATION OF FALLACIES, Mr. Mill regards all fallacies as divisible into two great heads—Fallacies of Stmpie INspEcTION, and Fallacies of INrER- ENce. By the first class he understands those cases where a presumption is created in favour of a fact or doctrine, on the mere inspection of it, and without any search for evidence ; natural prejudices are comprised under that head. By the second class he understands erroneous conclusivns from sup- posed evidence. This class is subdivided accurding to the nature of the evidence simulated ; which may be deductive, inductive, &c. A special division is indicated under the title ‘Fallacies of Confusion,’ where the error arises, not in the link between premises and conclusion, but in the incorrect handling of the premises themselves. There are thus five distinguishable classes of Fallacy, as set forth in the table :— of Simple Inspection - e« e« 1,Fallacies a priori. F Inductive | 2. Fallacies of Observation ee °°) Fallacies F Fallacies of Generalization conceived Deductive 4. Fallacies of Ratiocination Fallacies Fallacies from evidence : indistinctly 7 « - 5. Fallacies of Confusion of Inference conceived I. Fallacies of Simple Inspection, or a priori Fallacies.—Re- fraining from the discussion of the question, which this desig- nation might raise, what are the ultimate facts or premises at 600 MILL'S CLASSIFICATION OF FALLACIKS. the foundation of all reasonings, Mr. Mill adduces first the tacit assumption that the same order obtains among the objects of nature as among our ideas of them—that if we always think of two things together, the two things must exist together. He illustrates this tendency by numerous popular superstitions, as ‘talk of the devil and he will appear,’ &c. He also cites— the philosophy of Descartes, which, from the mere conceptions of the mind, inferred the existence of corresponding realities ; the doctrines that ‘ whatever is inconceivable is false,’ ‘ that a thing cannot act where it is not’ (applied by Newton to show the necessity of a gravitating medium), that ‘ matter cannot think,’ that ‘space is infinite,’ that ‘nothing can be made out of nothing,’ that ‘nature always acts by the simplest means.’ An allied Fallacy, or prejudice, is the tendency to presume a correspondence between the laws of the mind and the laws of external things, of which one form is expressed thus :—‘ whatever can be thought of apart exists apart.’ From this springs the personifying or re-ifying of Abstractions, as in the doctrine of Realism, and in mystical theories gene- rally, whether it be the mysticism of the Vedas, or the mysti- cism of Hegel; all which proceeds on ascribing objective existence to subjective creations— feelings, or ideas. Another kindred fallacy consists in representing nature as under the same incapacity with our powers of thought ; the great example being the celebrated Principle of Sufficient Reason, adduced in explanation of many first truths, such as the laws of motion. i ‘That the differences in nature correspond to the received distinctions of language,’ is another wide spread and baneful prejudice, which particularly weighed upon Greek philosophy, being prominent in the reasoning’s of Aristotle, and from which Bacon was unable to set himself free, as is shown by his futile — attempts to find a common cause for everything that goes under a common name, as heat, cold, &e. Lastly, there has existed the prejudice that ‘ the conditions of a phenomenon will resemble the phenomenon ’—like pro- ducing like: as that motion must necessarily arise from the impact of a moving body; that a sharp taste must be brought about by sharp particles; that our sensations must be copies of external things; that the law of causality can hold only between what is homogeneous, whence there can be no causa= tion between mind and matter; that the Deity must have the exact perfections discoverable in nature, __ II. Fallacies of Observation.—These do not apply to the . GENERALIZATION.—RATIOCINATION. 601 operation of observing, for which there is no logic strictly so called, but to the omissions and partialities in collecting facts with a view to the generalizing process. There may be Non- observation, or Mal-observation ; the one leaves out pertinent instances, the other distorts or misrepresents what is observed. Non-observation explains the credit given to fortune-tellers, to quacks, and to false maxims; the cases favourable being noted, and the other forgotten. The motive in this class of fallacies is a strong pre-conceived opinion or wish to find the dictum true. Farther, the Non-observation may be, not of instances, but of material circumstances, as when it is stated that lavish expenditure alone encourages industry, the circum- stances being overlooked that savings are capital for the employment of labour. Under Mal-observation may be placed the chief mistake connected with the proper act of observing, namely, the con- founding of a perception with a rapid inference, or the mingling up of inferences with facts. This is the common infirmity of uneducated witnesses and narrators of events. Iil. Fallacies of Generalization.—These are errors in the employment of the Inductive process. The chief instances adduced are these:—All inferences extended to remote parts of the universe, where no observation or verification can be carried ; all universal negatives and propositions asserting impossibility (not being contradictionsin terms) ; the theories professing to resolve all things into some one element, of which the most notable instance is the attempt to resolve states of consciousness into states of the nervous system; the placing of empirical laws, arrived at per enumerationem simplicem, upon the footing of laws of causation, largely exemplified in reason- ings upon society; the vulgar form of the same fallacy, desig- nated post hoc, ergo propter hoc ; and the fertile class of False Analogies. Under the same head are specified Bad Classifica- tions, or the asserting under one term, things that have little or no community ; of which the Greeks gave examples in such terms a8 Motion, Generation and Corruption. IV. Fallacies of Ratiocination. These comprise the errors _ against the laws of the Syllogism. Mr. Mill, however, properly includes under them the fallacies connected with the Conver- sion and Kquipollency of Propositions; remarking that the simple conversion of the universal affirmative, and the errone- ous conversion of Hypotheticals are among the most frequent sources of error. Of this last class, is the maintenance of some favourite doctrine, on the ground that the inferences from it 602 MILL’S CLASSIFICATION OF FALLACIES. are true. Connected with the Opposition of Propositions is the confounding of the contrary with the contradictory of a statement. Vicious syllogisms, whether from undistributed middle, or from illicit process, are tke more noted instances of this class of fallacies. There may be also included the fallacy of changing the premises, occurring frequently in the argument- ative discourses of unprecise thinkers (the schoolmen’s a dicto secundum quid ad dictum simpliciter) ; exemplified in the once favourite theory that ‘whatever brings in money enriches,’ Under the same head might be placed the misapplication of general truths, or the supposition that a principle true in the abstract must hold under all sets of circumstances. | V. Fallacies of Confusion. The first class under this desig- nation is Ambiguity of Terms, As there is no limit to that form of confusion, a logician can only select a few random instances ; those chosen by Mr. Mill are ‘scarcity of money,’ ‘influence of property,’ ‘tieory,’ ‘the church,’ the ‘laudable’ ina Stoical argument in Cicero’s De Finibus, ‘1’ in Descartes’ argument for the being of God, ‘necessity,’ ‘same,’ ‘ force,” ‘infinite,’ ‘right ;? to which he adds examples of the fallacy of Composition and Division, as strictly belonging to the same class. foe The second division is Petitio Principit, otherwise called ‘arguing in a circle,’ of which there are abundant examples. A certain species of terms received from Bentham the desig- nation ‘ question-begging appellatives,’ because they begged a | question under the guise of stating it; such is the word * Inno- vation.’ Plato, in the Sophistes, has an argument to prove that things may exist that are incorporeal, because justice -and wisdom are incorporeal, and they must be something: thereby begging the question that justice and wisdom are things existing apart or in themselves. One of the most re« markable examples of fallacy is furnished by the political theory of Hobbes and Rousseau, known as the theory of the — ‘social compact.’ We are supposed bound by the promise — entered into by our ancestors before society was called into existence ; but there is no such thing asan obligatory promise until society has first been formed. he The third class of Fallacies of Confusion is the Ignoratio Hilenchi. It is exemplified in most of the replies to the popu- lation doctrines of Malthus. A still more signal instance is — the stock argument against Berkeley’s doctrine of the nom existence of matter; Johnson’s kicking the stone was not the — point denied in the ideal theory. 5 ae a CHAPTER IL THE POSITION OF FALLACIES. The setting apart of a distinct chapter to the consideration of the errors against the laws of reasoning and evidence seems at first sight an incongruous proceeding. We cannot separate a law from its violations ; the one implicates the other. When good reasoning is exhibited, there must be exhibited at the same time the coresponding bad reasoning. If the rule be given that the middle term of a syllogism must be distributed once, whoever understands the rule must conceive, at the same time, cases of its fulfilment and cases of its non-fulfil- ment. If the method of Difference requires that the instances compared shall coincide in every particular save one, we are instructed by it that the method fails if any two instances do not coincide to this extent. If a good classification involves identity on one or more points of importance, there is implied in the same statement that a grouping under one name, with- out any important community, is a bad classification, a ‘fallacy ’ of classification. _ Any one would recognize the absurdity of a grammar that would reserve for a chapter at the end all the examples of grammatical errors. Yet such is apparently the plan pursued in Logic. The grammarian, indeed, frequently provides a separate collection of errors by way of practice to the pupil, but these are additional to what necessarily and properly occur under the rules that they severally violate; this, how- ever, is not avowed by the logician as the nature of his chapter on Fallacies. Without entirely exonerating works on Logic from the - inconsistency of distributing between two departments of the subject the fulfilment and the violation of the same rules, we can assign certain circumstances that account for the prevail- ing usage. The main circumstance is the narrowness of the field of logical precepts, from Aristotle down to the present generation. The part of reasoning reduced to rules was almost exclusively restricted to the syllogistic or deductive departments ; hence, in the exemplification of those rules, no errors could come to light except such as violated the forms 604 THE POSITION OF FALLACIES. of syllogism. But the Greeks had surveyed human knowleds wide enough to be aware that many errors passed current — that could not be reduced to errors of syllogism. The logician, a therefore, was driven to one of two alternatives—to make no allusion to some of the most notorious failings and mistakes of the human understanding, or to provide a chapter for enumer- __ ating such mistakes entirely apart from the body of logical theory. It was characteristic of Aristotle to choose the second — alternative—to be inconsistent rather than to be incomplete. His treatise on Fallacies comprises errors against the Syllo. gism, which he could not omit noticing under the Syllogism 7 (Undistributed Middle, Illicit Process); but these are a small — part of the mass of Fallacies; and the rest he had not any theory for. He had no Inductive Logic (or only mere ~ traces which his followers wiped away), and therefore he had no place for the exhibition of the rules siuned against by post — hoc, ergo propter hoc. For want of a thorough-going discussion — of the department of Classification and Definition, he could — not exhibit the errors connected with general language under precepts for the clheatyine of things and the defining of terms. ‘ It has been ee however, that even the thorough-going Logic of Mr. Mill does not dispense with a ‘ Book’ on Fallacies. This is explained in part, but only in part, by the autho Hol adhering to the usage of all former logicians, while using bis own extended system to re-arrange the recognized examples, | and to introduce new ones. Yet all the fallacies in the second, third, and fourth classes (Observation, Genetalautione Ratiocination) might with the utmost propriety be abeotbaail into the body of the work. The account of the inductive and — deductive processes unavoidably quotes derelictions from the sound performance of these processes, which derelictions are identical with the fallacies treated of under the heads just” named. The case is different with Mr. Mill’s first and last classes (Simple Inspection and Confusion), The chapters on these heads contain matter that would not readily find a place ey the systematic exposition of the logical methods. To take the first class, Fallacies of Simple Inspection, or a priori. Cnet these, the author dilates on certain fallacious tendencies ¢ the mind, the generating causes of errors. Now, the logic ti n might say that his business is to show how errors are to checked and corrected, not how they arise in the imperfect of the human constitution, If he is to handle this a, i, he NATURAL CORRUPTION OF THE INTELLECT, 605 vould not with propriety take it up in the detail of the Deductive and Inductive Methods; he would need to be allowed a corner apart. The demand is irresistible. -It would be most inexpedient to agitate, under the Syllogism, or under the Experimental Methods, enquiries as to the fallacious ten- dencies of the natural mind. Granting that all the deductive and inductive fallacies, and the mistakes of classification and definition, were taken up into the main body of the work, the fallacies @ priori, if included at all, must receive a separate handling. Some doubts might be raised as to the logician’s title or obligation to enter upon the subject, but there could be none as to his allocating a distinct chapter to the considera- tion of it. Socrates was the first person to urge strongly the natural corruption of the human intellect, and the need of a very severe remedial discipline, which, in the shape of personal _ eross-examination, he was wont to apply to his fellow Athen- ians. The theme was not again taken up in a vigorous manner, until Bacon composed the first book of the Novum Organum. The elucidation of the inevitable miscarriages of the untutored understanding, itellectus sibi permissus, and the classification of idola—false lures, in that renowned work, instead of being laid to heart and followed up by fresh ex- amples, became a matter of mere parrot repetition. The next | person to treat the subject independently, and to go systemati- cally over the ground, was Mr. Mill, in his chapter entitled ‘Fallacies a priort.. So important is the subject, and yet so far is it distinct from the proper field of Logic, that it might be embodied in separate treatises. It is a kind of homily or preaching, a rousing address on human frailty ; and although the logician is the person most likely to be impressed with the evil consequences, he is not the only person qualified to illus- trate them ; while the points to be adduced in the exposition are not precisely such as fall under either the deductive or the inductive logic. Mill’s concluding head ‘ Fallacies of Confusion,’ still remains extra-logical. The extension of the field of logic does not enable this class to be absorbed. They caunot be adduced as violating inductive, any more than deductive precepts. In reality, they are owing to the defective acquaintance with the subject matter of the reasonings, and toa low order of intellectual cultivation generally, rather than to misapprehending logical method. A considerable stretch of the logician’s province is implied in the taking up of this class ef errors. The ground that they the intricacies, the incoherences, the "sei platitian the per ments, possible to the human understanding. The only circumstance that justifies the attempt to handle them fie matically is the great frequency of a few leading forms; in ~ consequence of which they can be, to some extent, treated — comprehensively. Mr. Mill’s three classes of examples— ‘ Ambiguous Terms, Petitio Principii, Igroratio Elenchi—have — this character of extensive recurrence. Moreover, in ‘the elucidation of such classes, there come to view many prominent and practical errors, thus opportunely laid bare. am From these considerations, it follows that the most defensible course to be pursued in regard to Fallacies is to absorb into the main work all those that are the direct violation of logical | is precepts ; and to handle, in the chapters apart, the Fallacious tendencies of the human mind, and the Fallacies of Confusion. — This is not to debar the assembling of additional examples in a supplement or appendix ; it being understood that these’ are merely in continuation of the examples already furnished in the regular course, | Ae ae t. [ CHAPTER IIL fie FALLACIOUS TENDENCIES OF THE MIND. a The Fallacious tendencies of the mind may be traced throu gh an enumeration of the sources of Belief. wP The state of Belief is a form or manifestation of our nae vity. The import and measure of Belief is the readiness to act in the direction indicated by the thing believed. A man’s belief in the wholesomeness of a regimen is shown by his energy f 1d persistence in adhering to it. ' There are three distinct sources of belief. I. The inher Activity of the System—the disposition to act through m spontaneous vigour. II. The influence of the Fee Emotions, or Passions. III. The Intellectual Associatio acquired trains of thought. Excepting under the a there is nothing to guarantee soundness of belief, or the a ance of the thing believed with the reality. OUR EARLY BELIEFS OVER-VAULTING. 607 I. Inherent Activity of the System. From the spontaneous and inherent vigour of the system, we are induced to act somehow, to change out of the passive into the active condition, and to continue that activity while the energies are unexhausted, and while there is freedom from obe struction. There is no enquiry beforehand as to the proper course or direction to act in; opposition is not presumed until actually eneountered. A way now open is supposed to be al- ways open; the mind does not anticipate any future termination or obstacle. Blind confidence is the primitive attitude of our mind. It is only through the teaching of experience that we suppose any limit to our career of action. This state of mind shows itself in our early beliefs, which may be described generally as over-vaulting; as presuming that what holds now and here, will hold then and there and everywhere, The following are instances :— We are disposed to assume that, as we feel at the present moment, we shall feel always. After a certain number of checks, the tendency is somewhat restrained, but it continues very strong all through early life, and is seldom entirely conquered at any age. We begin life by reckoning with the utmost confidence that other persons feel exactly as we do. After lengthened experi- ence, this primitive tendency is greatly subdued, although perhaps in few minds is it fully sobered down to the measure of the actual facts, The consequences are shown in our not allowing for differences of character, in our inability even to conceive of types departing widely from ourselves. Without being the sole origin.of intolerance, this tendency greatly ministers to that prevailing vice of mankind. We can with difficulty avoid judging all men, in all circumstances, by the standard suited to ourselves and our own circumstances. From one or a few instances we are ready to infer a law applicable without limit. The mere infant parodies the induc- tive process; the most ignorant of human beings are the most unrestrained generalizers. From an acquaintance with one or two Frenchmen, Italians, or Russians, we conclude the characters of the entire nation. We feel assured that a remedy found to answer in a particular case will answer uni- versally. Happening to visit a place during fine weather, we are led to suppose that the weather there is always fine. The word ‘always’ isa familiar expletive to vent our generalizing temper. a ai y ‘TP. = "0 ne f 4 Tae 5 yu al si hin kee and harmony. Pythagoras was entranced by the mystery of number; Plato followed him; and Aristotle: was not exempt. from the spell. But the predominant source of fallacy quotable under the present head was the supposed Perfection, Dignity, — and Becomingness of certain arrangements in nature, which included numerical considerations among others. The superior worthiness of fire was declared in the Pythagorean philosophy ;, and even in the later Copernican controversy an argument was founded on the circumstance that the new system placed fire, the noblest element, in the centre of the universe. So only Mind, according to Plato, in Philebus, is sufficiently dignified to create the world. In the recital by Socrates, in Pheedon, of the phases of his intellectual history, on the subject of Cause, the doctrines of Thales and Anaxagoras are set aside because — they do not recognise the becoming as a power in the world. The adherence to the circular form of the planetary orbits, because of its perfection, was inveterate in the cool mind of Aristotle. The planets could be only six, because that was a perfect number. The dictation of a plan to Nature on a supposed orbshate has run through all times. Even in hard business affairs of. trade, Aristotle held it was against nature that money should breed money, that is, pay interest on loans. Lamarck argues that a Polype cannot have Sensibility, because it would be contrary to the plan that Nature is obliged to follow in all her works (Lewes’s Aristotle, p. 97). The fiction of Unity, which carried away the early Greek philosophers, partly proceeds from over-assimilation, and partly ministers to artistic emotion. The absolute unity of mind is still worshipped by German: philosophers. Herbart and others, rather than admit the radically distinct nature of Feel- ing, Will, and Intellect, insist upon regarding Intellect or Cognition as the basis of the two others. The artistic sublime dictates such exaggerations as ‘ Let justice be done, though the world collapse;’ ‘ Truth is great and all-prevailing.’ Only a mind driven off its calm centre — by the sublime of Force can exclaim ‘ Might is Right.” The — fallacy that makes Artistic Harmony the test of truth, almost — inevitable in poetry, is deliberately maintained in Wordsworth’s, Essay on Kpitaphs, and in his prose criticisms. ! gt The allegation is often made, on instances garbled to chime 4 in with an amiable sentiment, that great men derive thei J mental power chiefly from their. mothers, ae The influence of «esthetic qualities—beanty, hi: har- INTELLECTUAL ASSOCIATIONS. 615 mony, propriety—is constantly operating to twist the under- standing. The architecture, music, and colouring employed in religion, indispose the worshipper to canvass the validity of the doctrines. The art of the orator involves the tickling of the sense, and the charms of style. Such subjects as History, Criticism, Morality, the Human Mind, where literary polish is more or less attended to, are liable to distortion through that circumstance. Of Rhetorical devices, only a few are subser- vient to truth; while a great many are hostile, The interests of Morality and Religion, have, in almost every age and country, been thought to require a habitual exaggeration of the pleasures of virtue and the miseries of vice. Plato was the first openly to recommend the pious fraud of ‘preaching doctrines, in themselves false, as being favourable to morals and social order. And although only one society in modern times—the Jesuits—has formally avowed the same principle, there has been a wide-spread disposition to put it in : i practice. Various apologists for Christianity have contended — that, even supposing it untrue, it ought to be propagated on — account of its beneficial consequences. III. Influence of Associations. Belief is not founded in the intellect; yet the intellectual associations confirm tendencies pre-existing, and contribute to belief both in the true and in the false. When two things have been often associated together in the mind, the impetus thus acquired, in passing from the one to the other, counts as a force of belief. We are disposed, by our inborn activity, to proceed upon whatever we are told, there being no counter- acting tendency present ; the frequent repetition of the same declaration enhances our disposition to believe it. The force of iteration is one of the leading causes of men’s beliefs. What has often been said, and seldom or never contradicted, is all- powerful with the mass of mankind. Thus, one part of the iutluence of education, and of prevail- ing opinions, is due to an intellectual link, whose growth could be arrested by mere counter iteration. The same influence is at work confirming our modes of looking at things. There may be no reason, beyond the adhesion generated by length of time, why a man is reluctant to entertain a new opinion, and yet this may be enough to render his conversion impracti- cable. It was remarked that Harvey’s doctrine of the circu- lation was admitted by no physician past forty. Among our habits, we are to reckon beliets. ‘lhe inveteracy of preconceived Opinious is in great part due to their being long cherished. 27 CHAPTER IV. FALLACIES OF CONFUSION. These fallacies cannot usually be produced as direct contra- ventions of logical method. Many of them depend on imper- fect acquaintance with the subjects under discussion. A certain number may be regarded as snares of language (Bacon’s idola for). A logical discipline is good as against many; and their detailed exposure may have a slightly forti- fying influence. As already remarked, an exhaustive treat- ment is not possible; but certain genera may be selactethes as being both prevalent and deleterious. Fallacies of Language. Am Sitios and ill-defined terms.—The Fallacies of Equivoca- tion of the scholastic logic are fallacies of ambiguous langu- age; for which the remedy is an exact definition of all leading terms, and an adherence to the meaning so settled. It is one criterion of an advanced science to have its terms defined. In subjects not raised to scientific precision, we may expect vagueness in the use of language. The Mathematical and the Physical Sciences were the first to make progress in this direction; only in recent times has the progress been extended to thd Moral Sciences—Psychology, Hthics, Polities, Law, Political Economy. The exemplification of ambiguous words has no limit, unless we adopt some principle of selection. For a work on Logic, the most appropriate examples are terms of leading importance whose ambiguity is still a cause of error and perversion. © The word ‘ Nature’ is full of ambiguity. Butler pointed out three meanings. Sir G. C. Lewis, after a lengthened examination of particular uses of the word, found that they fall under two classes:—(1) A positive idea, as expressing essence, quality, or disposition ; (2) A negative idea as excluding art, or human regulation and contrivance. This last meaning occurs in the phrase state of nature, used to designate man’s existence before the introduction of law, government, and the arts of civilization. As human interference may sometimes be ~ AMBIGUITY OF TERMS. 617 good and sometimes bad, the meaning of nature varies accord- ingly. When men’s ‘natural rights’ are spoken of, there is great doubt as to whatis intended. ‘ Hvery man has a natural right to his liberty ’—is a jumble of uncertain sounds ; ‘ natural’ being probably used in Lewis’s second acceptation, as the antithesis of art, regulation, and interference. ‘Liberty ’ has various meanings. It isnot merely the absence of coercion or restraint, as being at large instead of being impri- soned ; it extends also to the possession of powers, rights, and status; thus in a community where there are slaves, being impri- soned ; it extends also to the possession of powers, liberty is a distinction, and freemen compose a privileged order of the state. The ambiguities of ‘Moral’ have been previously adverted to, Even in the one specific meaning of ‘right and wrong,’ it has a fluctuating signification, and has given occasion to erroneous views. The criterion of ‘moral’ and ‘immoral,’ in the accurate meaning, is Law; a moral act is imposed by a superior; hence a supreme power cannot do an immoral, any more than an illegal act. When the Deity is said to have a ‘moral’ nature, the word must be supposed to mean simply * goodness,’ or else ‘equity,’ both which qualities may attach to a supreme legislator; the sovereign power may do a mis- chievous act, and may be guilty of partiality or unfairness as between one man and another; which, however, is not the connotation of immoral or illegal, according to the proper definition of the terms. The sovereign has no moral duties ; his acts create these for his inferiors. _ The confusion of Law in the juridical sense, with Law as the uniformity of nature, is exemplified in Butler’s chapter on the Moral Government of God. Butler calls the ‘course of Na- ture’ a government, merely on the ground that it induces precautions to avoid pain. But these precautions have nothing moral in them; they may be used for criminal ends. Guy Fawkes most faithfully obeyed the laws of nature, when he placed his barrels of gunpowder so as to ensure the blowing up of Parliament, while he arranged for firing them in safety to himself. It is the object of a Law proper to prevent men from injuring one another; the uniformity of nature lends itself equally to good and to evil conduct. The word ‘ Utility’ has a narrow sense opposed to Art, elegance, and refinement; and a wider sense (as in the Utility theory of Morals), comprehending the whole circle of human gratifications and well-being. ‘Self’ has several meanings, which have to be disentangled in ethical reasonings. 618 FALLACIES OF CONFUSION. The words ‘same,’ ‘identity,’ have often been commented on. Similarity or sameness is a matter of degree, and in this consideration alone lies the ambiguity. A human being is called the same person all through life, although in many respects changed. ‘Probability’ is not always used in its proper meaning, namely, the expression of what is true, not in every case, but in most. Not unfrequently, the two sets of cases, pro and con, are called the probabilities for and against a thing. The wind blows from the east, say three days in seven, and from the west four days in seven; the proper expression then is, there is a probability of four to three in favour of west wind on a given day. To say that the probabilities are four in favour of, and three against, a west wind leads to a confounding of the probable with the improbable. A vacillation between the meanings is observable in Butler’s Introduction to his Ana- logy. He correctly expresses the nature of probability when he speaks of there being a greater presumption upon one side of a question than upon another, and remarks that if there be the slightest preponderance, prudence requires us to act accordingly. He goes on, however, to say that, in questions of great consequence, we have to be content with probabilities even lower; that is, where there is an equal balance on both sides; nay, even to less than this; in other words, we are to act with the majority of cases against us, which is to believe in the improbable. . The play of ambiguity is seen in the remark of Aristotle— ‘That which is naturally good is good and pleasant to the good man ;’ an equivocation too closely resembling what occurs in Plato’s argument to show that the wrong-doer, if unpunished, is more miserable, than if he were punished. ‘The wrong-doer’ says Plato, ‘when punished suffers what is just ; but all just things are honourable; therefore he suffers what is honourable. Now all honourable things are so called because they are either agreeable, or profitable, or both together. Punishment is not agreeable; it must therefore be profitable or good. Whence the wrong-doer when punished suffers whatis profitable or good, &e.’ Separate meanings ascribed to separate words.—This is one of the greatest snares of language. There is a strong tendency in the mind to suppose that each word has a separate meaning, and to be misled by tautologies and alterations of phraseology. The ramifications of this tendency are numerous and subtle; they include the master fallacy of Realism, or the conversion of Abstractions into Realities. DREAD OF CHANGES IN LANGUAGE. 619 The strong verbal associations formed with all our opinions and views make us alarmed when it is proposed to withdraw the customary phrases in favour even of such as are more suitable. Siillingfleet complained that Locke’s doctrine con- cerning Ideas ‘had almost discarded Substance out of the world.’ This feeling has been manifested against all the great innovations of philosophy. Because the Cartesian doctrine of Mind and Matter, as two distinct things, is declared to be. gratuitous and destitute of proof, people are shocked as if Mind were done away with. The same revulsion is experi- enced towards Berkeley’s attempt to reconcile the contradic- tion of the prevailing mode of regarding Perception. Whately disposes of Hume’s objection to miracles ‘as contrary to the Course of Nature,’ by the retort that, according to him, there is no such thing as a Course of Nature, there being nothing but ideas or impressions on the mind of the individual. The unproducible entity ‘Substance’ is upheld in man’s minds by the force of the word. The fallacy of the Identical Proposition is due to there being two different names for the same thing :— There’s ne’er a villain dwelling in all Denmark, . But he’s an.arrant knave. Ferrier complains of the phrase ‘ Perception of Matter,’ as a a duplication of words for one fact, leading people to suppose that there are two facts. So, between antecedent and conse- quent, in Causation, there is interposed the name ‘ power,’ to which there is nothing corresponding ; the fact being sufficiently stated by the uniform sequence of the antecedent and its consequences. There is a difficulty in satisfying men’s minds that Resist- ance, Force, Inertia, Momentum, Matter, are all one fact. So with the terms Motion, Succession, Direction, Distance, Situa- tion, Extension—which are modifications of one fundamental faet— Movement and the possibility of movement, The giving reality to Abstractions is the error of Realism and is not as yet fully conquered. Space and Time are frequently viewed as separated from all the concrete experi- ences of the mind instead of being generalizations of these in certain aspects. Certain things are said to be ‘ out of all relation to Time,’ which should mean that such things have no suc- cession and no endurance. ‘Time as the innovator,’ is either an unapt metaphor, or nonsense. So, ‘Truth’ in the abstract is a fiction; the reality is a number of true propositions. ‘ Chance’ lingers in men’s minds as an independent existence, 620 FALLACIES OF CONFUSION, instead of an assertion of identity between certain concrete situations. The word ‘Existence’ in its most abstract form refers to a supposed something attaching alike to the Object and to the Subject, over and above Quantity, Succession, and Co-existence, which are attributes common to both. The only meaning of the word is the Object together with the Subject; for which addition we also employ the synonymous names, Universe, Being, Absolute, Totality of Things. To predicate existence of matter or mind is pure tautology. ‘ Hxistence” means matter or mind, or both, as the case may be. The only use of the word is to express Object or Subject indiscriminately, there being occasions when we do not need to specify either. The valuable distinction, struck out by Aristotle, of Poten- tial and Actual, is made the occasion of giving reality to fictions. The potentiality has no meaning but by a reference to actuality; the power of moving means motion in given circumstances. ‘ Educability’ means education under certain conditions. Hamilton has created a fictitious intellectual faculty under the name ‘ Conservative Faculty ; @ pure re- duplication of his ‘Reproductive Faculty.’ We know nothing of the conservation of thoughts, except that under certain circumstances they are recalled or reproduced. Unsuitable phraseology and unreal questions.—Many purely artificial perplexities have arisen from applying to a subject terms incongruous to its nature. The words ‘true’ and ‘ false’ are properly applicable to knowledge or affirmations respect- ing the order of the world; they cannot be applied to pleasures and pains except by mere metaphor. A ‘false pleasure ’ is an incongruous jumble, like a ‘loud circle’ or a ‘ bright toothache.’ Aristotle puts the question—‘ Is happiness praiseworthy P’— to which there is no proper answer, because there is no apd meaning, The old puzzle respecting Motion is due to the improper use of language. Motion means ‘change of place.’ The puzzle is brought about by insisting that the phenomenon shall be expressed as im a place, that it shall be either in one place or in another. If we give way to this arbitrary restriction of language, we must allow, with Hamilton and many others, that Motion can be shown to be impossible. Allusion has already been made (p. 364) to the unsuitability of the word ‘hypothesis’ to express abstract notions, as the definitions of Geometry. : The application of terms of Extension and Local Position FALLACIES OF SUPPRESSED RELATIVE. 