CORNELL UNIVERSITY LIBRARY GIFT OF Miss Flossie D. Lortz The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924029142986 Cornell University Library BC108 .W76 1872 Logic, theoretical and practical : a tex olin 3 1924 029 142 986 TEXT-BOOK OF LOGIC. LOGIC, THEORETICAL AND PRACTICAL. . A TEXT-BOOK TEACHERS AND STUDENTS, W. D. WILSON, D. D., LL. D., L. H. D., V Professor in TTie Cornell XTnioersUy ; anO, AuOwr of Lectures on Psytiholpgy. ITHACA, N. Y. : ANDBUS, MdjCHAIN & LYOITS, 1872. Entered according' to Act of Congress In tlie year 1872, by » Andkus, MoChain & Lyons, In tie Office of the Librarian of Congress, at Washington. PREFACE. It is now some fifteen years since I published "An Elementary Treatise on Logic," which in its third edition is still before the public. I would not, howcTer, haye the reader regard this Book as merely a compilation, condensation, abridgement or re-ar- rangement of the former Work. On the contrary, it differs from it in many essential particulars. Since the time of the publication of that Treat- ise, my attention has been chiefly directed to the study of the Principles and Forms of reasoning, as they occur in the actual practice of men who are engaged in the various intellectual processes that are called for in the prosecution of- the affairs of life, and I am able to offer here a "Work, which, I think, will be found, in many respects, to be especially worthy of attention. It has been customary to regard Logic as a mere formal or instrumental science, dealing with "id^as," "notions" or "conceptions," as something interme- diate between the mind that perceives and reasons. Yi PBEtACE. and the substantial objects which it perceives and reasons about. I have fully adopted and carried out Cousin's declaration. " If by ideas is understood something real which exists independently, of lan- guage, and is intermediate between the mind and things that exist, I say that there are no ideas. There is nothing real, except things and the mind with its operations." I hold, therefore, that Logic deals with thikgs, and not any mere fictions, under whatever name they may be designated, whether "ideas," "notions," "concepts" or what not. And it uses words as representing things; and sentences or propositions as representing the relations which things appear to sustain to each other. What those, relations really are, is a question that belongs to a higher department of metaphysics, Ontology. This view of the itature of Logic has enabled me to sim- plify my discussions of the Formulae very greatly^ to dispense with an immense amount of technical- ities, and by constantly referring to things instead of mere "notions" about them, it has enabled me to make the general principles and laws of reasoning much simpler and more easily comprehensible. This view of the nature of Logic and of the func- tions of language in relation to it has led to, and rendered possible, a much more satisfactory account of the Fallacies, especially those in Diction, than has hitherto been attained. I think I have now made PREFACE. vii a classification that has enabled me to give an ac- count of them that is clear, complete and satis- factory. I l^ave endeavored to be brief and concise. Per- haps I have sometimes gone to an excess in this direction. But I believe that obscurity more fre- quently comes from prolixity than brevity. And of all the features of a text book, no one that I have encountered, has been more vexatious to me than the mere verbosity which seeks clearness through a multiplicity of words. Few persons, I apprehend, will ever study Logic without a teacher, and the teacher, as I believe, will find here as much fulness as he will desire. And even for one that studies by himself, a clear, concise statement, with one or two well selected illustrations is usually better than more. He may find occasion to pause and think; ■possibly, to devise examples for himself. But he becomes m ^he end, a better master of his subject for this exercise of his own faculties. And in any view, and with any amount or kind of help, Logic — anything that deserves the name, and does its work — cannot be read like a new novel, for amuse- ment or mere after-dinner recreajtion. In itself, , it is the most abstruse, and, in one sense the most abstract of all sciences; for it is the science that is comprehensive of the first principles and methods of all othets. » viii PREFACE. In the following pages, I haye followed the old, or Aristotlian nomenclature, so far as I hdVe had occasion to use any. I have given below, Part II, Chapter I, § 83, and Chapter II, § 140, my reas- ons for not adopting Sir "William Hamilton's theory of the Syllogism. It is but fair to say, however, that I have so far generalized the funda- mental principles or dicta of categorical and com- parative reasoning, as to provide for all possible cases, as I think; and I have in fact pointed out some forms that have not hitherto been recog- nized, so far as I know. And by referring each class of syllogisms or formula to that relation of things, one to another, out of which the Forms of reasoning arise, and on which they 'depend for their validity, I have been able,, not only to dispense with a large amount of technicalities, dry details and specific rules that have hitherto been used, but also, so to state the principles of reasoning that they will be readily understood without a familiarity with those technicalities, and may be applied to all cases, if there be any, not contemplated in, or pro- vided for by them. And yet, these terms constitute a part of the history of the science, and are still in use and often met with in the discussions which are found more frequently in metaphysics and theology than elsewhere. I have, therefore, thought it best, and PREFACE. ix no more than due to my readers, to introduce those terms pretty freely for the sake of explaining them, eren when they not only were not of use to my purpose, but often when they were quite in the way; for I have thought that it would not be very satisfactory to any one to have studied Logic, and not have learned the meaning of the terms that have been used in the discussions of Logic. But as I have elsewhere said in "the body of my Book, "Any one who will make himself thoroughly mas- ter of the Kules and Principles, which I have stated in common language and without technicali- ties, will hardly need trouble himself much about the details and technicalities of the Formulae, since he can hardly expect to retain the latter, while the principles, once thoroughly understood, will remain with him forever." In conclusion, I will merely add, that every term's experience, even now after twenty years, as a teacher of Logic, deepens my conviction of the importance of the study as a means of mental dis- cipline. It may be that very few of the students of Logic can retain a recollection of its Formulae, Terms and Eules so as to make conscious applica- tion of them in the mental work of their business of life. But as means of training one to a quick insight into subjects, a clear perception of important distinctions and a ready grasp of what is essential X PBEFAGE. while neglecting all mere accidental matter, Logic is, in my estimation, not only unsurpassed, but it is unequaled ' by any other branch of study. ^ And even the Eules and Formula become transformed, as it were, into habits, and thus enable the mind to act with the quickness and certainty of instinct in the ever varying processes of reasoning which the petformance of our duties in any station of life requires of us. Like the technicalities of Gram- mar and Rhetoric, they may all be forgotten while the habit of correct and ready speaking, which they contributed to form, remain as long as the mind itself retains its activity. W. D. WILSON. Cornell Univeesitt, ) Ithaca, M Y. f April, 1872. CONTENTS. PART I. — Introductory. THE NATURE AND SCOPE OF LOGIC page 13 Origin and NecessUyfor Logic 15 Elementary Mental Processes in Reasoning 22 Relations of TMngs on which Reasoning Depends 29 PART II.— Theoretical. CHAPTEK I.— THE LOGIC OF PROPOSITIONS 37 Hie Principles of Classification 41 Sir William HamHUm's Iheory of Quantification 48 Immediate Inference 52 CHAPTER IL— THE LOGIC OF FORMULA 59 Section I. — Categoeioai. Syllogisms 60 liUlaoies in Form 66 Hamilton's Theory of Syllogisms. 77 Compound and Incomplete Syllogisms 82 Section II. — Compaeative Stlloqisms 85 Comparison of Things 87 Comparison of Ratios 91 Various Methods of Completion , 95 Seohon III. — Conditional SxiiLooisMS 99 Different Sinds of Causes. /t, ' 100 Completion of Conditionals 103 Ccanputation cf Probabilities 107 Section IV.— Disjtosctivb Szllogisms 109 Different Kinds of Wholes 110 Completion of Disjunctives 115 Cumulative Arguments 119 CONTENTS. , xii PAKT III.— Practical. CHAPTER I.— THE LOGIC OF DICTION 125 Section I. — ^Woeds and Sentences ^. . . , 126 Section II. — Fallacies in Diction 135 CHAPTEE n.— THE LOGIC OF PEOOF..... 148 Section I. — The Cebtaintt of Pkopobitions 154 Tht Qrcnmds of Certairdy 156 Section II. — Ebduction to Identity and Conteadiotion . 160 Verbal Changes that may be Made 163 Section IH. — Indiytdual Pbopositions 169 Tliree Ways of Proving Them 171 Force of Testimony 175 Section IV. — ^Paetial Pbopositions 179 Their Advaniages .' 181 Section V. — Genebal Pbopositions 183 Prorued by Induction 1 Obtained by Average 190 Section VI. — Univeksal Pbopositions 192 May be Proved in Three Ways 192 Different Kinds of Demonstration 195 Section Vn. — ^Pbobable Pbopositions 199 Value of Analogy 201 Progressive Approach 203 Section VIIL — Extba Logical Fallacies 206 fallacies in Matter 207 Fallacies in Method 211 Section IX. — Eeeutation 213 Refutation of Beasoning 215 BefuUUUm of a Proposition 217 D^nitUm Necessary to Sefictation 219 Indirect Refuialion , , 220 Appebtdix. EXAMPLES FOE ANALYSIS AND CEITICISM 225 PART I. INTRODUCTORT. INTRODUCTION. NATURE AND SCOPE OF LOGIC. 1. Man depends for all he knows upon Obsbevation and Eeasoning. (1.) Observation, which consists in the exercise of (1) Sense-perception, as sight, hearing, etc., for all objects in the outward or material world, and (2) Consciousness for all the facts and phenomena of the activity of the mind within. But along with observation there is an Insight which is a process of seeing into the nature of the objects and phenomena which are seen or known by Perception and Consciousness. By this means, and by this alone, apparently, are we able to reason, and by rea- soning to come to know more than the brutes, and to rise above them in the scale of intelligence. It is doubtful whether Insight gives us, immediately, knowledge of any objects which had not been cognized otherwise^ that is, by Perception or Consciousness ; but it discloses to us their nature. (2.) Reasoning. This is the process by which we pass from observed facts and objects to general principles and laws ; and in many cases we come by this means to know the existence, nature and relations of objects which are not immediately subject to observation. Eea- soning is always carried on by means of Insight, and 16 '• TEXT-BOOK OF LOGIC. begins where Observation ends. In fact, what I have called Insight is often called Eeason, and thus the rela- tion of the two, Insight or Eeason, and Eeasoning, is made conspicuous. And in this view, that exercise of insight which is involuntary, follows upon and accompa- nies every act of perception or consciousness and of which, for the most p^.rt, we are conscious at the time, we call Eeason or Insight ; and the exercise of the same faculty, when we become conscious of its exercise, and when, therefore, its exercise passes under the control and and guidance of the will, we call Eeasoning. 2. No two persons ever begin to observe and think without differing in the statement of the results of their mental activity — even if they do not differ in the results themselves. And nothing is more natural and nothing more sure to occur at an early stage of our existence, in fact, before infancy and childhood will have passed away, than that we shall begin to dispute, to argue, and to try to refute and convince one another. Sometimes one will succeed and the other acquiesce. But it will often hap- pen that neither is convinced, and that we shall disagree as much about the validity and the value of the argu- ments that have been adduced, as we did about the original proposition. This naturally leads to a consider- ation of the reasoning itself. And then we have a be- ginning of the Science of reasoning — Logic ; or at the least the sense of the want of such a science. 3. But the science thus originating is rather Dialec,tics and the science of controversy than Logic properly so called. Logic comes in only as subsidiary and very sub- ordinate. The result would be a compound of Ehetorie and Logic, for as Whately has tersely said, "Ehetorie invents and arranges argurnents, Logic criticises them." Hence, as human culture advances the want is felt of NATURE AND SCOPM OF LOGIC. \^ some science of reasoning totally independent of any, subserviency to the mere conducting of a controversy, which shall give an explanation of all those measures and thoughts and influences that intervene between sim- ple observation and the highest results to which the human mind ever attains — a science which gives us truth ; and assists us to assert and maintain it, only as it shows us what it is and how to prize it. 4. The history of the science is conformable to this theory. The first writer on Logic, as Aristotle says, was" Zejto the Eleatic, who flourished about 475 — 300 years B. c, just after the uniting of the disciples of the two great schools of Magna Grecia and Asia Minor at\ Athens ; and after the transfer of the seat of Greek phi- ■ losophy to that section, had led to the discussion of the various and conflicting tenets of those two early philo- sophic evolutions. But his work, as Aristotle charac- terizes it, and as we knpw it front the remnant of it pre- served by Diogenes Laertius, was rather Dialectics than Logic. 5. Abistotle saw the difference between the two, and wrote what have since been called tis Logical treatises ; consisting of the Categories, the Prior and Posterior Analytics, the Topics and Sophistical Elenchi, in which he has included much of Grammar and Rhetoric as well as Logic. w 6. During the intervening ages, until since the revival of learning, the science was sedulously studied indeed ; though little was. done besides elaborating and applying what the Stagirite had written. At the time of the Ee- formation the deductive method, or the method of dem- onstration from mere definitions had been so extensively brought into" use, that it was thought, to be the only method that Logic could aflbrd, or knowanything about. 3 18 TEXT-BOOK OF LO&TC. It was characterized as the Scholastic method. The students of the natural sciences, among whom as an ^ p ound er of the method, the name of BACoisr stands pre- eminent, disliking the scholastic method, inaugurated the inductive method; and the study of Logic fell into dis- xepute with that class of men, and its use, or rather the use of its terms and formulas, was left to the theologiaps and philosophers. 7. About the beginning of this century, Archbishop "Whately wrote two treatises, one on Logic and the other on Ehetoric, which have done more probably, than all other causes put together to restore the study of Logic, and to put the science itself in a proper light. The books are remarkable in their chai-acter, of great value, doubtless,' and the student who has thoroughly mastered them knows something of Logic and a good deal of Whately. His work on Logic was assailed by Sir William Hamilton, first in the Edinburgh Eeview for April, 1833, and the paper is reprinted in Harper's Edition of Hamilton's Works, Ed. 1853. In this Eeview Hamilton handles Whately very severely, and proposes a new theory of his own. 8. But since thepublication of Whately's Treatise, the amount of attention to the subject has greatly increased and we have had works almost without number pub- . lished for the purpose of Improving and advancing the science, and bringing it within the reach and practical use of all educated persons. In Prance an(^ Germany also, neariy if not quite every school and evolution in philosophy has had its Logic. And in Hegel we find it assuming the proportions of " the universal science ;" not one among many only, but that which comprehends them all. One of Hegel's disciples has represented his ■views of the science in. these words: " The domain of NATURE AND SCOPE OF LOGIC. 19 Logic, says Hegel, is the truth as it is per se in its nature and character. It is the representation of God as He is in His eternal being."* 9. I propose, however, in the following pages a much more modest and unpretending view. I propose to view Logic as I have defined it, as the science of reasoning ; not Dialectics, not the science of disputation or discus- sion, but as the science of the methods of attaining truth. I shall hereafterf notice the basis of Hamilton's theory and give my reasons for not accepting it as an occasion for abandoning all that had been done before , him from Aristotle down. Notwithstanding, it must be admitted that Sir William's presentation of his theory has occasioned some modification of the statements that will hereafter be given to the science. 