621 to the mind has been the source of factitious puzzles and arti- ficial mysteries. ‘How the immaterial can be united with matter, how the unextended can apprehend extension, how the indivisible can measure the divided,—this is the mystery of mysteries to man’ (Hamilton’s Reid, p. 886). The answer ‘is, no attempt should be made to express the union of mind and matter in the language that would be suitable to the union of one extended thing with another. The most conspicuous example of an artificial difficulty created by incongruous language is the celebrated Free-will theory. The sequences of the Will consist of feelings followed by actions; they exemplify mental causes giving birth to activity, and are broadly contrasted with the physical prime movers—as water and steam —which are devoid of any mental element. There is no mystery in these peculiar sequences except the mystery of the union of mind and body, formerly remarked on (p. 357). The introduction of the idea of Free- dom or Liberty into the voluntary operation is totally without relevance; and the consequence has been a seemingly insoluble problem, a mesh of inextricable contradictions, Fallacies of Relativity.—A large class of Fallacies consist in denying or suppressing the correlatives of an admitted fact. According to Relativity, the simplest affirmation has two sides; while complicated operations may involve unobvious correlates. ‘Thus the daily rotation of the starry sphere is either a real motion of the stars, the earth being at rest, or an apparent motion caused by the earth’s rotation. Plato seems to have fallen into the confusion of supposing that both stars and earth moved concurrently, which would have the effect of making the stars to appearance stationary. Every mode of stating the doctrine of innate ideas commits, or borders upon, a Fallacy of Relativity, provided we accept the theory of Nominalism. A general notion is the affirma- tion of likeness among particular notions; it, therefore, subsists only in the particulars. It cannot precede them in the evolu- tion of the mind; it cannot arise from a source apart, and then come into their embrace. A generality not embodied in particulars is a self-contradiction unless on some form of Realism. Kant’s autonomy, or self-government of the will, is a fallacy of suppressed relative. No man is a law to himself; a law co-implicates a superior who gives the law, and an inferior who obeys it; but the same person cannot be both ruler and subject in the same department. 622 FALLACIES OF CONFUSION. In Ethical questions there are examples of suppressed rela- tives. Thus, it is often set down as essential to the highest moral virtue, that law and obligation should embrace every act of human life, that the hand ‘of authority should never, unfelt. Now, authority means operating by penalties, an appeals exclusively to the selfishness of men’s nature, _Uni- versal obligation is universal selfishness, which is not what is intended by the supporters of the doctrine. The view is sometimes expressed that the civil magistrate is bound to support (by public establishment) the true religion ; which, however, can mean only what he thinks the true reli- gion; and the correlative or consequence is that he is bound to establish a false religion, provided he believes it to be the truth. This is an offshoot of the fallacy arising from the suppression of the subject mind in affirmations. An affirma- tion correlates with an affirmer; a truth supposes a betianar. (See Part First, p. 80). A Fallacy of Relativity i is pointed out, by Mr. Voswes in the . doctrine of Fatalism; a doctrine implying that events, depend- ing upon human agency, will yet be equally brought to pass whether men try to oppose, or try to forward them. (Logic of Chance, p. 366). The doctrine of Relativity is carried to a fallacious pitch, when applied to prove that there must be something absolute, because the Relative must suppose the non-Relative. If there be Relation, it is said, there must be something Un-related, or above all relation. But Relation cannot, in this sma be : brought round on itself, ees by a verbal juggle... which thy or extended world). This is the final at of all ene oni tion. We may view the two facts separately or pe and we may call the conjunct view an Absolute (as Ferrier does), but this adds nothing to our knowledge. A self-con- tradiction is committed by inferring from ‘ encry idling is relative,’ that ‘something is non-relative.’ Fallacies of Relativity often arise in the hyperboles_ of Rhetoric. In order to reconcile to their lot the more humble class of manual labourers, the rhetorician proclaims the dignity —_ of all labour, without being conscious that if all labour is ‘ dignified, none is; dignity supposes inferior grades; a moun- ‘ tain height is abolished if all the surrounding plains are raised to the level of its highest peak. So, in spurring men to industry and perseverance, examples of distinguished success 7h et” ‘i... BEGGING THE QUESTION.—SHIFTING THE GROUND. 623 are held up for universal imitation ; while, in fact, these cases _owe their distinction to the general backwardness. Petitio Principii. - Petitio Principii, Petitio Quesiti, arguing in a circle, begging the question—are names for a fallacy always included by logicians in the List of Fallacies. ‘To assume somewhere in the premises the very point to be proved is frequent in dealing with ultimate truths. The attempts to prove causation or the uniformity of nature usually take it for granted in some form or other. The inductive syllogism is a petitio principu. As another instance, suppose, on the one hand, the continuity of motion were given as the proof of Persistence of Force, and on the other hand, the Persistence of Force given as the proof of the continuity of motion, the argument would revolve in a circle. | A chemical writer (Gmelin) assigns as the cause of chemical decomposition by superadded bodies leading to new com- pounds, that the forces tending towards the new compounds are stronger than those maintaining the old. Hamilton remarks that Plato, in Phezdon, demonstrates the immortality of the soul, from its simplicity, and in the Re- public, demonstrates the simplicity from the immortality. Ignoratio Elenchi. _ Ignoratio Hlencht, shifting the ground, or answering to the wrong point, is committed in many controversies. An example is furnished in the controversy relating to a Moral Sense. The opponents of the doctrine urge as an argument against , primitive or intuitive moral standard, that different nations differ widely in their notions of what is right and wrong. The reply is, that although they differ in the substance of the moral code, they agree in holding some things to be right and morally obligatory. This, however, is shifting the ground. The reason for appealing to an implanted sense of Right was to obtain for certain moral precepts a higher authority than human convention could give. It was not to prove us endowed with a sense that something or other is a moral obligation, but to establish the obligation of certain assigued rules (the morality of our own time). In books on Practical Ethics, there is usually a chapter on ‘Our duties to ourselves,’ Like the autonomy of the Will, this is a Fallacy of Relativity, being a contradiction of the very idea of duty, which implies a superior authority. The difii- 624 LOGICAL FALLACIES, culty is met by shifting the ground; the allegation being that the care of our person and our interests is a duty to society and to God. The ‘ Fallacia accidentis’ and the ‘a dicto secundum quid ad dictum simpliciter’ might be brought under “shifting the ground.’ The meanin g of a term is changed in its application ; ; ‘water quenches thirst,’ does not mean ‘ boiling water.’ So, the pleasures of duty are not pleasures attaching to it as duty, or as self-sacrifice, they are incidental consequences of the situa- tion, through the reciprocal conduct of the other party. False Analogies. The irrelevant comparison, or unsuitable analogy, is a usual form of confused and erroneous thinking, especially in the older philosophy. It abounds in Plato (see especially Timeeus) and is not unfrequent in Aristotle; it is also prevalent in Bacon’s attempts at scientific investigation. A familiar but highly illustrative example is the comparison of the history of a nation to the life of man, in respect of birth, growth, maturity, and inevitable decay. The comparison is irrelevant; the likeness palpably fails in the most important points. A nation’s losses are repaired ; the physical failure of a human being is irreparable. The reply to all such comparisons is to indicate the failure of identity. They are false minor propositions ; and the fale- hood is exposed by pointing out the dissimilarity of the subject with the subject of the major. a are of the same nature as a pleading in law where the relevance is unsound. The remedy is found in hostile criticism. CHAPTER V. LOGICAL FALLACIES. There may be advantage in providing a supplemental collec 4 tion of examples of Logical Fallacies properly so called, that is, — violations of the prescribed Logical rules and methods; it being ‘a fully understood that the exemplification of the roles thein- 4 selves, in the regular exposition, unavoidably affords instan- ces of their neglect or failure. io EQUIVALENCE, DEDUCTION, AND INDUCTION. 625 The proper arrangement of such an additional collection (unless made promiscuous to test the ingenuity of the student) is the arrangement of the general subject. Following the order—Deduction, Induction, Definition—we should commence with Deductive or Syllogistic Fallacies. Since, however, a separate department, inaueahiahs to the Piyibogiacn; is made up of Equivalent For ‘ms, called also Im- mediate Inference, and since mistakes may be committed in this department (some of them the proper sources of syllogistic fallacies), the first clsss of Fallacies should be Fallacies of EQUIVALENCE, or of IMmepIATE INFERENCE. ‘The chief heads where fallacies occur are the Opposition of Propositions, and Conversion. _ The acutest minds have been snared by confounding the Contrary with the Contradictory, of Propositions. ‘The reverse of wrong is right’ should be ‘The reverse of wrong contains something that is either right or indifferent.’ ‘There are objections against a vacuwm; but one of them must be true:’ the guarded statement is, ‘if there be not a universal plenum, there must be some unoccupied space, or vacuum.’ The chief fallacy of Conversion is Simple Conversion of A ; ‘all the geometrical axioms are self-evident; all self-evident truths are axioms.’ The connection of this mistake with the usual fallacies of syllogism, was sufficiently pointed out, The proper Depuctive Faubacies are errors against the syllogistic forms and canons. They are mainly resumed in Undistributed Middle and Illicit Process, which again usually involve the simple conversion of A. But for the snare of language that leads to this inadvertence, a fallacy of syllogism would be comparatively rare. The Inpuctive Fauuactes include the most frequent and the gravest of logical mistakes. Their exemplification would naturally follow the expository order of the subject of Induc- tion. We might commence with erroneous views of the nature of Cause, such as the suppression of important conditions and collocations. We might also connect with this part of the subject the error of assigning more causes than a pbeno- menon needs. It is involved in the very idea of cause, that the effect is in exact accordance with the cause; hence, _the proof that more causes were operative than the effect needed, defeats itself. If we have an adequate cause for slavery, or for the subjection of castes, or classes, in the mere love of domination on the part of the stronger, the explanation that the state of society demands such an arrangement is of no value, This is the error called ‘ proving too much,’ 626 LOGICAL FALLACIES. - Next are the Fallacies from insufficient employment or neglect of the Methods of Elimination. Under Agreement falls the mistake (exemplified in Medicine) of confounding induction with multiplication of instances, without variation of circumstances. Mr. Mill’s Fallacies of non-observation likewise sin against the methods. An induction is not com- plete till all the instances, or representatives of them all, have been examined. Paley, in affirming ‘ that happiness 1 is equally distributed through all classes of the community,’ must have left out of account the larger part of the facts. The assertion that ‘Species are never transmuted,’ even although not disproved by positive instances to the contrary, would require an examination of facts far beyond what has ever been made. Leibnitz generalize: his ‘ Law of Continnity ’ from a few unquestionable instances, without verifying it through all nature. The fallacious inferences named ‘ Non causa pro causa,’ ‘Post hoc ergo propter hoe,’ are fallacies of the inductive methods. Some circumstance coupled with an effect is held to be its cause, without due elimination. Thus, the luxury in the Roman empire is said to have been the cause of its down- fall; commercial restrictions, in spite of which trade has prospered, are made the cause of prosperity. The fallacy of not recognizing Plurality of Causes will be apparent from what was advanced on that subject. So, the fallacy of trusting to the Inductive Methods in Intermixture of Kffects was necessarily involved in the reasons given for coupling Deduction with Induction. Under Secondary Laws, there is obviously ‘ata the fallacy of applying a general law to a concrete instance, or to an intermediate law, without the due modifications; as if we were to infer from the Law of Gravity that all the planets are falling direct to the sun. Fallacies of Explanation. were expressly exemplified. A | non-compliance with the logical conditions of Hypotheses would yield fallacies on that subject, wm a Factactes or Derinirion would, in the first place, express — the use of ill-defined terms. Again, the failure to satisfy the — methods and rules of Classification is a sin against Logic. We need but instance the wide prevalence of the error of Cross-divisions. Bacon is prolific of divisions and sub-divisions, — which are never logical. His four classes of Idola are not — mutually exclusive; his Prerogative Instances will hee after- wards remarked on, eloeote a berg © APPENDIX. A.—CLASSIFICATION OF THE SCIENCES. It is here proposed to subjoin a short account of the different modes of classifying Science or Knowledge. The subject has various logical bearings. The concatenation of Knowledge is in itself a Logic. The mode of partitioning Knowledge that first gained atten- tion was Bacon’s threefold division into History, Puitosopny, and PoETRY; in correspondence with the three great modes of intellectual production, or faculties—Memory, Reason, and Imagination. History, the product of Memory, deals with in- dividual things ; PaiLosopuy, the product of Reason, compares, classifies, and works up these materials; Portry, the product of Imagination, is the department of fiction, fable, or creation, as opposed to the literal rendering of things in History and in Philosophy. In dividing and sub-dividing these leading departments, Bacon displays his usual copiousness. History is divided into Natural History and Civil History. Natural History is the col- lective matters of fact of the world, laid out under Celestial Bodies, Meteors, the Earth, &c. Civil History is Ecclesiastical, Literary, Political, with minor sub-divisions. Painosopny refers to God, to Nature, and to Man. The first head gives Theology. The second is a somewhat crude sylla- bus of Mathematics, Natural Philosophy, and Metaphysics. The Philosophy of Man is divided and sub-divided in much curious detail, but with no logical precision. He speaks of man in a three-fold aspect—(1) Man in general, (2) the human _ body, and (8) the human mind. The theoretical and the prac- tical aspects of our knowledge respecting humanity are indis- criminately mixed. As a first attempt at partitioning the totality of Literature, the scheme of Bacon deserves to be commended. But the lines of demarcation are for the most part vague and unsatis- factory. The distinction of Individual (as History) and Gene- ral (as Philosophy) is wholly unsuited to a primary division 628 CLASSIFICATION OF THE SCIENCES, of knowledge; we cannot divorce the particulars from the generalities in the same subject matter. The main outline, as regards the three-fold Division, was maintained in the classification of D’ Alembert, intended for the © plan of the French ‘Encylopédie’; but with great improvements in the sub-divisions. The sub- division of Philosophy, relating to Nature, is a methodical arrangement of the Mathematical, the Physical, and the Biological Sciences, together with the more Scientific Arts, as Medicine, Agriculture, and Metallurgy. The Natural History department of History includes Meteors, Geography, Minerals, Plants, and Animals, very much on the scheme of Bacon, with the curious detached addition (also after Bacon) of a division for Prodigies, or deviations from the usual course of Nature. The Science of Man is distributed under the two heads Logic and Morals. Logic comprises the arts of Thinking, Retention, or Memory, and Communication. Morals is General, that is, revards Virtue at large (Ethics); or Particular,— including Law or J urisprudence. This is the mode of ap- proaching the science of mind that has been embodied in our Universities. Excepting in recently founded schools, there is no chair for Psychology or the Theoretical Science of Mind ; the subject is left to come under Logic and Moral Philosophy ; the Intellectual Powers being described in the Logic miterne the Active Powers in Moral Philosophy. Thus, in D’Alembert, as well as in Bacon, there is total confusion of the Theoretical and the Practical. The plan of subjects in the ‘ Encyclopedia Motespaliiheed (begun to be published in 1815), is worthy of being eo There are four Divisions in the work. The First Division includes PURE SCIENCES, divided into Format—Grammar, Logic, Rhetoric, Mathematics, Meta- physics; and Reat, Law, Morals, and Theology. , The Second Division is the MIXED SCIENCES ‘ch Mealiaiia ics, Hydrostatics, Pneumatics, Optics, Astronomy [constituting the larger part of our usual course of Natural Philosophy]. — The Third Division is the APPLIED SCIENCKHS, sub- divided into Experimental ParLosopay— Magnetism, Electricity, Heat, Light, Chemistry, Acoustics, Meteorology, Geodesy ;— Fine Arts; Userun Arts; Natura History (with applications - a to Mchintnal \ ounedee These are the properly scientific divisions; the other sub- ’ NEIL ARNOTT.—AUGUSTE COMTE 629 jects are History, Biography, Geography, Lexicography, and Miscellaneous information. The designations ‘ Pure,’ ‘ Mixed,’ and ‘ Applied’ Sciences have characteristic meanings, although not precisely carried out inthe above scheme. The Pure Sciences are the more Abstract and Formal Sciences, not involving the consideration of objects in the concrete; the two leading examples are Mathematics and Formal Logic. The Mixed Sciences consider the applications of the laws of the Formal Sciences to actual things. The Applied Sciences, in so far as distinct from the Mixed Sciences, should be equivalent to the Practical Sciences. Dr. Neil Arnott, in his work on ‘ Physics,’ published in 1828, gave wide publicity to a division more in harmony with our present views. He distributed the leading sciences under four heads, representing the four classes of general Laws of Nature—namely, Physics, Chemistry, Life, and Mind. He viewed Mathematics as preliminary and indispensable to these, being the Science of Quantity, or Measure, but not a depart- mént of natural operations, in the same acceptation as Physics or Chemistry. All the sciences give foundation to Arts. _In his subsequent treatise, entitled ‘Survey of Human Progress,’ Dr. Arnott brought out more decisively the distinc. tion between Sciences and Arts, and between the Concrete and the Abstract Departments of Science. Concrete Science he calls the knowledge of TH1nas ; and he enumerates, under this head, Astronomy, Geography, Mineralogy, Geology, Botany, Zoology, the History of Man. Science, or Philosophy (Ab- stract), is the knowledge of PHrnomena, and comprises the four fundamental departments—Physics, Chemistry, Biology, Mental Science. The Arts are classified as Mechanical, Chemical, Physiological, and Mental. The work of Auguste Comte, entitled ‘ Cours de Philosophie Positive’ (1830-42), is both a classification of the sciences as a whole, and a minute sub-division of each, according to certain fundamental principles. He first draws the primary distinction between the Abstract and the Concrete Sciences, which he fully illustrates. The Abstract Sciences, being the fundamental or departmental branches of Knowledge, are susceptible of an orderly classifica- tion on the principles of Generality, Simplicity, and Independ- ence. Accordingly, he commences with Maraemartos, whose truths 630 CLASSIFICATION OF THE SCIENCES. are the most general of all, and wholly independent of the truths of any other science, while all other sciences depend upon it. Its sub-divisions are, the more abstract portion called Number, including Arithmetic and Algebra, and the applica - tions of these to Space (Geometry), and to Motion (Rational Mechanics). His second science is Astronomy, which is the ensbouimideik of the Law of Gravitation. It receives this position because the carrying out of gravity requires Mathematics alone, while the phenomenon of gravity is a prelude to Physics. Then come, in order, Puysics, CuEmistry, BioLoey, and SocioLoGy, whose mutual position and interior arrangements are governed by the same ideas of growing dependence and complexity, and decreasing generality. In addition to the singling out of Astronomy as a leading science, Comte’s arrangement has these two farther peculiari- ties, namely, the omission of Psychology, as a separate depart- mental science, (it being appended to Biology, under ‘ Cerebral Functions,’) and the inclusion of Sociology, or the Science of Society, as a fundamental department. Mr. Herbert Spencer, in his recent work entitled * The Classification of the Sciences,’ has criticised the scheme of Comte, and propounded one of his own, which he has devel- oped with circumstantial minuteness. He deals exclusively with the Theoretical sciences. Mr. Spencer’s fundamental idea is the important distinction of Abstract and Concrete, which he expresses in a@ variety of forms ; it is the distinction between the Relations of pkeno- mena and the Phenomena themselves, between the Analytical and Synthetical ; it is the separation of one or a few sequences from the total plexus of sequences; the wholly or partially ideal as contrasted with the real. Not content, however, with a simple binary division accord- ing to this leading contrast, Mr. Spencer proposes a three-fold division, by interpolating between the extremes a middle class partly Abstract and partly Concrete, to be termed Abstract- Concrete. The three classes are Absrract, ABsTRACT-CONCRETE, and ConcreTs. The only way that this is competent is to sub- divide the Abstract, according to degrees of Abstractness. ‘Concrete’ has no degrees ; ; it means the phenomena taken in their full totality, or individuality,—Stars, Mountains, Mine- rals, Plants, Animals; and there can be but one way of giving these totals, one mode of concreteness. There may, however, HERBERT SPENCER'S CLASSIFICATION. 631 be various degrees of the analytic separation—more or less abstract relations indicated ; quantity and form are more ab- stvact than weight, hardness, colour, life. The Apsrract Sciences by pre-eminence, are those that deal with the most abstract of all relations—Space and Time. Wichout affirming that Space and Time are intrinsically mere forms, conceived by us without any particular things extended and enduring, Mr. Spencer holds that they have acquired this character by hereditary transmission, and that we do actually possess them in their empty condition, or apart from any con- crete embodiments. Hence, whatever relations subsist with reference to these great conceptions, are the most abstract that the mind can possibly entertain; they are pure and proper ab- stractions; their hold of the concrete world has been almost, if not altogether, severed. Space is the abstract of all rela- tions of co-existence. Time is the abstract of all relations of sequence. Now there are two sciences that are occupied with these abstract relations of co-existence and of sequence—Logic and Mathematics ; which accordingly form a class by them- selves, being removed from the next class by a wider interval than separates the members of that class from one another. Proceeding from the blank Forms of existence, to Existences themselves, from the relations of phenomena, to the phenomena, we find two divisions, having different aspects, aims, and methods. In fact, we have the distinction of Abstract and Concrete carried out, without the same absolute divorce as in the previous class. Mr. Spencer illustrates the distinction thus :—LHvery phenomenon is a manifestation of force, usually a combination or complication of forces (the course of a pro- jectile depends upon at least three forces). We may study the forces either in separation, or in combination—the factors or the product. On the one hand, neglecting all the incidents of special cases (say of falling bodies), we may aim at educing the laws of the common force (gravity) when it is uninter- fered with. On the other hand, given all the incidents of a phenomenon (as a river), we may seek to interpret the entire phenomenon, as a product of the several forces simultaneously in action. The truths reached through the first kind of en- quiry, though concrete inasmuch as they have actual exist- ences for their subject-matter, are abstract as referring to the modes of existence apart from one another. Mr. Spencer thinks it proper to point out farther that the abstract must not be confounded with the general. Hach has its peculiar signification ; ‘abstract’ means detachment from 632 CLASSIFICATION OF THE SCIENCES. particulars ; ‘ general’ means manifestation in numerous cases. — The law of uniform rectilineal motion is abstract; butitis — never realized in any particulars, consequently it is ‘not gene- ral; while rotation on an axis is very general, Accordingly, he disapproves of Comte’s expression ‘ decreasing generality,” as belonging to the phenomena of the successive sciences —Mathematics, Physics, &c. This criticism indicates a pot — worth noting, but as regards Comte’s remark it might easily be evaded. There can be no abstraction without a prior generalization; the abstract law of rectilinear motion, is a generalization of the very highest order stating what would | happen in every case when a body is projected into space and left to itself. The other kind of generality is something more special and concrete, in fact, much less of a generality _ this great primary law. The Sciences, then, that treat of the forces of vhievsoasedill as analyzed and handled in separation, are the ABsTRACT-CONCRETE Sciences; as Mechanics, Physics, Chemistry. ‘The sciences that view phenomena in their aggregate, or their full actuality, are Concrete Sciences ; such are Astronomy, Geology, weap. j Psychology, Sociology, &c. A few words now as to the more precise definitions and divisions of the leading departments, on which hang various points of logical interest, 1 ah ABSTRACT SCIENCE considers, first, what is common to all — Relations, and next, what is common to each order of Relations. — Between each kind of phenomenon and certain other kinds of — phenomena, there exist uniform relations. It is a universal — abstract truth—-that there is an unchanging order among — things in Space and in Time. This is the most abstract truth — ofall, the subject-matter of the highest division of Abstract Sotonesi It has sub-divisions. First, and next in abstractness, © are the connexions of things in Space and Time, irrespective — of the things connected. This is the subject-matter of Logie, — where the nature and amounts of terms related are not considered, but only the relations themselves. The other sub- division takes in Quantity or amount, without any farther qualities. This is Mathematics, which is a statement of laws of quantity apart from any real things, that is, as occupying Space and Time. This statement is made upon certain ultimate — units occupying definite positions in Space and in Time. The- divisions of Mathematics follow according as the units simply separate, or according as they are both separate and equal; the one gives birth to an indefinite Calculus (applied wy ABSTRACT AND CONCRETE SCIENCES. 633 in Statistics), the other to the Definite Calculus, whose sub- divisions are Arithmetic, Algebra, and the Calculus of Opera- tions. When the computation of units refers to occupation of Space, the subject is Geometry. When Time is introduced, we have Kinematics and the Geometry of Motion. . _ So much for the sciences of pure Abstraction. The second class, the Apstract-ConorETE, are occupied with the general laws of Motion, Matter, and Force, in their disentanglement from the concrete phenomena, where they re-act upon, and modify one another. In Mechanics, for example, which is one of the sub-divisions, the laws of motion are expressed without reference to friction and resistance of the medium (?). So in Chemistry, another sub-division, the laws are viewed upon substances absolutely pure, such as Nature rarely supplies. The partition of this group is conducted on the same prin- ciple as in the former group. A distinction is drawn between Force considered apart from its modes, and Force considered under each of its modes,—a more abstract, and a less abstract department. The first part contains a statement of the Laws of Force, as deducible from the fundamental principle of the Persistence of Force, together with the theorems of the Com- position and Resolution of Forces. The second part comprises Molar Mechanics or Molar Forces (Statics, Hydrostatics, Dynamics, Hydrodynamics), and Molecular Mechanics—includ- ing the properties and states of matter (Physical), and Chemis- try ; together with Heat, Light, Electricity, and Magnetism. [The arrangement is a questionable one, in so far as Chemistry is interposed between the Physical properties and states of bodies, and the agencies—named Heat, Light, &c]. The division of Abstract-Concrete Science is thus co-exten- sive with what we have formerly termed Inorganic Physics. The third great group, the Concruts Scienczs, as repeatedly stated, embrace the totalities of phenomena. Astronomy is placed in this group. The meaning is, that the astronomer does not stop short after generalizing the laws of planetary movement, such as they would be if there existed only one planet; he solves this abstract concrete problem, as a step to- wards solving the concrete problem of the planetary movements as affecting one another. The ‘theory of the Moon’ means an interpretation of the Moon’s motions, not as determined simply by centripetal and centrifugal forces, but as perpetually modified by gravitation towards the Harth’s equatorial protu- berance, towards the Sun, and even towards Venus—forces daily varying in their amounts and combinations. So the 634 CLASSIFICATION OF THE SCIENCES. 2 wy geologist does not confine himself to the separate elements— water-action, fire-action, he aims to interpret the entire structure ; of the Earth's crust, And, in Biology, if different aspects of — the phenomena of Life are investigated apart, they are all helping to work out a solution of vital phenomena in their entirety, both as displayed by individual organisms and by organisms at large. The interpretation is no longer Syne z cal but analytical. These explanations premised, the enumeration of subjects in the Concrete division is as follows :—First, and most general — of all, are the Universal Laws of the continuous Re-distribution — of Matter and Motion. Next follows the application of these — toactual Matter. Asapplied to the Celestial Bodies (1) treated — as masses, it is Astronomy ; (2) as made up of molecules— Astrogeny (Solar Mineralogy and Solar Meteorology). On the earth, the same actions result in Mineralogy, Metcortiae 3 Geology ; ; when causing organic phenomena, they make up — Biology, which has various sub-divisions, Leruiareae im. 3 Psychology and Sociology. Dy Such is the outline of Mr. Spencer’s scheme. By way of criticism, the following remarks may be offered. In the first place, objection may be taken to his longue in discussing the extreme Abstract Sciences, when he speaks of the empty forms therein considered. To call Space and — Time empty forms, must mean that they can be thought of ~ without any concrete embodiment whatsoever; that one can think of Time, as a pure abstraction, without having in one’s © mind any concrete succession. Now, this doctrine is in the last degree questionable. For although we might concede the : hereditary predisposition to fall into these conceptions, we do — not thereby affirm that they can be bodied forth without any concrete examples whatever. We might rather say with Kant, and the later a priort schools, that when particulars are given they start forth into full view, This much is certain, — however, that without a very wide and familiar converse with — particulars, the exceedingly abstract relations of these Abstract — Sciences, are wholly incomprehensible to any human being. The extreme generalities of Logic, in order to be intelligible, need perpetual reference to particulars. The same is true wit the first elements of Mathematics, which are the foundations of all the rest. . Mr. Spencer’s account of the subject-matter of Logic, the first of all the sciences, is so extremely general that we can hardly discover what is the precise scope he assigns to it. LINES OF DEMARCATION. 635 From its position, however, it must be viewed as Theoretical Logic purely ; under which there would be included the funda- mental aspects of all knowledge—Difference (Relativity) and Agreement (Generality), the Laws of Consistency, Mediate Inference, the Uniformity of nature; and the various deduc- tions or consequences of those primary facts. These are points common to all sciences, and may therefore precede them all. At the same time, it should be remarked that the ascertaining of these very high generalities has been a great inductive effort, considerably aided by the special study of the human mind, or the science of Psychology. This observation slightly qualifies Mr. Spencer’s statement that none of the truths of the third group are of any use to the problems of the second, while the second group are of no use to the first. It may be farther noticed that, notwithstanding the strong terms employed to contrast the Abstract with the Abstract- Concrete Sciences, the contiguous subjects of each show but a narrow boundary line. The geometry of Motion, the last of the Abstract Sciences, comes very close upon the Universal Laws of Force, the first subject of the Abstract-Concrete vroup. These considerations, if they have any weight, tend to in- validate the alleged distinction between Abstract and Abstract- Concrete Sciences, a distinction without an adequate difference. _ Practically, however, the matter isof no moment. The succes- sion of subjects would probably be regarded as the same, and the manner of sub-dividing and treating them would be very much the same with or witbout this particular boundary. Mathematics must precede Mechanics; and Logic, conceived in its high theoretic aspects, may claim to precede Mathematics. A much more serious dispute arises out of Mr. Spencer’s proposed boundary line between the Abstract-Concrete and the Conerete Sciences. No one ever drew the line as he has done it. The Concrete Sciences have always been typified by the so-called Natural History Sciences— Mineralogy, Botany, Zoology, Geology—and by Geography. These are Sciences whose marked teatures are Classification and Description. They deal with large collections of objects, which they arrange and describe by means of careful generalization. It is, therefore, with a little surprise that we find inserted among Concrete Sciences, not merely Astronomy, but the whole of Biology, in which is included Psychology. Certain parts of these subjects would be properly concrete ; as Celestial Geography (under Astronomy); and the Races and Charac- ters of men (under Psychology.) 636 CLASSIFICATION OF THE SCIENCES. Let us consider how the case stands with Astronomy. This — science, since Newton’s time, is avowedly based on Theoretical — Mechanics. Newton, in the First Book of the Principia, which | may be pronounced Abstract Mechanics of the purest type, went far beyond Mr. Spencer’s limits to an Abstract-Conerete _ Science. These limits, indeed, are not a little arbitrary. We can suppose a science to confine itself solely to the ‘factors,’ or — the separated elements, and never, on any occasion, to combine — two into a composite third. This position is intelligible, and possibly defensible. For example, in Astronomy, the Law of — Persistence of Motion in a straight line might be discussed in pure ideal separation; and so, the Law of Gravity might be discussed in equally pure separation—both under the Abstract- — Concrete department of Mechanics. 1t might then be reserved — to a concrete department to unite these in the explanation of a projectile or of a planet. Such, however, is not Mr. Speucer’s — boundary line. He allows Theoretical Mechanics to make this particular combination, and to arrive at the laws of planetary movement, in the case of a single planet. What he does not allow is, to proceed to the case of two planets, mutually dis- turbing one another, or a planet and a satellite, commonly — called the ‘problem of the Three Bodies.’ This problem is | not to be touched in Theoretical Mechanics, but to be remanded ; to the Concrete Science of Astronomy. Yet, if we are allowed — ; to combine the two factors—projectile motion and gravity to one centre—why may we not take in an additional Saatod a second gravitating body? The difference is not between single factors and their combination, but between two grades of combination. In point of fact, such a line is never drawn. N ewton, i in the First Book of the Principia, took up the problem of | Three Bodies, as applied to the Moon, and worked it to ole haustion. So writers on Theoretical M echanics continue to include the Three Bodies, Precession, and the Tides. Nor is any reason apparent for making the break that Mr. Spencer suggests. Increasing complicacy of deduction and caleulation attends the inclusion of new factors, but this special difficu is not supposed to take the subject out of an abstract ten ment and to insert it in some concrete department. <1 Again, Mr. Spencer remarks that in works on Mechanies, the laws of motion are expressed without reference to fri¢ and resistance of the medium. Turning to ‘ Thomson Tait’s Mechanics,’ we find the Laws of Friction intro . with a reservation of the purely Experimental results to the = CHEMISTRY AND BIOLOGY. 