10. It falls within the ^rj^jjiee-xfi^ Psychology to de- scribe the facultieSr-fttficMons and laws of Observation and Insight, the extent to which and the limits within which they may be trusted ; and the nature of the know- ledge which we have from their exercise. It is the province of Logic, on the other hand, to explain the pro- cesses and laws of Eeasoning, or that voluntary exercise of the mental faculties by^whi^h we proce ed in the man- ufacture oifTEe raw material of knowledge — if^we"niSy rise sucBT an expression — given us by Observation and Insight, into those general views, principles and laws which make up the mass of our knowledge, our science and our wisdom or practical skill. 11. I have thus far spoken of Knowledge only. We have besides this much of what is commonly and prop- erly called Belief. For this we depend on testimony. *St^'n'^let's Histoiy of F-hilosophy. Appleton's Ed. p. 346, t Part n, 84, 140, 149. ^"0 ■ TEXTS OK OF L GTC. and this testimony may be either ordinary human testi- mony in regard to matters which have fallen under other men's observation, or it may be Revelation in regard to things divine. 13. This difference, hotvever, serves to distinguish Belief from Knowledge ; namely, into Knowledge there mip,vR no Y.alj,]p,ta,i;y p.lernent. whereas, in all Belief there is always a voluntary element. If I see an object before me, I know it to be there and cannot but believe it to be there, and to be what I see it to be. I have no choice about it. Even in the case of hallucination, we have no 'pow§r to distrust our faculties. We know we see the object although we may know at the same time; by other means, that there is no such object seen. But in Belief, if we choose to place confidence in any witness ; we be- lieve on his testimony what he says. Or if we choose to distrust him, we do not believe what he says. Whethe r, theref^ejjwe_believe or not, depends very much upon chgige — whether we choose to place confidence in the witness or not : and this is as purely a free maral act as any other that man can perform, or ever refuses to per- form. 13. Undoubtedly, testimony has its laws and condi- 1 tions, and there are eases in which it becomes so strong ,_;.and so circumstanced as that we do not hesitate, and in ^ which we ought not to hesitaite'to place confidence in and accept what is thus declared to us with as much as- surance and with a compliance as unhesitating in our actions as though the matter were one that depends up- fon our own personal observation. And in fact the whole •discussion of what is called "the Evidences of Chris- tianity " is a discussion of the testimony on which we ought to accept what is taught us in the Bible as a Rev- - elation from God. But the consideration of Testimony NATURE AND SCOPE OF LOaiC. 21 does not properly fall within thfe proyinoe pi Logic. It is in fact a science by itself and must have special rules and canons in each of the various departments of in- quiry ; and in the department of Law it has been es- pecially elaborated and reduced to system. 14. The distinction which I have pointed out is not always observed, and much ofwhat we actually receive on testimony enters into what we call our knowledge ; and both facts and principles which rest on this basis, enter with those based on observation and insight, into what I have called the raw material, with which our logical processes begin. And after they have been thus blended and combinded, no futher notice is taken of the differ- ence between them for any of the purposes or processes of Logic. 15. Logic is the Science of Eeasoning ; and in the word " reasoning" I include all the forms of mental ac- tivity that follow upon Observation, and intervene be- tween it and the most general principles and the most comprehensive truths at which the humari mind ever arrives. A fact must precede in the order of time the science, that explains the fact. Men must have reasoned before they had a science of reasoning. The very con- struction of a science is, itself, an exercise of flie faculty and process of reasoning. And hence Logic cannot be an explanation, or inculcation and demonstration of any one way or mode of reasoning ; it is, and must be an ex- planation of all the modes and methods of reasoning. 16. Eecurring now to the nature of Observation, we see that we observe facts one by one, and as individual objects. I may. see, for example, a dozen objects on the table before me at one and the same time, and these ob- jects do undoubtedly make a gronp or collective whole, and they make a class or genus ; but I see them, one by 32 TEXT-BOOK OF LOGIC. one, individually, and as detached individuals. And if our intellectual action were to go no farther but end here, we should have no science, no language — we might have sounds — one for nearly every object, but we could have no adjectives — no common nouns — most likely, no verbs, and, at any rate, no sentences, or propositions. 17. The first act after observation is called Analysis. Eeal analysis, however, is, as its etymology imports, al- ways physical. By it we resolve, water for example, into oxygen and hydrogen ; sugar, inito oxygen, hydrogen and carbon. In all these cases, the parts or elements, into which the object is resolved by analysis, are substantial realities, and are denoted by nouns, which, as gram- marians, we call concrete terms. But in what is called logical analysis, the case is otherwise. We suppose, in accordance with an old theory .of ideas, that the object is made up of certain properties, essences or entia ra- lionis, so that, by analysis, we can separate these prop- erties, one from another. What we actually do, however, in a logical analysis, is to think of the object as made up of properties, and then resolved into its ultimate ele- ments. And what we thus (by supposition), obtain by logical analysis, are only the properties of objects, and tliey are always denoted by what grammarrians call ai- str act, terms, a s wMteness,,. roundness, solidifcyj etc. On- tologically, as existing by themselves, they are nothing, and cannot even be thought of as existing distinct from their substance. Solid objects exist ; but solidity does not. 18. The next step is Adstraction. By this in one view of the word we draw away one property of an object to make it a special object of thought. But in a more correct view of it, we withdraw the mind, from thinking of any but one of the properties of the object, which NATURE AND SCOPE OF LOGIC. 23 property we are supposed, as described before, to have separated from the rest by analysis. This, process of abstraction is the origin of what are called abstract terms. 19. And now occur two other processes — both of which are synthetic in their nature ; and although they are different, they can hardly be separated, so that the one of them can be performed without the other.' They are Judgment and Generalization. 20.- By an act of Judgment, we form a sentence or proposition, in which a word denoting the object con- stitutes what is called technically the sttbject of the proposition, and some other word called by grammari- ans an adjective — denoting a px-operty of it, (which word — we had obtained by analysis,) is made what we call the predicate, as " snow is white," the verb " is," being regarded as the copula. Hence, a Proposition con- '- sists of a subject, a copula and a predicate ; and the act of judgment is that synthetic act of the mind by which , we affirm the agreement between the subject and predi- cate of the proposition. Hence the subject is the result of observation, the predicate, of analysis, and the copula, ^ of judgment. 31. But the property which we thus affirm of any subject, is a property of other objects also besides that from which we obtained it by abstraction, and is in fact obtained by abstraction in like manner from a great va- riety of other objectsA-as "whiteness " Irom snow, from paper, linen cloth, from petals of flowers, etc., etc. Now in the very act of judgment we are forming a generaliza- tion dlso; that is, we are referring all objects that are white, and from which whiteness may be obtained by analysis, to a class, and are grouping them, (in thought,) into what is technically called a genus, and hence the 34 TEXT-BOOK OF LOGIC. ■word " to generalize." And the property which we thus make constitutive of a genus, we call the essential prop- erty, the one which mak^s the class to be a genus — the only one that is distinctly seen to be common to all ob- jects in that class. 22. For the most part, however, in generalizing, we make several of the most prominent and obvious prop- .erties Essentia, as we call theni, and perhaps without exactly discriminating or noting them separately. We denote the group or class of objects by a general term ; called general, from the fact that it denotes a-genus, and is obtained by the process of generalization. As ex- amples we have in fact all the common nouns in a lan- guage, as man, horse, pen, house, etc. Any of these common names or general terms may also be used as predicates, as, " dogs are animals/' " horses are quadru- peds," etc., etCr 23. Having thus formed or grouped objects into gen- era, we next divide them into smaller classes called species or kinds ; and the properties by which we distinguish the species otk^ from another, we call by the technical term. Differentia. Thus we divide man into species, as Negro, Mongol, Caucasians, we divide horses into species and call the different kinds of horses by different names, as Arabian, Blood, etc. The properties which distinguish one individual from another, we call Inseparable acci- dents, or Individual marks ; and those which distinguish any state, mode, or condition of any individual from another mode or state of the same individual, we call Separable accidents, as sickness or health in man, warm and cold, etc., in nearly all the objects we know of. 24. It is obvious that there is no one property that is always either Essentia, or Differentia, but all properties are in turn one or the other, as we choose to use them NATURE AND SCQPK OF LOGIC. 35 for the purpose above indicated. Even the properties which are for the most part regarded as accidental, as sickness or health, become essential when we speak of the sick as a genus, and divide them into different spe- cies, as those that are sick with one or another of the various kinds of disease. Or sickness becomes a differ- entia when we distinguish the genus Man into the two kinds, sick and well. ; 25. Hence any property is said to be (1) essential to the individual object when it is inseparable from it or cannot be separated from it without changing its identi- ty, (2) essential to a species when it is one of the differ- entia of that species, and serves to distinguish it from another species, and (3) essential to a genus when it is one of the properties that include objects in that genus. But when a property does not perform one or another of these functions, it is regarded as accidental. 26. It has not been customary, however, to include all the mental processes above described, nor in fact any of them except one, within what has been considered to be the province of reasoning. The term has been used for the most part in a more restricted sense, to denote the mere processes of inference or deduction. Hence a very great mistake as to the nature- and scope — and we may gdd the utility of Logic. Many writers claim that Logic applies to and can explain only a small part of our rea- soning processes, so that, in fact, by far the largest part of the opinions we hold and act upon cannot be sub- jected to logical criticism, reduced to or judged of by the formulae and principles of, Logic. There are those ■tvho hold that all our higher convictions of religion and 4uty are of this kind. And again, another and more common misapprehension is that Logic is but one mode of reasoning, and is "reasoning by mood and figure," as 26 TEXT-BOOK OF LOOIG. the expression is — a method that is very stiff, awkward and incapable of accomplishing any good result that cannot be better and more easily accomplished without it. 27. But Logic really begins where Psychology ends, and the two together explain all the processes from first to last ; and whatever is true and leads to a correct result must be in accordance with the principles which they teach. Logic is the process in which from two proposi- tions considered as, and called Premises, we infer an- other called the Conclusion, which is true if (1) the premises are true, and (2) the process or inference is valid. The Conclusion can, however, contain no term or word that was not in the Premises. 28. From what has been said of the science of Logic, its scope and its aims, it must be manifest that a thor- ough mastering of it, if such a thing be possible, will be of great use to every one as an instrument and means of scientific investigation in search of truth,. and in pre- senting and proving the truth to others. It will not only point out the right way and put one on his guard against the dangers of the way ; but it will put him in possession of a knowledge of the ways and means so as to enable him to abridge his labor and save his time and strength to a great extent. It will enable him to know what he knows, and thoroughly to understand it. 29. And yet Logic is, after all, like mathematics, gram- mar, etc., chiefly an instrumental science — of no great value in itself, and valuable chiefly as it is 'a means to that which is valuable in itself and which can be better obtained with than without it, even if it never helps us to anything that cannot be obtained without it. 30. It is not to be expected, however, that' one who has studied Logic will be always stating his arguments in the complete formulae or pointing out th'eir character NATURE AND SCOPE OP LOGICK 37 iu the use of pgical terms and technicalities ; anymore than it is expected that one who has studied grammar will be always parsing his sentences or citing the rules of etymology and syntax thai justify the structure and turns that he has given to them. But, like grammar, it will help him to speak without violating its rules, and thus render himself intelligible and conclusive in his reasoning. 31. Besides this, as in grammar, and in fact in all other sciences so in Logic, technical terms and names for all the objects and parts of objects we have to deal with are necessary in order to discuss arguments — to talk about them, point out their defects if they have any, and to show wherein and why they ai-e of force if they are valid. T!he science, however, makes no claims to supply the place of insight, sagacity and tact. If these are wanting, it can do nothing for us. It may help us as spectacles do defective eyes. It may also serve as a microscope to render visible objects that would other- wise pass unnoticed; or as a telescope, to bring into view what wgre otherwise too distant for vision. But, after all, it is only a means or instrument. Natural insight, sagacity and comprehension are gifts and facul- ties that it aids but cannot replace. 32. If, therefore, one believes or assents without rea- soning, it may be a mere matter of observation and .insight. Or it may be a mere matter of feeling and willfulness of which perhaps no account can be given. But if he believes as the result of reasoning, Logic must explain the process. In all knowledge, therefore, in fact in all rational belief, we have these three : Observation, Insight, Seasoning. The first of these is Observation-; the last is Reasoning ; but the greatest is iiifSiGHT. Wow, if one believes or assents without reason, or 28 TEXT-BOOK OF LOGIC. reasoning yet even, then, Logic will dey elope that fact and show the unreasonableness of the course by showing what absurdities are involved in the opinions which those who proceed in this manner profess to hold. 33. Eeasoning in reference to its method is of two kinds, Analytical, called also a pr^iori, or demonstrative — which is reasoning from the nature of the subject, and Synthetical, called also a posteriori and deductive, which is reasoning from the relations of the subject. 34. Analytical reasoning, begins of course with logical analysis, and it takes its name from the notion that by unwinding or unfolding the conception of the subject we find the predicate we wish to affirm of it, either obvi- ously contained or necessarily implied in the nature of the thing itself. Thus, by considering a straight line we see from its very nature that it must be the shortest line that can be drawn between two points, and that it can- not enclose a space. All mathematical reasoning is of , this kind, as we shall see more fully bye-and-bye. 35. This kind of reasoning is called a priori, because it proceeds fi'om the very idea or conception, or what we are supposd to know of the thing itself before any ob- servation or experience'concerning it.* It is called demon- stration, because it begins with, and proceeds by means of, what is self-evident, needing no proof, and shows the conclusion to be true in the very nature of the subject. 36. Synthetic Reasoning is called a posteriori; because * ' ' Eeasoning is sometimes said to be a priori because it is reasoning from cause to effect. 'TTtoieZi/'s Ehetoric, Pt. I, Chap. 71. §2. The ambiguity is undoubtedly inconvenient ; but it is too late now to correct it. Whether we have any ideas or conceptions of things he- fore observation or experience, may be a matter of doubt, and in fact is disputed and denied. But that we have "ideas" as they are called, of things which we have never seen, by means of their definitions, NATURE AND SCOPE OF LOGIC. 39 it is based upon an examination of the relations and connections of things, which relations — or rather our knowledge of them, must be, for the most part, posterior to the cognition and observation of the objects about which we reason. 37. The relations of things, one to another, on which our reasoning about them depends, are four. (1.) The relation, of Quality or of classification. It depends upon the fact that every object of observation or of thought even, is an individual in a species, and that that species is a class in a higher or ,more compre- hensive class, called a genus, and so on, up to the highest and most comprehensive class — a class which compre- hends all things and has but one attribute common to them all. It is called the relation of quality, because it drpends upon and shows tvhat a thing is. (3.) The relation of Quantity. This may be (1) simple extensive quantity as greater or less, as in Geome- try ; it may be (3) numerical quantity, as in Arithmetic or Algebra ; it may be (3) quantity of time, as before and after in History ; it may be (4) quantity of space, as more near or more distant, as in Geography and Astron- omy ; it may be (5) quantity of intensity, as when we say of the weather, it is warmer or colder, or of a color, it is darker or paler; or it may be (6) a comparison of ratios, as, when we say 2 : 3 : : 4 : 6, or 3 : 4 > 3 : 3. can admit of no doubt. The mathematician reasons concerning a curve, the exact representation of which he has never seen. And in all oases we form "ideas" of things from which we reason a priori, to ^properties and relations concerning them, which have never yet fallen nnder observation and which perhaps never can do so. Such is the case witii regard to the infinite divisibility of matter, and the law of motion, which asserts that a body in motion, with nothing to ob- , struct or retard its course, will continue to move oti forever. 30 TBXT-BOOK OF LOQIG. (3.) The relation of OAUSALiTY^or of cause to effect. Everytliing that we see, and everything that we think of except One, is regarded as an effect of something else, and everything without exception, is also regarded as a cause. Everything within the reach of human thought is bound in the chain and concatentation of causality. The cause is always some proof of the reality and of the nature of the effect, and conversely the effect is proof of the reality of the cause, and discloses to us much of its nature. (4.) The relation of Totality. Everything we see or can think of, is part of a complex whole — not merely an individual in a species,. but a part of a whole. Not only a letter in a word, a word in a sentence, but the features on the face, the rocks and trees in the landscape, the stars in the constellations of heaven, nay even the constellations themselves, are all parts of more compre- hensive wholes, whose relation to the whole and to the other parts, is a means of reasoning and of knowledge in regard to the whole which they make up, and to the parts which, with them, make it up. 38. Demonstration or reasoning from the nature of the subject, must always precede Synthetic or Deduc- tive reasoning in the order of time. And although its validity does not depend upon the Formulae or Syllo- gisms in which it is stated, it is nevertheless always in the same form as the reasoning from the relations of things. We will therefore proceed first to consider these relations and the Pormulse that grow out of them. 39. I think that it will be obyious from onr review of the Nature and scope of Logic, that it comes within the province of that science to discuss all the processes and means of knowledge and belief except what is included in Psychology. There are, however, writers who hold NATURE AND SCOPE OF LOGIC. 31 what indeed is a very common opinion among unedu- cated people : that Logic is only one method of reasoning among many ; or, as some would represent it, it is only a mode or form of stating arguments ; and, there is still another class who seem to think that it is a science which is to furnish us with a certain dexterity in the use of general principles, formulae and technicalities, hy which we can always at least confound an opponent if we cannot make the worse appear to he the hetter reason. 40. But the view I take of the suhject is far different from any or all of these. It is no one mode of reason- ing; it is rather the science that explains all modes that are at aU valid or legitimate. It is not a mode or form of stating arguments, although it discusses aU the modes and forms in which valid arguments can be stated. And- yet the most skillful logician and the most thoroughly trained mind — which is always the most logical mind — will be the least likely of all, perha,ps, to state its argu- ments in the use of technicalities or with an obtrusive display of formulae. And, of course. Logic includes all subjects of thought, knowledge^ opinion or belief; for it begins with logical analysis, explains judgment and gives the terms as well as the processes of inference. But acts of mere imagination and fancy it does not ex- plain. It is no treatise on poetry and the fine arts, and is not very poetic in its character. But if there be an object in existence or out of it, of which we know any- thing, or about which we can make any affirmation, that object falls within the nature and scope of Logic. 41. What is commonly called an argument usually ex- tends through a book or discourse consisting of many smaller arguments or formulae called syllogisms. These syllogisms are the "little steps" of reasoning, out of 32 TEXT-^OOK OF LO&IC. which the discourse or argumentative treatise is made up. Any fault or fallacy in these, or in any one of them, will therefore vitiate the whole. And yet it is very sel- dom, if ever, that these syllogisms or formulae are fully ancl formally stated. Each one of them must of necessity have two premises besides its conclusion, thus making three propositions in all. But in a continual argument it is very seldom that both premises are stated, one being assumed as too well known to need express mention. And quite often the conclusion even, is not stated, but implied rather and assumed as a basis or condition of proceeding with the next step in the course of the rea- soning. 43. Now it happens that the fault of a general argu- ment or course of reasoning often lies in these assumed, but not expressly stated propositions, whether premises or conclusions. But, of course, we have no way of finding what these propositions are, except as we complete the formulas or syllogisms of which they are part. It is a sort of an evolution process by which we find the root of a given power. It is a reconstructive process rather by which we restore from a few fragments a completed whole, jiist as some skillful anatomist from a few frag- ments of fossil bone can reconstruct the entire skeletoli of the animal to which they once belonged. PART II. TEEORUTICAL, THEORETICAL LOGIC. ANALYSIS AND CRITICISM OF FORMULA. 43. There has been much dispute as to whether Logic should be regarded as an aft or as a science. If it is a science only, and as a science, it should teach principles and truths concerning reasoning. If it is an art, and as an art, it should teach the application of those principles and truths. The teaching of the application without the previous teaching of ■ the principles would, at most, make one a mere contemptiblfe pettifogger; and the teaching of the principles without, at the same time, their practical application would be of no great value. The last without the first would be but half of what any student should know: the first without the last would not be worth knowing at all, and in fact, eouM not be said to be known or understood in any pro-per sense of the word. 44. The simplest steps or processes of reasanimg, as I have already said^ must either be, or imply, a form or formula, called a syllogism. The number of possible forms that have validity is definite, well known, and each one of them may be described ; and the principles on which t£eir validity depends may be fully and satis- factorily set forth. 45. These syllogisms, however, are but the "little steps" 36 TEXT-BOOK OB LOOIG. of reasoning; the moulded brick or rough ashlers of which argumentative discourse is made up ; and their construction into a discourse or their use in proving a proposition depends upon entirely different principles. The validity of the syllogism depends upon principles derived from the relation of its parts one to another j the method of their application depends upon principles derived from the nature of the subject matter to which they are to be applied and the" circumstances under which the application must be made. Hence I divide the work before us into two parts, 1st, itheoretical, treating of the formulae and their validity, 3d, practical, treating of the methods of their applica- tion to the various uses and purposes of life. CHAPTER I. THE LOGIC OF PROPOSITIONS. 46. Knowledge begins with the perception of objects. These objects we see individually, and one by one. By analysis and observation, we think of their properties, and those properties are denoted by adjectives, (the objects being denoted by nouns), which we can predicate of the object, and thus instead of names of things, we have pro- positions or affirmations concerning them. With these propositions begins what is commonly regarded as the process of reasoning. 47. The predicates that are thus obtained, are all ad- jectives. It is manifest, however, that we may also predi- cate of any noun any other noun that denotes a class in which the object denoted by the subject of the propo- sition is contained. Thus, " John Doe is a man," "Horses are quadrupeds," etc. In fact the predicate, which in this case is a general term, denotes a genus by the properties that are common to all the individual objects in the class. Hence, in the former case, that is, when the predicate is an adjective, we are said, in scholastic language, tQ predi- cate the species. But in the latter, when the predicate is a common noun, we predicate the genus ; the predicate denoting a class in which the subject is comprehended. 48. Hence, for present purposes, we may regard it as 38 TEXT-BOOK OF LOGIC. altogether immaterial and unimportant whether the predicate be an adjective or a common noun. But one or the other it must be, unless the proposition be a mere verbal definition. In this case, the subject and predi- " cate are both merely different names for the same thing, denoting it by what are called alternate conceptions of it, as '■' common salt is chloride of sodium ;" the former term denoting it by its position in common use, the lat- ter by its chemical composition. Again, " the Queen of England is Victoria ;" the former denotes her by her of- fice, the latter by her personal name. 49. And in fabt, we may regard all the words used to denote or describe the subject of a proposition, as but one word — a compound word — making what we call a com- plex term. In this view, the simple term, or common noun denotes the genus, and the adjective or relative clause will limit the assertion to some part or species of the genus. Thus, "good men," "cold winds," "men lohofoUom Mahomet," — Mahometans, etc., etc. 50. In the same way, all the words that make up the predicate may' be regarded as one, for logical purposes, however compounded or complex it ma,y be, and it will be none the less either (1) an adjective denoting a property of the object denoted by the subject of the proposition, or (3), a noun denoting a class in which it is contained, as "good men are faithful to their trusts." Here, "faithful to their trusts " is virtually an adjective denoting a prop- . erty or quality of " good men." 51. In reference to what is .called the quantity of the iJi'oposition, it is obvious that it may bfe either- (1) indi- vidual and aflBrm a predicate of an individual object, (2) partial, affirming the predicate of some objects making part of a class, or (3) general, affirming the predicate of a class to which there may be individual exceptions, and TEE LOGIC OF PROPOSITIONS. 39 (4), universal, affirming the predicate of a claBS to which there are no exceptions. 53. The two last named — general and uniyersal — are not distinguished from one another in form at all, and the difference between them is found in the subject mat- ter of the propositions. Thus, if we say, " men are rational beings," the proposition is universal, in form, but there may be exceptions, as in the case of idiots, who are not rational, though I presume no one would deny that they are men. In fact, there are, or at least, may be exceptions to all the propositions, however general in form that are proved by any of the a posteriori methods ; that is, any of the methods that proceed from observa- tion and by means of induction and generalization. But if we say, " all triangles'have three sides," or " in all tri- angles, the length of one side is less than the sum of the other two," we have a universal proposition to which . there can be no' exception. And this is the case with all propositions that are proved by demonstration and a priori. (See Part Illf Chap. II, Sects. V and VI.) 53. But for all present purposes, we will leave this difference out of sight and proceed to consider the propo- sitions as one, and call them, as writers on logic have al- ways done, universal propositions. 54. Any proposition is regarded as individual when the subject is either (1) a proper name, as John, Thames, London, etc., or (3) any common noun with the pro- nouns, " this," " that," or the definite article " the " with a relative clause following, as " the man who did this," etc. 55. An individual proposition is, for all the purposes of formal logic, or the discussion of syllogisms, to be considered as a universal proposition ; in as much as it always speaks of the subject as a whole. We have, there- 40 TEXT-B OK OF L GIC. fore, really ta consider only the two kinds so far as Quantity is concerned, namely, Uniyersal and Partial. 56. But in reference to what is called the quality of propositions, there may be three kinds. (1) The propo- sition may be affirmative, and include the subject in the the predicate as a class, as " horses are quadrupeds," or (2) it may be negative, and exclude the subject from a* class, as " horses^ are not birds," or (3) the proposition may be what is called indefinite, that is, affirmative in form, and negative in force ; as when we say, " men are immortal." The predicate being a negative term denotes as such, no class, while the proposition is equivalent to " men are not mortal," ip. which the subject is excluded from the class denoted by the predicate. However, the ■ indefinite and the affirmative propositions are to be con- sidered Ss the same for our present purposes, and we have in relation to "Quality but the two kinds, Affirma- tive and Negative. Or combining quantity and quality, we have four, namely. Universal AJBrmative, Universal Negative, Partial Affirmative, and Partial Negative. These propositions are, for the sake of convenience, called respectively, A, E, I, 0, thus : Alls are P, A. No S are P, or S are not P, . E. Some S are P, I. Some S are not P, 0. 57. If we regard the form of propositions alone, as that upon which their force and efficiency for categorical reasoning depend, it is evident that there can be but these four kinds of propositions. If we speak of any thing, we must (1) speak of it either as a whole or of some part of it. In the former case, the proposition is universal, in the latter, partial ; and we must (3) either affirm or deny something of that of which we speak. THM LOGIC OF PROPOSITIONS. 41 ■whether it be a whole, or only the part of some thing. In the former case, the proposition is aflfimative. In the latter, it is negative. Hence, combining the two condi- tions, we have A, E, I, 0. 58. These propositions grow out of and sustain most intimate relations to classification. 1 59. Every object in nature is one — an individual — and is included in some class. Hence we have such words as " chairs," "pens," " tables," " horses," " dogs," " crows," " wrens," etc., denoting classes of objects. Any two or more of these classes are combined into a higher class, and we have such words as " furniture," " quadrupeds," " birds." Two or more of these are combined, and we have such words as " animal," " vegetable," etc., and thus on until we come to a class called the summum genus which includes all-things, and has no name. 60. The lower term, that is the common name that in- cludes the fewest- individuals, so that there is no terni between it and the individual name, is called the infima species ; and any other class is called a species, -if it be considered as included in a higher and more compre- hending class, or a genus if it be considered as compre- hending other and smaller classes. And those in the order ascending from the individual name up to the summum genus are called subaliernate terms. Thus, let K" denote an individual, and we have N, dog, quadru- ped, animal, etc., forming a series of subordinate or sub- alternate terms. 61. But at each step we have two or more classes uniting to form a class above, thus : Quadruped, I ^^j^^j_ That is quadrupeds and birds are both animals. 63. Any two words which are in different lines below 43 TMXT-B OOK OFLO 910. th^t in whicli they unite as " animal," are called co-or-. dinate terms, as "quadruped" and "bird" are co-ordin- ate. 63. The test of co-ordination is this : no one object can be in more than one of the classes denoted by any sjiaijjji- set of co-ordinate terms. And any two or more term&that have no indiyidual common are co-ordinate. 64. The class pext above any two or more co-ordinate terms in which they unite is called in reference to them the proximate genus. 