637 department called Properties of Matter. In Newton’s Second Book, and in all works of similar compass, the operation of a Resisting Medium is handled. The law of the radiation of light (the inverse square of the distance) is said by Mr. Spencer to be Abstract-Concrete, while the disturbing changes in the medium are not to be mentioned except in a Concrete Science of Optics. We need not remark that such a separate handling is unknown to science. Mr. Spencer’s illustrations from Chemistry are especially at variance with usage, while it is difficult to reconcile them with reason. Chemistry is an Abstract-Concrete Science. What does this mean? The reply is, the chemist is never satisfied with the crude substances of nature, but first purifies them, and ascertains the properties in the pure state. This, of course, is a necessary precaution. But if the insinuation be, that Chemistry does not give, or ought not to give, the pro- perties of any impure substance, or any alloy or mixture, the fact is quite different.. Every chemical writer describes all the prevailing species of carbon, including pure and impure kinds; the same with iron, and with every substance found in important varieties. Why should it be otherwise ? There is no dereliction of logical principles in stating the properties. of the iron ores, in connexion withiron. Thesame thing may be repeated in Mineralogy, but is not out of place in Chemistry. Again, no writer on Chemistry ever omits to describe the Atmosphere, which is the actual or concrete combination of Oxygen, Nitrogen, &c. lt may be noticed in addition that a substance purified is obviously not a substance in the abstract. Virgin gold, and the purest diamond are still objects in the concrete. These remarks on Chemistry pave the way for the conside- ration of the place assigned to Biology among the Concrete Sciences. Now, Biology is a science of increasing complica- tion; living bodies are subjected to all the Physical and Chemical Laws, and to Biological Laws in addition: so that a rose is a more complicated object than a diamond. But the objects of Chemistry and the objects of Biology are equally concrete, so far as they go; the simple bodies of chemistry, and their several compounds, are viewed by the Chemist as concrete wholes, and are described by him, not with reference to one factor, but to all their factors. The isolation of the one _ property, named Chemical combination, which would be an abstract handling of bodies in the chemical point of view, 638 CLASSIFICATION OF THE SCIENCES. must be considered to be impracticable; at all events it is never done. We may doubt whether anything would be gained by attempting it. But, whatever abstractive operation of this kind is possible in Chemistry, might be repeated in Biology ; there might be general laws— isolated factors—of life, as well as of inorganic matter. If so, to place one of these two leading departments among Abstract Concrete Sciences, and the other among the proper Concrete departments is to make a dis- tinction without a sufficient difference. 1, Nor is it possible to justify the placing of Psychology wholly © among Concrete Sciences. It is a highly analytic science, as Mr. Spencer thoroughly knows. The totality of mind is sepa- rated into factors, each discussed in isolation, before they are — brought together. There are many strictly abstract discussions to show the difference between the effect of a motive (as selfish- ness) acting in ideal purity or separation, and the same motive, combined with many others, in the concrete human being. But the force of the remark would appear to be dissipated if all the laws of Psychology are to be considered as expressions of the concrete facts of mind. A separation may be temporarily made between the purely theoretical and deductive treatment of a science, and the ex- perimental treatment. In Theoretical Mechanics, (as Hydro- Dynamics), the laws of a resisting medium may be inferred and computed from primary assumptions as to the nature of fluid particles; while, on the other hand, the subject may be investigated by experiments, as in gunnery. But the science is not completely presented unless both are taken account of together: the theoretical deductions have to be confronted, checked and verified, by the experimental results, in order to have any standing as laws of the department. Yet another method is possible. A subject, as, for example, Astronomy, may be exhaustively handled in a separate treatise ; wherein there shall be brought together from every department whatever bears upon the celestial bodies. This would be a ughly mixed department, yet not, on that account, a strictly concrete science. It would be full of the most abstract diseus- sions ; witness the ‘Mechanique Celeste’ of Laplace. It would draw contributions from various sciences, besides its parent science, Mechanics ; it would introduce Optics, Heat, Magnet- ism, and Chemistry; yet it would not treat the heavenly bodies as Minerals are treated in Mineralogy, or Plants in — Botany. It would have many practical bearings; in fact, it would have considerable claims to bea Practical Science. Any — ‘ 4 ee er ee ee ee Pes Sabor PRETENSIONS OF FORMAL LOGIC. 639 scientific department exhaustively treated would eschew purity, and draw contributions from many sources. Thus, it appears that Mr. Spencer, in abandoning the usual partition of the sciences, into the departmental or fundamental sciences, on the one hand, and the concrete or derived on the other, has abandoned the more real distinction in search of a fanciful and untenable boundary line of the Abstract and the Concrete. We see reason still to abide by the old specification of the Concrete Sciences, typified by Mineralogy, Botany, Zoology, Geology, &c. These sciences have marks peculiar to themselves; they are the classificatory and the descriptive sciences. They embrace large collections of individual things, which have to be classified, and to be described as concrete wholes. Moreover, they contain no new fundamental operation of nature; every variety of natural agent has been previously exhausted in the departmental sciences—Mathematics, Physics, Chemistry, Biology, Psychology. B.—THE PROVINCE OF LOGIC, It is contended by some logicians that the Province of Logic is Formal Reasoning and Thinking; by which they mean mainly the Syllogism, and what is subsidiary thereto. They would exclude everything that refers to the Matter, that is to say—Induction, and the greater part of Definition and Classifi- cation. We have, however, just grounds to complain that the dis- _ tinction of Form and Marter is too vague and unsteady to con- stitute a clear line of demarcation between the two departments of Hvidence—Deductive and Inductive. It will be expedient for us, therefore, to ascertain what precise meanings, if any, can be assigned to these phrases. Perhaps the most thorough and consecutive account of the severance of Formal Logic from Material Logic is that con- tained in the Introduction to Mansel’s edition of Aldrich. In that work, the author adduces every consideration that is of any avail in widening the distinction in question. Adverting to the first question raised in the definition of Logic, namely, whether it be a Science or an Art—whether it is principally theoretical or principally practical—Mr. Mansel holds that, in its essence, it is speculative or theoretical, and, in its accidents, practical. ‘There would be a body of prin- ciples or laws, although no one cared to apply them to the discipline of the mind, or to the improvement of the thinking faculties. 28 640 . . HE PROVINCE OF LOGIC. _ Nevertheless, the science is susceptible of application to practice; it may be brought to bear on our intellectual pro- cesses. Such is its scope as expressed in the second part of Whately’s definition— the Art of Reasoning ; which definition, however, as regards the word ‘ Reasoning,’ Mr. Mansel, in common with Hamilton and Mill, objects to as narrowing the province too much. Even as a Formal Science, Logic in- — cludes the processes named Apprehension and J udgment, and these not as mere aids to Reasoning, but as independent acts of thought. Accordingly, Mansel agrees with Hamilton in substituting for ‘ Reasoning,’ with suitable eee the larger term ‘Thought.’ He then proceeds to lay oat the distinction between the a Form and the Matter of the thought. His first indication of the difference is to this effect: Thought may violate its own laws, and so destroy itself; something may be set up that turns out wholly unthinkable. On the other hand, a Thought may be per- fectly consistent with itself, but at variance with facts of eeperience ; which, although quite thinkable, would be empiri- — cally illegitimate, or wnreal. [This is the distinction between — Self-Consistency—Immediate or Equivalent statements, and Inductive or matter-of-fact certainty |. 4 The next remark is that there must be material data in Saat : to thought of any kind, even formal thought; there must be concrete experience of things external and things internal, in order to understand even a syllogism. But the materials being q given, there is a vital difference between two modes of using ~ them. The distinction of Presentative and Representative thought — is an aid here; the distinction between the individual concrete — things—a building, a man, a star, and the generalities or con- — cepts—height, figure, brightness, which we may form by the — comparison of the concrete objects. The consideration of the Matter is the reference to the individual things; the considera- — tion of the Form is the general concept, or representative — thought. [So far we have the ordinary distinction between — Concrete and Abstract, only it is apparently pushed to a kind of Conceptualisn ; there being implied that the concept, or — notion, is Something more than an agreement among individuals. If it be true that a notion is unthinkable, except as one or more individuals, the ‘Form’ is still ‘ Matter,’ only in a Somer what different arrangement]. it es But farther, the thinking process may be distinguished | as material or formal. It is formal when the matter given is sufficient for the product derived, with no other addition but FORMAL THINKING EXPLAINED, 641 the act of thinking. It is material when the data are insufli- cient, and the mind has to take in more matter, in the act of thinking. Given the attributes, A, B, C, we can think them as co-existing in an object, without any fresh appeal to facts ; which is formal conceiving. [This is quite intelligible too; all the operations of Arithmetic are formal in this sense ; we pro- nounce six times four to be twenty four, without an appeal to pebbles or coins, or any real objects. We have put together from primary realities a machinery that can operate independ- ently of the realities]. As conditions of formal conceiving, are laid down the laws of Contradiction and Identity. We must not introduce Con- tradictory attributes—A and not-A. The author is a little more obscure as regards the condition of Identity. Thought, he says, is representative of all possible objects ; but Intuition (cognition of the individual, as opposed to Thought, or the general) must be conscious of differences; every object of intuition is marked off, limited, and individualized ; it is atsedf and no other, To this circumstance corresponds the Law of Identity, ‘Ais A’; ‘every object of thought is conceived as itself.’ A somewhat novel rendering of that well-known Law of Thought. These laws are the key to logical conceiving (Conception is the first logical product). Next, as to formal judging, or the forming of Judgments. Affirmation takes place when one concept is contained in another; Negation, when one contra- dicts another. Here, too, are involved the laws of Identity ~ and Contradiction. Finally, as to reasoning. This is formal when the given judgments are connected by a middle term, under such condi- tions of quantity and quality that the mere act of thought necessarily elicits the conclusion. If there be required any addition to the data, the consequence is material. Formal Mediate reasoning, no less than Immediate inference, is achieved through the laws of Identity (for affirmative syllogisms), and of Contradiction (for negative syllogisms). In the immediate inferences of Opposition [Obversion] and Conversion, there is a further demand for the subordinate law of Excluded Middle. Thus, then, if a thought professes to be based on formal grounds, to be guaranteed by the laws of thought alone, its pretensions can be adjudicated on by Logic; if it professes to rest on sensible experience, or on suppressed premises, it must come before another tribunal. _ It is, of course, open, the author remarks, for any innovator 642 THE PROVINCE OF LOGIO, to propose an extension of boundaries, by the inclusion of the Matter of propositions; but he does so in the teeth of Kant’s demonstration, that a criterion of material truth is not only ~ impossible, but self-contradictory. Moreover, the attempt to enlarge the field renders impossible the assigning of any definite field whatever. v7i5 eer We are interested to know in what way Mr, Mansel makes ood these very strong allegations. The steps are these. — (1) The Aristotelian or Formal Logic seeks the laws whereby a the mind thinks; the Baconian seeks the laws whereby the phenomena of outward things take place; that is to say the one _ refers to mind, the ego, the other to matter, the object, or non- ego. Consequently, the one enquiry is the interrogation of self-consciousness, the other is an examination of external nature. ‘3 Such is Mr. Mansel’s first position. Tt seems to involye some confusion of ideas. We strongly doubt whether the contrast ae Formal Logic and Inductive Logic can be reduced under the — contrast of Subject and Object, or Mind and Matter. a For one thing, the study of Mind, or Psychology, is, nm — modern times, universally considered to be properly Inductive. _ How can we reach the important laws of Mind—such as Rela- _ tivity, Association of Ideas, the operation of the Feelings, and the Will—except by observation and induction of the facts of — - self-consciousness, occasionally aided by external indications. — Again, the laws of Thought, called Identity, Contradiction, and Excluded Middle, apply alike to the outer world and to — the mind. If so, they may be gathered from either source. — Probably, however, the supposition is that these laws are got at without investigation ; that they work themselves out with- — out being expressly studied. We unconsciously and irresistibly — declare that the same thing is not at the same instant white and black ; just as we walk without thinking how we walk. These invincible tendencies of the mind, if such there be, are — no doubt facts of our mental nature: but so is our belief that — Nature is uniform, or that every effect must have a cause; on — which reposes all Inductive investigation. In both cases, the mind is the instrument, although the material may be some- _ times mental phenomena and sometimes phenomena of the — outer world. Deduction and Induction have equally their seat in laws of the thinking mind; and have equally, for their field of operation, both mind and matter. ‘ae (2) The next position is this—The Aristotelian laws are laws — of thought as it ought to be; the Baconian laws are Jaws of MANSEL’S ARGUMENTS. 643 nature as itis. The author adds, as explanatory and synonym- ous statements, what seems to involve a new and distinct idea, namely, that the one rest on their own evidence, the other on the evidence of the facts concerned. To this we may reply that ‘thought as it ought to be’ is certainly not confined to Formal Reasoning. Wherever we think wrong, and have to be put right, we are in the domain of ‘thought as it ought to be.’ Lord Bacon’s inductive logic professed to substitute right thinking for wrong. We commit fallacies of Deduction and of Induction equally ; and if Logie does not put us right upon both, it must be for some other rea- son than the one now assigned. The addendum given, professedly to explain the above posi- tion, namely—that the Aristotelian laws are self-evident, and irreversible in thought, while the Baconian laws are inductions from facts and contingent or reversible—is merely a re-state- ment of the general thesis as between self-evident or necessary truth, and inductive or contingent truth. (3) The third position is that the Aristotelian Logic pro- ceeds from the law to the facts, constructing types or genera- lities, and rejecting what does not conform thereto; while in the Baconian Logic, the procedure is from the facis to the law, rejecting every law that does not account for the facts. This | is a direct opposition of Method. Now, we may readily grant this position. But what is its bearing on the question in dispute? The methodsare different, but both are methods of arriving at truth; both may be alike in want of precautions, and if so, both may, so far as appears, equally receive attention from the logician. (4) The fourth position is perhaps the most remarkable. It is this: Law, in the Aristotelian system, implies a conscious- ness of obligation; whereas, in the Baconian system, Law means only uniform sequence. Here is that confusion of thought, so well pointed out by John Austin, in connexion with the term ‘ Law,’ whereby there is introduced into the order of natural phenomena the notion of authority and obedience. Law, as regards the order of nature, whether in mind or matter, is purely figurative ; it is applicable merely as expressing wniformity of sequence; the Hthical and Political definition—a rule set by intelligent superiors to intelligent inferiors, accompanied by the infliction of pain on neglect—cannot be transferred to the sequences of nature, whether mental or material; the application to these contains only the single incident of law—uniformity. There 644 THE PROVINCE OF LOGIC. can be no moral right or wrong in Logic, except only in so far as we are all morally bound to seek the truth, an obligation extending equally to truth Deductive and to truth Inductive. | (5) A fifth position maintained by the author is, that, in the field of Thought, the cause is the conscious self; the effects, the thoughts produced by that self, through its own power, and under its own laws. To which we may reply, that both causes and effects are equally self, equally mental, but not thereby | ; radically contrasted, in manner of investigation, with external nature. Cause and effect in mind must be discovered induct- ively, if at all. Should the sequences be very prominent, little attention may suffice for their discovery; but that does not alter the method of proceeding. So much is Mr. Mansel carried away by the application of — the term Law, in its Ethical sense, to the process of thinking, that he censures Mr. Mill for applying ‘ physical causation ’ (meaning uniformity of sequence, ascertained by induction) to the moral and intellectual world; as if there ever was any other mode of discovering the facts and laws of mind than the same processes, observation, and generalization, that apply to the material world. In short, he brings us round by a series of verbal ambiguities to the question of Free-Will and Neces- sity, which becomes thus a principal turning-point of the controversy as to whether Logic should, or should not, be confined to Deduction. The combined force of these five positions does not appear to establish either of the two allegations, namely (1) that a criterion of material truth is not only impossible, but self- contradictory, or (2) that to enlarge the field of Logic, is to assign it no definite field. We shall not here attempt a direct reply to the first, inasmuch as the exact basis of inductive truth will be fully considered in another place. (Appenpix D.) The second allegation is a challenge to assign a definite boun- dary to Logic, while over-stepping the limits of the Formal Logic. ; Bhi Mr. Mansel puts so much more stress on the Theoretical than on the Practical side of Logic, that he would not be satis- fied with a reply based on the practical side. Let us enquire, — then, whether a Theoretical Logic, embracing Induction, could be laid out and so circumscribed as not to be confused with any other scientific department, such, for example, as Mathe- — matics, Physics, or Psychology. Pa In the InrropuctTioNn, we have indicated a field of Theoretical — Logic, according to the larger meaning of the Province; and SCOPE OF THEORETICAL LOGIC. 645 in Apppnpix A; we have given Mr, Spencer's survey of the field in the same larger meaning. In summary, we may repeat 9 topics. he Laws of ConsistEncy, or Equivalence of Propositions, —€ understood as the Laws of Thought. These give necessary (in the sense of analytic) inferences. They also give, in the view of Hamilton and Mansel, the basis of the Syllogism. _ IL The Laws of Depucrivz or Mediate Inference, as repre- sented by the Dictum de omni et nullo. This we hold to be more than mere Self-consistency, or Equivalence. It might be called Mediate Consistency, the consistency of a conclusion with two conjoint premises, as contrasted with the consistency of an equivalent transmutation of a single proposition. Mr. Mansel would hold that this consistency is necessitated and self-evident; and such an impression is not uncommon with thinkers generally. In opposition to that view, we have con- tended that nothing less than the induction of material in- stances would justify the conclusion. Ill. The Law of the Uniroxmity of Nature, which is the basis of all material truth, and of all induction; consequently the basis of the syllogistic axiom of mediate consistency. The consideration of this law may well precede the ordinary sciences, for itis an assumption running through themall. It may, there- fore, receive its first announcement in the science that deals with the criteria of all truth, namely, the separate science of Logic. It is followed out into a series of formule, known as the Inductive Canons, which, in their own sphere, may be com- pared with the syllogistic forms, in the Deductive sphere. Now, it seems to us, that a science may be constructed so as to include the Laws and Formule of Immediate Consistency, Mediate Consistency, and General Uniformity, without trans- gressing the sphere of any other science. It need not run into Mathematics, the kindred Formal Science; it need not trespass on the Physical Sciences, merely because it considers the pos- tulate necessary to them all, that is, Uniformity; it need not run into’ Psychology, although it derives from that science the _explanation of the ultimate nature of Knowledge, as Difference and Agreement. And there does notappear to be any other conterminous region. But we cannot concede to Mr. Mansel that Logic is essen- tially, or in the main, a theoretical science, and only incident- ally practical. We contend that the science would never have heen called into existence, but for its supposed practical utility. 646 THE PROVINCE OF LOGIC, Indeed, the same might be said of its splendid giant brother, — Mathematics. However agreeable and recreative to some ~— minds may be the contemplation of this great creation of ages, yet, but for the necessities and difficulties of measurement, it would never have been heard of. Mr. Mansel supposes a race of intelligent beings, subject to the same laws of thought as we are now, but incapable of transgressing these laws; and declares that in the presence of such a race, the Logie of the Formal Concept, Judgment, and Syllogism, would remain the same. Unfortunately even for the illustration, there is a fallacy of Relativity in the very statement of the case. Toa being that never committed an error, truth and error would be alike unmeaning; to appreciate the valid moods of the syllogism, as contrasted with the invalid, such a being would have first to be told of an erring race, capable of confounding the two. Only after Adam fell did he know good and evil; only by committing fallacies is any one competent to under- stand Logie. Postponing for a little the enquiry into the prictioal oi of the Inductive extensions of Logic, we shall advert more particularly to the distinction of Form and Matter, on which so much stress is laid in the present dispute. To some Formal Logicians the distinction does not appear in all respects satis- factory. Thus, Dr. Thomson (Outline of the Laws of Thought, § 15) remarks :—‘ The philosophic value of the terms matter and form is greatly reduced by the confusion which seems in- __ variably to follow their extensive use. Whilst one writer ex- plains form as ‘the mode of knowing’ an object, another puts _ it for ‘distinctive part,’ which has to do with the being or nature of the thing rather than with our knowledge of it 5 8 where it means ‘shape’ in one place, which is often a mere accident, in another it means ‘essence;’ so that it may be brought to stand for nearly opposite things. I will add, that — probably there is no idea which these terms represent that ue be conveniently expressed by others, less open to con- usion a Mr, De Morgan says :—‘ When it shall be clearly vedical ae out, by definite precept and sufficiently copious example, what the logicians really mean by the distinction of form and matter, _ I may be able to deal with the question more definitely than — I can do at this time.’ (Cambridge Transactions, vol. X. Part II. p. 8.) Again, ‘ The truth is, the mathematician as yeh is ' the only consistent handler +f the distinction, about © es 'FORM AND MATTER. 647 nevertheless, he thinks very little. The distinction of form and matter is more in the theory of the logician than in his practice; more in the practice of the mathematician than in his theory.’ (Syllabus, p. 48). Hamilton illustrates Formal Truth in Mathematics thus :— ‘To the notions of Space and Time, the existence or non- existence of matter is indifferent. If matter had no existence, nay, if space and time existed only in our minds, mathematics would be still true; but their truth would be of a purely formal or ideal character,—would furnish us with no know- ledge of objective realities.’ (Logic II, p. 66). But, in another place, he quotes, with approbation, from Esser, a passage to the effect that truth consists not in any absolute harmony of thought, but in the correspondence of our thoughts with their objects. ‘'Ihe distinction of formal and material truth is thus not only unsound in itself, but opposed to the notion of truth universally held, and embodied in all languages.’ (Logic L 106). And again (Reid’s works, p. 687), he remarks of Reid’s eriticism on the Predicables, that Reid, like our British philosophers in general, was unaware of the diiference between the Logical or Formal, and the Metaphysical or Real. The Predicables are forms or modes of predication, and not things predicated: in the language of the schools, second notions, not first.’ Let us adopt Mr. de Morgan’s suggestion, and refer to Mathematics for examples of Form, in the opposition to Matter. In so doing, however, we are merely taking up an old subject under anew name. In Mathematics, we have the most com- plete development of reasoning by Symbols, called also Abstract reasoning. ‘There will be other opportunities for examining the special processes of Mathematics (Loaic or tHe Sciences, Mathematics). For the present, let us note what bears upon the question before us. The abstractions of Mathematics, like all other abstractions, are embodied in concrete instances; the Form is always given in some kind of Matter. But the matter needed is so very spare and attenuated, that, by a stretch of language, we may say it is no matter at all. Yet, the circles of Enclid are circles of printer’s ink; they have colour and a definite size. If we compare them with the round shield of Achilles, or a gorgeous centre ornament in the roof of a palace, we may describe them as void of matter and substance ; but they have their own substance, nevertheless. The symbols of Arithmetic (still more, of Algebra) are material, although their peculiar shape has nothing representa- 648 THE PROVINCE OF LOGIC, tive in it. They are the signs of concrete facts—one, two, three—which are inconceivable by us, except in concrete instances. The simplest material will answer the purpose— _ bread crumbs, pebbles, mud specks; but we must have, in the mind, a series of discrete impressions, derived somehow or other ; even thoughts would do; but we find it easier to work upon things of sense. Without some concrete basis, we cannot possess in thought any number whatever. This is merely to repeat the received nominalistic view of Abstract Ideas. There is, however, an important step that can be made in Mathematical Reasonings, whereby we can altogether leave out — of sight the concrete things (which is to refrain from realizing the very meanings of the numbers that we are handling). We — can devise rules of operating upon the symbols, which, when ~ duly constructed and checked by the proper precautions, will — give us the same results as actual experiments upon the con- crete numbers. Having constructed our decimal notation, we can base upon it a multiplication table, containing equiva- lent formations of numbers; and by mere force of memory, recalling these symbolical equivalents, we can perform opera- tions of multiplying, without thinking of the concrete numbers at all. In getting out the product of 94 by 116, we can leave the world of numbered realities out of view for the time: com- ing back to it only when the product has to be practically turned to use. . Now, by this dwelling among symbols, and rules and signs of operation, we are as far away from Matter, or things in the © concrete, as we can possibly be. If anything represents pure — Form, the multiplication table does. The higher operations of _ Algebra keep us for longer periods withdrawn from concrete reality ; but the principleis the same. Thesymbolical creations are more numerous, the rules of operation more complicated, the operations themselves more protracted; yet there is no- thing new in the principle of working. . hpet The question then arises, Do these rules of operation upon — symbols bear out the pretensions of Formal Logic, as to the — self-evident, necessary, and non-material character of Formal Thinking? Are all such rules, in their origin, completely withdrawn from the tests of concrete experience, as they are in the working? The full answer to this question is the theory | of Deductive Reasoning in general, and of Mathematical Rea- soning in particular. It is enough here to make two observa- tions. First. If it be true, as the a posteriori thinkers maintain, that the final axioms of all Mathematics,—on which repose th FORMAL RULES OF OPERATION. 649 rules for Arithmetical sums, for Algebraic equations, and for Geometrical demonstrations,—are inductions from experience, then these various rules of operation have, after all, a purely material source, and are not evolved by the mind in abstract or formal thinking. . But secondly. It is notorious and undeniable, that the rules of operation, before they are trusted to, are tried and checked by the results. A great many of them are so paradoxical, so unpromising, and even repugnant, to the ordinary mind, that they are admitted only because of their being instrumental in bringing out true results (as proved by reference to the matter). Who would put faith in such a rule as ‘ minus mul- tiplied by minus gives plus,’ unless fully assured by concrete trials that it leads to correct conclusions? The impossible quantities of common Algebra, the infinitesimals of the higher Calculus, have been a perpetual stumbling-block, as regards their Form ; their sole justification is the test of actual facts. Seeing how many ingenious tricks can be played upon us _by formulas and formalities, the most unexceptionable in their appearance, there probably is not a single rule in the whole compass of Mathematics that any reflecting person would trust to merely as a ‘ Law of Thought,’ without an appeal to the matter by actual trials. The reason why we are so confident in these rules, is that their verification is so easy, and has been so complete. But in the absence of verification, we should be very chary indeed in admitting such rules as the multiplica- tion and division of fractions, vulgar and decimal, the extrac- tion of the cube root, and the like. We have often been deceived by more plausible formalities than these ; dolus latet im generalibus, is true of all alleged ‘ Laws of Thought.’ The same remark as to the necessity of inductive verifica- tion applies to Logical Forms. Not one of the valid moods would be received by mankind upon formal evidence alone. The dictum seems very evident, the nota note even more evi- dent; but the nota note conducts us most plausibly to false conclusions, until by examination of the actual cases we have laboriously fenced it with circumlocutions and qualifications. _ When we examine carefully the various processes in Logic, we find them to be material to the very core. Take Conversion. How do we know that, if No Xis Y, No Yis X? By exam- ining cases in detail, and finding the equivalence to be true. Obvious as the inference seems on the mere formal ground, we do not content ourselves with the formal aspect. If we did, we should be as likely to say, All X is Y gives All Y is X; we 650 THE PROVINCE OF LOGIC. are prevented from this leap merely by the examination of cases. itm N07 Again, the laws of Hypothetical Equivalence are dependent on our knowledge of the material circumstance called Plurality of Causes, but for which the formal directions as to Hypor thetical Inference would be quite different. oa Mr. Mansel complains that the rules of Definition commonly. given in logical treatises are extra-logical; that is, they step __ out of Form into Matter. The charge is well founded; the _ writers obviously felt that Definition, confined within the — narrow limits of the Formal, would be a very meagre affair. What would be logical defining in strict form? Why, this. A Formal Definition consists in giving, as the marks of — the thing defined, the marks of some higher Genus, together with the Diffinendei We have, then, these forms:—The Genus together with the Difference (in Connotation) is the Species; the Species minus the Difference is the Genus; the Species minus the Genus is the Difference. Thisis the whole | theory of Defining, according to Formal Logic; and it is worth | nothing. me Still more would a logic of Classification, to be of any value, a trench upon material considerations. Logical Division is another name for classification. The rules of Logical Division — are Formal, but they have to be held in check by the — otherwise they may lead us astray. > It may be maintained that Deduction and Tndtiebteh are — properly continuous operations; they are the parts of one ~ whole. Within certain small limits, Deductive processes are possible, upon rules of symbolical operation solely, these having — been well fenced by a study of the matter ; but real deduction, % the extension of a principle to new cases, supposes an exami- nation of the cases in their concreteness or actuality, exactly — as in the inductive generalization of the rule. The judge who — applies the law must look to the matter; he must not commit — paralogisms of form; but he cannot stop short at mere formal A correctness. sdf Within the Inductive sphere, we might construct rales of Formal operation, such as ought to commend themselves to ¢ rigid formalist. Thus, A, B, and C, being joint causes of an- effect X; if A be foducadl: in sittin ts B or C must be corre pondingly raised to keep up the effect; if A be increased; 4 others are so far dispensed with, and so on. These are e: mathematical considerations, which: wa':kniows to. be corr = 10 | 4 VALUE OF A LOGIC OF INDUCTION. 651 generally, and can therefore use formally without regard to the matter. But the question at issue cannot be adequately stated, unless we view Logic as a Practical Science. If its practical character is conceded, the propriety of extending the Province rests upon the utility of rules for Induction. The presumptions in favour of such rules are these :— First. It is admitted that Aristotle included in his scheme both Deduction aud Induction, however imperfect may have been his view of their respective spheres, and however inade- quate may have been his handling of Induction. Thus, the testimony of the Founder of Deductive Logic is opposed to its exclusive pretensions. | Secondly. In the table of Fallacies, sketched by Aristotle, and retained by the scholastic logicians, with slight modifica- tions, there are comprised Fallacies of the Matter, and of these some are fallacies of Induction (non causa pro causa, S§c.). From this we may infer, that, in the opinion of logicians generally, people are liable to commit mistakes in regard to matter, no less than in regard to fourm. We may infer farther, that it is not useless to give a reminder of these material and inductive mistakes, which is, in fact, a Logic of Induction. Thirdly. The scholastic period was marked by an almost exclusive attention to the formal or Syllogistic part of Logic. At the revival of letters and philosophy in the 15th and 16th centuries, public opinion revolted against the narrowness of the conception, and found a spokesman in Bacon, who inaugu- rated, amid very general applause, a Logic of Induction. For the last two centuries and a half it has been the pride of both physical and metaphysical philosophers to call themselves his disciples as regards the methods of pursuing science and philosophy. Fourthly. The renovated Physics, or Natural Philosophy, of Galileo and Newton was accompanied with a professed Logic of Induction—the famous Regule Philosophandi prefixed to the Third Book of the Principia. These rules, meagre as they are, were a guiding star in physical research to the enquiries of the 18th century. Fifthly. In the present day, when physical science has been s0 far advanced as to exemplify sound methods of procedure, the most distinguished physical philosophers still feel and ac- knowledge the need of a systematic guide to research, for the more abstruse and subtle departments. The Introduction to 652 THE PROVINCE OF LOGIC . Natural Philosophy, by, Sir John Herschel, and the ssdoagil « and Logic of the Inductive Sciences, by the late Dr, Whew ell are testimonies to this want. Sixthly. Since the publication of the work of Mr. Jahn. 4 Stuart Mill, in which the Inductive Logic is methodized with — a completeness previously unknown, applications have been — extensively made of the Inductive canons to the Experimental — Sciences. The investigations of Medical science have especi- — ally profited by Mr. Mill’s teaching; a higher and surer stan- dard of evidence has taken the place of the loose eeaitiads 08 reasoning formerly prevalent. ui Seventhly. The Science of Politics is an equally atribiniist > ample. The valuable work of Sir George Cornwall Lewis on — the ‘ Methods of Observation and Reasoning in Politics,’ makes _ perpetual reference to the Inductive Logic of Bacon, Her- schel, Whewell, and Mill, and only once or twice alludes to © Formal Logic, although the author’s education was such as to incline him to view that department with the utmost possible — favour. He complains strongly of the wide-spread abuse. of the Method of Agreement (the enwmeratio simplew of Bacon) in Politics, as mm other subjects; and endeavours by Per and by example, to counterwork the vicious tendency. ; Kighthly. Sir William Hamilton occupies a considetablal j portion of his Course on Logic (nine Lectures out of Thirty- six), with Modified Logic, in which he considers Truth and — Error, on the material side; Observation; Induction; the — Credibility of Testimony ; and various other points related to, the acquisition and communication of knowledge. The plan — of his course would have allowed him, without contradicting his views of the Province of Logic, to have gone as minutely — as Mr. Mill does, into Induction, and the operations a to Induction, such as Classification and Naming. ify heh Dr. Thomson, in his Laws of Thought, follows the example of Hamilton, in ‘the enlargement of the Province. In Part IV., entitled ‘ Applied Logic,’ he considers (shortly) the Search for — Causes, the Inductive Methods, Definition, Analogy, Chance, — Classification, Fallacies generally, and the Division ofr the Sciences. | Alt C.