65. It will be very easy for any person who chooses to do so, to make for himself a table or diagram that will illustrate to the eye the principles of classification. It would be something like the numberless springs issuing from the mountains and hill-sides that surround and form the boundary of any great river basin. Each spring is an individual object. Two of them unite and form a rill or stream ; a few of these streams unite and form a creek ; the creeks form a river, and several rivers unite in their courses to the ocean. In the same way, the twigs of a tree unite to form a branch ; a few branches form larger branches, and these, at last, unite in the trunk or main stalk. So objects unite to form species, species form genera, genera unite in still higher classes, until we reach the summum genus, which in- cludes, in fact, all things that are real. And, in theory, and for certain purposes of discussion, it is supposed to include all things imagined or imaginable as well. And the terms are called higher or lower as they stand in this order nearer to the name of the summum genus on the one hand, or to that of the individual object on the other. 66. From the nature of classification it is obvious that. THE LOGIC OF PB0P08ITI0NS. " 43 (1) The lower the term, the fewer individuals it will include. (2) The higher the term, the fewer the properties by which it will denote them. Thus the word " dog " includes fewer individual ob- jects than " quadruped," or " animal " ; but it describes those objects more definitely ; that is, it ascribes to them more properties. 67. But besides this, there is no one object or class that is not included in several classes which are neither co-ordinate or subalternate. Thus, sulphur is a " drug," it is a " mineral," etc., etc., and yet not all dr?igs are minerals ; nor are all minerals drugs. That is, " mine- ral " and " drug" are not terms in the same line or as- cending series ; nor yet are they co-ordinate terms ; and we juay represent their relation thus : The terms " drug " and " mineral " are called alternate terms, and they differ from co-ordinate terms in the fact that they always have on» or more individuals common to them all ; as in the above example, the same thing is both' a drug and a mineral. 68. Again, the same genus may be divided into species in reference to different tests or properties as differentia. Thus, we may divide man, in reference to religion, into Jews, Mahometans and Christians ; in reference to race, into Negroes, Mongols, Caucasians, etc. The terms pTo- duced by these co-ordinate divisions, as Negro, Mongol and Jew, are called disparate in reference to each other. No af&rmation cah be made between them ; no inference can be drawn from them. 69. Thus, the principles and the processes of classifica- tion are essential to all knowledge, and enter into all the 44 TEXT-BOOK OF LOOIO. processes of understanding and compreliension as well as into those of reasoning — all I say, after the very first, which is mere observation, and which the animals per- form, as well as man. These principles are very simple, and when once understood, all the "necessary axioms or maxims of reasoning become self-evident. The principles of division are also implied in classi- fication. ^ 70. There are three kinds of division. (1) Numerical, in which we divide, as in Arithmetic, mere numbers, (3) Physical, in which we divide any individual object into parts, as a loaf of bread, into slices, and, (3) Logic- al division, in which we divide genera into species ; spe- cies, into individuals, and then, when logical division can go no further, physical division begins. 71. Logical division can go no farther than the indi- vidual, because in dividing the individual, we resolve it into parts and destroy its individuality. A man divided into parts would be a man no longer. Nor could the parts, each and separately, be called a man ; they are merely parts of a man, and a? such, would be ' called hands, feet, etc, etc., but not men. 73. Those classes in which the same individual object is included are called alternate species, whereas those which have, and, can have, no individual in common are called co-ordinate parts or species. 73. In division, we have Several self-evident axioms. (1) The whole must be greater than any one of its parts. (3) The sum of the parts must be equal to the whole, whether we count them and reckon them by number or weigh them for example, and compute them in units of weight. (3) In logical division, moreover, it holds that no in- THE LOGIC OF PB0P081TI0N8: 45 dividual can be in more than one of the co-ordinate parts. But in regard to alternate species, this last rule is reversed, and one individual at least, is always include ed in more than one of them ; as " Coleridge was both a poet and a philosopher." 74. I have thus far been speaking of what are called natural classifications, based on the essential pi'operties of the individuals included in the classes. Thus, if any animal is once a dog or a horse, etc., it is always a dog, a horse, etc. But if we use accidental properties, the classes are artificial and fluctuating. Thus, if we speak of men as sick and well, we have the two species denoted by these words. But any individual may belong to one species or class to-day and the other tomoiTow. 75. If now, we recur to our four propositions. A, E, I and 0, we shall see that : (1) AH affirmative propositions either grow out of or \ make, in the process of the affirmation, subordinate I terms. Horses are quadrupeds, quadrupeds are animals, etc.; this is true because such is the natural relation of the objects we are speaking of. But if we say certain men are " sick," " asleep," " laughing," " weeping," etc., we. make of them, for the time being, a class. And, in this cascy as in the other, the subject and predicate of our proposition are subordinate terms. If the proposi-' tion be universal (A), the subject is the lower term ; as " aU horses are quadrupeds." But if the proposition be ' partial (I), the subject may be the higher term in the ' natural classification ; as " some quadrupeds are horses." (1) All negative propositions either grow out of or malce, in the process of negation, c oordinate terms. « Quadrupeds are not birds," and " birds are not quadru- ^ peds." If the classification be founded in the nature of ; the objects we speak of, then the negation grows out of ' ^46 TEXT-BOOK OF LOGIC ^ tlie relation, and the objects are permanently co-ordin- ate. Otherwise, the co-ordination maybe merely trans- sient, based on some accidental property. 76. In all universal propositions, the subject is spoken . of as a whole. Hence, it is said in technical terms to be ^distributed. In all negative propositions, the subject is wholly excluded from the class denoted by the predicate. I Hence, in this case, the predicate is said to be dis- ! tributed, or: ' ; UniTersals distribute the subject. Negatives distribute the predicate. Or again, and more definitely : A distributes the subject. w~v..i.>-«^«-<^ ^f> >->^ -^ B ' " both subject and predicate. '>' ^'i-^- ' I " neither. (P^^tL^ ci-f^.^....^^.-.i " the predicate. - ^-O-a^M^^ 77. Propositions are either didactic or figurative. A didactic proposition describes a thing by its properties, and the predicate will always be either (1) an adjective, denoting a property of the subject, or (3) a common noun, denoting a class in which it is contained; as " snow is white," " horses are quadrupeds." All others are figurative, or poetic* 78. Didactic propositions are either analytic or syn- thetic. An analytic proposition is a mere definition. It is obtained from a logical analysis of the subject, states only its nature, and adds nothing to our knowledge of it, beyond the mere fact of knowing what it is. Thus, the definition of a triangle, though the beginning of trigo- * This, however, is not exactly the meaning given to the word " figurative " when used in treatises on Bhetoric, and for purposes of rhetorical criticism. But it is founded in the nature of the case; and is a distinction, the importance of which we shall see in the chapters on Language and on Fallacies in Diction below. TEE LOGIC OFF B OF 08ITI0NS. 47 nometry, is far from explicitly stating all that is true con- cerning the triangle. Any proposition that predicates of a subject anything more than its mere definition — that is, its proximate genus and its differentia — is called a synthetic proposition ; it adds to our knowledge of the subject. Definitions are either real or verbal. 79. In a' verbal definition we have two words of the same kind or logical quality — the one explaining or giv- ing the meaning of the other ; such as we have itf dic- tionaries, etc. ; as " common salt is chloride of sodium." Hence, if one term be abstract, the other must be ab- stract also, or if one be concrete, the other must be con- crete. And again, a verbal definition can always be .simply converted. Thus, if " common salt is chloride of sodium," " chloride of sodium is common salt." 80. In the case of definitions, both the subject and predicate are distributed; not indeed because they are affirmative proposi-tions ; for aflBrmative propositions, as such, distribute nothing, but because they are definitions and would fall short of being definitions if they did not distribute the predicate as well as the subject, so that nothing could be included in the predicate that was not also included in the subject. 81. In a real definition, there must always be in the predicate (1) a common noun denoting the class or prox- imate genus, and (3) an adjective. If the thing defined be a species, the adjective will be the differentia of the species ; if it be an individual object, the adjective will denote some inseparable accident ; as " triangles are three sided plane-figures," " quadrupeds are four-footed verte- brates," " Napoleon was the general who commanded the French at Waterloo," and "Cousin was the Frenchman who founded the eclectic philosophy. 48 TEXT-BOOK OF LOGIC 82. Real definitions also haye the important property, already ascribed to verbal definitions ; they can be sim- ply converted. If triangles are three-sided plane-figures, " all three-sided, plane-figures are triangles." If " quad- rupeds are four-footed vertebrates," then " all four-footed vertebrates are quadrupeds." 83. There has of late years been an effort made to show that in the case of some negatives, the predicate is not distributed. Sir William Hamilton has distin- guished himself as the author and advocate of this view. But he has adduced from the range of argumentative lit- erature no examples. He cannot even make one, without violating in form the idioms of our language, and of all languages, and thus, in fact, failing to make his proposed sentence an exainple. 84. Practically, fhe answer to Sir William's doctrine is that no such propositions as those that he proposes to recognize, have ever been found among the utterances of men, nor have any syllogisms of the class that he would provide for, ever been made, so far as appears from either his own citation of examples, or the researches of his dis- ciples. Those that have been offered as examples were all manufactured for the occasion, and are manifest fallacies in form, and so of course, ought not to be recog- nized and provided for. 85. But I think it easy to show a priori that all th« propositions and syllogisms that he proposes to provide for are impossible. We have recognized the four propo- tions. A, E, I and ; A and E being universal, distribute the subject; E and 0, being negative, distribute the predicate. But Sir William thinks" we may have af- firmatives that do distribute the predicate, and negatives that do not. Hence he proposes to reckon eight proposi- tions instead of four. Thus denoting the - four already THE LOGIC OF FROPOSITIONS. 49 discussed in this treatise, as usual, by A, E, I and 0, and denoting the other four by the symbols he proposes, we have: Affirmative : U, toto-total, - ' All (— ) is all (— ) A, toto-partial, - All ( — ) is some ( — ) Y, parti-total, -' Some ( — ) is all ( — ) I, parti-partial, - ^ Some ( — ) is some ( — ) Negative : E, toto-total, - Any ( — ) is not any ( — ) H, toto-partial, - Any ( — ) is not some ( — ) 0, parti-total, - Some ( — ) is not any ( — ) £1, parti-partial, - Some {—) is, not some ( — ) The blanks included in the parentheses are supposed to be filled with any nouns we please. Thus, in U, "all triangles are all three-sided figures," etc. 86. Now it seems to me that if we correct Sir Wil- liam's grammar, we shall dispose of his four additional propositions at once. (1) In the first place, the yerb which he uses is in the singular, — " is," " all is all," " all is some." This never occurs in English at all ; the adjective pronoun " all,' qualifying ov\j plural nouns, and plural nouns of course, require their verb to be plural. We should, therefore, write, " All are all," " All are some," etc. And so with the pronoun " some ; " we use it indeed before nouns in the singular number, but then it is followed by either (1) an adjective, as " Some man is sick," or (3) a noun in the singular number, with the article "a" or "«w," as "some man is a poet," etc. But if " some " is used before a noun in the plura;l, the verb is plural also, and that is required in the examples above given. Hence, we should read, " Some are all," " Some are some." 4 50 TEXT-BOOK OB ZOGIC. (2) But, in the secoad place, the pronouns " all " and " some " are not used in English to qualify the predicates at all. This being a negative proposition, it is of course impossible to illustrate it by examples. After compound verbs, it is true^ " all" and " some" may be used, as " He told all the men." But if we resolve this into the simple verb and its compounds, vre have a different result, " He ■was telling all the men," etc., where, it is manifest that not the word " men " alone, which is a noun, but " tel- ling the men^" which is an adjective, (when all the parts are taken together), is the real predicate. And hence we see that although " all " is used in the predicate, and as a part of it, it does not qualify the predicate at all, but is only the limiting modal of it. 87. Make these grammatical corrections, and Sir Wil- liam's eight propositions are reduced at once to the four propositions we have recognized. A, All (— ) are (— ) E, ISTo (— ) are (— ) I, Some {—) are ( — ) 0, Some ( — ) are not ( — ) And what is thus true and necessary for intelligible ex- pression in English is true also of all other languages that I know anything about. And I think it might be shown to be a necessary result of the very laws and na- ture of language as a means of expressing thought ; re- sulting from the nature and necessary laws of language, because resulting from the laws of thought itself. 88. But, as a further refutation of his theory, we may remark (3) that from the nature of negation, the predi- cate must be taken as a whole, or distributed. Negation is negation, exclusion ; and that negation which does not exclude one from being another is no negation at all. Af- firmation afiBrms identity in some respects, at least, al- ^ THE LO QIC OF PR OPOSITIONS. 5 1 ways; but negation affirms diversity. 'S is not P. In this case, it is manifest (1) that S and P, as terms, do not and cannot denote the same thing, and hence the things denoted cannot be, or be thought to be^ the same. Nor (2) can S denote any object or class of objects in the class P, for if it did our proposition would-be no S •is not P, which is the same in logical effect as S is P. And the same is true if we take ; some S is not P ; for we can make " Some S " one word, Some-S (Some S), and substitute it for S in the above demonstration, and the result will be the same, no (Some S) is not P, or Some S is P.* 89. Hamilton's whole theory with all its errors and mistakes, comes, I believe, from the assumption that Logic deals with "notions," "ideas," "cpnceptions," or something of the kind, rather than with things. It deals with realities, with things,'and -uses words to de- note and represent things, as we use the letters of the alphabet in Algebra to denote quantities, with this dif- ference only, that whereas in Algebra, we can make x, y, etc., denote any quantity we please, and a different one if we choose to do so in each equation, in Logic, on the other hand, the same word must: always denote the same object or class of objects, and for the obvious reason that words denote things by their properties. But when ob- jects are considered as units, as in Mathematics they.al- ways must be, their properties — ^which make them indi- viduals, distinguish them from one another, and group them into classes, species and genera — are not taken into account at all. 90. There are certain important relations which these four propositions. Universal Affirmative, (A,) Universal *For a oontiauation of this discussion of Sir William Hamilton's theory of Syllogisms, see below Part ll, Cliap. 11, Sec. I. § 140. 53 TEXT-BOOK OF LOGia ]^eg^tive, (E,) Partial Aflfirmative, (I,) Partial Negative, (0,) sustain to each other, which will be readily under- stood as soon as we shall have understood the principles of classification and division, already stated. 91. We shall assist ourselves towards the comprehen- sion of- the relations of these propositions, as, well as to- wards the understanding of the inferences and changes we are about to discuss, if we represent p the propositions to the eye, which we may do by the accompanying wood cut. ( (. Sj A, All S are P, is represented by one circle inclosed in another; E, No S are P, by two circles exclusive of each other; (g) ( p I, Some S are P, by two incomplete cir- ^-^ cles, cutting each other, and thus having ^^.