—ENUMERATION OF THINGS. ¢ S As The Classification of Names (p. 61) leads.by a ‘paiell al transition to the Classification of Things. Moreover, in order i to establish the most generalized propositions, we must nee 288 correspondingly generalized Notions, tae _ BASIS OF RELATIVITY. 653 _ The totality of Existing Things may be divided in various ways, under different principles of classification and division. We may partition the whole universe into Celestial Bodies and Terrestrial Bodies; into Minerals, Plants, Animals ; into Solid, Liquid, Gas; into Ponderable and Imponderable ; into the Four Hlements of the ancients, which division crudely gives the three states of matter, and the imponderables—Heat, Light, &c. Lastly, we may make a division into Matter and Mind. These various modes of sub-dividing the totality of things are useful for their special purposes. The purpose of the Logician is to arrive at a division that will correspond to the distinct methods of enquiry, so as to partition the field of knowledge according to the best division of intellectual labour. We begin by re-stating, as an essential preliminary, the principle of Universal Relativity, by which all objects of know- ledge are two-sided, or go in couples. This statement is necessary to obviate the error, committed by Aristotle and others, of placing ‘ Relation’ in an inferior or subordinate place in the classification. If Relation is recognized at all, it is fundamental and independent; everything comes under it, it comes under nothing. The supreme position given by Logicians to the ‘ Law of Contradiction’ is a mode of admit- ting this primary fact. I. The deepest of all Relations is Opsecr and Sussect, com- monly called Mind and Matter, the External World and the Internal World. When we pass from being engrossed itl pleasure or pain to the consciousness of some extended thing, as a tree, we are affected with a marked shock of difference; we have made a transition the broadest and deepest that the mind can ever pass through. These typify the two ultimate or final modes of the human consciousness ; they mutually constitute each other, on the principle of Difference or Relativity; they cannot, therefore, be resolved one into the other, or into any more fundamental experience. The contrast must be accepted as the chief division of all things, on the principle of dividing upon the maximum of difference. One portion of knowledge we term the Object world, the Extended World, and, less correctly, Matter, and the External World. The other portion we call the Subject world, the Unextended Mind, and, less properly, the Internal World. Indeed, when we talk of these two departments as dividing between them the universe of existence, we are using fictitious and unmeaning language; the ultimate universe, according to the law of Relativity, is a 654 ENUMERATION OF THINGS. couple; the highest real grouping of things is this ‘lag: grouping, called Object and Subject, &e. These are “the proper swmma genera. Hxistence is a mere name. . If. Ossucr has been variously represented and aisle Some have contended that it is an ultimate fact, given in our earliest consciousness. Others have resolved it into simpler — states of the mind. ‘The different views on this subject be- 3 long to the Metaphysical and Psychological question called | the ‘Theory of External Perception.’ We here assume that the 4 = notions expressed by ‘ Object’ and ‘ Subject,’ can be analyzed, a and we give one mode of the analysis. Object means (ia what calls our muscular and bodily energies into play, as Stipe | i to passive feclings; (2) the uniform connexion of definite feel- 7 ings with defimte enerytes, as opposed to feelings unconnected with energies; and (3) what affects all minds alike, as opposed to what varies in different minds. wae (1) The greatest antithesis existing among the phenomen a of our mental constitution is the antithesis between the Active — and the Passive ; the muscles (with the out-carrying nerves) — being the bodily instrument for the one, the senses (with the — in-bringing nerves) being the bodily instrument for the other. To this fundamental antithesis we are able to link the opposi-— tion of Object and Subject. Although developed by other circumstances, the contrast appears to be rooted in our Grotaat t Psychological contrast. ns (2) The circumstance of our feelings being definitely cherie with definite active exertions on our part is a most notable ac- companiment of our objectivity. When we move across @ room, and feel our optical prospect definitely ante passions and emotions. (3) It is a characteristic of the Object world, that differ persons are affected in the same way. Those definite ae sense, accompanying definite movements, as in walking a street, or in entering a room, arise in each person alike other class of feelings—hunger, fatigue, fear—run a ditt course in different persons. rs These are probably the main features of the fandaindhel trast of Subject and Object; other subsidary cinched been pointed out, but their discussion is not suitable to this 5 ATTRIBUTES OF BOTH OBJECT AND SUBJECT. 655 _ IIL. The Supsecr is explained by what has been said of the Object ; it concerns our passive states; our feelings not de- finitely changed with definite energies ; and the states wherein different persons vary in the same circumstances. IV. There are attributes common to Object and to Subject, and attributes special to each. Notwithstanding the fundamental contrast of these two ex- periences, we can affirm some attributes of both. Thus, within the sphere of each, we are variously affected; we recognize object distinctions and subject distinctions. So we identify and compare object facts with one another, and subject facts with one another. From the very nature of human know- ledge, these possibilities of discerning agreement and difference must hold in both departments. Hence :— First. The contrasting attributes of Lixennss and UNLIkz- ness belong equally to Object states and to Subject states. We identify and discriminate magnitudes, forms, colours, &., which are object facts; we identify and discriminate pleasures, pains, volitions, ideas, which are subject facts. Hence, affir- mations of likeness or of unlikeness may apply to every kind of knowledge whatsoever. Being in fact the fundamental cir- eumstances that define and constitute knowledge, such aflfirma- tions are analytical propositions. Secondly. Quantity or Degree belongs to both states. This is Agreement and Difference in one important fact or feature, called more and less; the states of the subject mind are all of varying amount or intensity, as well as the states of the object consciousness, which we call object properties—size, weight, hardness, &c. We may and do predicate quantity, therefore, of everything knowable. The laws of Quantity, of which Mathematics is the complete developement, pervade all modes of existence. It is true that numerical calculations are mostly confined to object properties—as space, dimensions, weight, and so on; we have no numerical ratios in pleasures and pains. This circumstance, however, which is a great drawback to the science of mind, is not due to the absence of — degree from mental phenomena, but springs from our inability to set up an exact common standard of degree in the states of the mind, and to take precise measures according to that stan- dard. We are conscious of inequalities in our pleasures, emotions, and desires, but we have a difficulty in fixing the degrees in an understood expression, such as may be communi- cated to others, and permanently recorded. It is usual to specify the leading modes of Quantity under 656 ENUMERATION OF THINGS. Intensity, Duration, and Extension: the last being a uaa special to the object. Intensity and Duration apply in’ both | regions of phenomena. Intensity is usually marked with Te- gard to each special property—intensity in colour, heat, pres sure, &c. Duration, which is a degree of continuance, is more commonly abstracted from things, and enters into that great — and all-comprehending generality, called Time, to be noticed z more fully under next head. ninety Thirdly. The great and important contrast named Co-existe ENCE and Succession is found in both departments of pheno- — : mena. Oy PRs Co-existence is not an ultimate experience of the mind. | We begin with modes of Succession, which are developed into | Co-existences. vi To the mind, which, with very slight qualification, can — attend to but one thing at a time, all distinctive states of con- sciousness are successive. Succession is the law of our mental being. The succession may be rapid or slow, which accep gi the estimate of duration above noticed. In succession — grounded the important fact called Number or Discrete aca tity, as opposed to the measure of continuance, or Continuous” Quantity. We identify groups of successions as twos, 0 threes, fours, and so on. Thus the forms and modes of Quan- — tity are involved in the modes of succession of our sensations, feelings, and thoughts. to TS ae 7 Duration and Succession (with Number) thus belong alike to states of the Object and states of the Subject. The eleme nb of Time, which is duration and succession generalized to the utmost, ‘and reduced to a common measure, 1s @ propel if both worlds ; ; a circumstance that has been noticed Pon the very beginning of philosophy. “aE The predicate of Succession also involves order of ped rity, which can apply to object and to subject states equally, Co-existence is an artificial product, a peculiar mode of suc es cession, which in its highest form is Simultaneity in Speen r Extension, a property of the Object sphere exclusively. There attaches to Mind an inferior mode of Co-existence, the 20+ existence of two or more awakened sensibilities at one momen of time. bsanids : oe Of Attributes common to both spheres, we naval thus - uike Unlike, Quantity, Succession, Co-existence ; but as the predi cation of Like-Unlike in the widest sense is, from the nature of knowledge, a purely identical proposition, we need stat only Quantity, Succession, and Co-existence. These ar ATTRIBUTES SPECIAL TO THE OBJECT. 657 three attributes assumed as distributing knowledge into differ. ent heads of Logical Method. _V..The attributes special to the Ossxcr, are as follows :— (1) Hatension—This property is the fundamental circum- stance of the object world, the one fact common to whatever is not mind, or not subject. When we are in a purely subject state, as a pleasure or a pain, we have no consciousness of ex- tension or space. The distinction between extended matter and the unextended mind, explicitly made in the 5th century, A.D., was the commencement of correct views of mind and matter. Psychologically considered, Hxtension is a mode of our active or moving energies, assisted by our senses. Motion is essen- tial to the consciousness of things as extended. Extension is a real property whether with or without matter; as scope for motion, evenempty space is an actuality. The total of the Hxtended World is sub-divided imto Extended Matter and Extended Space without matter. (2) Resistance, Inertia, Momentum, or Force.—This is the characteristic property of Extended Matter, in its opposition to an Extended void. The putting forth of our energies in the peculiar mode called Resistance is perhaps the simplest situation that we can be in, as regards the active side of our being ; hence, resistance may be considered our fundamental consciousness of the object world. Resistance is Matter; the giving way of resistance, followed by movement, is Space. In no subject state have we the peculiar sensibility called force, energy, or resistance; where that feeling is present, we apply the name matter. fixtension and Inertia are the two generic facts entering into the long known group of attributes called the primary qualities of matter; the radical and identifying peculiarities of the so-called external and material world. Still, these are in close association with other properties, based on passive sensibility, or sense proper, as colour, tactile feeling, &c. (secondary qualities) ; which properties, of themselves, would not be object properties, but become so by their dependence upon the object class. (3) Colour.—The pure and proper sensibility of the eye, the susceptibility to mere light, is not properly an object fact. The conjunction of the feeling with visual extension (the mus- cular sensibility of the eye), and with locomotion, is necessary to give objectivity to light and colour, Our notion ot the extended or simultaneous in space is based on movements, but 658 ENUMERATION OF THINGS. © filled up and defined by our optical sensibility to (eden i. light. Our feelings of illumination are definitely connected — with definite movements and in that way comply with one ¢ of ; the grand conditions of objectivity. a (4) Touch.—The commonly recognized sense of Touch is a compound of muscular energy with pure skin sensibility. — This last, or touch proper, is scarcely ever separated from th 2 fundamental experience of Force or Resistance (we may make — the separation by supporting the outstretched arm or leg). Hence, touch is adopted and embodied among object properties. — The tactile effects, called hard, soft, rough, smooth, are ‘eali= 2 ties of Matter. Sight and Touch are the senses most completely i incorpora ed with our activity, or with our object experience. The remain- ing senses have a looser connexion with our energies, but, so far as connected, we rank their indications among object, qualities. i (5) Sound.—Mere noise might be a form of simple subjec- tivity. When related to movements, as when steadily increasing or diminishing with our locomotion, it falls into a connexion” with objectivity. So regularly is this connexion observed, th a the fact is enrolled among properties of matter. zs (6) Odour.— An exact parallel to Sound. The objectivity of odour is established by its definite changes under ges is movements on our part. m (7) Taste.—There is here a compound ofa peculiar sensibili iy —the proper gustatory feeling—with touch proper ; whence Me comes readily into the object sphere. (8) Heat and Cold.—This property needs no other comme ot than the foregoing remarks on Sound and on Odour. The various organic sensibilities of our body—Diges Respiration, &c.—have a strongly subject character; yet, contract object relationships whenever they are defin changed with definite movements, as when we connect re tion with taking food, or suffocation with impeded breathing. But, in so far as they suggest no activities, or attitude energy, they are pure subject states, modes of self-conscions! These are the various sensible properties of the sp ‘matter’ in the genus ‘extended ;’ they are the mode primitive sensibility that we call material. There are o properties of a more subtle and abstruse kind, arrived the help of our intellectual processes—such as we call A tions, Repulsions, Molecular structure and arrangements- which are necessary to completeness in the enumeration. — Bi os. = seme p = ATTRIBUTES SPECIAL TO THE SUBJECT. 659 The Sciences of the so-called External world are occupied with the various attributes now described. One portion of Mathematics is occupied with quantity in Extension; Mechanics embraces the essential fact of Matter, together with its other incidents; Physics and Chemistry include Light, Sound, Odour, Heat, &e. VI. The attributes special to the Sunszcr are the defining marks or essential attributes of Mind—Feeling, Will, and Thought. All these are in full antithesis to the great object facts, as above detailed. Of Feelings, the greater part are pleasures and pains, which are our most unequivocal types of subjectivity. We never confound two such things as comfortable warmth, and lifting a chair; the heterogeneous is at its utmost stretch in such a contrast as this. - Our states of Will, or Volitions, have a purely subject origin, namely, our feelings, with outcomings in the object sphere. The two departments are here, as often happens, in close proximity, but are not therefore confused. Voluntary action is always reckoned a special characteristic of mind. For, although it is activity, directed often upon material things, yet its origin in the pleasurable and painful modes of sensi- bility gives it an indelible stamp of the subject. Our Thoughts, Ideas, or Intellectual states, have in them a considerable amount of object reference; still there is a broad distinction between Sensations and Ideas, in the circumstance that the one class is, and the other is not, connected with de- finite bodily movements. The succession of our sensations is in uniform accordance with our locomotive and other move- ments; the succession of our thoughts is totally different. Hence, although our ideas are the reflexion or repetition of our sensations, yet their manner of occurrence assimilates them with subject states. In the complex fact called Sensation, we have incessant _ shiftings of the scene, from the object to the subject. A sen- sation, as cognisant of extension, resistance, colour, &c., is an object fact; as a pleasure or a pain, it is subject. Now, un- mistakeable as the contrast is, wide as is the chasm, we may leap it a great many times in a minute; we flutter to and fro, between the pleasurable consciousness of a sensation, and the intellectual measure of it as a thing of size, form, or colour. The sciences of the Subject World have thus to deal with our Feelings, Volitions, and Thoughts. They have, moreover, 660 ENUMERATION OF THINGS. to draw the delicate boundary line between the two worl ds, | to divide the spheres, where they become entangled. _ ie a Sigs ada If it were now asked what, in the final analpeuy is the : nature of predication, we are able to affirm—Attributes of the Object, and Attributes of the Subject, declared as related in Quantity, as Co-ewisting or as Successive. a VII. Sussrance is not the antithesis of all Atghiba tase ba 5 the antithesis between the fundamental, essential, or defining ~ attributes, and such as are variable or inconstant He wal} Bs From the relative character of the word Attribute, the fancy grew up that there must be a substratum, or something dif. ferent from attributes, for all attributes to inhere in. Now anything that can impress the human mind — Extensi Resistance, &c., may be, and is, termed an attribute, we seem driven entirely out of reality, if we would find a something that. could not be called an attribute, and might stand as a sub- e stance, +e But ‘substance’ cannot be rendered by non-entity. T antithesis that we are in search of is made up without violent a supposition. Substance is not the absence of ¢ attributes, but the most fundamental, persisting, inerasible, or essential attribute or attributes in each case. ‘The substance of gold is its high density, colour, lustre, &c.—everything that we consider necessary toits being gold. Withdraw these, a gold itself would no longer exist: substance and oxpry ti ng else would disappear. ive ee The substance of Body or Matter, is the permanent, o essential fact of Matter—Inertia or Resistance. This is feature common to everything we call Body—whether § Liquid, or Gas; the most generalized, and therefore the ing property of Matter. The remaining attributes of m vary in each separate kind; they make the kinds or spi varieties—air, water, rock, iron &e. The real distinction thus between the Essence and the Concomitants, the Invaria and the Variable, the Genus and the Species. | The substance of Mind is no other than the esrogate three constituent powers— Feeling, Will, Thought. — present, mind is present; these removed, mind is gone. — three facts named do oe exhaust shi mind, there mu some fourth fact; which should be produced and established a distinct mode of our subjectivity. The substance would be four-fold. But the supposition of an ‘ego’ or ‘self, powers to inhere in, is a pure fiction, coined from non-¢ - MILL’S CLASSIFICATION, 661 by the illusion of supposing that because attribute applies to something, there must be something that cannot be described Mr. Mill, as the result of his analysis, gives the following as an enumeration and classification of all Nameable Things :— ‘1st. Feelings, or States of Consciousness, ‘2nd. The Minds which experience those feelings. ‘3rd. The Bodies, or external objects, which excite certain of those feelings, together with the powers or properties whereby they excite them; these last being included rather in compliance with common opinion, and because their existence is taken for granted in the common language from which I cannot prudently deviate, than because the recognition of such powers or properties as real existences appears to be warranted by a sound philosophy. — ‘4th; and last. The Successions and Co-existences, the Likenesses and Unlikenesses, between feelings or states of consciousness. Those relations, when considered as sub- sisting between other things, exist in reality only between the states of consciousness which those things, if bodies, excite, if minds, either excite or experience. ‘This, until a better can be suggested, may serve as a sub- stitute for tne abortive Classification of Hxistences, termed the Categories of Aristotle. The practical application of it will appear when we commence the inquiry into the Import of Propositions ; in other words, when we inquire what it is which the mind actually believes, when it gives what is called its assent to a proposition. ‘These four classes comprising, if the classification be cor- rect, all Nameable Things, these or some of them must of course compose the signification of all names; and of these, or some of them, is made up whatever we call a fact.’ (Logic Book I., Chap. III). The Categories of Aristotle. We owe the Categories to the opposition made by Aristotle to Plato’s Realism of Universals. Plato viewed Hns or Real Being as belonging only to Universals separated from their particulars; they only being permanent as contrasted with the Generated and Perishable. Aristotle held, on the contrary, that Real Being attached only to the Particulars ; that certain varieties of Being might be predicated of an individual—Hoe aliquid, That man, This horse, &c.—but that no Being had 662 ENUMERATION OF THINGS. any reality apart from the individual. The varieties of E that might thus be predicated of a particular individual, enumerated in a schome known 48/the Categories («aty yop Predicamenta). They are as follows :-— 1. Oveta—Substantia—Substance. 2. Tooov—Quantum— Quantity. 3. Tovev—Quale— Quality. 4. Tpos 1—Ad aliquid—Relation. 5. lod—Ubi—Location. 6. Tlore—Quando—Period of Time. 7. KetoOac—Jacere—Attitude, Posture. aga 8. "Exew—Habere—Hquipment, Appurtenance, Property. i 9. Tlovetv—F'acere—Active Occupation. tikes 10. [1doxew—Pati— Passive Occupation. Mr. Mill points out the more obvious defects of the. Cat gories considered as an enumeration of Things. aOR ‘The imperfections of this classification are too obvious t require, and its merits are not sufficient to reward a minu ie ne examination. It is a mere catalogue of the distintic rudely marked out by the language of familiar life, w ao little or no attempt to penetrate, by philosophical analgeie O- the rationale even of those common distinctions. Such an analysis, however superficially conducted, would have shown the enumeration to be both redundant aad defective. ‘Som eo. objects are omitted, and others repeated several times under different heads. It is like a division of animals into men, quadrupeds, horses, asses, and ponies.’ a Hamilton endeavours to obviate this last obioonte by c ing it into a scheme of successive grades of subordination. .- elucidation is as follows :—‘ Being (70 ov, ens) is primal divided into Being by itself, (ens per se), and Being by accid (ens per accidens). Being by itself corresponds to the - Category of Aristotle, equivalent to Substance: Being accident comprehends the other nine, but is, I think, m properly divided in the following manner :—Being by accid is viewed either as absolute or as relative. As absolut flows either from the matter, or from the form of tinge | from the matter,—it is Quantity, Aristotle’s second category If from the form, it is Quality, Aristotle’s third a relative, it corresponds to Aristotle’s fourth category it and to Relation all the other six may be reduced. The arrangement would stand thus :— — “an . 4 ai erry cn HAMILTON ON THE CATEGORIES, 663 L Substance (1) . Quantity (2) Il. Attribute <~ Quality (3) Relation (4) /Place (5) Time (6) Posture (7) Appurtenance (8) Activity (9) Passivity (10) There is no evidence that Aristotle saw the division in this light; if he had done so, he might have adverted to the mis- placement of ‘ Relation,’ which, if it includes any of the others, equally includes them all; Substance and Attribute, Quan- tity, Quality—are all relationships. Still, the arrangement is useful as showing how some of the worst defects may be remedied, and as an aid to remembering the list. The four first are easily remembered; the remaining six (under Relation) may be cast into three couples—Place and Time, Activity and -Passivity, Posture and Possession or Appurtenance. The Categories do not seem to have been intended as a classification of nameable things, in the sense of ‘‘ an enumera- tion of all kinds of Things which are capable of being made predicates, or of having anything predicated of them.” They seem to have been rather intended as a generalization of pre- dicates, an analysis of the final import of predication, including Verbal as well as Real predication. Viewed in this light, they are not open to the objections offered by Mr. Mill. The pro- per question to ask is not—In what Category are we to place sensations, or any other feelings or states of mind, but—Under what categories can we predicate regarding states of mind P Take, for example, Hope. When we say that it is a state of mind, we predicate ‘substance :’ we may also describe how great it is (‘ Quantity’), what is the quality of it, pleasurable or painful (‘ Quality’), what it has reference to (‘ Relation’). Aristotle seems to have framed the Categories on the plan— Here is an individual: what is the final analysis of all that we can predicate about him P The proper comparison of the Categories is to the Predi- cables, and to the Import of Propositions, or the Universal Predicates. Comparing the Categories with the Predicables, we see that through both runs the distinction between Funda- mental and Concomitant, Essential and Accidental. The four _ predicables, genus, species, differentia, proprium, are predications of ‘substance :’ accidens,—concomilance (vp BeByxos) embraces 29 664 THE UNIVERSAL POSTULATE, all the categories except substance. Other categories than "9 substance might be propria, or predications deduced from #l 10 % ussence of the subject; but it is probable that Aristotle, in speaking of ‘fundamental’ and ‘concomitant’ in connectialill . with the categories, meant to include propria in the category — of substance. Probably Aristotle’s list of propria had been — smaller than the list that could be made out now. Secondly, — if we compare the Categories with the Universal Predicates — (Co-existence, Succession, Quantity), we see that the Categories are more superficial and less ultimate than the later analysis. — The category of ‘substance’ (if we do not include propria) — belongs to the department of Verbal predication: the remain- ing Categories are Real predicates, corresponding to the final — analysis ‘of propositions. As such an analysis, they are open to the objection of not being ultimate ; for example, the Pee cations concerning ‘space’ and ‘ time’ may regard ‘co-exist- — ence’ or they may regard ‘succession.’ More than this, they are not adapted to any logical purpose; they cannot be gar) a the basis of logical departments. While these comparisons show the bearings of the, dates’ = gories as regards Logic, it should be kept in mind that their original purpose was simply to exhaust the possible predicates — regarding an individual, and not either to exhibit a classification — of nameable things, or to analyze the import of proponieeaay with a view to the arrangement of logical Se ys D.—THE UNIVERSAL POSTULATE. ag The theory of Demonstration supposes that we come at as ; to something that cannot be demonstrated. Dermonsttyeaeaa the referring of a fact to a higher generality, already es blished ; to demonstrate such higher generality would ‘be + jo find some principle still more general; a few steps must lea us to something that is absolutely final, something whose e i- dence is not demonstrative, something believed in withou ot extraneous support. i ee The edifice of demonstration is not complete until we clea re out these ultimate foundations, and state distinctly the natur of the certainty attaching to them. Let us then ask what a the facts to be received without proof, as underivable, unde ducible, undemonstrable P ioe In probing to the deepest foundations of id wld ae certainty, there has often been a confusion of two classe primary facts—the Logical and the Psychological. — oa Logical primordia are meant the indemonstrable assumptions TESTIMONY OF CONSCIOUSNESS, 665 at the foundation of all demonstrable truth; by the Psycho- logical, are meant the elementary sensibilities of the mind, whence our complex intellectual products are evolved by growth, ag_ regation, or association. What the logical founda- tions are, will be stated fully in this note; the Psychological foundations are the primary sensibilities arrived at in an ultimate analysis of the mind—such as Resistance, Motion, Colour, Sound, &c. There may be a partial coincidence of the two classes of ultimate data; but the coincidence is not neces- sarily total; and each must stand on its own grounds, The _ propriety of an Analysis of the mind needs to be established by evidence; hence it must appeal to some first principles different from itself; so that the priority belongs to the Logical foundations of our knowledge. ‘The phrase ‘ Universal Postulate,’ proposed by Mr. Herbert Spencer, to express the ultimate foundations of certainty, is adopted from Huclid. While the subject-matter is quite differ- ent in the two applications, there is this common feature, that in both something has to be begged on one side and granted on the other; one person cannot force another person into the admission. The basis of all reasoning is something mutually conceded between the different reasoners, When an opponent accepts a certain first principle, and declares that he will abide by all its consequences, we may compel him to accept whatever we can show to be a consequence; but we have not the same fulcrum with the first principle itself In reviewing the modes of stating the primary assumptions, we may commence with the so-called Laws of Thought— Identity, Contradiction, and Excluded Middle. These, how- ever, are too limited for our purpose. As explained in this work, they are laws of Consistency and Equivalence ; the Formal Logicians suppose them to include also Syllogism, or Mediate Consistency ; by no one are they held as furnishing a criterion of material truth. Hamilton has put forward ‘the testimony of Consciousness ’ as the ultimate and infallible criterion of certainty. He ex- presses the reference to consciousness in these three maxims or precautions :— . *(1) That we admit nothing, not either an original datum of consciousness, or the legitimate consequence of such a datum. * (2) That we embrace all the original data of consciousness, and all their legitimate consequences ; and— 666 THE UNIVERSAL POSTULATE. ‘(3) That we exhibit each of these in its individual agen / neither distorted nor mutilated, and in its relative er ‘a whether of pre-eminence or subordination.’ eae Works, eo 747 Res in general terms, this criterion seems cnimpoachable, But when we come to specific enquiries, we are aware of its vagueness and uncertainty. Our present consciousness must — be admitted to be our present consciousness; when we feel — hungry, we have the fullest certainty that we are hungry. The question, however, arises—what does consciousness say to facts in the past, and to facts in the future. And strange as the thing may appear, people may differ as to what things we are actually conscious of, as will be seen presently. 4 Mr. Spencer expresses the Universal Postulate under ‘the — form of the Inconceivability of the Opposite. The only reason — assignable, he says, for our primary beliefs, is the fact of ‘ in- variable existence tested by an abortive effort to cause non- existence.’ When the opposite of an assertion is utterly 4 unthinkable by us, we can do nothing but receive that assertion | as true. a The difficulties attending the employment of this test are a these : First. The examples that are most in its favour are cases” ; where the opposite is a self-contradiction. I cannot think that I do not at present exist, because the two suppositions are in- compatible ; the attempt is a violation of the law of consistency. — So,—‘ Motion cannot be thought of without an object that moves being at the same time thought of’ is an instance where the two statements give the very same fact; ‘motion’ oN ‘a thing moving,’ are two slightly different " phrases for an- identical conception. The opposite is pure self contradiction a Now, for all such instances, a postulate of self-consistency would answer the same end as a postulate of unthinkableness of the negation. Eg Secondly. In assertions where there is not mutual i implica- tion but difference in things conjoined, the inconceivablene of the disjunction has arisen from unremitted experience, indissoluble association. This is the case with extension : colour; we cannot think of an object as extended with thinking it as of some colour; the visible form, althou different fact from colour, has alw ays been embodied optical impression of colour. Again, ice cannot, without difficulty, be thought of but as cold; the visible appee INCONCEIVABILITY OF THE OPPOSITE. 667 of ice and the sensation of warmth are repugnant because of the strong opposing association. | | The same remark applies to the (proper) Axioms of Mathe- matics. The iteration of them in experience creates an almost indissoluble link of thought in their favour. We are practi- cally unable to think their opposites. So with the Logical Axiom of Mediate Consistency. Now, with regard to this class of beliefs, it is an open ques- tion, whether the stress should be laid upon the acquired inconceivableness of the negations, or upon the circumstance that has brought about the inconceivableness, namely, the unbroken iteration of the facts. Whether are we to lay hold of the primary condition, or of its consequence or concomitant ? There seems to be a presumption in favour of the primary condition, namely, the unbroken experience. Mr. Spencer himself attributes our inability to conceive the opposites of axioms and other strong beliefs to the experience of the race accumulated and transmitted to us. ‘ Objective facts are ever impressing themselves upon us ; our experience is a register of these objective facts ; and the inconceivableness of a thing implies that it is wholly at variance with the re- | gister.’ Thirdly, There are propositions admitted by us to be uni- versally true, but whose opposites we can well conceive. Such is the law of gravity. We can easily suppose that law to be suspended. ‘The reason in this case is, that although the greater number of unsupported bodies fall to the ground, some do not; smoke and dust may be seen ascending. We learn to regard these as exceptions, but they prevent us from having an overpowering strength of association between the absence of solid support and the descent of a body to the ground. Fourthly. Some examples given as unquestionable applica- tions of the principle of Inconceivableness are denied by a whole school of thinkers. Both Sir W. Hamilton and Mr. Spencer maintain that we are under the necessity of believing the Persistence of Force; that we cannot conceive either Matter or Force as absolutely created or absolutely destroyed. It is under the first kind of inconceivableness (where the opposite is a self-contradiction) that this case is brought; there is no attempt to affirm it on unbroken experience. The self-contradiction, however, is by no means apparent; Force is one thing, and its commencement or termination is seemingly a different thing. That aspect of Force whereby, in communi- cating itself, it loses the numerical equivalent of what is 668 THE UNIVERSAL POSTULATE, communicated, becomes familiar to us after we are educated in — mechanical facts; and we are then prepared to receive the ~ doctrine of Persistence. But prior to this experience, which, — to be sure, is requisite to a clear and precise cognition of — Force, we can form a conception of force beginning we know ~ not how, and ending we know not how. We are not at first struck with any self-contradiction in force arising out of no — prior force; the contradiction that we discover at lastisa — contradiction of our experience. ' A still more doubtful example is furnished by the question of questions—Material Perception, which Mr. Spencer upholds _ * in its popularly received form, on the authority of the test of — inconceivableness of the negative, Mysterious asis the con- — sciousness of something out of consciousness, we are, he says, — obliged to think it. ‘The current belief in objects as external independent entities, has a higher guarantee than any other — belief whatever.’ Yet thisis the belief that would have re- mained undisturbed to this hour, but for its glaring self-contra- diction, first exposed by Berkeley, and since by others. (See, — in particular, Ferrier’s Review of Berkeley). Any test of belief that guarantees this assumption must needs be repudi- ated by the numerous believers in its self-contradictory — character. There is an evident incongruity in laying down, — as a universal postulate, what begs the very point in dispute, — in a leading controversy. 4 ha Fifthly. Mr. Spencer’s view, that inconceivableness (where — there is no self-contradiction) represents ‘the net result of our experience up to the present time,’ supposes a theory of the sources of belief which is liable to great objections. He considers that our habitual contact with actual things has — engrained in our minds an intensity of connexion between the — ideas of those things proportioned to the frequency of their recurrence. For example, Space relations are the most iterated of any, and, consequently, our minds are moulded to these with — the highest possible tenacity. Next are Matter and Force | , relations. In this way, as already remarked, our repugnance — to form even an idea of the opposites is a proof of the persis ence of the corresponding facts. So that, experience and inconceivability of the opposite are convertible statements, _ Now, it may be granted that the contact with actual thi is one of the sources of belief; but it is not the only nor th greatest source. Indeed, so considerable are the other sou as to reduce this seemingly preponderating consideration to comparative insignificance. The competing elements are 0 O e SOURCES OF BELIEF, 669 briefly the following :—(1) The innate impetuosity of believ- ing that what is will continue; and (2) The influence of our strong emotions and predilections. Both influences will be illustrated afterwards as prevailing causes of error or Fallacy (Book VI). There should also be taken into account the circumstance that our strength of association does not represent the comparative recurrence of the fact, unless our position is such as to encounter the facts in proportion to their exact frequency. What is most familiar to nature, may not be the most familiar to us. We may not see the world from a zentral or commanding point of view. The best example of this is our excessive familiarity with one type of causation— the human will; in consequence of which, we represent that as the proper and natural type; whereas, it is an exceptional and narrow instance of causal agency. There still remains the effect of society in propagating and iterating certain propositions in language; by which iteration, no less than by confronting the facts in our own person, we are moulded to belief in certain doctrines. On the whole, therefore, when the various agencies operating to form our convictions are taken together, the one circumstance assigned by Mr. Spencer is so overborne as to render our strength of belief no just criterion of the facts believed. Sixthly. Nothing is gained by putting under one head, and subjecting to a common test, two classes of beliefs so distinct, as Self-Consistency and Consistency with Facts. Hitherto, in philosophy, these two departments, under various names, have been kept distinct. The one is known as Formal Truth, Necessary Truth, the Laws of Thought; the other is Material Truth, Contingent Truth, Inductive Certainty. Although the most strongly iterated of the laws inductively arrived at tend to indissoluble associations, and to a difficulty of thinking their opposites—in that way approximating to the truths of consist- ency, this is a mere incident belonging unequally to things that are alike true. When the inconceivability occurs, a reason can be given for it; and the reason not being always the same, there is no propriety in disguising the deeper dif- ferences by the superficial agreement. We are not obliged to have only one Universal Postulate. Should there occur two very different kinds of certainty, neither reposing on the other, our proper course is to assign different postulates. On these various grounds, we demur to the test of the ‘Inconceivableness of the Opposite’ as the basis of all cer- tainty, or as the matter that cannot be proved, but must be 670 THE UNIVERSAL POSTULATE. asked and granted, before demonstration can begin. We should propose, instead of that test, at least two Postulates, accord- — q ing to the distinction last noted ; perhaps more may be oo uisite. i First and foremost, we should place the Postulate of Consis- TENCY, or Self- Consistency—the absence of self-contradiction. — This is the basis of Immediate Inferences, or Equivalent Forms. — It must be conceded as a prime condition of all reasoning, discussion, and intelligent communication, Hnough has been — said in regard to it. Secondly, there must be some assumption or assumptions eS the foundation of all inferences or conclusions from Experience — “4a —some grounds of Material or Inductive certainty. There is much more difficulty in deciding what the postulate should be — for the department of real inference, or whether a single postulate is enough. We here enter upon a totally new sphere. In order to guarantee the conclusions of our experience, ; or to support us in such allegations as—‘ water quenches thirst,’ — ‘unsupported bodies fall’—there is clearly demanded, in the first instance, a trust in present consciousness. We must assume | that what we feel, we do feel; that our sensations and feelings — occur as they are felt. Whether or not we call this an irresisti- — ble belief, an assertion whose opposite is inconceivable or unthinkable, we assume it and proceed upon it, in all that we do. The calling the negation unthinkable does not constitute any reason for assuming it; we can give no reason better than that we do assume it. ‘The importance of stating this primary assumption is not apparent, till we proceed beyond it. We are carried a very little way into knowledge by the admission taken by itself’; we must make some steps in advance, and assume thing seemingly precarious in their character when compared with a the decisive certainty of immediate consciousness. It is requisite, in the second place, that we should believ 7 2 in past consciousness, or memory. Unless we trust our lection, our knowledge is limited to what is now present ; we cannot compare two successive experiences, or declare facts to succeed one another. We have, one moment, consciousness of thirst; the next moment, we have the | sciousness of a certain act called drinking ; ; the next foll ing moment, we have the farther consciousnees of relief thirst. The succession of the three steps is a fact or ex] ence; but we cannot believe it, unless we believe in , ee h® - 7 . ne THE LEAP TO THE FUTURE. 671 recent fact, given in memory, as well as the present, given in consciousness. The belief in memory must therefore be postulated. It may be asked, however, are we to believe our memory without limits, or, if nitt, what are the limits to our belief? If there be any circumstance qualifying or defining the belief, that circumstance should be produced as something more funda- mental, and therefore proper to take the place of the assump- tion that it limits and qualifies. In short, memory must be believed in; yet the postulate of the belief is not wholly independent and isolated, but leans to some extent on another and a different postulate. Granting, however, that the belief in memory, as well as the belief in present consciousness, is a primary assumption, we next remark that it comes short of our needs. The most authentic recollection gives only what has been; something that has ceased, and can concern us no longer. A far more perilous leap remains ; the leap to the future. All our interest is concentrated on what has yet to be; the present and the past are of value only as a clue to the events that are to come. Now, it is far easier to satisfy us of what has been, than of what is still to be. The postulate that we are in quest of must carry us across the gulph, from the experienced known, either present or remembered, to the unexperienced and unknown—umust per- form the leap of real inference. ‘ Water has quenched our thirst in the past ;’ by what assumption do we aflirm that the same will happen in the future? Experience does not teach us this; experience is only what has actually been; and, after never so many repetitions of a thing, there still remains the peril of venturing upon the untrodden land of future possibility. The fact, generally expressed as Nature’s Uniformity, is the guarantee, the ultimate major premise, of all Induction. * What has been, will be,’ justifies the inference that water will assuage thrist in after times. We can give no reason, or _ evidence, for this uniformity ; and, therefore, the course seems to be to adopt this as the finishing postulate. And, undoubtedly, _ there is no other issue possible. We have a choice of modes of expressing the assumption, but whatever be the expression, the substance is what is conveyed by the fact of Uniformity. As nature is not uniform in everything, we have to apply a test to discriminate the uniformities from the varieties. There is a uniformity in the manner of animal generation, but 672 THE UNIVERSAL. POSTULATE, not an absolute sameness in the individuals born even of the — same pair. Now experience will not establish uniformity, but it will establish exceptions to uniformity ; it will sift the natural | ye sequences and enable us to reject all that are not uniform. ae me) does not prove that anything will always be in the future a what it has been in the past, but it will prove that some things | a have been uniform in the past, and others not uniform. oe has at least a destructive certainty, og Let us word the postulate thus :—What has uniformly been in the past will be in the future. Otherwise, ‘ what has never — been contradicted in any known instance (there being ample a means and opportunities of search) will always be true.’ in aa the course of our experience, we have seen a great many pro- mising uniformities break down, Again, we have found in- — stances that have never failed; on “such cases, we venture, and it is a mere venture, to predict the future continuance of a the same state of things. We go forward in blind faith, until a we receive a check; our confidence grows with experience ; a: yet experience has only a negative force, it shows us what has” i never been contradicted ; and on that we run the risk of Ey Ss ing forward in the same course, 7 This assumption is an ample justification of the poe operation, as a ara of eM inference, Without it, we can ie4 it other wise than as begged at the very outset. If there be a reason, it is not theoretical, but practical. Without the as- sumption, we could not take the smallest steps in practical matters ; we could not pursue any object or end in life. Un- less the future is to reproduce the past, it is an eni ma, & labyrinth. Our natural prompting is to asswme such i entity ; to believe it first, and prove it afterwards. This third Postulate i is, properly speaking, the Postulate of m4 Experience. Not only does it involve a hazard peculiar 1 0 ; itself, making a broad line between it and the postulates of present consciousness and of memory, but it seems to remove — all the doubts and ambiguities connected with these appar- . ently more facile assumptions. Nothing can be better evidence than present reality, provided we do not mistake an act ul consciousness for an inference, or a recollection. This d culty is got over by comparison of instances, and by the ap; cation of general principles, which repose ultimately 1 upon Great Postulate. a So with Memory. We trust implicitly a recent recollee- FALLACIES IN LANGUAGE, 673 tion ; but as the interval of time enlarges, our trust diminishes. A limit has thus to be prescribed, through a comparison of experiences, followed by an inference from the past to the future, which brings us round again to the assumption of the future from the past. Hence, whichever way we turn, we find this to be the one resting place for the sole of our foot. E.— ARISTOTELIAN AND SCHOLASTIC FALLACIES. The Aristotelian is the basis of all subsequent classifications. It proceeds upon the distinction between fallacies in Language, and fallacies in Thought, L ‘Pallacies arising in Language (In Dictione, of rapa tiv hefiv). 1. Aequivocatio, Homonymia, opwrunia; ambiguity ina single term. This is a very comprehensive class of fal- lacy. One of the examples given by Aristotle illustrates an ambiguity in the word ‘necessary.’ ‘ Hvil is good, for what is necessary (ta deov7a) is good, and evil is necessary.’ What is necessary aS a means to a desired end is good; but what necessarily results from antecedent conditions may be evil. Whately gives, in his Logic, an enumeration of words often used ambiguously in discussion. This task belongs as much at least to the lexicographer as to the logician. Thus: ‘ Ex- pect’ is either what is possible, as that the sun will rise to- morrow, or what is right, as ‘ England expects every man to do his duty.’ ‘Old’ means either length of duration, or dis- tance of time. As age gives experience, and experience often teaches wisdom, there is a disposition to regard the ancients as wiser than ourselves. To this Bacon replied, ‘we are the ancients ;’ we inherit the wisdom of the old, and can add to it more experience. _ A chief cause of ambiguity is that the signification of words is constantly shifting. The word ‘publish’ formerly meant ‘communicate’ or ‘show,’—‘ The unwearied sun publishes to every land.’ This is now the legal meaning of publish: to publish a libel is not necessarily to print it, any communica- tion of written libellous matter to another is sufficient. The law still speaks of ‘ uttering’ coin. ‘Some’ is of interest to the logician, in its two chief senses ‘some at least,’ and ‘someat most,’ or some = not none, and some = not all. The remedy for ambiguity is Definition. 2. Amphiboly, amphibolia, dug¢.Bodréa. A sentence may have two grammatical renderings, but by preference suggest the one intended to mislead. This was an occasional trick of the O74 ARISTOTELIAN AND SCHOLASTIC FALLACIES. ancient oracles. ‘Aio te, Avacida, Romanos vincere pos reads as well whether the Romans are victors or vanquish ‘I hope that you the enemy may slay.’ iy 8. Fallacia compositionis et divisionis. Whately define th is fallacy as the use of a term collectively in one premise, and distributively in another. If the term is collective in major premise, and distributive in the minor, it is a fallacy ae a division ; if the collective is in the minor, and the distributive in the major, it is a fallacy of composition. Five is one number, i Three and two are five, Fallacy of Division Three and two are one number. (ae Three and two are two numbers, ‘od HB ; Fallacy of Composition. 2 bi ith ; Aristotle gives a similar division,—ovv0eats, or the aa = of wrong disjunction, and d:atpeors or the possibility of wrong conjunction. His example of é:atpeors is :— Sa Fe Five is two and three ; Two and three are even and odd ; Five is even and odd. th This would be a fallacy of composition, according to Whate and Mr. Poste observes that it is not easy to understand exactly Aristotle’s distinction, and not worth the trouble. mm 4. Fallacia Prosodiae or Accentus, rpoowdia, This is very trifling consequence, and chiefly noticeable because the different meanings that may be given to a sentence varying the emphasis. Mr, De Morgan remarks that commandment, ‘ Thou shalt not bear false witness against neighbour,’ is often read with the emphasis so placed as suggest that subornation is not forbidden, or that anyth false except evidence is permitted, or that it may be given him, or that it is only against neighbours that false witness may not be borne.’ Most of the old examples are mere puns. — ‘Tu es qui es; quies est requies ; ergo, tu es requies.” 5. Fallacta figurae dictionis, oxijua deEews. According t to Aristotle's view, this fallacy is a species of grammati a mistake, arising from the circumstance that unlike th have names with a like inflexion. Thus, ailing and cuttong have the same termination, but one applies to a state or quality, the other to an action, dees. IT. Fallacies in Thought (Hxtra Dictionem, ot é€w ths KeFews l. Fallacia aceidentis, or a dicto simpliciter: add dict Three and two are five, Five is two numbers. FALLACIES IN THOUGHT. 675 secundum quid, nupd 76 cuvpBeByxos, A fallacy assuming that subject and predicate have all their attributes in common. It is taking a predicate as co-extensive with a subject, when it is not. 2. Fallacia a dicto secundum quid ad dictum simpliciter, 70 amos 7 fA) GrdBs adda TH i} Tod 7) Tore } pos te éyeaOas, confusion of an absolute statement with a statement limited in manner, place, time, or relation. What you bought yesterday, you eat to-day; You bought raw meat yesterday ; You eat raw meat to-day. This is the converse of the fallacia accidentis; many of the examples of both are instances of erroneous conversion of an universal affirmative. 3. Ignoratio clencht, ro mapa rv tod édéyxXov dyvov, an inadequate notion of confutation. A debater undertakes to contradict and overthrow a thesis, and proceeds to destroy some different position. [tis the common error of arguing beside the point, of proving what has only a superficial resemblance to the conclusion, or of simply trying to distract attention from the point at issue. Mr. de Morgan classifies, along with this, any attempt to transfer the onus probandi to the wrong side. 4, Fallacia consequentis, non sequitur, ro mapa 70 émopevoy. To mistake gall for honey, because it is yellow, is a non sequitur. Kain wets the ground, therefore wet ground implies that it has rained. Every one in a fever is hot, but every one that is hot is notina fever. In this case also, the ex- amples are generally instances of wrong conversion of an universal affirmative. 5. Petitio Principii, 70 rapa 76 év dpxG AanBaverw Aristotle describes five forms of this fallacy. (1) When one begs the very thing that ought to be demonstrated. (2) When one begs universally, what ought to be demonstrated particularly. (3) When one begs the particular to help to prove the uni- versal. (4) When one begs all the particulars that compose the universal. (5) When one begs something necessarily con- nected with the conclusion. Logicians discuss the question whether the syllogism itself is a petitio principii. 6. Non causa pro causa, 70 py aitiov ws attiov 7Oévar, an inductive fallacy, for which another name is, post hoc, ergo proper hoc, which is the vice of the delusive induction called per simplicem enumerationem. Whitfield attributed his being 676 ARISTOTELIAN AND SCHOLASTIC FALLACIES. overtaken by a hailstorm on a certain occasion to his having in not preached at the last town. ‘ ie ie 7. Fallacia pluriwm interrogationum, 70 74 metw peor ware Re év oetv, is the fallacy of putting more questions than one as one. Why did you strike your father? It is an easy snare to ask a reason for a fact that has no existence. ‘The fir sb members of the Royal Society were in this predicament, a they tried to explain why a dead fish weighed more Af? | living fish. The auswer was, it did not, Hardly any addition has been made to Aristotle? s list of Fallacies by modern writers on the Syllogism. Aristotle's _ principle of classification has been pronounced illogical, and — new arrangements have been proposed; but his enumeration has not been materially increased. aa ce The arrangement followed in most Manuals of Syllogistic Logic, is that adopted by Whately. sh Rejecting as indistinct the division of Fallacies into those in the words (in dictione) and those not in the words (cotra dictionem), Whately divides them into Logica and Non- Mrz Loeican. The Logical include all cases of insufficient premise 3. advanced as sufficient; all cases ‘where the conclusion does — not follow from the premises.’ Such cases only, he contends, | are logical in the strict sense: logic having to do only with the sufficiency of the premises given for the conclusion based upon them. As Non-Logical he reckons all cases where ; premises are sufficient for the conclusion, ‘where the conclu- sion does follow from the premises,’ but where either the premises are unduly assumed, or the conclusion is irrelevant to the point in dispute. To settle whether the premises are a legitimate or whether the conclusion is in point, passes beyond the proper sphere of Logic. ic Such are Whately’s main divisions. The grouping of t Aristotelian fallacies under them is as follows:—I. He: cube divides Logical fallacies into the Purrty Locicat and the Sry I> LOGICAL. The Purely Logical are Undistributed Middle, al | Iilicit Process of the Major and of the Minor: two errors which Aristotle did not enumerate in his list of Fallacies (sophisma whether because he considered them too palpable to be fra lently used by a sophist, or because he had sufficiently ex them in treating of the syllogism. The Semz-logical em all instances of ambiguous middle term. The ambiguit be in the term itself, or may depend upon the context. ambiguity being in bes term itself, we haye Fallacia a 41.00 WHATELY’S CLASSIFCATION, 677 cationis, and Fallacia Amphiboliae. Our author takes an opportunity of remarking that a term may have two meanings from accident (as the term ‘ light’); or from some connexion of resemblance, analogy, cause and effect, &c., between the different senses. The ambiguity arising from the context, we have Fallacia Compositionis et Divisionis,and Fallacia Accidentis, and a dicto secundum quid ad dictum simpliciter. In these cases the middle term is not ambiguous in itself, but is used with different adjuncts in the two premises. II. In the Non-logical or Material group, the premises may be unduly assumed, and the conclusion may be irrelevant. A premise may be altogether false and unsupported. The only guarantee against this is a knowledge of the conditions of In- duction, The major premise may beg the conclusion (petitio principti,; being either the very same as the conclusion, and differing only in form, or not quite the same as the conclusion, but unfairly implying it. So much for premises unduly assumed. ‘Turning now to the other sub-division of the Non- logical fallacies (ignoratio elenchi, or irrelevant conclusion), we find various modes of shirking the question particularized. One way is to lay great stress upon the objections, taking no notice of what may be said in favour. Another way is to shift ground, either to something wholly irrelevant, or from one premise to another. A third way is to escape under cover of vomplex and general terms. And a fourth way consists in appeals to the passions and sentiments, ignoring altogether the rational grounds of the point in question. (See Book VI). THE AXIOM OF THE SYLLOGISM. (Supplementary Note to the Second Edition.) In pp. 18, 156, 226, 237, 247, 269, the Logical Axiom of the Syllogism has been placed under the head of Inductive truth. This has not been done without misgivings, as the following remarks will show. The drawing of a broad line between Immediate and Mediate or Syllogistic Inference, and the laying down of a Deductive Axiom founded on experience as the basis of the Syllogism, will be seen to be attended with difficulties. The first is the anomalous middle position of the Hypo- 678 SUPPLEMENTARY NOTE. — thetical Syllogism. If we are bound to bring hy pothetic inference under one or other of the two forms, we feel tha % our decision is not satisfactory; the case passes somewhat beyond Immediate Inference, and yet does not reach vg Syllogism. "ye There is the same unpleasant doubt about the cases di cussed in p. 109, and p. 157, where a singular preposition has to be treated as a Universal, We cannot, without con- siderable straining, make these out either Equivalent a Si. 4 tions or Syllogisms. 4 The second difficulty is still greater. The question hagaih O- be raised, whether syllogistic inference is or is not Self J consistency. Is the conclusion the mere equivalent of the premises, so that to deny it, while admitting the premises, would be self-contradictory ? ae That the conclusion of the Syllogism flows necessarily fi from. the premises, is generally insisted on. To refuse the con- clusion would be to contradict the premises. Indeed, the self-contradiction would be as unequivocal as in the denial « of an immediate inference—all A is B, some A is B. In what then consists the distinction, as regards the logical foundation, or the kind of certainty, between Mediate and Immedia te inference P In the Syllogism, the bond of necessary Sit vallonaal ‘ies between one proposition and two others; in the immediate inference, it lies between one proposition and one otl This makes the case a degree more complicated, withou apparently altering the generic character of the inference ; it is an inference contained in the premises; it cannot | * refused without contradiction in terms. This circumstance of necessary, or self-consistent relatio ship should appear in the axiom of the Syllogism. It ‘ae so in the dictum de omni et nullo. That axiom seems to be 2 necessary truth ; we feel that to deny it would be not mer to deny a fact, but to deny in one form of words what have already affirmed in another ; which expresses wha’ 8 meant by ‘contradiction in terms,’ and by the denial « of a ‘necessary ’ truth. The other form of the axiom—WNota note—‘ whatever | mark has whatever that mark is a mark of, must al necessary, if it is an exact equivalent. We cannot st that the Syllogism under one form of axiom is an implies or necessary inference—an analytic judgment ; and, 1 an another form, an inductive or contingent inference—a THE AXIOM OF THE SYLLOGISM. 679 thetic judgment; such a supposition could arise only from _ some great confusion of ideas. If, under the guise of nota note, the axiom is exactly equiva- lent in substance, as it is in appearance, to the mathematical axiom of mediate equality—-equals of the same are equal— it would not be an axiom of self-consistency, or an analytic judgment. That axiom may be very evident, may be styled by courtesy self-evident, but it is a synthetic judgment ; the subject and the predicate are not mutually implicated; its denial is not a contradiction in terms. The subject is ‘ equals of the same’—things severally compared to a common stan- dard or measure; the predicate is—equal by ‘ coincidence,’ or by being compared immediately—a totally distinct mode of comparison. These two modes are said to concur; the trial by the one mode is a test or mark of what would happen in a trial by the other mode. We have an opportunity of comparing two things with the same third; we have no opportunity of applying the two things to each other; we are assured by the axiom that the coincidence of the two with the common third is proof that they would coincide if we could apply them to each other. There would not be a contradiction im terns, there would only be a contradiction of experienced facts, if we denied that mediate coincidence infers immediate coinci- dence. Mr. Mill, in the new edition of his Logic, p. 208, states that he regards Formal Logic as the logic of mere consistency, and the dictum de omni as its axiom; he does not insist on apply- ing to it the nota note, although he regards that form as the proper axiom for the logic of the pursuit of truth by way of Deduction ; the recognition of which can alone show how it is possible that deductive reasoning can be a road to truth. So viewed it is, not self-consistency, but an inductive, con- tingent, or synthetic proposition, like the mathematical axiom of mediate equals. The difference between formal deduction and real deduction is the difference between syllogism and inductive or experi- mental truth. Real deduction is the following out of an induction, and assumes the uniformity of nature. That the men living and unborn will die is a necessary inference from ‘all men are mortal,’ but not a necessary inference from the actual premise, which is confined to the men that have actually died. The real deduction contains three steps :— certain individuals possess the attributes called humanity, and also the attribute mortality ; these two attributes have been 680 SUPPLEMENTARY NOTE, 9 © conjoined through all our past experience; hence the prese of the one marks the presence of the other. Now, John Brown — and William Smith possesses the first fact, humanity, therefo ro they possess what it marks, that is the second fact, mortality. ye This is the application of the nota note in its purity and sim plicity ; the uniformity of nature being supposed in addition. — ; For greater clearness, take another instance. ‘ All inert substances gravitate ; ‘ ‘throughout all our experience, the property ‘inertness’ is a mark of the property ‘ gravity.” Now, the etherial medium in space has the mark inertia ( (by resisting the comets); it therefore gravitates. > But still the question recurs, might not the infonenbaals n both these instances be given under the dictum de omni # For, basing on the uniformity of nature, we at once convert — the special observations into a general law; men in the past b have died, men in the future will die; whee all men a A mortal. Ghitis has the marks of man, is a man; Caius is mortal. Inert matter gravitates; the ether is inert ; ¢ he eo ether gravitates. a It would thus seem that the attainment of new ta tia by. the way of deduction, does not imperatively demand any change of axiom. ‘The dictwm and the nota note are equally ly suitable. If so, the inference must still be a case of necess implied, or self-consistent truth. Of the dictwm and the note alike, we must declare that their denial is a self-contra- diction. ‘2 Necessary or self-consistent inference, instead of being con- fined to the manipulation of the equivalent forms of positions, takes a wider sweep and embraces the Syllog which we should have to characterise as ‘ mediate self-c sistency,’ ‘mediate necessity,’ ‘complex implication” forms lying between immediate inference or propositi equivalence, and mediate inference or syllogistic equiva would be regarded as incidental varieties of Self-consistency ; they need not be forced under either of the two principal genera. ht whi hb When we say ‘ Socrates was wise, ‘Socrates was poor ; therefore ‘one man was wise and poor,’ we draw a nec or self-consistent conclusion, but not by the way o Syllogism, as representing deductive reasoning. ‘Socrates is wise,’ and ‘ Socrates is poor,’ we can Ct ‘Socrates is wise and poor;’ ‘wisdom and poverty ¢ joined in Socrates ;’ the axiom or assumption here is properties can be affirmed of a subject separately, or in separate THE AXIOM OF THE SYLLOGISM. 681 propositions, they may be affirmed conjunctly, or in a com pound proposition. Again, to proceed to the farther variation —one man was wise and poor—we perform the, process of sub- stituting for ‘Socrates’ the designation ‘one man,’ which prop- erly applies to him. ‘This is the mode of equivalence con- stantly assumed in working algebraic equations; where, for any expression, we insert at pleasure another equal to it. Neither of these modes is the same as the dictum de omni, and, there- fore, they need not be forced under the syllogism, although they amount to something more than stating an equivalent form of a single proposition. F.—ANALYSIS AND SYNTHESIS. The common idea—Analysis and Synthesis—is difficult to express adequately, owing to the variety of its applications. Chemical Analysis, Mathematical Analysis, Logical Analysis, with the corresponding Syntheses, have a basis of agreement, but with points of difference. The general idea of Analysis is separation; of Synthesis, composition or combination. Yet the contrast does not alto- gether correspond to the distinction of Abstract and Concrete. Analysis is Abstraction, but Synthesis is not the negative or the absence of Abstraction; it is not the wn-abstracted Concrete. While the scientific man is, by the law of his being, an analyst, the poet or artist, who does not analyze but combines, is not a synthesist. Synthesis in contrast with analysis, is combining after analyzing. The simplest exemplification of the two correlated processes is seen in Cuemicat Analysis. The Chemist operates upon an unknown mixture or combination of substances, as a strange pro- duct from a furnace, or the stomach of a poisoned man. He. separates and identifies the various ingredients of the compound. The obverse Synthesis would consist in making up the given compounds by means of the several elements in their proper proportions. Thus, having ascertained the precise constituents of a mineral water, it is then possible to form the water artifi- cially. If the artificial water is exactly identical with the natural water, both the analysis and the synthesis are successful and complete. It is by the analysis, however, that the synthesis has been possible. The analysis is the foundation of a new means of production; it enables us not merely to imitate and rival the spontaneous products of nature, but also, if need 682 ANALYSIS AND SYNTHESIS. be, to vary those products on a definite plan or purpose. W To may introduce beneficial variations into the ayathease bd mineral waters, So, having analyzed some crude substance medicinally valuable, we may artificially compound it, firs literally (which proves the sufficiency of the analysis), | and next with improved adaptations for the end. The most notable application of Chemical synthesis is fo the formation of organic compounds in the laboratory. By foregone analysis, the chemist has discovered the constituen elements of these compounds, and the peculiarities of their — union ; he then uses his knowledge to re-produce by laboratory — processes what has been produced in the course of living ~ growth. In this way, urea, acetic acid, and many other or- ganic products have been obtained by laboratory 7 Such synthetic efforts are the trophies of analysis. Our next example may be termed Loaican Analysis; it i: the ordinary Scientific Analysis, the peculiar case of Mathe: matics being reserved. Here, Analysis is substantially i iden- tical with generalization, whether of the notion or of the pro- position. What Synthesis is will appear presently. ath The processes of assimilating, identifying, classing, general ale izing, abstracting, defining, are the various sides, aspects or stages, of one fundamental ‘operation. Now Analysis is merely a farther aspect, another side, of the same proteus. To ident classify, and abstract, is to separate or analyse, so far as the case admits; the separation being no longer actual, as in Chemistry, but mental or ideal. To identify and class y transparent bodies, is to make abstractive separation, or ana- lysis, of the property called transparency ; or to view its fu tions, powers, or agencies alone and apart from all the ot powers possessed by the individual transparent bodies. W. is liquid, but this aspect is disregarded ; diamond has e: ordinary refractive power but no notice is taken of it two substances are studied merely in their agreement in w we call transparency. Shia Now the investigation of nature turns exclusively on this abstractive separation. Bodies are constituted with a ch of powers or properties inseparably combinated, yet pursuing its independent course without any distur bance | the others. Water, as transparent, has a power exaetly i tical with diamond and rock er ystal, as transparent; the peculiarities wherein the two bodies stand widely con have no seen? exercise no interference, as regar ANALYSIS MEANS ABSTRACTION AND INDUCTION. 683 of attention, and being easily impeded and thwarted by dis- tracting circumstances, finds the advantage of neglecting all allied properties, and concentrating its powers on the one subject of study at the time. Thus, Abstraction and Analysis, if not identical, are the same fact viewed with a slight difference. Abstraction means separately viewing one point of agreement, and leaving all other accompaniments in the shade; the transparency is studied by itself, the specific gravity and all other incorpo- rated properties being left out of sight. Analysis means the very same thing; only, proceeding a little farther, it supposes that every one of the powers of a given concrete, as water, may be abstracted by turns,—transparency, liquidity, specific gravity ; so that water as a whole may be analyzed, or sepa- rated (mentally) into a number of different powers, whose enumeration is a full account of the agency of water. The farther we push abstraction and generalization, the farther we push Analysis. When, after generalizing all mechanical movements, and forming an abstract idea, or analytic separation of molar or mechanical force, we proceed to identify mechanical momentum with molecular forces, we make a new analysis; we separate the property of force from its exclusive connexion with the movements of masses, and view it as the movement of matter, whether in larger or in smaller aggregates. It is now requisite to assign a correlative meaning of Syn- thesis. As Analysis is the ideal separation and separate exhi- bition of all the functions of a concrete thing, as water, iron, blood, Synthesis is the re-statement of the whole in their ageregate. Its efficacy would be shown in supposing a new aggregate, asa liquid diamond, a metal with all the properties of lead except its corrosion. It would also be exemplified in the act of communicating, by description, the knowledge of a mineral, apart from a concrete specimen, Another step is inevitable. As these abstractive properties, or notions, are what enter into the inductive generalizations of nature, each inductive law being two or more coupled together, Analysis becomes applied to Inductive discovery. There can be no wide induction without a correspondingly wide genera- lization of at least two notions, that is, without an equivalent analytic separation. The summit of generalization, in the notions Quantity, Inertia, Gravity, Persistence, is the summit of Analysis. The highest generalities of Mind are attained through the most thorough Analysis of Mind. 684 ANALYSIS AND SYNTHESIS. The employment of Analysis to signify Induction appears in Aristotle, and pervades the logicians after him. (See Mansel’s Aldrich, App. G., Hamilton’s Logic, II., 2). By an easy transition, Synthesis would be applied to Deduction. The deductive operation of following ont the law of gravity to lunar perturbations, to the tides, to precession, &c., would be called synthetical, as reuniting abstract elements into new combinations. Having mastered the laws of central force, and the composition of forces, Newton deduced or inferred the orbits of bodies governed by other forces than gravity. Synthesis, however, scarcely applies to simple Deduction, the following out an induction to a new case, as when we infer the death of the reigning pope from the mortality of the men that have died. There is no element of combination in such cases, there is but the filling up of the Induction, which is only formally complete so long as any particulars are still outstanding. The synthetic operation is best realized by the complex deductions, or the union of several deductive laws to a composite or concrete case—a secondary law. . There is nothing gained by using the terms Analysis an Synthesis to the Inductive and Deductive processes respec- tively. We may show in what way the application is proper or admissible, and that is all. The use of the Syllogism may be expressed as analyzing or separating, out of regard to our mental infirmity, the three parts of a step of reasoning, so that they may be studied in _ separation. The premises, instead of being confused together, - can be looked at apart, and each judged on its merits in its isolated condition. ‘This is an advantage belonging to Method, or Discovery. Wherever a separation of this kind can take place, a great relief is given to the understanding, with a corresponding enlargement of its powers. ons An accountant separates his columns of debit and of credit, and classifies under different heads payments that relate to different subjects and follow different rules. i Grammatical Analysis may be followed by Grammatical Synthesis, as in constructing sentences upon new types sug- gested by putting together the component elements in various e WAYS. ae Criticism is a species of analysis; and the composition of an Oration or a Poem, by the guidance of critical and rheto- rical rules, is a strictly synthetic operation; the previous — analysis is the foundation of the method. Composition, with: — 1 Fy out any rules, is not synthesis i on hea MATHEMATICAL ANALYSIS, 685 it is a weakness of the unscientific man to suppose that a concrete thing, as, for example, a political institution, can be viewed only as a whole—that its operations are an indivisible totality. Thus, the obtaining of justice by the procedure in a court of law is through a series of steps and processes—raising the action, appearing by counsel, summoning a jury, and so on. The effect of the whole being good, the un-analyzing mind distributes the merit equally over all the parts, and is shocked when a doubt is raised as to the utility of any one constituent, as, for example, the jury. To advert finally, to the special instance of Mathematical Analysis and Synthesis. A new step in geometry may be taken either by analysis or by synthesis. The various Geo- metrical properties are said to have been first discovered, by analysis, while in exposition they are in the form of synthesis ; which is not strictly the fact ; we may proceed from the known te the unknown in both ways; discovering new properties by synthesis no less than by analysis. Let us take Synthesis first, as suiting the case of a science whose onward march is by the way of Deduction. Let us assume that a certain proposition has been arrived at, ‘no matter how, say, ‘ Parallelograms on the same base, and be- tween the same parallels, are equal.’ Now any one consider- ing this proposition might readily see, that the axiom of mediate equality applied to it, would show that the same thing might be predicated of equal bases ; such an inference would be an effort of pure deduction, or the skilful combin- ing of two already established propositions to yield a new third proposition. So, by a repetition of the same apposite union of truths possessed, one might also infer that ‘ Z7'7- angles on the same base, or on equal bases, and between the same parallels, are equal.’ By farther combinations, the rea- soner might go on to deduce or infer the 47th, and so forth. All which is a purely synthetic operation; and geometrical truths may be evolved to any extent in this way. Corollaries are usually deductive inferences, of short leap, from the main proposition. The operation is seldom one of simple deduc- tion, there is usually a certain concurrence of two or more propositions to the new result; and the mental effort lies in bringing these together. Geometrical synthesis and deduc- tion are thus the same thing. What then is Geometrical Analysis ? Is it Induction? We are told that it proceeds from the unknown to the known. If one were to suspect or surmise (without being sure) that the 686 ANALYSIS AND SYNTHESIS. square of the hypothenuse of a triangle is equal to the sum of the squares of the sides, and assuming it, were to endeavour to connect it by a thread of geometrical reasoning with the established propositions of geometry, the operation would be called analytic or regressive, as compared with the synthetic or progressive course above described. Yet in reality, the mcntal operation is substantially the same in both; the two differ only in superficial appearance, like the enquiry from cause to effect, and from effect to cause. Assuming the truth of the surmise first, we have to consider what prior proposi- tions would be requisite to support it; and, again, what other propositions would support these; until we come at last upon admitted theorems. The real operation at each step is a deductive one; we feign a proposition and try its conse- quences ; if these coincide with the case, such proposition or propositions are what we need; and if they are found among the true propositions of geometry, we have made good our point; we have proved our surmise, and put it in the train of geometrical deductions. The facilities for this inverted deduction are so greatly mvl- tiplied by Algebra as to give to the algebraic processes the designation ‘analytical’ by pre-eminence. In an Algebraic equation, we work backward from the known to the unknown ; yet it is by a series of properly deductive operations—the application of axioms and theorems already established. Algebraic Geometry is called ‘ Analytical ;’ the more recon- dite processes of Algebra are called the Higher Analysis. Thus, while Synthesis has throughout a reference to the deductive and combining processes of science, Analysis relates to generalization or inductiou, everywhere except in Mathe- matics, in which it is merely the mode of deductive synthesis adapted to the solution of special problems. The geometer, when he has no special end in view, evolves new propositions by direct or progressive synthesis ; when he has a problem to work out, he confines his deductions to those that lie in the approaches to the desired solution. The course of discovery ina Deductive science can be only Deductive; it consists in following out generalities in hand to new applications; usually by combining several in one application. The art, the labour, hes in the union of several propositions to a result. The operation must be tentative ; it cannot be foretold; yet it is amenable to a certain general method, which practice instils, and which is not altogether beyond the reach of precept. ’ oe BACON ON THE NECESSITY OF FACTS. 687 G.—GROWTH OF THE LOGIC OF INDUCTION, Previous to Mr. Mill, the principal contributors to the Logie of Induction were Bacon, Newton, Herschel, and Whewell. Bacon.—The essential part of the service rendered by Bacon to Science was his protest in favour of basing generalities on a patient collection and accurate comparison of facts. It was too much the custom, he complained, to ‘just glance at experi- ments and particulars in passing ;’ in place of this, he proposed to ‘dwell duly and orderly among them.’ With the whole force of his eloquence he discouraged flighty speculation and rash conjecture, and urged that generalities must be founded upon a wide comparison of particulars. Following up his emphatic enunciation that men must have done with rash speculations and rashly abstracted notions, if they desire to make progress in their knowledge of Nature, he devised modes of elucidating truth by the comparison of instances on a methodical plan. He directs the arrangement of facts in three different tables. The first table is to contain instances agreeing in the presence of the phenomenon to be investigated; this he calls a Table of Essence and Presence (Tabula Issentiae et Praesentiae). The second table is to con- tain instances wanting in the phenomenon, but otherwise allied to the instances where the phenomenon occurs, each instance corresponding as far as possible to some one instance in the first table; this he calls the Table of Deviation, or of Absence in Allied Instances (Tabula Declinationis, sive Absen- tiae in Proximo). The third table contains the phenomenon in different degrees, and is called the Table of Degrees or Table of Comparison (Tabula Graduum, sive Tabula Comparitiva). The constitution of the three Tables is exemplified upon an enquiry into the phenomenon of Heat; for the prosecution of which are assembled no less than 27 instances agreeing in the presence of heat, 32 allied instances agreeing in its absence, - and 41 instances of heat manifested in different degrees. The three Tables seem designed for the convenient applica- tion of the three leading methods of Inductive elimination— Agreement, Difference, and Concomitant Variations; but we must not suppose that Bacon realized anything like the precision of those methods. He did not conceive the idea of choosing his instances so that they should differ in every point but the phenomenon under investigation, agreeing only in that —the fundamental idea of the method of Agreement. Nor did he conceive the aces of the decisive method of Difference, the 688 GROWTH OF THE LOGIC OF INDUCTION. choice of two instances agreeing in every point save the given phenomenon. Having collected his Tables of Instances, he went to work by excluding according to certain canons the irrelevant instances, then making a hypothesis or guess at the truth, and finally verifying this by farther enquiry. Bacon takes especial credit for his process of Exclusion or Rejection. He contrasts it with the popular method of pro- ceeding by Simple Enumeration, that is, by counting only the favourable instances, overlooking the unfavourable; and he claims to be the first to make it prominent. The problem of Induction being to ‘ find such a quality as is always present or absent with the given quality, and always increases or decreases with it,’ ‘the first work of true induction is the rejection or exclusion of the several qualities which are not found in some instance where the given quality is present, or are found in some instance where the given quality is absent, or are found to increase in some instance where the given quality decreases, or to decrease when the given quality increases.’ It will be observed that this process of exclusion, although — a great advance upon generalizing without regard to contra- dictory instances, is very rudimentary. Bacon does not dis- tinguish between laws of simple’ Co-existence and laws of Causation. The first of his principles of Rejection is suited only to the establishment of co existences, and amounts to this, that we are not to declare two qualities universally concomi- _ tant, if in certain instances we find one absent when the other is present. His other principle of rejection is the reverse of the method of Concomitant variations, a disproving of causal connexion on account of independent variation; and applies to causation alone. As to the modes of certifying the hypothesis allowed after this process of collecting and sifting instances—the Logic of Proof, Bacon has left us but a fragment. Of his nine divi- sions of aids to Induction, he completed only the first, Prero- gative Instances. Under this head, he dictates a farther enquiry into particulars, and dwells upon instances of special value to the inquirer, calling them Prerogative from that cir cumstance. To call this division of his subject an aid te induction is misleading; we expect to find an account of — instances particularly suitable for founding inductions upon, and find instead illustrations of various maxims applicable to Definition, Observation, and even Experiment, as well as Sorte specially adapted for Inductive Elimination, BACON’S INDUCTIVE METHODS. 6389 It is among the Prerogative Instances, if anywhere, that we are to look whether Bacon had conceived any practical device for bringing the process of Exclusion or Elimination to a po- sitive result, as is done in the modern methods of Agreement and Difference. Under the heading of Solitary Instances, we _ do find a crude approach to the selection of instances implied in these methods. Solitary Instances are either instances that exhibit a phenomenon without any of its usual accom- paniments, as colour produced by the passage of light through a prism; or instunces agreeing in everything except some particular phenomenon, as different colours in the same piece of marble. He says in a vague way that such instances shorten very much the process of Hxclusion. They contain really all that is demanded for the methods of Agreement and Difference. Yet in Bacon’s hands they are comparatively useless, and, as part of his method, could not even furnish a suggestion for more perfect contrivances. The reasons are to be found in his vague conception of the problem of Induction. His methods of Exclusion are of avail only for problems of Cause and Effect ; they are superfluous for problems of simple concomitance, a single instance of disunion being sufficient to disprove such a connexion; yet he speaks throughout as if his elaborate comparison vf instances were designed only to prove two properties co-existent. To this confusion he was inevitably led by the subjects he proposed to investigate. He seems to have thought principally of investigating abstract qualities of bodies, such as density, weight, colour, volatility, porosity, heat; his purpose being to establish their Form, by which he seems to have vaguely understood something inva- riably present with these qualities and endowing them with their peculiar nature. Such an investigation gave ample scope for numerous assemblages of instances ; but the methods of sound knowledge were not likely to be perfected in a region that can be approached only by hypothesis. Under Migratory Instances, keeping still in view the same class of subjects, he recommends attention to cases where qualities are produced in bodies ; giving, as examples the pro- duction of whiteness by pounding glass and by agitating water into froth. From this’ we gather that he was sensible in a measure of the advantage of studying the introduction of a cause into known circumstances, although in his narrow field of investigation it could lead to no result. In these two first instances we see how far he anticipated the Methods of Agreement and of Difference. Few of the other 690 GROWTH OF THE LOGIC OF INDUCTION. twenty-five instances bear strictly on the Inductive Process. With Migratory Instances, he compares Instances of Companion- ship or Ennuty, such as the universal concurrence of heat with flame, and the universal absence of consistency in air; just as when a change is produced, we must seek the cause in some - added influence, so when a quality is always present in a sub-— stance, we must seek the cause in some property of that sub- stance. In Striking or Shining Instances, and Clandestine Instances, he urges the importance of the two extremes in a variable phenomenon. His seventh and eighth Instances, Singular Instances (as the magnet among stones, quicksilver among metals), and Deviating Instances (individual monstro- sities), are important for alike reason ; their novelty sharpens investigation. His twelfth case, Instances of Ultimity or Linut, is of the same nature. The five last go together ; the stimu- lating efficacy ascribed to them is a favourite topic with Bacon, and is the real characteristic of several other Instances. Instances of Alliance or Union and Instances of Divorce, the thirteenth and fourteenth, form a natural couple. The one constitute instances reconciling apparent contradictions; the heat of the Sun cherishes, the heat of Fire destroys; a con- ciliatory instance is found in the growth of grapes in a house heated by fire. The second constitute instances disproving an alleged universal connection; it is asserted that Heat, Brightness, Rarity, Mobility are always found together; we point to air, which is rare and mobile but neither hot nor bright. In exemplifying Instances Conformable or of Analogy, he breaks clean away from Inductive caution; he gives as ana- logous cases the gums of trees and most rock gems, and refers the splendour and clearness of both products to the same cause, fine and delicate filtering. Such fancies show how little Bacon was removed from the rash speculation he condemned in the works of his predecessors. on His fourteenth case, the famous Instantia Orucis (Fingerpost Instance), is mentioned in the Chapter on Hypotheses, § 7, (p. 135), and is there placed in its true light as an instance decisive of rival hypotheses, Such instances are otherwise called Decisive and Judicial or Oracular and Commanding. These are all the instances that have a direct bearing on Induction. Of the remainder, two are of importance for Defi- nition, the fifth and the ninth, Constitutive Instances, and Bordering Instances. Constitutive instances give the constitu- ents of a complex notion; Bordering instances make the baffling transition border between two classes. i - - PREROGATIVE INSTANCES OF BACON. 691 Five instances are classed together as Instances of the Lamp, or of First Information; and relate to Observation, Under Instances of the Door or Gate he comments on artificial aids to the Senses—the Microscope, the Telescope, and measuring rods. By Swmmoning or Hvoking Instances, he means indica- tions of things not directly accessible to observation ; such are the pulse and the urine, as symptoms of the condition of the human body. Instances of the Road, otherwise called Travelling and Articulate Instances, display stages of growth and of other gradual changes :—the study of these is strongly recommended. Supplementary Instances or Instances of Refuge are said to supply us with information when the senses entirely fail us ; when we cannot remove an agent altogether we may vary its influence, and when a phenomenon defies observation we may study analogous phenomena. Dissecting or Awakening Instances are such as great effects produced by small causes; they appeal to our wonder, and stimulate enquiry. The seven concluding instances embody advice on the prac- tical conduct of investigations. The four first of the seven instruct us how to attain precision by definite determination and measurement (Mathematical or Measuring Instances) ; the three last how to economize our resouces (Propitious or Bene- volent Instances). The Mathematical Instances are Jnstances of the Rod or Rule, otherwise called of Range or of Limitation (where measurement of Space is required) ; Instances of the Course (measurement of Time) ; Instances of Quantity, or Doses of Nature (where attention is called to the quantity of an agent); and Jnstances of Strife or Predominance, under which title he gives a confused enumeration of various ‘ Motions,’ or tendencies to motion, and represents the movements of bodies as determined by the victory of one or other of these conflict- ing tendencies—for example, when water runs out of a crack, the motion of Continuity is overcome by the motion of Greater Congregation (the tendency of bodies to the ground). Nothing could be more fanciful and illogical than this enumeration of ‘Motions.’ The Propitious Instances are—Jntimating In- stances, which point out what is most useful to mankind; Polychrest Instances or Instances of General Use, (contrivances useful for a variety of purposes, as various modes of excluding air from bodies to prevent decomposition) ; finally, Instances of Magic, the use of small causes to produce great effects, We have given no account of the tenth division, /nstances of Power, otherwise Instances of the Wit or Hands of Man. It is partly identical with awakening Instances: we have singled 692 GROWTH OF THE LOGIC OF INDUCTION, * it out here as containing a homily against being led away by admiration of skilful contrivances from better ways of accom. plishing the same end. In concluding this brief account of the Baconian method we may reiterate that the merit of Bacon lay neither in the machinery he provided nor in the example he set, but in the grand impulse he gave to the study of facts. . Nuwron. Newton cannot be said, any more than Bacon, to have made a direct contribution to the methods either of Discovery or of Proof; but he set an example of rigorously cautious enquiry that did more than all the precepts of Bacon to raise the standard of Proof, and to purify science of fanciful hypotheses. He even went to an extreme and was over- rigorous in his requirements of proof; such was his dislike to making hypotheses (in the sense of assuming causes not known to exist), that he wished to banish them from science altogether. | The Rules of Philosophizing (Regule Philosophandi) pre- fixed to his Principia were long quoted «as authoritative. Although worded with an express view to the establishment of Gravitation, they are necessarily applicable to other induc- tive generalizations. The Frst rule is twofold, and may be thus explicated. (1) “ Only real causes’’ (vere cause, actually existing causes) “are to be admitted in explanation of phenomena.” We have stated the limits to this under Hypotheses (p. 131), (2) “No more causes are to be admitted than such as suffice to explain ‘the phenomena.” This is an echo of the maxim known as ‘Occam’s razor’ (‘ Entia non sunt multiplicanda preter neces- sitatem’), and means that when one cause is proved to be present in sufficient amount for the effect, we are not at liberty to suppose the presence of other causes. From a few words of explanation affixed to the rule, we should gather that he meant also to suggest that there was a presumption in favour of an explanation accounting for the phenomena by the fewest agencies—a special pleading for his theory of gravita- tion: ‘Nature does nothing in vain, and a thing is done in vain by several agents when it can be done by a smaller number.’ The Second rule is—‘‘ In as far as possible, the same causes. are to be assigned for the same kind of natural effects,”” For example, respiration in man and in beasts; the fall of stones in Kurope and in America. An aspect of the Uniformity of Nature designed to favour his view of Solar attraction as the NEWTON’S RULES OF PHILOSOPHIZING. 693 sume kind of effect with the attraction of the Earth for the Moon or for terrestrial bodies. The Third—“ Qualities of bodies that can neither oe increased nor diminished in intensity, and that obtain in all bodies accessible to experiment, must be considered qualities of all bodies whatsoever.” Another aspect of the Uniformity of Nature, also specially adapted to his extension of Gravity to the heavenly bodies. The Fourth‘ In philosophical experiment, propositions collected from phenomena by induction, are to be held, not- withstanding contrary hypotheses, as either exactly or ap- proximately true, until other phenomena occur whereby they are either rendered more exact or are proved liable to excep- tions.’ This is indirectly aimed at the Cartesian explanation of the celestial movements by Vortices, the word hypothesis being used in an opprobrious sense, as involving an element of fancy operating upon imperfectly known materials. The rule may be held to imply that the test of a theory is its accordance with facts, which is not altogether correct. Herscuer. Sir John Herschel devotes a considerable por- tion of his Discourse on the Study of Natural Philosophy to an account of ‘the principles on which Physical Science relies for its successful prosecution, and the rules by which a syste- matic examination of Nature should be conducted, with illus- trations of their influence as exemplified in the history of its progress.’ His introductory chapters on this head reiterate with greater clearness the admonitions of Bacon; enforcing recourse to experience as the sole fountain of knowledge, illustrating the dangers of prejudice, and urging the import- ance of recording observations with numerical precision. Farther, he dwells upon the value of Classification and Nomenclature ; although he suggests no leading principles for either process. In these preliminary remarks we recognize the sagacity of the practised experimenter; but it is when he comes to analyze what is involved in the notion of Cause, and to state his rules of philosophizing, that we become fully aware of the advance made in the investigation of Nature since Bacon and Newton, and of the advantage possessed by the expounder of scientific method in having a large body of successful observations and experiments to generalize from. From the characters implied in the connexion between cause and effect, he derives nine ‘ propositions readily appli- cable to particular cases, or rules of philosophizing.’ Four of them, the second, seventh, eighth, and ninth, are the four 694. GROWTH OF THE LOGIC OF INDUCTION. Experimental Methods ; which are stated with snfficient pre- cision, although not exalted into the prominence given them by Mr. Mill as the sufficing and only methods of Proof. By Herschel in fact, the four rules are regarded solely as aids to Discovery ; the ‘idea of Proof. does not seem to have crossed his mind. His other rules are more purely suited for Dis- covery. The first is a more precise statement of Bacon’s main principle of Exclusion, the foundation of the methods of Agree- ment and of Difference :—‘ that if in our group of facts there be one in which any assigned peculiarity or attendant circum- stance is wanting or opposite, such peculiarity cannot be the cause we seek.’ The third is ‘we are not to deny the exist- ence of a cause in favour of which we have a unanimous agreement of strong analogies, though it may not be apparent how such a cause can produce the effect, or even though it may be difficult to conceive its existence under the circum- stances of the case ’:—a maxim identical with the principle of analogy, that we may sometimes infer the presence of one phenomenon from the presence of another, although no causal connection has been established between them. As an example he states that though we do not know how heat can produce light, we yet conclude that the sun is intensely hot because it is vividly luminous. The fourth rnle is that ‘contrary or opposing facts are equally instructive for the discovery of causes with favourable ones.’ The fifth recommends the — tabulation of facts ‘in the order of intensity in which some peculiar quality subsists,—perhaps the most valuable art of Discovery. To this precept Herschel very properly appends that the value of the device may be frustrated by the interfer- ence of counteracting or modifying causes. The sixth rule reminds the enquirer ‘ that such counteracting or modifying causes may subsist unperceived,’ and urges attention to them as a means of explaining exceptions. In some general remarks following the enunications of his rules, he illustrates the necessity of combining Deduction with Induction in complicated enquiries, and explains the nature of Empirical Laws, glancing at the fact that they are limited in their application to new cases, without stating more pre- cisely what their limits are. The concluding chapter treats ‘ of the higher degrees of Inductive Generalization, and of the formation and verification of theories.’ He insists that the assumed agents must be vere causm, ‘such as we have good inductive grounds to believe do exist in nature.” The value and the test ofa hypo- Pe alee i g i Bee A, 4.) i Ti a a al lite he WHEWELL’S FACTS AND IDEAS. 695 thesis he places in its accordance with the facts, and its enabling us ‘ to predict facts before trial.’ Wuewett. The scheme of the late Dr. Whewell’s Novum Organum Renovatum commends itself as strikingly thorough and exhaustive. It professes to be ‘a revision and improve- ment of the methods by which Science must rise and grow,’ founded upon a comprehensive History of Scientific Discovery and a History of *cientific Ideas. Now, theoretically, there could be no more perfect way of elaborating a body of maxims for the aid of the discoverer, than to pass in review, chronolo- gically or otherwise, the great physical discoveries that have been made, and to study the essentials of the process in each case. The distinguishing feature of Whewell’s scientific writings is his persistent driving at an antithesis that he conceives to be fundamental, between Ideas or Conceptions and Facts. This antithesis is the shaping principle of his system and meets us at every point. It regulates the division of his history into two parts: the History of Scientific Ideas tracing the gradual development of the so-called ideas, such as Cause Affinity, Life, that form the subject-matter of various depart- ments of science ; and the History of Scientific Discovery, illus- trating how by the instrumentality of Ideas (the highest generalities), and of Conceptions (the lower generalities), the particular facts of Nature are united and bound together. The same antithesis divides scientific method into two pro- cesses. Generalization consisting not in evolving notions from a comparison of facts, but in superinducing upon facts con- ceptions supplied by the mind. There are two requisites to satisfy before this operation can be perfected, namely, that the Conceptions be clear and distinct, and that they be ‘ appro- priate’ to the Facts, capable of being ‘applied to them so as to produce an exact and universal accordance:’ whence there are two scientific processes, the Explication of Conceptions and the Oolligation of Facts. The grand problem of Science is to superinduce Ideas or Conceptions upon Facts. The business of the discoverer after familiarizing himself with facts, is to compare them with con- ception after conception, in the view of finding out aftera tonger or shorter process of trial and rejection, what concep- tion is exactly ‘appropriate’ to the facts under his consider- ation. When the investigator has at length, by a happy gues. hit upon the appropriate conception, he is said to ‘colligate’ the facts, to ‘bind them into a unity.’ No distinction is 696 GROWTH OF THE LOGIC OF INDUCTION. drawn in this operation between the generalization of Notions and the generalization of Propositions ; the difference between | them is merged in the one grand purpose of procuring for facts clear and appropriate conceptions. It is difficult to understand what he supposes to have been the origin of the conceptions thus superinduced upon facts. He speaks of them as being struck out in the gradual march of Science by the discussions and reflections of successive thinkers, a view not inconsistent with their derivation from the comparison of particulars and the gradual evolution of decp and pervading agreements. But he says also that they are supplied by the mind, while facts are supplied by sense; and the language he holds regarding the suiting of facts with their ‘appropriate’ conceptions, is consistent only with the assumption that the mind is a repository of conceptions accu- mulated there independently of the experience of particulars. By this initial severance of generalities from the particulars they repose upon, he excluded from his method definitions formed by the comparison of facts and the precise statement of common features. He rather decries the value of Definition, and allows it no place of hononr in his Lxplication of Conceptions. The meaning of a conception is, he thinks, oftener apprehended from an axiom than a definition—another instance of his total neglect of the distinction between notions and propositions. His ‘methods employed in the formation of Science,’ the title of the third Book of the Novum Organon, are three in number, Methods of Observation, Methods of obtaining clear _ Ideas, and Methods of Induction. As a preliminary to Obser- vation, he recognises an Analysis or Decomposition of Facts. Under Observation, he discusses chiefly the modes of obtaining precise measurement; he speaks also of the education of the senses, but does not attempt to lay down any definite precepts farther than recommending the study of Natural History and the practice of Experimental manipulation. His Methods of ac- quiring clear scientific ideas, are neither more nor less than the study of the various departments of science where the ideas occur ; the very method that would be recommended by a preceptor believing in the evolution of general notions from — particulars. An aid to the acquisition of clear ideas is Discus- sion. We find no trace of the three leading Experimental Methods in his Methods of Induction, nor indeed of any methods of Proof. He conceived that his province was to furnish arts of Discovery, in so far as anything was of avail beyond natural mw a et eee ee le Le i sla WHEWELL’S METHODS OF INDUCTION, 697. sagacity; and he seems to have thought slightingly of the efficacy of the Three Methods as a means to the attainment of new laws. His principal arts of Discovery are given under the title of ‘Special Methods of Induction applicable to Quan- tity.” The Method of Curves isa device for making apparent to the eye the result of observations on the concomitant varia- tion of two phenomena. It ‘consists in drawing a curve of which the observed quantities are the Ordinutes, the quantity on which the change of these quantities depends being the Abeissa,’ The Method of Means is the familiar device of eliminating the effects of a constant cause from the conjoined effects of accidental accompaniments by striking an average of several observations. The Method of Least Squares is a some- what complicated supplement to the Method of Means. When more than one mean is proposed, they are each compared with the series of actual observations; the deviations from each case in the series are squared, and the mean is affirmed to be most probable, the sum of whose squares is lowest in amount. The Method of Residues is the method we described under that name. Under the title of ‘Methods of Induction depending on Resemblance,’ he illustrates the Law of Continuity (‘that a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate magnitudes according to the intermediate conditions’); the Method of Gradation, a name given to the process of proving that things differ not in kind but in degree); and, in the Method of Natural Classification, enforces the importance of. grouping objects according to their most important resem- blances. Perhaps the most valuable part of the Organon is the con- eluding Book on the Language of Science. Of this subject Whewell had made a special study ; his aphorisms on the requisites of philosophical language contain nearly all the important points. H.—ART OF DISCOVERY. It was the distinction of Mr. Mill’s handling of Logic to draw a clear and broad line between the Art and Science of Proof and the Art of Discovery. The main business of Logic, according to him, is the proving of propositions; only in an incidental way does it aid in suggesting them. There is, in the laws of evidence well understood, a power- ful indirect incitement to original discovery. A thorough 698 ART OF DISCOVERY. means of testing whatever is propounded for acceptance leads to the rejection of the false, and, consequently to a renewed search, ending at last in the true. For this reason alone — would discovery be more rapid in the Mathematical and Physical sciences, where verification is easy, than in the Mental, Moral, and Political sciences, where the facts are wanting in the requisite precision. Kepler was not left in any doubts as to whether he had arrived at the true law of the periodic times of the planets; psychologists could not so easily satisfy themselves as to the thorough-going concomitance of mind and body. The Arts and methods of Discovery embrace (1) the Facts, that is, Observation ; and (2) the Reasonings on Facts, namely, Deduction, Induction, and Definition; which are all compre- hended in the one process, generalization. As regards the accumulation of Facts, there is little to be said, and that little is apparent at a glance. Facts are ob- tained by active search, enquiry, adventure, exploration. For some, we must travel far, and visit many countries ; for others we have to lie in wait till occasions arise. For a third class, we have to institute experiments, involving contrivance and devices, and the creative ingenuity of the practical mind ; all which is itself a department of discovery, the least of any amenable to rules. The arts of Observing were remarked on, in the Introduc- tion, as being special for each department, and not a fit sub- ject for general logic. The precautions common to all kinds of observation, in regard to accuracy and evidence, would be worthy of being recited, provided there could be given a sufli- ciency of illustrative instances to make the desired impression. From the limitation of the human faculties, the highest powers of observation are not usually accompanied with high speculative force. Hence, among other consequences, a not unusual misdirection of the energies of great observers. . Passing from the region of fact, we come to the region of Generality. A number of individual observations being sup- posed, the next thing is to discover agreements among them— to strike out identities wherever there are points to be identi- fied; these identities ending either in Notions or in General Principles. It may seem a work of vast labour to exhaust all the facts of the material and of the mental world; it is nota less labour, although of a different kind, to exhaust all the identities among the facts. Although the main condition of success, in bringing about : : ad :=—s) ai i ee a ee et ee B= PSYCHOLOGICAL AIDS TO DISCOVERY. 699 identities, is a peculiar intellectual aptitude, belonging to some men in a pre-eminent degree; yet there are aids, methods, and precautions, for increasing the power. Some of these aids are suggested by intellectual psychology, others grow out of the methods unfolded in logic. The methods growing out of the psychology of the intellec- tual powers are briefly these :—to possess the mind of a large store of the related facts; often to refresh the recollection of them ; to come into frequent contact with subjects that seem likely to afford comparisons and analogies; not to stand too near any one set of facts so as to be overpowered by their specialities ; not to be engrossed with the work of observing the facts ; and in general, as to matters of great difficulty, to keep the mind free from attitudes and pursuits antagonistic to the end in view. Newton alternately devoted himself to mathematics and to the observation and collection of facts in the various subjects of natural philosophy; and this alternation doubtless makes the perfect physical enquirer. Frequently an identification has to be embedded in some conception apart from the facts ; as Kepler’s laws in numerical and geometrical statements, the law of sines, &c. In such cases, proximity to the sources of the conceptions will help to bring about the coalition. If mathematical relations, the mathematical knowledge should be kept fresh, and so with other subjects. These constructing instances alone give any meaning to Wheweil’s much iterated antithesis of Fact and Idea. The identification and generalization of facts often happens without any ‘idea,’ any central form, or representa- tive beyond the facts themselves; there is no idea for a circle but round things, abstractedly viewed ; and no idea for gravity, but gravitating bodies compared and regarded in their points of agreement. In certain other cases, a conception is obtained (not from any intuitive source, but) from some already existing generalization, either in the same department, or in another department. The ‘idea’ for embracing water waves, and sound vibrations, was found by Newton in the ‘ Pendulum;’ and apart from the facts themselves, no better ‘idea’ has yet been given. The connexion of Body and Mind has its ‘idea’ yet to seek. There has hitherto prevailed the bad idea of External and In- ternal. Inshort, the most suitable comparison wherein to em- brace therelation has not been obtained from any source, intuitive or other. One approximation is a ‘ union of distinct states.’ 700. ART OF DISCOVERY. The arriving at difficult identifications, that is, the tracing of similarities shrouded in diversity, by such devices as have been advanced in logic with a more special eye to proof, may be viewed in the first place with regard to generalizution as such; not distinguishing the notion from the principle or proposition: What pertains specially to the induction of the general proposition, namely, the conconwtance of distinct pro- perties, is best considered apart. _ Under the Deductive Method (p. 96) attention was called to three helps to the discovery of generalities—multiplication . of instances, close individual scrutiny of instances, and selec- tion of the least complicated instances. A wider view of the available resources must now be taken. We have to see how far the thorough explication of the reasoning processes, and of all the adjuncts to reasoning, called forth by the comprehen- sive Logic of Proof, can be brought to bear also in the striking out of suggestions to be submitted to proof or disproof. The first great practical lesson derivable from Logic, and applicable in a much wider sphere than proof, is to impress us with Generality as the central fact of science and of all know- ledge transcending individuals. After we have gained posses- sion of a certain range of facts, the next great aim is to generalize them to the uttermost. This is not all. In pro- portion to the compass of any agreement, ought to be the pains taken with it, and the prominence given to it. We have urged, under the Logic of Medicine, the prime import- ance of generalizing the Diseased Processes and General Thera- peutics, because of the wider compass of their application. In everything else, the rule holds. The biologist should take no rest until he has exhaustively accumulated instances of the great fact of Assimilation, under every possible variation of circumstances’. In like manner, the physical concomitants of mental processes need to be searched out in all their innumer- able modes, in order to rise to the generalities of the connexion. The severest etiquette of the most punctilious system of ranks and dignities in society is as nothing compared with the graduation of estimate and of respect to be shown to generali- ties of different grades. It is a grave logical misdemeanour ever to give an inferior generality precedence over a superior, or to treat the two as of equal consequence, or even for a moment to be unaware of their relative standing. We may give all due consideration to the phenomenon of falling bodies as a wide fact co-extensive with the surface of the earth; but — in presence of the superior sway of the law of gravity through- VALUE OF ORDER AND METHOD. TO1 out the solar system, the terrestrial fact must sink into a second place in our esteem. The next great application of Method, as an aid to discovery, consists in the use of the various Forms or Formalities, ela- borated with a view to proof. This is the largest part of the present subject. « Logicians have always striven to set forth the value of Order, method, and explicitness, in complicated statements. Hamil- ton’s dictum—making explicit in the statement what is implicit in the thought—has been received as a happy enunciation of one function of logic. Mr. Mill remarks,—‘ One of the great uses of a discipline in Formal Lggic, is to make us aware when something that claims to be a single proposition, really con- sists of several, which, not being necessarily involved one in another, require to be separated, and to be considered each by itself, before we admit the compound assertion.’ This is the disentangling or analyzing function of the syllogism, and is deservedly extolled as perhaps its highest utility. It is a direct remedy for the weakness of the mind formerly adverted to (p.398). We may, however, go farther back than the exposition of - Syllogism for valuable aids growing out of the logical formali- ties. All the Equivalent Propositional Forms are instrumental as means of suggestion. They enlarge the compass of any given proposition, by unfolding all its implications; many of these not being disposed to rise to view of themselves, or without the stimulus of the formal enunciation. Of all the modes of Hquivalence, probably the Obverse is the most fruit- ful and suggestive ; this has become apparent on many occa- sions, in the course of the present work; we may instance especially negative defining. Next in value is Conversion ; the converting of A by its legitimate form is.a check to the blunder of supposing the subject and predicate co-extensive in uni- versal affirmations ; and the arresting of the mind on the road to impending error seldom ends there, but is also a start in the search for truth. Even the immediate inference from the Universal to the Particular is suggestive of facts not previously in the view. Much could be said as to the unsystematic but wide-ranging mode of Equivalence by Synomyous terms, or by varying the ways of expressing the same proposition. Although some- what ensnaring, this is a fruitful and suggestive operation. Its power consists in resuscitating from the stores of the past all the various known examples of the proposition ; to which 702 ART OF DISCOVERY, also may be added even illustrations and analogies. We know from many celebrated instances, how mere opulence of phrase- ology gives the semblance, and occasionally the reality, of superior insight. The Shakespearian wisdom, the stirring apothegms of Pope, have their source, not in the scientific process of the intellect, but in the suggestiveness of exuberant phraseology. The Methods of Inpuctive Elimination, both directly and indirectly assist in Discovery. The collection and comparison of instances, to comply with the method of Agreement as a method of proof, will in many cases lead to new and improved » generalizations. A man can scarcely go through the labour requisite for establishing a law of high generality upon ade- quate evidence, without adding to his knowledge of the law. Hspecially is this likely to happen in working the Method of Agreement, whose exigencies are exactly those of inductive discovery. The same remark applies to the union of Agreement in Absence with Agreement in Presence ; and there is the addi- tional force and incisiveness that always belongs to the working of the negative side. The method of Residues, to which Sir John Herschel called special attention, was by him expressly commended as an aid to Discovery. The importance of Concomitant Variations has already been signalized, and will be again referred to. Without dwelling farther on the specific virtues of the ‘several methods, we would call attention to the value of a complete scheme of Inductive Proof, in urging a search for instances to fill up all its requirements. He that has thoroughly mastered the experimental methods, desires to bring up in favour of every important principle a series of particulars under each one of them separately ; an operation as fertile for discovery as it is thorough-going for proof or disproof. The remark is not confined to the methods of experimental elimination. The greater number of propositions or laws may derive evidence through the Deductive Method, and through Chance and Probability also. The wish to satisfy all possible methods of establishing a law is a wholesome stimulus to enquire after the very facts that improve the character and extend the application of the law. The consilience of Indac- tion and Deduction is the very highest art that the human intellect can command, not merely for proving difficult propo- sitions, but for getting hold of propositions to be proved. INDUCTIVE ELIMINATION, 703 All this is to repeat in another shape, and in a grander sphere, the function of the Syllogism in insisting that there should be produced an explicit major and an explicit minor premise in any pretended ratiocination. Every inductive in- stance should be viewed in its proper character, by reference to the method that it subserves. An instance of Agreement should be given as such; a Deductive proof should be quoted under that description. If the Logical rules are not arbitrary, but founded on a correct analysis of the scientific processes, the conscious reference to them, on all different occasions, must be a relief and a comfort to the perplexed enquirer. _ The Deductive operation, understood not formally as in the syllogism, but really and materially, as in finding new appli- cations and extensions of inductions, is a pure generalizing process. It consists in identifying particulars with other par- ticulars, exactly as in the properly inductive operation. It is the same march of mind continued and prolonged. An induc- tion so called is merely a certain collection of particulars, with a generalized expression superadded ; deduction is the bring- ing in of new particulars. The difference of the two is not in the mental operation; it is in the end thatis served. The inductive particulars are those necessary for giving the gen- eralized expression, and for proving it as a law of nature ; the subsequent deduced particulars, not being required for esta- blishing the generality, receive illumination from the other class. In both cases the effort of discovery is identical ; it is the bringing together in the mind by the force of resemblance a host of particular facts from all times, places, and subjects. Before the induction is gained, the particulars contribute to its establishment; after it is gained, the new particulars are receivers and not givers of benefit. The processes included under Derinitron—the canons for Defining, General Naming, and Classification—are processes of Discovery directly, and of Proof indirectly. Mr. Mill calls them subsidiary to Induction, meaning Inductive Proof. Every step indicated under those several heads has an imme- diate efficacy either in suggesting generalities, or in purifying them from ambiguity, perplexity, and confusion. It is impos- sible to make a single well concerted move in any of the paths marked out in these several departments without gaining an enlargement of views, or the means of some future enlarge- ment. Everything of the nature of an antidote to inadvertent and confused tainking, everything that reduces information to the TO4 ART OF DISCOVERY. shape best suited for recollection and reference, everything that facilitates the comparison of resembling facts—must be enrolled among the means of Discovery. These various ends are explicitly aimed at by the prescriptions contained under Definition, Naming, and Classification. To substantiate the allegation would be to rehearse the methods explained under those heads. The amassing of particulars, positive and negative, with a view to Definition, is the express act of gen- eralization, and brings with it discoveries of concomitance, as well as generalizes notions. All the devices of Naming are intended primarily to ease and assist the understanding in arriving at new truths. The machinery of Classification is stall more strikingly the economizing of the faculties in amassing and in manipulating knowledge. | When the generalizing process has expressly in view the discovery of laws, or concurring properties, a most material help (as formerly seen) is afforded by Tabulation, espe- cially according to a scale of degree. Failing this, great stress is always laid upon extreme instances. These are the glaring and striking instances of Bacon and Herschel (see the Re- search on Dew, p. 68). The method of exhibiting gradation by Curves is considered one of the best ways of suggesting numerical laws. Mr. Darwin has given an account of the steps that Jed him to propound the doctrine of Development under Natural Selection. It affords an interesting commentary on the fore- going enumeration of the causes that prompt original sugges- _ tions. ‘When I visited, during the voyage of H.M.S. Beagle, the Galapagos Archipelago, situated in the Pacific Ocean about 500 miles from the shore of South America, I.found myself surrounded by peculiar species of birds, reptiles, and plants, existing nowhere else in the world. Yet they nearly all bore an American stamp. In the song of the mocking-thrush, in the harsh cry of the carrion-hawk, in the great candlestick- like opuntias, I clearly perceived the neighbourhood of America, though the islands were separated by so many miles of ocean from the mainland, and differed from it in their geological constitution and climate. Still more surprising was the fact that most of the inhabitants of each separate island in this small archipelago were specifically different, though most closely related to each other. ‘The archipelago, with its imnu- merable craters and bare streams of lava, appeared to be of recent origin ; and thus I fancied myself brought near to the ate ie a Saal oe Ne he akg 8b A i iy CONSTRUCTIVE INVENTION, 705 very act of creation. I often asked myself how these many peculiar animals and plants have been produced: the simplest answer seemed to be that the inhabitants of the several islands had deseended from each other, undergoing modification in the course of their descent; and that all the inhabitants of the archipelago had descended from those of the nearest land, namely America, whence colonists would naturally have been derived. But it long remained to me an inexplicable problem how the necessary degree of modification could have been effected, and it would have thus remained for ever, had I not studied domestic productions, and thus acquired a just idea of the power of Selection. As soon asI had fully realized this idea, 1 saw, on reading Malthus on Population, that Natural Selection was the inevitable result of the rapid increase of all organic beings; for I was prepared to appreciate the struggle for existence by having long studied the habits of animals. ’ (Domestication, vol. I., p. 9). Throughout the entire logical scheme, the analytic separation already insisted on, is an invaluable help to the faculties under the complications of natural phenomena. Toenable us to view separately whatever can be separately viewed is the motive for such artificial divisions as Structure and Function in biology, Physical Side and Mental Side in psychology, Order and Progress, Theory and Practice in politics, Conservation and Collocations in cause and effect, Description and Explana- tion every where. The process of Invention in the Arts and business of life, is amenable to the general rule of keeping the mind fresh upon the most likely sources. The mere cogitating process in prac- tical constructions is exactly the same as in the solving of geometrical gp other problems. Certain data are given, a certain construction is required ; there is an intervening chasm that has to be bridged. The habit of analytical separation is of avail in this instance also. The mind should steadily view one poiut at a time, drawing out connexions with each by turns. Thus, to t..ke a simple geometrical construction : given the vertical angle, the base, and the altitude of a triangle to construct it. Now the base is given, and we have to follow out the deductions and implications of the two other data— altitude and vertical angle—with a view to arrive at some known process that will construct the triangle. Let us con- sider separately what the altitude will suggest. Now, a certain fixed altitude implies that the apex of the triangle will lie somewhere in a line parallel to the base; consequently, if 706 ART OF DISCOVERY. we draw such a parallel, we limit the place of the apex to that line. Turn next to the given angle. Considering how to erect upon a given base a triangle with a given vertical angle, we are reminded that upon the given base may be constructed an arc of a circle, such as will contain that angle. The next step is to find a means of constructing the proper arc; the operation of discovery is exactly the same; and brings us at length to some construction that we can perform. We then unite our two threads hitherto followed out in separation. The parallel line first suggested, and the arc next found out, give by their intersection an apex to the desired triangle. It is our previous knowledge that must forge the links of con- nexion between what is given and what is required; but the analytic habit concentrates the attention by turns on each datum, and each outgoing from it; and this is probably the utmost that mere art or method can do for us in constructive inventions. . The uncertainty as to where to look, for the next opening in discovery, brings the pain of conflict and the debility of indecision. This is a case fit to be met by the collective wisdom of a generation. There might at intervals be held a congress on the condition-of-science question, to decide, accord- ing to all the appearances, what problems should be next taken up. Lessons may be drawn from the history of Hrrors, as well as of Truths. All the Fallacies are beacons both in discovery and in proof. Every source of confusion is an incubus on in- - vention. More particularly, the excessive devotion to the con- crete, and to the artistic interests nourished by it, may amount to a total disqualification for scientific originality, whose very existence is in the domain of abstraction. Certain widely prevailing tendencies of natural phenomena have been indicated as of value in prompting discovery. Such are the Law of Continuity, and the maxim that Nature works by the Simplest Means. Both these principles are uncertain in their scope ; which, however, does not prevent them from being used to give suggestions ; it only disqualifies them from being conclusive evidence. If we are careful to verify our hypotheses, we are at liberty to obtain them from any source. Still, the mind that has become largely conversant with the ways of nature will find many more fruitful sources of suggese tion than either of those principles. - RECITAL OF FACTS, [07 I.— HISTORICAL EVIDENCE. Two leading branches of Evidence, applied in practical life, are Legal Hyidence and Historical Evidence. The two depart- ments have much in common. The evidence both in courts of law and in matters of history is probable, and approaches to certainty by the summation of probabilities. The following abstract of Historical Evidence represents the maxims in use among historians at the present day, as summarized by Sir G. C. Lewis. _ The object of History is the recital of facts—of events that have actually occurred. In the case of contemporary history, the writer may be able _to rely upon his own observations, or upon original documents obtained from authentic sources. Personal knowledge was the basis of much of Xenophon’s Anabasis, Polybius’ History, Cexsar’s Gaelic War, and Lord Clarendon’s History of the Rebellion. But the greater part even of contemporary history must repose on the evidence of witnesses. To a historian, not himself cognizant of the events he nar- rates, the sources of information fall under one or other of two classes :—(1) Monuments, ruins, coins, and generally all ancient remains; and (2) the evidence of Witnesses. From the former exclusively is derived whatever we know of the pre-historic age; in the same way as geology is built on in- ferences drawn from fossils and the nature and position of rocks. It is only with regard to history resting upon the tes- timony of witnesses that rules of historical evidence apply. Two points demand the notice of one seeking to verify any alleged historical fact. (1) Does the evidence of the witness exist in an authentic shape? and (2) Is it true? The first regards the accuracy wherewith the evidence has been trans- mitted to us; the second, the worth of the evidence itself. The means of knowledge of the witnesses, the goodness of their memory, their judgment, their general veracity, their special interests,—are all to be considered. This the historian has in common with a jury or a judge, except that he has to deal with men long since dead, and whose character there is more or less difficulty in ascertaining. What forms the pecu- liar subject-matter of rules of historical evidence is not there- - fore the worth of the evidence, but the accuracy of its trans- mission. | The supreme canon of historical evidence is that all testi- 708 HISTORICAL EVIDENCE. mony must be contemporary, or received directly or through trustworthy tradition, from contemporar.es. ‘ Whenever any event is related in histories written after the time, and not avowedly founded on contemporary testimony, the proper mode of testing its historical credibility is to enquire whether it can be traced up to a contemporary source. If this cannot be done, we must be able to raise a presumption that those who transmitted it to us in writing received it, directly or through a trustworthy tradition, from contemporary testi- mony. If neither of these conditions can be fulfilled, the event must be considered as incurably uncertain, and beyond the reach of our actual knowledge.’ (Lewis’s Methods of Politics, I. 270.) This rule is universally recognized as inclusive; whatever is established by such testimony is credible. There is not, however, the same unanimity, in admitting it as exclusive; or that whatever is not authenticated by external evidence is uncer- tain. 7 Sis ‘ ee pares Se! We TRANSMISSION OF WRITTEN EVIDENCE. 709 and fact; from the Secession of the Plebs io the war with Pyrrhus (213 years) is solid history. It would perhaps be too much to condemn Niebuhr’s efforts on a priori grounds. To what extent a license of guessing may be permitted will best be seen when it has been tried by different men. If the result should be a general concordance of opinion, we might reasonably infer that the ancient narratives, although they. conceal, nevertheless betray the truth. If, however, this method lead to irreconcileable and endless diversity of opinion, it must cease to be regarded as valuable or trustworthy. Evidence may be transmitted in two ways, by writing or by oral tradition. These may be considered separately. The value of a written memorial consists generally in this, that its credibility is not impaired by the mere action of time. An English mathematician named Craig held that all testi- mony was enfeebled by mere lapse of time, and thus the evi- dence of Christianity would at length be reduced to zero. Assuming that that event would coincide with the end of the world, he calculated when the end would come. Laplace adopts the same view, and says that even in spite of printing, the events that are now most certain, will, in the course of ages, become doubtful. But this must be regarded as an error. The only deterioration that a document can suffer from mere lapse of time is the increased difficulty of weighing the credi- bility of the writer. A written memorial has none of the disadvantage of a statement handed down orally from one person to another, and losing value at each transmission. Yet the evils of transmission are not wholly overcome even with written records. Two doubts may arise, (1) whether the writing is ascribed to its real author, and (2) whether it is free from interpolation and mutilation. ‘In many cases the original memorial is preserved; as in ancient inscriptions upon stone, brass, or other durable ma- terial. Such are the inscriptions, in the arrow-headed cha- racter, on the Babylonian bricks, and on other Assyrian monuments ; the hieroglyphics engraved on the remains of Egyptian architecture; and the numerous Greek and Latin inscriptions found in different parts of Asia Minor, Africa, and Europe, and belonging to different ages. Ancient coins, with their legends, are another original record of the same kind, as well as historical sculptures or paintings, such as the bas-reliefs on the column of Trajan, or the Bayeux tapestry. Ancient documents, likewise, containing the authentic records of many important events and public acts, are preserved in the original 710 HISTORICAL EVIDENCE. in national archives. Such, for instance, is Domesday-book, the rolls of Parliament, court records, charters, and other official registers and documents kept in public depositories.’ (Lewis, I. 201). In authenticating books and documents, whose safe-keeping is not specially provided for, great difficulty is often expert- _enced. A mere tradition regarding the origin of a document would be exposed to nearly all the doubts that attach to oral tradition. ‘Hence the importance of archives, chartularies, public libraries, and other safe places of deposit, which are under the care of trustworthy guardians, appointed and con- trolled by public authority.’ The law of England requires that written documents, before they can be tendered as evid- ence, be produced from the proper place of custody. The difficulty of ascertaining the genuineness of ancient books, is forcibly illustrated by the controversy regarding the Platonic Dialogues. Until the close of last century, thirty-six dialogues were attributed to Plato on the authority of Thra- syllus, whose list dates from about the commencement of the Christian era. As, however, Plato died more than three hundred years before, the canon of Thrasyllus stands in need of corroboration and support. Most of the German Critics allow it very little weight, and test each dialogue upon own evidence, external or internal, but chiefly internal. This unavoidably gives rise to great diversity of opinion, and there is little agreement as to what ought to be rejected or retained. Ast, the least sparing critic, leaves only fourteen out of thirty- six. Mr. Grote, on the other hand, discards the German criticism, and putting little stress upon the indications of authorship contained in any reputed dialogue of Plato, searches for more decisive evidence, so far as it can be got, in the history of the books mentioned by Thrasyllus. Plato died B.C. 347, and left his works to the care of the schoal continued under Xenophanes and Speusippus. We do not possess any list of their master’s works resting on their autho- rity, and the first solid ground we reach (apart from the few incidentally mentioned or alluded to by Aristotle) is an extract from the works of the Grammaticus Aristophanes, who lived at Alexandria from B.C. 260 to B.C. 184. He comes thus a century after Plato, and nearly two centuries before Thra- syllus. He divided the dialogues into trilogies, and several of these are mentioned by Diogenes Laertius. They are re- markable as containing the names of some of the compositions — that are least acceptable to the critics, and that would be hard EXAMPLE OF PLATO’S DIALOGUES. 711 to vindicate on internal evidence. These are Leges, Epinomis, Minos, Epistolae, Sophistes, Politicus. It would be interest- ing to know what means Aristophanes had of distinguishing the genuine from the spurious works, if any such then existed. For two centuries after the death of Plato, the Academy was kept up as a philosophical school, with an unbroken suc- cession of presidents. The chief treasure of the school was . the works of the master. It cannot be too much to assume that there was provided a safe custody for the MSS. of Plato, and a ready means of verifying any alleged works. Plato is better off in this respect than any of his great contemporaries, . Socrates, Demosthenes, Euripides, or Aristophanes. Aristophanes, the Grammaticus, was head of the Alexan- drian Library. He was taught by Callimachus, who preceded him in the office of Chief Librarian. Callimachus is the author of the ‘Museum,’ a general description of the Alexandrian Library ; and less important authors than Plato, as e.g. Demo- critus, are mentioned by him. It is then highly probable that such a library as that of Alexandria would contain copies of oue of the foremost Greek philosophers. And, considering the ease of verification, it is most likely that the Librarian would assure himself that his copies were authentic. There were, in the time of Thrasyllus, spurious dialogues. . Whence came these, and by what criterion did he discard them? If Aristophanes and Thrasyllus (who appears also to have been connected with Alexandria) depended upon the lib- rary there, they must be allowed to speak with great weight ; but if'they proceeded wholly or partially upon internal evidence, they have less claims on our attention than the better-equipped modern critics. Mr. Grote supposes that the spurious works were made for the demand in Greece and Asia Minor, and for the library started by the Kings of Pergamus as a rival to the Alexandrian. So much for the difficulty of settling the real authorship. The other point to be determined is the freedom of existing copies from spurious additions or omissions, accidental or intentional. In the first place, errors will accidentally creep in, by the mere act of copying. It is impossible to guarantee strict accuracy in transcription. This is recognised in jurisprudence, and the English law refuses to admit any copy where the original can be produced. But the reason of the law does not apply with the same force in history. A very slight alteration in a deed might sometimes alter the meaning of it; and, more- 3] 712 HISTORICAL EVIDENCE. over, there is often an exceedingly powerful temptation to tamper with deeds. Now, the value of a copy of MS. depends on its accuracy, and the motives for falsifying history are far weaker. It is therefore considered that the works of classical authors are preserved to us substantially as they were when published. Such variations as there are do not affect the general accuracy of the copies that have reached us. _ In the second place, changes may be made intentionally, to suit a purpose. We are told that Solon inserted a verse in the Iliad with a view to confirm the title of the Athenians to the possession of Salamis. At an early period, authentic lists or canons of authors and their works were prepared to guard against deception. Short writings are most easily forged, and hence there are numberless forgeries of letters; but we find examples of falsification at greater length in the poems of Ossian. Ecclesiastical writings contain many forgeries, made for the purpose of propagating or confirming opinion. The motive for executing forgeries is often to make money by arousing curiosity ; but in such cases as Ossian, it is merely the pleasure of deceiving the world. Literary forgeries. are generally detected by internal evidence—by inconsistencies, anachron- isms, imitations of subsequent writers, and other, maria of recent composition. When we have sufficient assurance that a work is both authentic and genuine, written by its reputed author, and not tampered with in the course of transmission, we have still to consider the worth of the testimony. Besides examining our - author’s means of information—whether he writes as an eye- witness or at second hand, or at what other remove from eye- witnesses—we must enquire into his character for versaiigiend his motives to depart from the truth. sine There is often intentional perversion or enppression of the truth, especially in Autobiography, as Ceesar’s Gallic Wars, and Napoleon’s Memoirs of his Campaigns. Vanity, a love of the marvellous, and party spirit, operate in the same direction. There are Catholic and Protestant histories of the Reforma- tion; Whig and Tory histories of England. The accounts of modern campaigns and military operations differ very much according to the side the writer belongs to. Many inaccuracies arise from not taking the trouble to investigate the truth. History may be blended with fiction for a didactic or moral purpose, as in Xenophon’s Cyropeedia. The ancient historians departed from strict truth, by intone, ducing into their works speeches composed by themselves. it ia ie re. a MYTHICAL HISTORY. 713 One fourth of the history of Thucydides is composed of such speeches. Lucian thought it a sufficient excuse for introduc- ing fictitious speeches, that they were suitable to the charac- ter of the speaker, and appropriate to the subject. Polybius is the only writer of antiquity who condemns the practice, for, he says, the object of the historian is not to astonish the reader, but to record what was actually done or said.. This opinion has been followed by modern historians, and the manufacture of speeches has therefore ceased. The same thing, however, in substance, is still done, although introduced as part of the history, namely, interpreting acts and suggesting motives. It is a great, though perhaps not uncommon, error, to treat as history what thus owes its origin to conjecture. Another perversion of history is mythical history. ‘The original author of such a legend must, no doubt, be at first conscious that it is the spontaneous product of his own inven- tion, unattested by any external evidence. But the fiction is suggested by prevailing ideas and feelings; it interweaves existing facts and customs into its texture; it furnishes an apparent support to institutions or practices for which the ular mind seeks an explanation; it fills a void which is sensibly felt, and supplies food for an appetite whose demands are at once urgent and general. The inventor of such a legend, therefore, differs altogether from the author of a novel or romance, who lays before the public a tale avowedly fictitious, and which they accept as such.’ Hxamples may be found in Greek mythology, in the fabulous heroes of medieval chivalry, and in the lives of medieval saints. Such legends havea use, not as describing events, but as throwing a reflected light on the circumstances and character of those who invented, believed,and circulated them. The most difficult case to the historian is not pure mythology, but the blending of myth and history, which lures men on to search for fact, but leaves them un- able to distinguish it from fiction. The history of Greece, from the first Olympiad to the Persian war, and of Rome, from Tullus Hostilius tothe Punic wars, illustrates this inter- mediate period of twilight and uncertainty. The second mode of transmitting evidence— Ora TRADITION, loses credit very rapidly with the lapse of time. An account of an event, diminishing in evidentiary value at each remove from the original eye-witness, very soon ceases to have any value at all, This has always been more or less recognized. Polybius confined himself to what he learned from eye- witnesses of the preceding generation, and thus begins his 714 HISTORICAL &VIDENCE, consecutive history about twenty years before his birth. Newton thought that oral tradition might be trusted for 80 or 100 years; and Volney remarks that the Red Indians had no accurate tradition of facts a century old, . The average value of oral tradition may be enhanced in various ways. During the panic caused by the mutilation of the Mercuries, and the fear of treasonable attempts to esta- blish a despotism, the Athenians recurred to the government of Pisistratus and his sons, which had begun nearly 150 years and ended 100 years before that time. Thucydides describes the Athenians as referring, entirely by oral tradition, to the attempt by Cylon—a fact at the time 180 years old. That event had however created a hereditary curse in the powerful family of the Aicmaeonidae, and the memory of it was revived at different times by public acts. The Dies Alliensis, the anniversary of the fatal battle of the Allia, was doubtless kept up by uninterrupted usage from B.C. 390. Festivals, emblems, antiquated offices, serve to fix tradition, and keep alive the recollection of events. The Interrex, in Rome, who continued to be appointed during the Republic in the vacancy of the consul- ship, was a reminiscence of a period of elective kings. The King of the Sacrifices, like the King Archon at Athens, is also a decided indication of the regal period. There were, more- over, many buildings, monuments, and public places in Rome associated with the names of kings. The existence of laws, like the Twelve Tables, inscribed on metal or stone, may serve to perpetuate a correct oral tradition. Rubino, the author of a work on the early Roman Constitu- tion, has laid down some rules on this subject. He divides oral tradition into two classes, one referring to the constitution, and the religious and civil institutions connected with it, the other embracing the more common material of history, wars, negotiations, and the striking events that give interest to the history of Rome. This last alone was committed to the ex- clusive keeping of oral tradition, and was much more liable to error and uncertainty than the traditions relating to the constitution. ‘T'o some extent, constitutional usage implies a knowledge of precedents. Such information in all probability existed at the beginning of the Second Punic war; but it might not reach far back without the help of documents, There is no reason to suppose that accurate knowledge would have gone back beyonda century. It is not possible to draw any broad line between constitutional history, and the common events of history ; we could not discuss the changes in the ARGUMENT.-—CATEGOREMATIC.—DICTUM. 715 English Constitution during the seventeenth century, without a knowledge of the events that gave birth to them. There is one case where oral transmission makes an approach to the value of transmission by writing. This happeus when the memory is assisted and checked by a set form of words, especially if the form be metrical. Czsar tells us that the secrets of the Druidical religion were contained in a great number of verses, in committing which to memory a druid would spend twenty years of his life. In like manner, the Iliad and Odyssey were perpetuated by a race of professional reciters and rhapsodists. K.