^.^_ a part common to both ; and 0, Some 8 S ()P are not P, by one complete circle to _X— ' denote the predicate and an incomplete ^— ^-^ one for S the, subject to show that the (S f P , subject in is not distributed. ^""^ It would assist imagination somewhat if these circles were filled with little dots, each one being supposed to represent an individual object as the circles do classes of objects. 92. Immediate inference, by the opposition of Propo- sitions. (1) The propositions A and E are the Universals, and I and 0, -the subordinates, respectively, I to A and toE. If now, the Universal is true, its subordinate must be true also. If All S are P, Some S are P. If No S are P, Some S are not P. If, however, the subordinate be true, the Universal is only problematical, that is, it may be true. If Some S are P, all S may be P, that is, there is nothing THE LOGIC OF PROPOSITIONS. 53 in the nature of the assertion to prevent it. There may be insuperable objections, however, in the nature of the subject matter in regard to which the assertion is made, that renders it impossible that it should be so. If we say " some horses are quadrupeds," there is nothing implying that they are not all so. If we say that some triangles are isosceles, there is nothing in the proposition to show that not all triangles are isosceles, though we know from the nature of triangles that they are not so. (2). The two Universals A and B are called In refer- ence to each other contraries. And if one is true the other is false. • If All S are P it cannot be true that No S are P. And so, if No S are P it cannot be true that All S are P. But if one of the Universals be false, no inference can be drawn from that fact in regard to the other. Thus, " All men are good " and " No men are good " are both equally untrue ; for some are good, and some are bad (not good). Hence, both universals may be false, but they cannot both be true. (3). E and I, A and 0, are called in relation to each other- Contradictories. If one of them is true the other is false, and vice versa, if one is false the other is true. If No S are P, Some S are ^ is"false. If Some S are P, No S are P is false. If All S are P, Some S are ^ot P is false, etc. Hence, of two contradictories, both cannot be either true or false. (4). I and^O are called in reference to each other sui- contraries. They may both be true, but cannot both be false. If it is true that " some men are good," it is equally true that " some men are not good." Now, sup- pose both of them to be fafee. Then the contradictory of one of these, say I, which is E, is true, " No men are 54 TEXT-BOOK OF LOfirlG. good." But if E is true, its sub-contrary 0. is true alsow, And thus 0, one of the sub-Contraries, is proved to be. true by the very supposition that makes both of them to be false. 93. Contraposition of Propositions.. A. term denoting an object by its properties is called a, positive term.. A term denoting an object or a class of objects by the absence ol some property is called a priva-. tive term, as " blind," " deaf," etc. Hence the positive term and its corresponding privative make two co-ordin- ate species in the same proximate genus. As all animals, are either " blind " or " seeing." But we do not speak of a tree, a rock, a mountain, etc., as " blind." We, how- ever, make another class of terms, which we call negatives,, by prefixing a negative particle to them. As wHpossible,, Mifinite, etc. These words do not really denote or de- scribe anything. They are really the complement of the positive term in the summum genus. Thus let S denote any species, and then non-S will include all things, real or imaginary, that are not included in the species S. All things are either possible'or impossible. All things are either finite or infinite, etc. 94. By means of these negatives we can change what ■ is called the quality of propositions from afiSrmative to negative, and vice versa, from negative to affirmative. (1). Thus, if S are not P, S denotes a species that are not included in the class P ; and if not included in P, they are in non-P. That is, S are not P. Hence, by substituting the negative of the predicate itself and dropping the negative from the copula, or, in other words, by connecting the negative with the predi-i cate instead of with the copula, we have an affirmative' proposition" with a negative terra for its predicate, instead of an affirmative proposition with a negative copula. [It THE LOGIC OF PEOPOSITIONS. 55 should be noticed that no S are P is the same as " All S are not P.] (2). If we have the TJniTersal Afifinnative All S are P, we can by means of two negatives make it a negative proposition. This is most likely to be done by using the negative copula "no" or "not" with a negative predi- cate. As No S is non-P. Or we may say there ia no S that are not P. " There are no horses that are not quad- rupeds." This is' called stating a proposition by contra position, and the two forms may be called the first exposita, and the second contra-posita. (3). I can never be stated by contra-position, for it has no term that is distributed. But is frequently stated so, for the purposes of logical analysis and resolution. Thus, Some S are not P is the same as some S are non-P. (4). And for E, the Universal Ifegative, we may have a negative term for a subject if we will use it as an undis- tributed term. Thus, if " no men are horses," " Some non-men," that is some things that are not men, are horses." This will hold true if we remember that the summnm genus includes all things conceivable or incon- ceivable, all things that can be thoiight of or spoken of, whether real or unreal, possible or impossible. 95. By Conversion of Propositions. In the conversion of propositions we change the rela- tive position of subject and predicate. Thus, S are P becomes P are S. The first form of a Proposition is called the Exposita, and the second is called the Converse. (1). It is manifest that B and I can be converted sim- ply, as it is called. If ISTo S are P, No P are S. The two are co-ordinate species, totally exclusive of each other. Or, if some S are P, " Some P are S." The two are al- 56 TEXT-BOOK OF LOGIC. ternate species, and are mutually inclusive in part of each other. " Some poets are Americans." " Some Americans are poets." (2). But in the case of A, the Universal AfiBrmative, this mode of conversion cannot be practiced. Por in A the subject is but a species in the class denoted by the predicate, — the predicate, as we have so often said, being the more comprehensive claa*. If "All poets are artists" it does not follow that "^ZZ artists are poets." Hence, A may be converted into I by limitation ov per accidens, as the Schoolmen say, "Some artists are poets.'' In case, however, the subject and predicate of a Uni- versal Affirmative are syiionymous, that is two words denoting the same thing, the proposition may be con- verted, simply. As "lunar caustic is nitrate of silver," therefore, " nitrate of silver is lunar caustic." Such prop- ositions are called identical. 96. By both contraposition and conversion combined. (1); We have seen that 0, the partial negative may be contraposed into I, by substituting for its predicate, terms of the opposite quality, (that is a negative for a positive, and vice versa), and dropping the negation from the cop- ula, as Some S are not P, Some S are non-P. In this form it may be converted thus,' Some non-P are S, " Some men are not poets," " Soine things that are not poets are men." can^be converted in no other way. (3). By the same two-fold change, A may be made into an exclusive proposition, as " All civilized pen^ns are white." By contraposition as before explained, we may have " No civilized persons are not white." But we may convert this into the exclusive form, " None but whites are civilized." That is, if all the species civilized are included in the genus white, none that are not included in the genus white, can be in the species civilized. %' THE LOGIC OF PROPOSITIONS. 57 97. There are one or two forms of double propositions that it may be well to notice in this place. ■ (1). One we may call the exceptive, thus, " All S except X are P." Here we have the proposition A, All nou-X are P, and the negative, No X are P, " AU but the Apos- tles fled." " All non- Apostles fled," and "No Apostles fled," are both contained in the exceptive proposition. (2). We may also have another form of the exclusive propositions, thus if " None but whites are civilized," we can say "whites are the only civilized persons," "Virtue is the only thing worth living for." Here we have the double proposition, " Virtue is worth living for," " All other things are not worth living for." 98. As covering the whole ground, we have the two following canons : EuL2 I. Two negatives in whatever form are equiva- lent to an affirmative. EuLE II. No term may be distributed in the converse that was not distributed in the exposita. 99. These transformations of propositions are of use not only in the analysis and criticism of arguments,* but * Let the student resolve each of these sentences into their three parts, Subject, Predicate and Copula ; state the QuaUty and Quan- tity of each Proposition ; convert them ; state them by contraposi- tion ; show what inference can be drawn from them by the opposition of propositions, and resolve those of them that are compound into their simple and elementary propositions. I 1. Birds fly. 2. There is a fish in the tub. 3. Great is the work of life. 4. That man's heart is not in the right place. i 5. It is wrong to put an innocent man to death. 6. A soft answer turns aw3,y wrath. 7. There is no possibility of proving' his assertion. ' 8. Few treatises contain truth unmixed with error. 9. The French are among the best soldiers in the world. S8 TEXT-BOOK OF LOGIC. also and to a far greater extent, for giving emphasis to truths which might otherwise appear comparatiyely tame. Thus the proposition " all men are sinners," is trite, but it becomes more emphatic when it is put in the form of a double negative, "there is no man that is not a sinner." And in fact, it is one of the most constant and most im- portant of the rhetorician's efforts to so arrange the wofds in his sentences that they may arrest attention^ and fix themselves in the memory of the reader or hearer. Hence a knowledge, nay more, a thorough comprehension of the Logic of propositions is essential to the thorough mastery of the best skill in the art of using them. And on the other hand, a knowledge of the Logic of Proposi- tions is quite as indispensable as a means of preventing our being misled by the mere rhetoric of propositions that sound large and mean but little or nothing. 10. Not all that glitters is gold. 11. AU that glitters is not gold. 12. Nothing is heavier than platinum. 13. Feathers are heavier than nothing. 14. There is no place like home. 15. None but the brave succeed in life 16. None are civihzed but the Caucasians. 17. All but the bad wiU be saved. 18. Virtue and vice are ahke in some respects. 19. Integrity is the only thing that can save a man. 20. A true man is a public benefactor, though he be not appreciated. 21. Neither wealth nor knowledge can wholly satisfy man's wants. 22. When the Israelites came out of Egypt, Moses was their leader. 23. In studying the history of a nation we must take note of the physical features of the country they live in. CHAPTER II. THE LOGIC OF FORMULA. 100. A Syllogism is any combination of two proposi- tions called Premises out of which, or from which, can he derived a third proposition called a Conclusion. . 101. Out of the first named relation, (§ 37, 1) — that of quality — arise categorical propositions, as they are called. They simply aflSrni an object or class of objects to be, or not to be, in a certain class ; as " Horses are quadrupeds," " Birds are not quadrupeds ; or to have, or not to have certain, properties; as " Snow, is cold," "Ice is not warm," etc., etc. Any syllogism that has both premises categorical is called a categorical syllogism. 102. Out of the second relation, (§ 37, 2) — quantity — arise comparative propositions, as already stated ; and any syllogism that has one or both of ^its premises com^ parative is a comparative syllogism. 103. The propositions that arise from the relation of causality, (§ 37, 3), are called, for the purposes of discussion in Logic, conditional propositions. They consist of two simple categorical propositions, one of which is aflBrmed to be true on condition that the other is true. Thus, if A is B, is D, in which the former is considered as a cause, in some sense, and the latter an effect. Any syllogism that has one premise conditional is called a, conditional syllogism. 60 TEXT-BOOK OF LOGIC. 104. The propositions that arise from totality (§ 37, 4) or the relation of parts to wholes, are called disjunetiye propositions; and they alscf consist of two categorical propositions, one of which is asserted to be true on con- dition that the other is not true ; as Either A is B, or C is D. And any syllogism that has one premise disjunct- ive is called a disjunctive syllogism. 105. But as the three last named kinds of propositions presuppose, and in a measure depend upon categorical propositions and the relation of classification, we will consider that class first. * SECTION I. CATEGOBICAI/ SYLLOOISMS. 106. If any one has mastered the princif)les of classi- fication discussed in the last chapter, the following propo- sitions will be self-evident : (1) Whatever may be aflBrmed or denied of any class may be affirmed or denied accordingly of whatever is contained in the class. The terms are subordinate. 107. The rule just stated above, is what is commonly known as Aeistotlb's dictum de omni et nullo. We have from this canon the following as corrol- laries : (a) The predicate of a predicate is predicate of its subject, also, and (5) The subject of a subject is subject of its predicate also. Thus, A is B, B is 0, therefore, A is C ; that is, is predicate of B, and therefore, predicate of A, which is CATEGORICAL STZL0GISM8. Qi B's subject. And A' is subject to B, and therefore, sub- ject to C which is B's s whJGc t. f^ rvxJU_c,cL»-^ And thus, the terms in any ascending series [§ 60], are so related that ea ch one m ay be subject in a proposit ion t o any one aboye it. and ■pi^'p.diflat? ^r, any one that is [2] Wherever a term may be afiBrmed of one object or class of objects and denied of an other, the two may be denied of each other reciprocally. The terms are co-or- dinate. « That is, if terms or species are not included in any one class or genus, th'ey cannot be included one in another. If A and B are not species which are included in C, they cannot be either subordinate or alternate to each other. Hence, they must be co-ordinate, and may be denied of each other.f [3] Wherever two terms may be predicated of one and * Under tMs rule there are but four syllogisms, called respectively (for reasons which I will explain below), (§118), Barbara, Celarent, _, Darii and Ferio, for example, we have S" GaJ-- T ■^ Barbara, All injustice is wrong ; persecution is injustices there- J fore, p^ecution is wrong. V^ S'^i-'V*-/ « ^ t> K/'^Cdarent, No valuable acquisitions are within the reach of , the idle; science and literatare are valuable acquisitions Liherefor&..ih6y are not within the reach of the idle. ^^ V ^^^^ < JtTVt^ y Darii, AH minerals are dug out of the earth ; some of the most useful things are mineral ; therefore, some of tie most useful things ^ are dug out of the earth. ^ /. f ctAJL-J^ «j^rw.*_ ' Ferio, No upright man should be treated with contempt ; some ignorant men are upright ; therefore some ignorant men should not 1 be treated with contempt. t Under this rule there are four syllogisms, namely : r^ Cesare, Birds are not viviparous ; bats are viviparous ; therefore, '' bats are not birds. ~#-a- 62 TM:KT-ii OOK OF LO GIG. the same object, they may be predicated of each other partially. The terms are alternate. But in case one is affirm ed and the o ther denie d of the common term, that term which is denied of it in the premises may be denied partially of the other in the con- clusion. Thus, " If whales live in the sea, ajjfl yet ■whales are not fishes," it is manifest that some things that live in the sea are not fish. Or, this third rule may be stated in two forms, as follows: 9(rT«^."5 cuiA- / [a] Any two predicates that_ are afB^ed of the same > subject may be predicated partially of each other. [5] If of two predicates one is affirmed and the other denied of the same subject, that one which is denied of it may be denied of the other partially ; as M are S, M are not P, then some S ^-re notP/^-^^^^jl^ Camestres, Mere natural ineKnations are common to man and | brutes ; the virtues are not commbn to man and brutes ; therefore, ♦ Uhe virtues are not mere natural inclinations. >^ i\ ^ ^T * ^ ^ Fesiino, Nothing really expedient is dishonest ; but sSme things ^ that appear to be expedient are dishonest ; therefore, some things / that appear to be expedient are iMt/ap. CWwfS^'^W^''^'*'*^" /. .^Baroko, The contented are happy ; some Christians are not happy ; therefore, some Christians are not contented. <-■ f^^^^j^ (b > Cn^yji. ^ ^ <' O,', ■v^ / * Under the third rule there are six syUogisnis, as follows : '^ O-'i y' Darapti, Governments are necessary to the welfare of man ; hut's governments are always a restraint upon the governed ; therefore, t some restraints are necessary to the welfare of man. Disarms, Some acts of Mendship are unjust ; all acts of frien(S? ship please those that are' benefited by them ; thfefefore, some things that please those that are benefited by them are, nevei:theless, un- just. ^ Datisi, Every form of pride is sinful ; some forms of pride are \ commended by mankind ; therefore, some things commended by / manMnd are sinful. CATEGORICAL SYLLOGISMS. 