—EXPLANATION OF SOME LOGICAL TERMS. The following terms, not being deemed essential to any of the important doctrines of Logic, may not have been made fully understood in the previous exposition. As they occasion- ally occur in logical discussions, short explanations of them are here appended. ARGUMENT is used in severa! different senses. Apart from its more popular significations, a disputation, a chain of rea- soning, and even a chain of events (the argument of a play), its meaning is not fixed and uniform among logicians. Some apply it to an entire syllogism, premises and conclusion, some to the premises only as the grounds of the conclusion, while Hamilton maintains that its proper meaning is the middle notion in a reasoning,—‘ what is assumed to argue something.’ So Mansel holds that the word should be applied only to the Middle Term. CaTeGcoREMatic.—A distinction is drawn between words that can stand alone as subject or predicate of a proposition, as man, stone (Categorematic) ; and words that can stand only in company with other words, as all, none (Syncategorematic), DictoM DE OMNI ET NULLO.—This applies directly to the First Figure alone. It is usual to give similar principles for the other Figures, and among these we may notice the dicta given by Mr. Mansel in his notes on Aldrich (p. 86). ‘Principle of second figure. Dictum de Diverso. If a cer- tain attribute can be predicated (aflirmatively or negatively) of every member of a class, any subject of which it cannot be so predicated, does not belong to the class, * Principles of third figure. I. Dictum de exemplo. Ifa certain attribute can be affirmed of any portion of the members 716 EXPLANATION ON SOME LOGICAL TERMS, of a class, it is not incompatible with the distinctive attributes of that class. Il. Dictum de excepto. If a certain attribute can be denied of any portion of the members of a class, it is not inseparable from the distinctive attributes of that class.’ EnrHyMEME.—A syllogism with one of its premises sup- pressed in the enunciation. Hamilton argues against the prominence given to Enthymeme as a division of syllogisms, on the ground that they are not a special form of reasoning, but only an elliptical mode of expression. He also shows (what is done more elaborately by Mr. Mansel) that Aristotle understood by Enthymeme not an elliptical syllogism, but ‘a syllogism from signs and likelihoods,’ or a syllogism with the major premise only probable. Tanava Ratio or Sophisma pigrum is the master fallacy of Fatalism. It might be classed with fallacies of Non-observa- tion. The Fatalist argues that, if a thing must happen, it will happen whether he interfere or no; overlooking oe his own agency is one of the co-operating causes. InruitIve—SyMBOLICcAL.— We often employ words itd sym- bols without fully realizing their meaning. This Leibnitz called Symbolical as distinguished from Intuitive, Knowledge, ideas and sensations fully realized in consciousness. We can conceive a yard, a mile, or even ten or twenty miles, in the full reality of the extent; but of the distance between the earth and the moon, the sun, or one of the fixed stars, we have no proper conception; we may, however, express such dis- _ tances in figures, which are intelligible as such. This would be a symbolical conception. | | Mopvats.—(See Part I, p. 99). The opposition of Pro- positions has been applied to Modals, in the following state- ments, If the matter be necessary, all affirmatives must be true, and all negatives false, If the matter be impossible, all negatives must be true, and all affirmatives must be false. If the matter be contingent, all particulars must be true, and all wniversals false, Here the meaning of ‘ necessary’ is no more than univer- sally true, as all men are mortal, all matter gravitates. ‘* Im- possible ° is universally false ; all men are gods. ‘ Contin- gent’ means partly true and partly false; Some men are wise. Porpuyry’s TreE.—This is a tabular arrangement showing different grades of generality. The example chosen ranges from the summum genus Substance, to the infima species Man, PROPHYRY’S TREE. 717 ending with two individuals. It may be exhibited thus, in a form better described by the Greek name, Porphyry’s Ladder (jue) — ie | Substance Corporeal Incorporea] (Body) Animate Inanimate (Living Body) Sensitive Insensitive (Animal) Rational Irrational (Man) Socrates Plato PREDESIGNATE is a term applied by Hamilton to propositions, laying their quantity expressed by one of the signs of quan- tity, Ail, None, &. The contrasting term is Preindesignate. The terms commonly used in logic are Definite, Indefinite. SmpLe APPREHENSION is defined by Whately as ‘ the opera- tion of the mind by which we mentally perceive or forma notion of any object.’ It is the same as Perception, whereby we know things in the actual or concrete—a house, a tree. By another faculty, designated Abstraction, we conceive things in the general. Surricient Reason.—Under this title Leibnitz stated the law of Causality. Everything that exists must have a ‘ suffi- cient reason ’ for its existence. The attempt has been made to prove certain truths, such as the law of perseverance of uni- form motion in a straight line, on the ground that no suffi- cient reason can be given why a body should either lose its velocity or deviate to one side or the other. The same line of remark has been used with the principle of virtual velocities. Sopuisma PoLyzerescos and SopuisMA HEev1eROZETESEOS are two ingenious Greek Sophisms. ‘The first was alluded to under Definition. Choosing a word having a doubtful margin of application, the sophist asks whether it applies to such and such a case, and goes on putting the question to one contiguous case after another, until he has drawn the respondent palpably _ beyond the range of the word, when he demands the difference between the last case admitted and the first refused. Such words as heap, calf, &c., are suitable: the sophist asks—Was it a calf to-day, will it be a calf to-morrow, next day, and so on ; the respondent cannot say on what day it ceases to be a calf, and becomes a heifer. The Heterozeteseos (Soplism of 718 EXPLANATION ON SOME LOGICAL TERMS, Irrelevant Question) decoys a person into committing himself by a categorical answer—‘ Have you cast your horns ?—If you answer, I have; it is rejoined, Then you have had l.orns: if you answer, I have not, it is rejoined, Then you have them stall.’ he Niel) Bp Xt ApstRAcTIoN, allied to Analysis, 683. Abstract Ideas, dispute regarding, 5. Abstract name, completion of gener- . alizing process, 52. value and abuse of, 53. Accidens, 76. Accidentis, fallacia, 674. Activity, a source of fallacies, 607. Adjectives, connotative, being gener- alized names, 49. Aiquivocatio, 673. A dicto secundum quid ad dictum simpliciter, 602, 624, 675. Assthetic emotions, a source of fal- lacy, 6138. A dicto simpliciter ad dictum secun- dum quid, 674. Affinity, chemical, defined, 473. maximum of, 417. in Mineralogy, 524. in Botany, 532. in Zoology, 540. in diseases, 596. A fortiori, 164. Agreement, intellectual property of, 3 the basis of Reasoning, 8. basis of Definition, 385. defines the limits of Explanation, 351. stated in classification, 422. in the arrangement of chemical elements, 476. statement of, in Mineralogy, 529. in Botany, 535. in Zoology, 548. in diseases, 596. Method of, 279. fundamental maxim of, 278. in Biology, 500. Agreement, Method of, in Politics, 565. in Medicine, 590. frustrated by plurality of causes, 308. protected against plurality of causes, 309. an aid to Discovery, 702. in Absence, basis of, 279. Universal, the sole evidence for Inductive truths, 2377. the test of uniform co-existence, 244, proof of concomitant properties in Natural kinds, 245. the sole Inductive Method, 277. fundamental mode of Proof, 344. Algebra, notions of, 4382. account of, 443. highest operation of, 445. Algebraic Geometry, notions of, 432. account of, 448. All, two meanings distinguished by De Morgan, 187. Ambiguity of terms, 602, 616. Amphibolia, 678. ‘Analysis, Chemical, 627. Logical, 628. allied to Abstraction, 39, 629. applied to Induction, 684. Grammatical, 684. Critical, 684. Mathematical, 685. preliminary to elimination, 272. in Psychology, 511, in Society, 570. conformed to rules of division, 427. an aid to Discovery, 705. Analytic judgment, 76. 720 Analogy, as a form of Inference, 373 does not amount to Proof, 373. examples of, 375. Analogies, false, 372, 624. Analogical Hypotheses, 377. Animals and Plants contrasted, 495. Antecedence, invariable, not causa- tion, 268. causal usually complicated, 271. Apprehension, simple, 717. Approximate Generalizations, 365. probability of, stated in numbers, 366. how brought nearer certainty, 368. open to sophistry, 369. A priori, applied to knowledge, 10. Argument, 715. Aristotelian contrasted with Bacon- ian logic, 642. Arithmetic, definitions of, 433. ultimate notions of, 434. account of, 442. proof in, 443. Associations, a source of fallacy, 615. Astronomy, its place among the Sciences, 630, 636. Averages, 321. Axiom of Syllogism, various forms discussed, 155. proof of, in experience, 159. Hamilton’s forms, 160. as given by Thompson, 161. as given by De Morgan, 162. not derivable from the “ Laws of Thought,” 162. Axioms, nature of, 224, requisites of, 294, only two Mathematical, 224, of Inductive origin, 225, Bacon, contributions to inductive methods, 687. Belief, the nature of, 12. inherently excessive, 607. law of, explains intense convic- tions, 225. Biology, scope of, 488. divisions of, 492. notions of, 494, propositions of, 496, INDEX. Biology, conservation of Force in, 498. Empirical laws in, 498. logical methods of, 500. Hypotheses of, 502. as basis of Medicine, 577. Body, substance of, 660. Body and Mind, 357, 376, 505. Botany, arrangement of characters in, 531, maximum of affinity in, 532. grades in, 534. agreement and difference in, 535. peculiarity in exhibition of differ. ences, 586. index in, 538. CaLcuLts, notions of, 432. account of, 448. Canons of Syllogism, 149. according to Hamilton, 151. special for each Figure, 152. Canons, special, derived from Axiom, 163. Categorematic, 715. Categories, of Aristotle, 661. Categorical Imperative, meaningless, 376. Causation, law of, 20, 226. uniformities of, as a branch of Logic, 239. law of, expressed, 245, obverse denied, 246, three aspects of, 247. practically viewed, 24/7. scientific, 249. fallacy of, 250. as Conservation of Force, 251. as an instrument of elimination, 276, unfolded in three maxims of elimi- nation, 277. induction of, 843. rests on Agreement alone, 845. as an Empirical law, 845. discriminated from’ Co-existence, 381. not distinguished from Co-exist ence, 688. propositions of, in Biology, 497. in Polities, 556, 564. contradiction of, incredible, 379, A”) Para INDEX. Cause, an alleged intuition, 11. to be sought ameng the antece- dent circumstances, 267. not proved by invariable antece- dence, 268. the unconditional invariable ante- cedent, 268. material, formal, efficient, final, 248. : Causes, composition of, 268. combination of, 327. real, 359. . _ Chance, computation of, a resource under Intermixture of Effects, 313. coincidence explained, 315. principle of computation, 316. applicable where other methods fail, 316. combined with law, 319. submerging a small uniformity, 319. in Biology, 501. in Psychology, 516. in Medicine, 592. elimination of, an aid to Discov- ery, 702. Character, Science of, based on Psy- chology, 516. elements of, 518. as affected by Conservation, 518. influences on, 519. not classified like Natural History, 520. peculiarities of, 521. human, in Politics, 556. Characters, descriptive, sequence of, 414, in Chemistry, 478. in Mineralogy, 528. in Botany, 531. in Zoology, 588. Chemical force, conservation of, 355. combination, not a union of forces, 370. defined by contrast, 398. Chemistry, fundamental fact of, 472. propositions of, 473. arrangement and methods of, 474. elements of, classified, 474. descriptive method of, 478. agreement and difference in, 483. 721 Chemistry, empirical laws in, 484. law of Conservation in, 484. hypotheses in, 485. nomenclature of, 486. notation of, 487. Class, two meanings of, definite and indefinite, 280. Classification, golden rule of, 383, Methods of, 414. descriptive characters in, 414. grades of, 418. terminates with Species, 420. statement of agreements and dif- ferences in, 422. Index, 424. of Characters, 520. Sciences of, 522. an aid to Discovery, 704. Co-existence one of the three Uni- versal Predicates, 108. as Order in Place, 103. as Co-inherence of Attributes, 104, uniformities of, as a branch of Logie, 289, 248. induction of, 241. proof of, by Universal Agreement, 244, propositions of, in Biology, 296. in politics, 556. and Succession, common to sub- ject and object experience, 656. Collective names, singular or gener al, 48. Colligation of Facts, 695. Collocation of Circumstances, 251. degrees of complexity, 260. elliptically spoken of as the Cause, 262. as Potential Energy, 264. the effect of expended force, 265. in Politics, 564. Colony, example of positive defini- tion, 388. Colour, not intrinsically objective, 657. Complex Propositions, how far mat- ter of Logic, 85. Complications of Cause and Effect, 271. 722 Compositionis et Divisionis, fallacia, 674. Comprehension, 50. practically more important than extension, 333. Hamilton’s syllogism in, criticized, Conceptualism, 6. Concept, formation of, 383. Conception, formal, 473. Concomitance, discovery of laws of, 419. in Zoology, 539. Concomitant, a predicable, 76. separable and inseparable, 77. Variations, 292. fundamental maxims of, 278. interrupted by critical points, 294, as a means of suggestion, 294. tables of, for Discovery, 295. under intermixture of effects, 403. in Biology, 500. in Politics, 567. in Medicine, 591. Concrete names, 54. Conditional Propositions, 85. Syllogism, involves no inference, 117, Confusion, fallacies of, 602, 616. Consciousness, 507. testimony of, 665. Connotation, of General Names, 49. Conservation of Force, law stated, 251. proved ae universal agreement, 23 explained, 250, 252. evidence of, 844, has same proof as Causation, 266. not an @ priori conception, 267. in Chemistry, 484. in Biology, 498. in Medicine, 589. under re-distribution, 460, in Character, 518. Consistency, Principle of, 14, 108, 645, 670. Contiguity, extension through, 403. Jontinuity, law of, empirical, 338, of names INDEX. Continuity, a help to Discovery, 697, 706. Continuous Comparison, 295. Contradiction, principle of, 16. Contradictory, propositions, 93. misapplication of the name, 94, Contraries, expression of, made pre- cise by De Morgan, 56. basis of De Morgan’s additions to syllogism, 184, Contrary propositions, 92. Contrast, in defining, 385. animals with plants, 495. exhibition of, in Chemistry, 483. Conversion, Simple, 113, Fallacies of, 114. by Limitation, per accidens, 114. obverted, or by Negation, or Con- traposition, 116. Copula, 44. meanings of, 182. Correlative names, 55. Correlation of Forces, see Conserva- tion, Credibility, consistency with proved inductions, 379. Crystallization, an example of Agree- ment, 284, explanation of, confirmed by Joint Method, 291. Curves, method of, 697, 704. Depvcrtiov, first principles of, 17. explained, 40. why placed before Induction and -Definition, 41. laws of, 645. as general presumption, 284, involves observation of facts, 825. two stages of complexity, 32'7. simple, extension of a law, 327. combination of causes, 329. fallacies of, 625. Deductive Method, three requisites of, 325. in Psychology, 513. in Politics, 567. in Medicine, 592. me insufficient in Politics, 572 Sciences, how constituted, 216. INDEX. Definition, as verbal predication, 71. exhaustive and unexhaustive, 71, 72. explained, 38, 384. fundamentals of, 385. Positive Method of, 386. margin of transition, 890. Negative Method of, 392. deductive, 395. the language of, 395. by synonyms, 396. per genus et differentiam, 74, 396. by Analysis, 396. notions not susceptible of, 398. mixed with Real predication, 582, 587. fallacies of, 626, neglected by Whewell, 696. an aid to Discovery, 706. De Morgan, divisions of Terms, 51. on Positive and Negative names, 56. enumeration of Propositions, 90. additions to syllogism, 182. Demonstration, based on Induction, 219. Denotation, of General Names, 49. Derivative laws, 334. various kinds of, 334. limited application of, 336. of wider application than Em- pirical, 342, in Politics, 568. Description, of chemical bodies, 478. not to be mixed with explanation, 483, 584. Descriptive terminology, 407. characters, sequence of, 414. Development hypothesis, 502. Dew, research on, an example of elimination, 298, Dictum de omni et Nullo, 155. Difference, Method of, fundamental maxims of, 278. explained, 287. where indecisive, 289. in Politics, 566. in Medicine, 591. exhibition of, in Chemistry, 483. Differences, statement of, in Classi- fication, 422, 529, in Botany, 535. 723 Differences, statement of, difficult in Botany, 536. in Zoology, 543. in Diseases, 596. Differentia, 73. Dignity, a source of fallacies, 613. Dilemma, 121. Discovery, Art of, 697. distinguished from Proof by Mill, 697. three aids to, 326. secondary in Logic, 327. Disease, definition of, 575. Disjunctive Propositions, 85. Disjunctive Syllogism, involves no inference, 119. Division, an aspect of classification, 425, rules of, 426. a mode of grades, 427. fails with undefined classes, 428. Documents, invalidated by two doubts, 709. Erricient Cause, 248. Electricity, Conservation of Force in, 257. characters and branches of, 468. Elimination, of Cause and Effect, 271. weapons of, 276. is Proof, 279. of chance, 314. Empirical laws, explained, 333. various kinds of, 334. criteria of, 335. limited application of, 336. established by Universal Agree- ment, 237. more precarious than derivative, 842. in Chemistry, 484. in Biology, 498. in Psychology, 514. in Politics, 568. Enthymeme, 716. Equality, uniformities of, as a branch of Logic, 239. Equality and inequality, one of the three Universal Predicates, 103. Equivalence of propositions, 107. 724 Equivalent terms, as an aid to Dis- covery, 702. Essential attributes, 74. predication, in Psychology, 509. Excluded Middle, principle of, 17. Exclusion, Bacon’s process of, 688, Existence, has no real opposite, 59. propositions of elliptical, 107. means Object and Subject indis- criminately, 620. Experience, the source of knowl- edge, 9. the proof of the Axiom of the Syl- logism, 159, 226. the proof of Causation, 226. Hxperiment, advantages of, 278. in Biology, 500. in Politics, 563. Experimental Methods, apply only to Cause and Effect, 240. deductive, in character, 277, 345. explained, 279. examples of, 297. frustration of, 306, 312, 3138. in Psychology, 512. in Politics, 565, 572. in Medicine, 590. how far anticipated by Bacon, 687, 689. given by Herschel, 694. neglected by Whewell, 696. Fixperimentum crucis, 865. Explanation of Nature, a joint effect, 347. intermediate links, 348. subsumption of laws, 349. limits of, 351. fallacious, 354. Extension, 50. fundamental property of the Ob- ject, 657. Evidence, assertions beyond reach of, incredible, 382. Historical, 423. supreme canon of, 707. internal and external, 708. two modes of external, 709. transmitted by writing, 709. transmitted orally, 7138. Facts anp Ipmas, 695, 699. INDEX. Fallacies, Aristotelian and Scholastic, 673. Whately’s division, 676. Mill’s classification of, 599. a priori, 599. of observation, 600. of generalization, 601. of ratiocination, 601. of confusion, 602, 616. © position of, 603. extralogical, 605. tendencies to, 606. logical, 624, . knowledge of, = Discovery, 707. in Politics, 572. Fear, a source of fallacy, 612. Feeling, two-sided, 2. Feelings, a source ‘of fallacy, 609. Fever, definition of, 581. Figures, 136. relative value of, 146. reasons for different, 146. Figure dictionis, fallacia, 674, Fina] Cause, 248. Food, an example of positive defini- tion, 388. Force, definition of, 251. chief predicates of, 251. Conservation of, 21. Form and Matter, 639. Formal Logic, too narrow, 645. Cause, 248. thinking explained, 640. requires inductive verification, 648. Freedom of the will, 844, 621. Functions of living bodies, 491. Function and Structure viewed separately, 493. GENERAL Name, explained, 48. Generality, Names classed according to, 47. higher and lower, 54. degrees of, in Notions, 64. fixed grades of, in Botany, and i in Zoology, 65. degrees of, in Propositions, 78. of Proposition follows Notion, 78. as classifying Propositions, 78. as a basis of Definition, 385, — 7 INDEX. Generalization, identical with Expla- nation, 446. the highest ambition of Science, 456. approximate, 465. fallacies of, 601. ' excessive tendency to, 608. as an art of Discovery, 279, 698. Genus and species, movable names, except in Natural History, 65. a predicable, 73. Geometry, notions of, 432. definitions of, 434. ultimate notions of, 436. axioms of, 438. » postulates of, 439. order of topics in, 446. proof of Euclid’s fourth proposi- tion in, 447. Glaring instances, 690, 704. Government, forms of, 549, 553. definition of, 551. functions of, 552. local and central, 554. defines Public and Private, 554. Grades of generality, great import- ance of, 700. in classification, 418, Statement of, suited to discovery of concomitance, 419. in Mineralogy, 528. in Botany, 534. in Zoology, 542. in Diseases, 596. Gravity, an example of Hypothesis, 460. contraction of, incredible, 379. Hamintoy, additions to syllogism, Quantification of Predicate, 178. syllogism in Comprehension criti- cized, 180. Health-Disease, indefinable, 264. Heat, generated by collision, 253. conservation of, 254. unprofitable dissipation of, 255. definition of, 467, heads of the science of, 467, propositions of, 470. structural, should be stated in chemical formula, 487, 725 Herschel, contributions to Induc- tion, 693. History, Philosophy of, 548. basis of Politics, 561. perversions of, 712. Homonymia, 505. Hypothesis, various meanings of, 358. of known agencies desirable, 359. of a new agent permissible, 361. as a representative fiction, 362. differs from geometrical abstrac tions, 364. analogical, 377. in Chemistry, 485, in Biology, 502. in Psychology, 515. in Politics, 569. in Medicine, 593. Hypothetical Inference, 116. IDEA AND Facts, 695, 699. Identification of a Minor, when dif ficult, 218. not an induction, 235, 328. Identity, principle of, 16, Idola, Bacon’s, 609. Ignava Ratio, '71'7. Ignoratio elenchi, 602, 628, 675. Immediate Inference, 107. by Added Determinants, 109. fallacies of, 625. Import of Propositions, 100. Hobbes’s view, 100. not the reference of something to a class, 101. Inconceivability of the opposite, ex- plained, 223. rejected as ultimate test of truth, 665. Incredibility, inconsistency with proved inductions, 379. Index, to a classification, 424. in Mineralogy, 530. in Botany, 538. in Zoology, 544. in Diseases, 597. Individual, our idea of, a conflux of generalities, 7. Induction, first principles of, 19. explained, 40, 231. would furnish Formal processes 650. 726 Induction, a branch of Logic, 651. improperly so called, 233, 235. cannot be brought under the syl- logism, 233. a prerequisite of deduction, 325, in difference of subject, 371. postulate of, 502. fallacies of, 625. growth of, 687. Inductive, Discovery, 326. Methods an aid to Discovery, 702. Syllogism, 233. Infime species, 63, Inflammation, definition of, 583. Intermixture of Effects, 310. in Politics, 565. in Medicine, 591. International law, 548. Intuition, an alleged source of knowl- edge, 10. Intuitive—symbolical, 716. Invention, how assisted, 705, Joint Mernop of Agreement and Difference, 291. counteractive to plurality of causes, 310. in Politics, 566. in Medicine, 591. an aid to Discovery, 703. Judgment, formal, 641, as a synonym for proposition, 80 its significance with Aristotle, 80. Jurisprudence, 548, KNOWLEDGE, the act of, includes al- ways two things, 3. conjoins Agreement and Differ- ence, 4. of two kinds, called Object and Subject, 5. Individual or Concrete, and Gen- eral or Absiract, 5, 22. origin of, in Experience, 9. limited by our sensibilities, 13. nature and classification of, 21. should be true, 22. conveyed in propositions, 44. relativity of, appears in language, 54 Kinds, 63. INDEX. Kinds, exemplify co-inhering attri. butes, 241. LanauaGeE, truths expressed in, 42, fallacies of, 616. Law, confused meanings of, 643, 617. metaphorical use in “ Laws of Na- ture,” 239. involved in Government, 552. combined with Chance, 319. Laws of Nature, by preéminence, 239. Liberty, 550. Life, definition of, 488. Light, undulatorg theory of, 361. commutation of, not established, 258. production of, an example of Agreement, 286. definition and subsidiary notions of, 468. Likeness and Unlikeness, common to subject and object expe- rience, 655. Love, a source of fallacy, 612. Marain, doubtful, in definition, 390. Mathematics, Logic of, 429. the best example of a Deductive Science, 429, 647. notions of, 430. propositions of, 482. definitions of, 433. axioms of, 437, leading branches of, 442. Materia Medica, 581. Method, expresses part of the func- tion of Logic, 35. an aid to Discovery, 701. — Mind, substance of, 660. definition of, 505. difficult to estimate quantity in, 517. Mind and Body, 357, 876, 505. Mineralogy, scope of, 522. relations to Chemistry, 522. arrangement of characters in, 523, maximum of affinity in, 524, grades in, 528. agreement and difference in, 529, — index for, 530. Material Cause, 248. INDEX. Material, names of, singular, 48. Matter, as Resistance, 657. defined by positive method, 391. by negative method, 393. constitution of, a hypothesis, 363. Force, Inertia the same fact, 455. ‘physical properties of, 464. Mechanics, 462. Medicine, scope of, 575. based on Biology, 577. definitions of diseases in, 581 general diseases in, 579, 581. specific diseases in, 586. propositions of, 588. _ experimental methods in, 590, elimination of chance in, 592. the deductive method in, 592. hypotheses in, 593. classification in, 595. Minor, identification of, not an in- duction, 235. Mnemonics, 147. Modals, 99, 717. Molar forces, conservation of, 252. Molecular attractions, 464. Molecular forces, enumerated, 254. Motion, laws of, reduced to one, 458. Monarchy, example of positive defini- tion, 887. Moods, 138, _ usual enumerations justified, 153. Muscular Irritability and Putrefac- tion, an induction, 303. Mystery, 356. Names, why considered at beginning of Logic, 45. defined, 46. denote things, not ideas of things, 46. variously classified, 4’7. De Morgan’s divisions of, 51, go in couples, 54. meaning of, increases with oppo- site, 60. loosely extended, 402. transitive application of, 408. class, 409. of generalities should be short, 410 new, 410. 127 Names, precautions in appropriating old, 412. expressive, 414, different, held to imply different things, 418. improper use of, 420. Naming, general, value of, 401. first requisite of, 402. second requisite of, 407. Nature, explanation of, 346, ambiguity of the word, 616. Negation, variously expressed, 58. Negative names, 55. singular or plural, 57. of a real property, also real, 58. Necessary Truth, 14. Necessity, meanings of—certainty, 220. implication, 221. inconceivahility of the oppo- site, 223. Nerve force, conservation of, 258. Newton, contributions to Induction, 693. Nomenclature, 412, 414. of Chemistry, 486. Non causa pro causa, 675. Non sequitur, 675. North-east wind, an example of Agreement, 283. Nota note est nota rei ipsius, 156. Notation, of Chemistry, 487. Notion and Proposition, not distin. guished by Whewell, 696. Notions, contrasted with Proposi- tions, 61. disguised as Propositions, 66. of singular or plural constitution, 63. indefinable, ultimate, 398. Ossect, analysis of, 486. attributes special to, 657. Dhyecksmuiees highest real couple, opie of all antitheses, 653. attributes common to, 655. Observation, why not a department of Logic, 36. the basis of Induction, 234. compared with Experiment, 278. in Biology, 500. 728 Observation, in Politics, 561. erroneous, causes of, 562. fallacies of, 600. as an art of Discovery, 698. Opposition, of propositions, 92. error in common square, 94. amended square, 97. Aristotle’s square, 98. Obversion, formal, 109. material, 111. Order, valuable aid to Discovery, 701. Order and Progress, 555, 570. Oxygen, exemplary description of, 479. Parity of Reasoning, 235. Pathology, general, 579. Per genus et differentiam, 885, 396. Persistence of Force, see Conserva- tion. Petitio Principii, 602, 6238, 675. Physics, Molar, divisions of, abstract, and concrete, 452. notions of, 452. propositions of, 454. definitions of, 455. axioms of (laws of motion), 458, concatenation and method of, 462. Physics, Molecular, departments of, 463. notions of, 464. propositions of, 469. predominant methods of, 472. Plants and Animals contrasted, 495. ' Plato’s dialogues, how authenticated, 710. Plurality of Causes, 246. how far subject to uniformity, 246. bearing of, on the Experimental Methods, 307. in. Politics, 565. in Medicine, 591. Plurium Interrogationum, 6'76. Political Economy, 648. Politics, two divisions of, 547. embraces several sciences, 549. province of, 549. Descriptive, 550. Theoretical, defined, 556. propositions of, 558. universal propositions of, 559. INDEX. Politics, Theoretical, limited proposi- tions of, 560. methods of, 561. experiment in, 563. causation in, 564. method of agreement in, 565. other experimental methods in, 566. deductive method in, 567. hypotheses in, 569. simplifying of, 570. fallacious methods in, 572. Practical, End in, 573. based on Theoretical Politics, 574, origin of political devices in, 575. Porphyry’s tree, 716. Positive names, 55. Post hoc ergo proplter hoc, 675. Postulate, the universal, 664. Potential energy, 259. an aspect of Collocation, 264. Practice, logic of, 545... maxims of, in Politics, 575. Predesignate, 717. Predicables, 73. Predication, verbal, 76. confounded with real, 68. in plural notions, 69. in Natural Kinds, 69. verbal not tautological, 70. final analysis of, 660. Predicates, three universal, 102. Mr. Mill’s scheme of, 106. Premises, 135. Prerogative Instances of Bacon, 688. Presentative and Representative, 7, 640 Primary qualities of matter, 657. Probable Inference, explained, 365. may be estimated, 366. ~ how made more precise, 368, Probability, 320, explained, 321. principle of, 321, rules of, 322. n applied to Causation, 824. an approximate generalization, 366. aeons . comparison of, 381. in Biology, 501. bs vA INDEX. Probability, in Psychology, 516. ambiguity of the word, 618. Progress and Order, 555, 570. Proof or Evidence, the scope of Logic, 34, 279. Proposition, a, contains two names, and two notions, 274, 292. verbal, 67. Propositions, 78, Proprium, 74, exemplified in Mathematics, 432. Psychology, scope of, 505. subordinate notions of, 507. propositions of, 509. logical methods of, 511. empirical and derivative laws in, 514. hypotheses in, 515. chance and probability in, 516. suggesting arts of Discovery, 699, oncrete Science ? 636. Quatity, of Propositions, Affirma- tive or Negative, 83. an ineradicable distinction, 83. designations of, 84. Quantification of ‘Predicate, 86. makes two propositions in one, 88. cack a to syllogism, basis of, 178. Quantity, of Propositions, Total or Partial, 81. Universal and Particular, inapt names, 82. Indefinite, 82. one of the three universal Predi- cates, 333. common to Object and Subject ex- perience, 655. subject-matter of Mathematics, 429, designations of, 81. sciences of, Deductive, 103. uniformities of, as a branch of Logic, 239. RATIOCINATION, fallacies of, 601. Realism, 5. fallacy of, 619. Reasoning, ‘used in defining Logic, 30, 729 Reasoning, founded on Similarity, 8, 370 from particulars to particulars, 209. chain of, reducible to a series of syllogisms, 215. causes of}, complicated, 217. formal, 641, Reductio ad impossibile, 141, Reduction, 147. Relativity, law of, 2. Names classed according to, 54. universal, 61. as affecting Notions, 66. as classifying Propositions, 78. as a basis of Definition, 385. basis of an enumeration of things, 485. fallacies of, 621. of Proposition follows Notion, 79. Relative. terms, for special relation- ships, 60. names, 55. Representative Fictions, 362. in Medicine, 594. Residues, Method of, 279, 295. in Politics, 569. an aid to Discovery, 702. Resistance, 657. SANGUINE TEMPERAMENT, & source of fallacy, 611. Science, the perfect form of Knowl- edge, 23. characteristics of, 23. problem of, as conceived by Whewell, 695. Sciences, classified, 25. Abstract and Concrete, 25. Abstract, 25. Concrete, 28. Practical, 28. defined, 545. Classification of, Bacon, 6217. D’Alembert, 628. Engyclopedia Metropolitana, 628. Neill Arnott, 629. Comte, 629. Herbert Spencer, 630, criticism of Spencer’s scheme, 634. 730 INDEX, Secondary qualities of matter, 657. Laws, importance of, 332. Self-interest, a source of fallacy, 620. Series, Classification by, 295. Serial order, in classification, 417. Similarity, law of, 3. the foundation of Reasoning, 8 370. basis of scientific explanation, 346. extension of names through, 402, 405. Singular Name explained, 48. Propositions, syllogism of, 159. Smelling, due to oxidation, induc- tively proved, 297. Society, notion of, 547. structure of, 550. Solid defined by positive method, 390. by negative method, 393. Sophisma Heterozeteseos, 717. Pigrum, 15. Polyzeteseos, 716. Sorites, or heap, 390, 717. face, an abstraction, 11. characterized, 657. Species, a predicable, 73. Species, importance of in classifica- tion, 420. -infima, 421. in Mineralogy, 528. in Botany, 535. in Zoology, 542. Statistics, Political, 549, 562. Medical, 592. Structure of Living Bodies, 490. and Function viewed separately, 463. Subject, explained, 655. attributes special to, 659. Teter i highest real couple, reas of all antithesis, 653. attributes, common to, 655. Substance, a supposed intuition, 11. fundamental attribute, 660. Succession, one of the three Uni- versal Predicates, 105. as Order in Time, 105. as Cause and Effect, the chief part of Induction, 106. Sufficient Reason, 600, 717. Sumption and Subsumption, 146. Syllogism, defined, 138. examples of, 165. additions to, by Hamilton, 178. by De Morgan, 182. by Boole, 190. Numerically Definite, 188. functions and value of, 207. how far a material process, 211. axiom of, reposes on experience, 226, an aid to Discovery, 703. of the Will, meaningless, 376. Sympathy, a source of fallacies, 610. Symbolical—Intuitive, 716. Symbols, of Propositions, 86. Synonymous Propositions, 123. Synonyms, definition by, 396. as an aid to Discovery, 701. Synthesis, Chemical, 681. Logical, 683. does not apply to Simple Deduce- tion, 684. Grammatical, 684. Mathematical, 685. Synthetic judgment, 76. TABULATION, as an Index Classifica- tion, 580, 597. as an aid to Discovery, 704. Tabular arrangement, Bacon’s, 687. Terminology, descriptive, 407. Terms, of syllogism, 364. Therapeutics, general, 580. Things, enumeration of, 652. Mr. Mill’s enumeration of, 661. Thought, Laws of, 16, 641. definition of Logie, 30. too limited to make a Universal Postulate, 664. Time, an abstraction, 240. Tradition, oral, value of, 7138. approaching to written evidence, 715. Truths, known immediately, 32. known by the mediation of other truths, 32. Uttimate Laws or Narurg, pei in number, 353. Uniformity of Nature, supposed’ in Deduction, 19. See eee INDEX. 731 Nature, enters into | Verification, in Politics, 567. — - tt etical Logic, 645. Vere Cause, 359. te major premise of all tion, 671. WHEWELL, contributions to Induc. nat a unity, 238, tion, 695. Wonder, a source of fallacy, 612. S “among effects of same eeu 335. Zooioey, difficulties of, 588. ited in application, 341, 342. arrangement of characters in, oon connection, 334. 538. laws of Concomitance in, 539. ‘ maximum of affinity in, 54¢. , souree of fallacies, 603. grades in, 542. of circumstances, 278. agreement and difference in, 548. ion, } index in, 544. c cae fos nee tet ie ape other - a: Ca hla ® abe Bo hal) Sea's eee ¢ ra ¥ > ~ yr a ¥y Mise + ee cs ? a a - he ' i » + #8 a i *AG ar ¢ wv? " sy ARO oe » Te 5 / iF ‘ ¢ . « 4 Ts +e SS paltlot at cola dtitin’ | ahi pela 1 4 ‘ aN A ' r i ‘ 4a 74h shy j ; ¢ ' nw ’ } im ; itt Gi oe ba ) ' YY Cr . at : . } 2 «fight ‘ \y ti 5 arr 7 ~Y YAbewe” §e a eth: Toe tei t Irivp its 5 ‘ ‘ 1 ~~ on a7 vie ; . ‘ ' ’ 3 : r' 7 5 thy ’ : ‘ ‘ = : P ¥ “5 fen . if sie PO. SI : i : ; ures x aad "4 : } or. hte operas fe 7%) \ : en (} ; . e ‘ ; fry ti 4 LP : hinti nokenn..| etn eee mi nt ta ; nis j wet 7 be i , i eRRRE AS a8 : : eys 0 nfea a weal 4 J tS 2G > e ‘ 2 ‘ . i ie x? 2 x ; “ ‘ Bh ye ie @ x Rei inf « < : é WORKS OF ALEXANDER BAIN, LL. D., PROFESSOR OF LOGIO IN THE UNIVERSITY OF ABERDEEN, ENGLISH COMPOSITION AND RHETORIC. Revised and enlarged edition. Part —Tue InTELLEcTUaL ELEMENTS or STYLE. Including—Order of Words; Number of Words ; the Sentence ; the Paragraph; Figures of Speech; and, finally, the Qualities of Style. $1.20. Part IJ.—EmotionaL Quauities or Sryte. Including— Art Emotions classified; Aids to Emotional Qualities; Strength; Feeling; Vituperation,—The Ludicrous; Vituperation; Ridicule; Humor; and Residuary Qualities. $1.20. ENGLISH COMPOSITION AND RHETORIC. Old edition. 12mo. $1.22. LOGIC, DEDUCTIVE AND INDUCTIVE. New revised edition. 12mo. Cloth, $1.40. MENTAL SCIENCE: A Compendium of Psychology and History of Philosophy. 12mo. Cloth, $1.22. MORAL SCIENCE: A Compendium of Ethics. 12mo. Cloth, $1.22, AMERICAN BOOK COMPANY, Publishers, NEW YORK, aE 8 CINCINNATI, se CHICAGO, JOHONNOT’S WORKS. The Sentence and Word Book. A GUIDE TO WRITING, SPELLING, AND COMPOSITION BY THE WORD AND SENTENCE METHODS. By James Jononnor. 12mo, 184 pages. In teaching reading, those who practice the word and sentence methods have met with a serious difficulty. They can not find, in sufficient number, simple lessons with words expressing the ideas of home and of youthful experience. The ordinary reading-lessons do not contain these words, and the teacher has not time to search them out, and arrange them in proper sentences. Johonnot’s ‘‘Sentence and Word Book” has been prepared with special reference to the difficulty here encountered. It selects and arranges words. It deals with familiar topics. It groups words that ex- press ideas upon the same topic. It uses new words in such combinations that their meanings are understood. 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Its selections are from the best standard authori It is embellished with thirty-one beautiful and instructive illustrations. AMERICAN BOOK COMPANY, Publishers, NEW YORK, aie 6 CINCINNATI, eae _CHIC 0. ~ fr - tk, Maha lila acts Gar AK AE AR ali tas tai ahh, Lig bh pte tae tht Tipp lta Saipan ni Meg g S pean cent acai ns igen ALAS ptt i tinh tare tctipg Ng nh a AGO APOIO ttc A ta anos a i ie Laas re oe Ts i / . rf — , A - tas! ' y 5 i wc} iit