63 "[$] Any term of which another has_J)een predicated may be predicated partially of that term and of any term ^ which-^may be predicated, r^ \JS . In this case the terms are subominate, as under the first rnle, but here they are taken in the reverse order, . " animal," " quadruped," " horse," and we have " Some animals are horses." If we would regard negative propositions as aflSrma- tives with negative predicates [§ 56, ], we should need no further rules. But to provide for considering andL treating them as negatives, we have S CX't ^ 'Ti [a] If any term be denied of that which has been predicated of another, that other term may be denied of it. Thus, " All horses are quadrupeds ; no quadrupeds have wings; therefore, nothing that has wings is a horse." [5] Again, if a term has beeji predicated of another, any term of which that other has been denied may be partially denied of it. Thus, " No fish have lungs ; but some animals that have lungs live in the water ; there- fore, some animals that live in the water are not fish."* Felapion, Empty pretensions are inconsistent with true integrity ; \ .yet they are often successful in life ; therefore, some things that are ' successful are inconsistent with true integrity. _ ^ Bokardo, Some lawful money has no intrinsic value ; yet aU law- '^ (1 ful money passes current in the market ; therefore, some things that ■^-jpass current have no intrinsic value. Ferison, No virtues can be acquired without effort ; but sonie vir- M* tues are necessary to respeotibility ; hence, some things necessary to ^ respectibility cannot be acquired without effort. * The five syllogisms under this rule are as^foUows : Bramantip, Worldly honors are transient vanities ; and transient 'f vanities are always sources of disappoihtment ; therefore, some of ' our sources of disappointment are worldly honors. / '5vvi 64 TEXT-BOOK OF LOGIC. 108. For the convenience of discussion, it is custom- ary to speak of the subject of the conclusion as the mi- nor term and the premise that contains it as the Minor Premise, and the predicate of the conclusion as the ma- jor term and the premise that contains it as the Major Premise ; thus, S are M, M are P, therefore S are P. S being the minor term, P the major, and M the middle, and the minor premise, in this case, stated first, though it is most common to state it last. 109. It will be obvious on a moment's reflection that if we combine the four propositions. A, E, I and 0, in triplets, we can have, in all, sixty-four combinations, called Moods. Thus, let the major premise be A, and for the minor premise we may have either A, E, I or 0, and in lite nianner, with each of these for minor premise, we can have either of them for conclusion. And each of these sixty-four moods may be stated in either of the four different ways, called Figures, thus giving in all two hundred and fifty-six syllogisms. Of ' these, however, only ten moods and nineteen syllogisms are found to be valid and valuable. Thus, if we have the mood A, A, A, in which all the propositions are universal affirmative, we may have B, Cammes, All virtues ennoble their possessors ; but nothing that en- nobles its possessor is to be lightly esteemed ; therefore, nothing that may be lightly esteemed is a virtue. Dimaris, Some good men meet with great misfortunes ; but all J^ that meet with great misfortunes are under discipline ; therefore, q some of those that are under discipline are good men, nevertheless, c> ) Fesapo, Nothing that is vicious should be permitted as an amuse- ment ; but everything permitted as an amusement is a recreation ; therefore, some recreations are not visions. ^Y Fresison, Reason is not instinct ; instinct is a natural capacity ; ; .therefore, there are some forms of natural capacity besides reason, [or that are not reason]. CATEGORICAL SYLLOGISMS. 65 E, E also, in which they are all universal negative ; or E, A, E, in which the major premise is universal nega- tive, the minor, universal affirmative and the conclusion is universal negative. And this comhination we may vary so as to produce sixty-four moods. H 110. But with any one of these varieties of moods, we may have four sub-varieties, called Figures, according to the position of the middle term. Thus, calling the minor term S, the major P, and the middle term M, we have P are M, rv,>\ tS S are M, - '^..xjr r-^ .-. S are P. X^;, , ^ P are M,- r^§,'^i~^ M are S, .A .-. S are P. ^ ' \ That IS, m the 1st, The middle term is subject of the major and predicate of the minor, premise, 2d, It is predicate of both' premises, 3d, It is subject o'f both premises, ■ 4th, It is predicate of the major and subject of the minor premise. We have thus exhausted the possibilities of form and structure qf categorical syllogisms. With but the three terms there can be but the sixty-four moods and but the four ways or figures of stating the moods. 111. So too, there can be but the four relations of terms, subordinate, co-ordinate, alternate and disparate, [60-68]. The first of the four rules provides for sub- ordinate terms taken directly, and the fourth provides for thern if taken indirectly, or in the inverse order j as 5 [1] J M are P, S are M, •. S are P. -VN -^v. oriv - [3] ^^ M are P, ( K. M are s. <--- -•> , •. S are P. 66- TEXT-BOOK OF LOGIC. will be seen if we refer to the first and fourth figures, (§ 110). The second rule provides for co-ordinate terms and the third, for alternate. Disparate terms, having no constant relation to each other, and no relation, as dis- parate, from which any inference can be drawn, there can of course be no principle or rule of inference from them. They may ie alternate or co-ordinate ; they may be made subordinate and then, of course, inferences can be drawn from them as subordinate, as alternate or co- oj^dinate. ~3>^ 113. The Fallacies as they are called, that is the faults whereby these possible forms fail to fulfill the conditions of any one of the four rules, are also reduced to four classes' as follows : (1) If ioth premises are negative there will be no con- clusion. (3) If one premise be negative, no affirmative conclu- sion. (3) If the middle term be not once distributed, there will be no conclusion. (4) If any term be distributed in the conclusion which was not distributed in the premises, the conclu- sion will not be valid. It will be remembered that a term is said to be dis- tributed when it is the subject of a universal, or predi- cate of a negative proposition. 113. It will often be found in analyzing a syllogism that there are really fo,ur terms when there had appeared at first to be but two. Thus, in Hume's famous sophism, " My hand touches the pen ; the pen touches the paper ; th.erefore, my hand touches the paper," we have really four terms: (1) my hand, (3) touches the pen, (3) the pen, (4) touches the paper. This is called the Fallacy of many terms. CATEGORICAL SYLLOGISMS. 67 114. A proposition can be Teftuced to the three parts « S," " is " and " P," etc. Thus, « John eats," " John is eating." And it will sometimes happen that when this analysis of both premises gives us four terms, as in the case just cited, there will yet be a possibility of supply- ing a third premise, thus making a Sorites, as it is called, that will be valid, (§ 152, 160). And in some cases, also, the premise to be supplied will need to be a comparative proposition, (§317). Thus, "John eats meat; meat is expensive ; therefore John eats what is expensive." Here we have four terms, (1) "John," (2) " meat eating," (3) " meat," (4) " expensive." But if we have " Whatever is true of meat is true of meat-eating, in this respect," we have a complete Sorites. Or, we can put all the words into three terms, (1) "John eats," (2) "meat," (3) "ex- pensive." Wherever this can be done — for a reason that will appear below — the syllogism is valid, though it may appear to be a fallacy of many terms. This, it will be seen, cannot be done with Hume's sophism. We have at least, (1) " my hand touches," (2) "pen," (3) " pen touches," (4) " paper," and no ingenuity that I know of can reduce the words to less than the four terms. And the third premise that would be required to make the Sorites, is "What touches the pen is the pen," which is of course absurd, or " Whatever may be said of that which touches the pen may be said of the pen, in this respect," which is also absurd. 115. A violation of the first or second rules gives what is called the fallacy, of Negative Premises. It will often happen, however, that the two negatives may be made modals of the middle term, and then we have a valid conclusion. Thus, S are not M, not M are P, therefore, S are P. We might write the modal term as a negative term, non-M, and make it and the negative particle one word. 68 TEXTS OOE OF LOGIC. 116. A Tiolation of the third rule constitutes what is called Undistributed Middle, thus Dogs are animals ; Horses are animals ; From this we could not infer that dogs are, or are not horses. 117. A yiolation of the fourth rule constitutes what is called Illicit Process' and may occur with either the ma- jor or minor term. (1) Thus, for an Illicit process of the Minor we have All horses are quadrupeds ; All horses are useful animals ; Tlierefore, all useful animals are quadrupeds ; whereas, the premises prove only that " some," not all useful ani- mals, etc. (3.) For an Illicit of the Major we have. The Negroes have black skins ; The Arabians are' not N"egroes ; Tlierefore, the Arabians have not black skins. 118. Applying these rules and tests, we find that there are only nineteen syllogisms that are valid and useful, four in the first figure, four in the second, six in the third, and fiVe in the fourth. The Scholastic writers have put the names of these nineteen syllogisms, into Hexameters, as follows : BAibArA, CElArEnt, DArH, FErlOgae, priom. CEsAiE, CAmEstrEs, FEstInO, BAiOkO, secundcB. TeHia, DArAptI, DIsAmIs, DAtlSI, EElAptOn. BOkArdO, EErlsOn, habet ; Qaaria inswper addit. BrAmAntlp, CAmEnEs, DImArls, FEsApO. ErEsIsOn. The vowels used in;forming the names of the syllo- gisms were selected to indicate the Propositions, A, E, I, 0. All beginning with B can be reduced to the form CATEGOBIOAt SYLLOGISMS. 69 of Barbara ; all with C to Celarent ; all with D to Darii ; all with P to Perio. The Consonants indicate the changes that are necessary to reduce them to the First Figure.* * "m" indicates transposition of the Premises, so that the Major becomes Minor, and vice versa. "s" denotes that we are to convert simply the proposition before it as in Cesare for No S is P, read No P is S. "p" denotes that we are to convert per acddens or by limitation, the proposition before it, as in Darapti, for All M is S, we are to have Some S is M. "fc " denotes (in the old method,) that for the proposition before k, we are to substitute the contradictory of the conclusion. This will give for a new conclusion the contradictory of the old, which from being false or absurd, will imply by immediate inference the truth of the old conclusion. But by means of the contra-positions and conversions described above, (§ 93-95,) we can accomplish the same result more du'ectly as will be seen below. Thus, Cesare to j Celarent. No P are M, s converts simply, No M are P. All S are M AU S are M. . -.No S are P. . -.No S are P. Disamis. Some M are P, ) „ ^ ■■ ^ ( All M are S. AU M are S. [ ""'^^'"^ ^^"^ transpose, | g„^^ p ^^^ ^_ . -.Some S are P. . -.Some P are S. ' , and by conversion. Some S are P. Pelapton. NoMareP, No Mare P. All M are S, convert "p" Some S are M. . -.Some S are not P, . '.Some S are not P. Baroko becomes Fertb, instead of Barbara. Thus for the Major Premise of Baroko, we have, AU P are M, then No non-P are M, and No M are [non-P]. "With this for Major, we have, No M are non-P. Some S are no M, . -.Some S are [non-P,] or Some S are not P. which is Perio of the first figure. With Bokardo of the third figure we can effect a Kke transforma- 70 TEXT-BOOK OB LOGIC. 119. I have also discussed the Formulse thus far as If all the terms were siraple and consisting of only one word. But this is seldom the case ; in fact, it never is the case with what are called material syllogisms. And it will often happen that a modal that is used with a term in one part of a syllogism will, for the sake of variety of expression, and to avoid stiffness and awkwardness of ex- pression, be varied, or dropped entirely, when the term occurs in the other part. And on the other hand, there is often a disposition, for the purely rhetorical purpose of emphasis, to insert a modal in the conclusion that did not appear in the Premises. For this reason it becomes hecessary to consider the function of Modals a little further. 120. A Modal, unless it be a mere expletive, adding nothing to the meaning of the proposition, is of the na- ture of an adjective, if it be not a mere adjective, as "men," "white men;'' "men" "men who keep their promises." And it is a mere question of idiom and rhet- ■ tion. It then becomes Darii. For the Major Premise Some M are not P, write the Minor Premise as Major, and then include the neg- atiive in the Predicate of the Minor, and we have, ■ ^ V , All M are S, Some M are [non-P,] then we have, Some [non-P] are M. , and by conversion, Some S are, [non-P,] Some S are not P. These conversions are rather ourions, more amusing than useful. A famiUarity with them will, however, well ;f6pay the labor it will cost to any one who aims to make himself thoroughly master of- the science and formulse of reasoning. And I know of nothing that wiU be of more service in giving one that fiimiUarity with the form- ulae and that insight into their force, and that quickness in detecting fallacies in form, than an exercise in converting not merely the abstract forms, made in the use of the letters S, M and P, but also the fuller examples of syllogisms given above, pp. 61-65 Notes. CATEGOBICAL SYLLOGISMS. 7I oric whether the modal can be expressed or is expressed in one way or the other. 121. The dictum of Arisotle stated above (§§ 10,6, 1, 107,) is, in fact, about the most general of all the prin- ciples of deduction. It results from it : (1). That we may replace the subject of a universal or the predicate of the negative proposition by any term that is lower in the subordinate series, as " All men are mortal," "white men are mortal," "Englishmen are mortal," "Birds are not quadrupeds," "birds are not horses," etc. (3). We may replace the subject of a partial proposi- tion or the predicate of an affirmative proposition with a higher or more comprehensive term, as " Horses are quadrupeds," "horses are animals," "Some Americans are poets," " some men are poets." 132. But as the subject of universals and the predicate of negative propositions are always distributed and the subjects of partial and the predicates of affirmative prop- ositions are undistributed, the two rules just stated are equivalent to : We may replace a distributed term by a lower and less comprehensive one, and an undistributed by a higher and more comprehensive term. 133. We might prove this rule in another way, as fol- lows : Any noun that occurs in a proposition may be made the subject of the proposition and all the other words will then become predicate. Consequently for a distributed term occurring anywhere, even as part of a modal, we may substitute a lower one and for a partial term a higher one, as " He had a majority of the votes in all the wards." " All the wards " is a distributed term and but part of a modal, and yet we may substitute for " all the wards," " the first ward," and the proposition wiU still be true, if it was so before. 72 TEXT-BOOK OF LOGIC. Of course it will make-no difference whether we insert for a lower term another word or limit the one used, by an adjective, as for "man" either "negro" or "black man." And in the other direction the omission of an adjective or raodal enlarges the sphere of the noun, as for " Englishmen," " men," for " white horses," " horses." 134. Now it so happens that in fifteen, at least, out of the nineteen syllogisms there occurs a Universal AfiBrma- tive; and this of course makes the subject the lower and subordinate term to its predicate. Taking then the other proposition for a Major proposition [as we may call it in this connection,] and we may replace 'either of its terms by one or the other of those in the Universal Af- firmative according to the rules just laid down and we 'have at once a vindication of the validity of the syllo- gism. 135. And even with regard to the remaining four, Ferio, Festino, Ferison and Fresison, it would be easy with a little ingenuity to state the major premise E, by contraposition, as a Universal Affirmative, and thus bring them under the same rule. I have given in the last Chapter diagrams represent- ing the'four Propositions, A, E, I and 0. 136. Now we can always add to these a third circle so as to indicate a syllogism and the nature of its conclu- sioh, if it has any that is valid. Thus, take AAA in the first figure and we have All S are M, All M are P, and we may write it with three circles in this form when it is -manifest thafS is in P^ or All S.are P. For the Fi g uy^ EAE^we shall Mare one circle S in the circle M and another circle P, exclusive of the other from which it is manifest, that S is not in P or No S are P. CATEGORICAL SYLLOGISMS. 73 For All we shall have two circles M in — ^gp P, and since some S are M we shall have J_Y'^\ \ S an incomplete circle cutting M, and of .^"TrvM j j course, therefore partly included in P or S some S are P. 127. In the first two examples it is manifest that there is but one way of constructing the syllogism ; but in the last we might have left the ends of the incomplete circle S wholly within P, in which case the conclusion indicated would be All S are P. Hence in this case there are two ways of completing the construction, the one giving a universal and the other only a partial conclu- sion in the same quality. 128. The diagram that illustrates the third Figure affords another example of the two fold construction P are M and S are M. The circle P must include M as must also the circle S. Hence, S and P must have so 1 \;---^ jy' much as M, at least, in common, and Some S^ S are P and conversely Some P are S. But the whole of S might be in P or the whole of P might be in S. Hence, two ways of construction, and the partial is proved to be true while the universal conclusion is shown to be probable only. 129. But besides this there will sometimes be three different ways of completing. Suppose we try AEE in the first Figure; All M are P,No S are M, therefore No S are P. We have for Major Premise, All M P are P : but for the Minor, No S are M, we must put S out of M, indeed, but this may be | done with S, (1) in P between M and P, (2) with S out of P entirely, or (.3) partly out of and partly in P. • In the former case the conclusion in- dicated would be All S are P, in the second, No S are P, 74- TEXT-B 0.0K OF LOGia and in the third, Some S are P and Some S are not P. Hence it is manifest that AEE in the first Figure proves nothing ; it is invalid, it is Illicit of the Major. In this way it is easy to show that if both Premises are negative there can be no Conclusion. Either Prem- ise will give two circles exclusive of each other, S and P, (§ 91,) the other will make a third term T. If now T is not P, we have a third circle exclusive of P indeed, but it may be (1) in S, (2) out of S, or (3) partly in and partly out of S. 130. Hence we have the following Eules : (1). If there is but One way of constructing the Syllo- gism, the Syllogism is valid and the construction indicates the conclusion. (3). If there are two waj^"* of constructing the Syllo- gism, the inferior or partial conclusion indicated is valid, I rather than A, rather than E. (3). If there are three ways of constructing the Syllo- gism, there is no valid conclusion. 131. It is also worth considering that (1.) If we have both Premises affirmative and the Middle Term alone distributed we may have a conclu- sion in I. (2.) If both Premises are affirmative and the Middle Term and one extreme be distributed we may have a conclusion in A, the distributed extreme being subject. (3.) If we have one Premise Negative and the Middle Term and one extreme distributed we have a conclusion in 0, the distributed extreme being predicate. (4.) If we have one Premise Negative and all three terms distributed we may have a conclusion in E, either extreme being subject. But, of course, if both Premises are Negative, there will be no conclusion. CATEGORICAL SYLLOGISMS. 75 132. The validity of either of the Nineteen syllogisms may also be deduced from Aristotle's dictum, stated as Rule I [§ |06,] by what is called the conTcrsion of syllo- gisms ; that is such conversions and contra-positions of the Premises as may be made in accordance with the rules given in the Note on page 69, 133. We have considered syllogisms thus far as made up of universal and partial propositions. But, in fact, many propositions that are universal in form, are only general, having exceptions. And, of cours/e, therefore the subject of the partial proposition may include only those that are exceptions ; thus, " all men are rational beings ; some men are insane ; therefere, some insane men are rational ;" or, " some rational beings are insane." In a sense this might be true, insanity being but a priva- tive term, iniplying that those who are actually insane are in an abnormal condition ; that they are essentially rational, only accidentally insane. 134. Again, if the Minor term be an individual term, it is quite possible that it is one of the exceptions to the general rule, of which the Major Premise is a statement. Thus, "all human beings are born of human parents. But Adam was a human being, therefore Adam was born of human parents." The proposition, "all human beings," etc., can, of course, be only general, since in any event and on any theory, the first human being was not born of human parents. Hence, if the Premise which is universal in form be only general in fact, the conclusion can be considered as made probable only by the syllogism. 135. Writers usually make a distinction between formal and material syllogisms. A material syllogism diflfers from a formal one only in that while it contains all that is necessary to a syllogism it is not stated in syllogistic 76 TEXT-BOOK OF LOGIC. form. Bat, of course, it can be reduced to such a form. In the reduction of material syllogisms to the syllogistic form great ingenuity is often requisite, and there is no little risk of error. It is believed, however, that a thor- ough mastery and a dilligent application of the rules a!nd principles already discussed will be amply sufficient for all cases. 136. It must be carefully noted that we have discussed the formulfE thus far only in reference to what appears in the form of the propositions and is implied in their very nature. If, however, by any peculiarity of the structure of a sentence, it appears that a term is distrib- iited where by the nature of the simple proposition, as either partial or affirmative, we should not expect it, this fact will often give validity when otherwise we should have either Illicit process or undistribilted Middle. 137. It will sometimes happen that the' Middle term of a categorical syllogism will consist of two nouns con- nected by a conjunction. This conjunction will require to be changed from copulative to disjunctive, or the reverse, in case the Premises are of different quality, one being affirmative and the other negative, thus : M and N are P. But S are neither M nor N. therefore S are not P. Or, again : P are neither M nor N". But S are either M or N". therefore, S are not P. Were it not for this change in the quality of the con- junction, we should have — as a little thought will show — an Undistributed Middle. 138. When, however, either the Minor or Major term is a double term, no such change of the conjunction connecting them is required. ' CATEGORICAL SYLLOGISM. 77 139. Any categorical syllogism that is at all valid may be put into one or another of the fore mentioned Nine- teen. If not already so stated, it is merely a material syllogism not stated in technical form. 140. The assertion, however, that there are but the nineteen valid Formulae, and that all valid categorical syllogisms can be reduced to one or another of these forms, is based on the fact that there are but the four varieties of categorical propositions already discussed, A, E, I and 0. I have, (§ 83-89) referred to Sir William Hamilton's theory of " quantification," as he calls it, for the purpose of showing that there can be no such prop- ositions as he proposes to recognize as constituting the additional four. It may be well, however, now to recur to the subject again for the purpose of showing that the syllogisms that he proposes to recognize are either inva- lid, Fallacies in Form, or are only, material syllogisms that can be reduced to one of the Nineteen forms. 141. His theory may possibly be more simple and satisfactory as an explanation ; but I think not. On the contrary, it seems to me much more complicated and less satisfactory than the one I have given above. It is, in fact, so long and so complicated that I have not thought it worth the while to discuss it here. 142. Sir William proposes to recognize what he calls the Intensive Syllogism as distinct from what he calls the Extensive, to which class he refers those .we have been considering. He is much mistaken, however, as I think, in regarding it as a Categorical Syllogism at all. His example is : The notion 'A comprehends the notion B. The notion B comprehends the notion 0. .•. The notion A comprehends the notion C* * Lects. on Logic, p. 192. 78 TEXT-BOOK OF LOGIC. As such it contains four terms, and can in no way^ be made a Sorites without involving a manifest absurdity. But here is a maniest mistake in the terms. The terms are not A and B and 0, simply, but (1) "the notion A" (3) "comprehends the notion B," (3) "the notion B," and (4) " comprehends the notion C," and in order to complete this as a categorical at all, it must be a Sorites with three premises, the supplied premise being the man- ifest absurdity " that which comprehends the notion B is the notion B." But his example, if we take it in reference to its mean- ing, is only the material syllogisln, which may be stated in form, thus : All B is A All is B, Therefore, All C is A. " The proposition "the notion A comprehends the notion B," being in his use of terms just equivalent to the proposition " All B is A." ■ 143. But Sir William's example, and in fact, all the examples of what he calls Intensive Syllogisms, involve a fallacy of another kind. His example, which I have abridged by the substitution of letters for his terms at length, is "the notion man, comprehends in it the notion of responsible agent," etc. What he says is, " in common language." " Man is a responsible agent. But a responsible agent is a free agent. Therefore, Man is a free agent." Surely we need nothing more to assure us that what he has called Intensive Syllogisms, are not Syllogisms, in form at all, but a certain artificial, unnatural, or at least ^^^eojnmon" way of stating common Syllogisms. But to our criticism. The real subject of the CATEGORICAL SYLLOOIBMS. 79 premises cited at length above, " the notion man," etc., is not "man," bu-t "the notion man." How are we to understand this grammatically? Are "notion" and " man^" which are certainly two nouns, in apposition ? or are they to be understood as connected by the prepo- sition " of," and thus equivalent to the "notion of man ?" The difference is material. And it seems that the latter view alone is tenable, since two terms can never be in apposition except when they denote the same thing, and to denote the same thing, they must be of the same quality. " Man," we have seen, is a general terjn. But what is " notion ?" If it means something in the mind representing external objects, as some metaphysicians hold, and as Sir William's philosophy seems to imply, then the word is concrete indeed, but individual also, and cannot comprehend a class in any sense, however it may denote or represent one. If, however, the word is abstract and denotes only as Descaktes and Cousiif, with others, have taught, then it can in no way be in apposition with man. 145. But further than this, the sentence itself implies a division, which in this case, is impossible, and thus asserts what is not true. And as the Minor Premise and the Conclusion are like the Major Premise in this respect, they are also like it, untrue in fact. He states his con- clusion with the remark, " Therefore on the principle that the part of a part is a part of the whole" " The notion man comprehends," etc. 146. Now whatever is a whole containing parts may be resolved in£o those parts, in one of the six ways al- ready described. Analysis, Physical and Logical. Divis- ion, mathematical, logical and physical, and that to which I have given no name by which a collective whole, as a family, etc., is resolved into its parts. * Bpt by no 80 TEXT-B OK OF 10 GIG. one of them can the " notion man " be resolved, divided or analyzed into "the notion, responsible agent." Not logical analysis, for that gives only abstract terms, but " agent " is not abstract. Not physical analysis, for that analyzes only material things, "notion " is not material- We say water comprehends oxygen, etc., only when the oxygen can be obtained from it by physical analysis. There can be no pretense of mathematical division. Logical division divides the class genus into species, and ~Bp§cies into individuals, and that which is subject of logical division must be denoted by a noun in the plural, as we divide "men" into Caucasians, Mongols, etc. Physical division, like physical analysis, divides only physical or material objects. There can be no pretense that " notion " is a collective whole, and hence none of the other division which resolves that kind of wholes into three parts. 147. Or if one should say that " notion " is something in the mind that represents external objects, as is so often implied in most of our metaphysical writers, we should indeed make of it something that would be subject to physical analysis or physical division, one or both of them ; but neither of them could give the result here required. The " notion," " idea," " concept," etc., are all of the same kind and quality, and when regarded as con- crete realities at all, they are supposed to be made up of elements, each one of which either is or represents a property of the object itself. 148. Hence, as said above, the only analysis to which it could be subjected would be that which would resolve it into parts which are properties and must be denoted by abstract terms. And in this view we cannot say that the " notion man, comprehends the notion agent," but only th^ notion of man comprehends the notion of free- CATEGORICAL SYLLOGISMS. 81 dom, or better still, " comprehends freedom." And even if " notion " be a concrete term, a physical division or - analysis of it is too absurd to be thought of. Hence, there is no sense of the word, as I apprehend, in which it can be said literally, " the notion man, comprehends the notion free agent." We may indeed say " the class man, includes free agents, " or that " free agency is es- sential to the class." But in no proper sense can we speak of notions or ideas as " including " or " doing " anything ; they are nothing themselves. 149. I consider therefore, Sir William Hamilton's theory of Syllogisms to be unfounded in fact and absurd in theory. It is not, however, a mere question of theory. As I have undertaken to show, no syllogisms were produced that call for or justify the extension he would give to the list named, which cannot, if they are categorical at all, be regarded as mere material syllo- gisms, needing only some modifications of their state- ment to reduce them to the form of some one of the Nineteen, whose names and forms have been already given. 150. It will seldoih happen in practice, that an argu- ment is stated simply as a syllogism with two Premises and a Conclusion. We have either, (1.) A series of more than two Premises followed by a Conclusion to which they are all necessary, how many soever they may be, or, (2.) One Premise only, followed by a conclusion, as if the Premise stated were the only one that is used. In the former case we have a complex argument called a Sorites, and in the latter an incomplete syllogism called an Enthymeme. 151. The Sorites can be reduced to two or more of the Nineteen Formulae, and the Enthymeme can always be 6 83 TEXT-BOOK Oi LOGIC. completed into one of them, unless it involves some fallacy in form. 152. A Sorites consists really of several syllogisms consolidated or abridged into an argument, thus : All A are B, . All B are C, All C are D, Therefore, All A are D. This may be reduced to two simple syllogisms, thus : All B are C, All C are D, All A are B, All A are 0, Therefore, All A are 0. Therefore, All A are D. 153. In this case we make the gecond Proposition, the Major Premise of the first syllogism, the first Proposi- sion the Minor Premise. The third Proposition is the Major Premise of the second syllogism, and the Conclu- sion to the first syllogism is the Minor Premise of the second syllogism, and so on until we arrive at a Conclu- sion which is the same as that of the Sorites. 154. The principles already laid down, with a slight modification, apply to Sorites, as well as to Syllogisms. (1). There may be no more terms than the whole num- ber of Propositions including the Conclusion. (2). After two negative premises there -can be no Con- clusion^ and after one negative premise there can be no affirmative Conclusion. (3). Each middle term, (of which there will be as many as there are premises,) must be once distributed. (4). No term may be distributed in the Conclusion that was not distributed in the Premises. 155. It'will result from these rules as in the case of simple Syllogisms, that (1). After two negative premises no Conclusion. (3). After one negative premise no affirmative Conclu- sion. CATEGORICAL SYLLOGISMS. 83 (3). After two Partial premises no conclusion. (4). After one Partial premise no uiiiTersal Conclu- sion. 156. We must consider, however that most of t^e Ar- guments that consist of a series of propositions which are to be regarded as Premises, are not Sorites — they have not the succession of Middle terms necessary to that Form. Thejf consist rathei-, when stated in due form, of a series of propositions, with either one subject, or one predicate common to them all, as n is P, m is P, is P, etc. or, S is m, S is n, S is o, etc., in which case we have one premise stated in detail rather than » succession of Premises as in the Sorites. IST. The incomplete form usually called an Bnthy- meme, consists of one Premise and the Conclusion — the other Premise being omitted and left to be supplied by the hearer — thus, " A B is guilty, therefore he ought to b6 punished." .Here it is manifestly assumed that " whoever is guilty ought to be punished." 158. Whenever a Premise is omitted, whether from a Simple syllogism or from a Sorites, it is very easy to re- store it by means of the rules already given, though for this purpose we would state them a little differently. EuLE 1. If the Conclusion be Universal Affirmative, both Premisses must be cfffiirmative and the Minor and Middle terms must be distributed. fiuLB 2. If the Conclusion be Partial Affirmative, the Premises must be affirmative, and only the middle term, needs to be distributed. 84 TMXT-BOOK OF LOGIC. EuLE 3. If the Conclusion he Partial Negative, one Premise must ie Negative, and the Middle and the Major terms must ie distributed. EuLE 4. If the Conclusion ie Universal Negative, one Premise must be Negative, and all three terms distributed. 159. The suppressed Premise is, of course, part of the syllogism, and is asserted by necessary implication in the assertion of the conclusion as a proposition that is to be regarded as proved by the asserted Premise. 160. We have considered Categorical syllogisms as having but three terms and two Premises. The Sorites - may, of course, have as many terms as there are proposi- tions, or as many terms as there are Premises and one more. And conversely, in the Sorites, as well as in the simple syllogisms, there must be as many Propositions as terms, and one Premise less than the entire number of terms. And as one of the Premises of a syllogism may be suppressed, so one or more of the Premises in a Sorites may be omitted from the statement of the argu- ment. In fact, in a Sorites each alternate Premise and thus one half of them, may be omitted, and we shall have a series of Premises with no term common to any two succeeding ones, thus ; A are B, are D, E are P. 161. In this case there is a Premise to be inserted be- tween the 1st and the 2d, the 2d and 3d, and we have B is and D is E, to be supplied, and the rules for supply- ing them that have already been given will apply to all the cases in which the suppressed Premise is categorical. We shall see below, that a Comparative proposition has sometimes been suppressed, and that consequently noth- ing but a comparative Premise will complete the logical connection that was broken by the omission. CATEGORICAL SYLLOGISMS. 85 163. And in any case, when we have a fallacy in form of many terms, we can treat it as an abridged Sorites and restore the Premise that is needed for completing the formula as a Sorites. If it be really a fallacy of many terms and not merely an abridged Sorites, the proposi- tion which is thus required will be either a contvadiction in terms or a contradiction of one of the given Premises. 163. A proposition is sometimes thrown in as proof of one of the premises. It is called a prosjWogism, and together with the premise which it was designed to prove makes an Enthymeme, thus, A is B, B is 0, (C is X), therefore A is 0. Here we have C is X therefore B is d for an Enthymeme. It implies that X is B. 164. It will also frequently happen that immediately upon the conclusion to a syllogism another conclusion is drawn from it. This is called an episyllogism and to- gether with the conclusion from which it is drawn, makes an Enthymeme also. Thus, A is B, B is C, therefore A is C, consequently A is D, which implies that all is D . •165. Again we sometimes have a series with the same term common to them all, thus A is m, B is u, C is u. This is the form that is generally used in induction. Thus, dogs are carnivorous, foxes are carnivorous, wolves are carnivorous, hyenas are carnivorous. But dogs, foxes, wolves are the canidse, therefore the canidse are carniv- orous. SECTION II. OOMPABATTVi: SYLLOGISMS. 166. The reasoning that'is Based on Classification re- lates to the quality of objects, to what they are. We observe, we generalize, we predicate properties of classes, we include some objects in the classes we have made, and 86 TEXT-BOOK OF LOGIC. exclude others from them. The whole process is con- cerned with the properties of objects, that make their quality, their essence, and their differences. And even properties which are accidental to the individual are made essential to the class by classification, and thus brought within the range of categorical reasoning. But nothing is said of quantity, or comparisons of .time and place, in- tensity, etc., nothing of^ catisation and law, nothing of relative properties and combining proportions, nothing of the relation of objects to the complex wholes of which they are parts. 167. There are those who think that every argument can be stated in one of the categorical formula already considered. This, I think, is an error. Take the follow- ing as an example. Air is lighter than water, Water is lighter than earth, therefore, Air is lighter than earth. This syllogism is at once seen to be good, and yet re- garded as a categorical syllogism, it has four terms, (1) "air,'- (3) "lighter than water," (3) "water," (4) "lighter than earth." If -we regard it as an abridged Sorites, as A is B, CisD, therefore, A is D. We may complete it, indeed, by introducing the proposi- tion B is C, and then we should have AisB, B is 0, CisD, therefore, A is D. But B in this case is "lighter than water," and C is. "water," and the proposition B is C becomes " that which is lighter than water, is water," or "water is lighter than itself," which is absurd. IpOMPABATirS SYLLOGISMS. 87 But aside from this difficulty, the Principles of reason- ing by comparison are totally different from those of reasoning by classification. 168^ Comparisons are of two kinds, (1) comTPai iaons ofoiijficts^nd ( 2) compariso ns of ratios ox JelatLojis; the former having three terms, and the latter four, either expressed or implied. ■Comparisons with three terms are of two kinds, (1) comparisons of quantity and (3) comparisons of compre- hension. Of the first kind we have A_^B, etp., and in the latter, A co ntains B. 169. Objects may be compared in reference to four kinds of quantity, (1). Quantity of number, as more or. less. (3). Quantity of time, as before and after. (3). Quantity of space, as above or below, farther or nearer (4). Quantity of intensity^ as whiter or less white. But these four kinds of comparisons, which are apparently different, are all comparisons of quantity. Quantity itself is sometimes spoken of as of three kinds. (1). Continuous quantity when the object is considered as something substantial, but a unit, that is as one but larger or smaller, longer or shorter, etc. In this class we have not only simply the size of objects, but also time and space, they being considered as entities extending from event to event, and object to object. (3). Discrete quantity or number, in which objects are considered as many, that is as made up of parts, as five, six, etc., and one is hardly said to be larger or smaller than another, but rather, more or less, as six is more than five. (3). Intensive quantity in which we consider and compare not things, but properties, and make the comparison for the most part by the use of adjectives in the comparative degree, as " iron iBjiarder than lead," "platinum is Aeaw- ier than gold," etc. In all these cases we compare objects 88 TEXT-BOOK OF LOGIC. with reference to their intensity in the possession of some one or more of their properties. But the difference between these three kinds of quan- tity make no difference with the principles and formulae of comparative reasoning, 170. A comparison may be one of equality or inequal- ity, as A := B, or A > B. And all such comparative propositions may be converted. (1). Simply, as A = B, then B = A. (2). By change of the comparative adjective, as A > B, therefore B <; A. (3). But in the third place, if the comparison is inde- terminate, as A is as great as B, there can be no conver- sion, for in this case A may he greater than B for all that is said of it, and therefore *ve cannot say that B is either equal, to or less than A. We can only say for it that B is not greater than A. • 171. The principles of comparative reasoning are ob- vious and well known. (1). If two things are separately equal to a third, they are equal to each other, as A = B, B = C, therefore A = C. (2). If of three things one is greater than the second,- and the second greater than the third, the first is greater than the third, and vice versa, as A ]>► B, B > C, tJiere- fore A > 0, or A < B, B < 0, therefore A < 0. (3). If two -things are both either greater or less than the third, no inference can be drawn with regard to'their relation in either continuous or intensive quantity, thus A > B, C > B, no inference. Or A < B, B > 0, again no inference. 172. But if we apply to continuous or intensive quan- tity discrete quantification, we can make a comparison of any two objects by means of a third, whatever may comparative: syllogisms. 89 be their relations in regard to equality or inequality. This quantification brings them within the domain of number, of Arithmetic and of Algebra, and constitutes, in its application to continuous quantity, Analytical Geometry and the Calculus. Thus A is twice as great as B, and B is half as large as 0.' This gives us the means of a comparison between A and 0, that is, A and are equal. But this always has reference to an assumed unit of measure, B, in the above example ; and may therefore always be represented by numbers simjaly, as 3, 4, 7, 9, etc., and thus we have addition, subtraction, multiplica- tion, division, etc. The principles of this kind of reasoning fall so com- pletely within the domain of Mathematics, that it does not seem worth while to pursue them any farther in this place. 173. There is, then, the other form of comparison, with three terms — three, if we regard them as compara- tires, but four, if we regard them as categorical syllo- gisms — remaining to be considered under this head. They are not comparisons of quantity of any kind, but rather, as we have said, of comprehension. As " A con- tains or comprehends B," etc., or " A is in B," " B is in C," etc.. It is manifest that we cannot regard them as categori- cal without making them fallacies of many terms. If we complete them into Sorites we have the manifest ab- surdity : " B is whatever contains B," or something of that kind; 174. And yet the reasoning is complete and satisfac- tory. It rests upon "the self-evident Eules that (1.) Whatever contains anything contains whatever is contained, in it. And conversely. 90 TEXT-B OOK OFLO GIC. (2.) Whatever is contained in anything is contained in whatever contains that thing. 175. The syllogisms that come under these Rules are precisely the same in form as those that are founded upon relations of quantity. Thus we may have the 'example, "John is in Paris; Paris is in Prance, therefore John is in Prance." But no one of the propositions may be converted. . If John is in Prance it does not follow that Prance is in John. So too with a class ; the genus canis contains the species fox ; therefore " all foxes are canidse," and " some canidse are foxes." 176. Hence it is manifest that in comparatives of this class, the two terms that characterize its two members may be either (1) synonyrhous, denoting the same thing or (3) they will be, one more comprehensive than the other, but subordinate terms in ascending series. They cannot be either co-ordinate, alternate, or disparate. 177. In the comparisons of things there are but three terms needed for a syllogism, and in fact there can be only three in a simple syllogism ; with moi-e than three it becomes a Sorites, with more than two premises. But in the comparisons of ratios or relations, there are four terms either expressed or implied, and there may be or not, one or even two more new ones added in the Minor premise. 178. We shall do well to consider these comparative syllogisms under two heads. (1.) Those in which theTe is a comparison of (a) quantity, of (b) time, of (c) place, as (a) 3 : 4 : : 6 : 8, (5) this occurs when that does, (c) the boy is where his father is. In the second class we have a comparison of predica- tion, which we will explain more fully after we shall have discussed the first kind named, those of quantity, time and place. COMPABATim SYLLOGISMS. 91 179. When the comparison is of ratios as between numbers, we generally put them so that one ratio is equal to the other, as in the example 3:4: : 6 : 8. But it might be stated otherwise, thus, 3 : 4 > 3 : 7, or the reverse, 2 : 4 <; 3 : 5. In this case, however, for any practical operations, it would become necessary to con- vert the ratio into a single number, as 2 : 4 is the same as 2-4, or 1-2 of the assumed unit of measure. 180. When, however, the comparison is not of ratios, but rather of relations, we say that one relation is the same as the other, or identical with it, thus, "the seed is to the plant, as the egg is to the chick," the relation be- tween the seed and the plant is the same as that of the egg to the chick. 181. It will be seen at once that identity of relations constitutes what we call an analogy. It is true that we speak of one object or thing as analogous to another. But the similarity is rather a resemblance than an anal- • ogy, when we compare objects one with another. How- ever the confusion of terms is of no great importance^ 182. We may have (1) the four terms given witl» the ~)\ ratio of one part given, to find that of the other(^r (2), 7 both ratios given with two terms, to find a third that will ^^ be common to both. If the four terms are given in the comparative propo- sition, the comparison is of the relations between them, and we have only to state explicitly for a Minor Premise, what the relation of one pair, of the terms is, and then for conclusion we affirm that relation of the other pair thus: 3 : 6 : : 4 : 8. But three is half of six, therefore, four is half of eight. 183. In case, however, only two terms are given, an- 92 TEXT-BOOK OF LOGIC. other is implied, which is to be a member of both ratios. As " the boy is where his father is." Here " where " stands for the unknown third term, which is to be com- mon to both ratios, and we complete by saying, Theboy is in the city, therefore, the father is in the city, and " in the city " is the third term common to the two ratios. 184 There is a very important difference in thi« re- spect among the comparatives that have or imply four terms. In all purely mathematical comparisons or prop- ositions the wanting term, which here as elsewhere, must be common to both ratios or members of the compara- tive, must be consequent of one and antecedent of the other, whereas in the purely real ' comparisons, that is the comparison of things and not of numbers, the want- ing term must be either " antecedent or consequent in both members. Thus, if we have 3 : x : : a; : 13, or a; : 3 : : 13 : 2), we multiply the known terms 3 by 13, and have 36, extract the square root, and we have 6 for the value of X, and then we have 3:6: : 6 : 13, etc. 185. But If we say the boy is where is father is, the term expressing or making definite " where " must be predicate of both members, as " the boy is in town," "the father is in town." Or, when A occurs B occurs. At nine o'clock A occurs, at nine o'clock B occurs. But either the subject or the predicate must be common to both member of the comparative. 186. If we have one ratio given to find the other it will make no difference which is stated as the first ratio of the comparative, or proportion, although we shall, of course, be obliged to state the one that is known or ad- mitted as the Minor Premise, and then afiirm the same as the meaning or expression of the ratio' or relation between the term of, the other member, thus. COMPARATIVE SYLLOGISMS. 93 3 : 4 : : 6 : 8. we may say 3 : 4 is three-fourths, therefore 6 : 8 is three-fourths, ' or we may say, 6 : 8 is three-fourths, therefore 3 : 4 is three-fourths. ■Or the boy is where his father is, the boy is in town, therefore the father is in town, or the father is in town, therefore the boy is in town. 187. But when the ratios or relations are botli given, the object is to find the nommon term, and that common term is, as in all, except mere mathematical proportions it must be, either the subject or the predicate of both members, and we shall not haye the sahie liberty of state- ment and completion as we have when all four of the terms are given. 188. In comparisons of this kind, that is, comparisons of ratios with but two terms given and a third wanting, which is to be common to the two members, we have a certain relation between the two terms that character- izes the members. We have three cases. (1). When the terms are mere synonyms, two names for the same thing, thus, " whatever can be said of common salt, can be said of .chloride of sodium," because common salt is chloride of sodium. In this case it can make no difference which member we complete for the Minor Premise. We can say, " salt is an antiseptic," therefore " chloride of sodium is an an- tiseptic," or the reverse, "chloride of sodium is an antiseptic," therefore " common salt is," etc. (2). In the second place the terms may be two in a series of subordinates as quadruped, animal, etc., or the one inferior to the other in comprehension, as Paris, Prance, etc. 94 TEXT-B OOK OF LO Gia And here we may have two cases, (a) the case in which the subject of both is wanting, as " whatever is a qnad- ruped is an animal," or "whatever is in Paris i& in France." In this case we must complete for Minor Premise, that member which has the narrower or lower sphere, as '•■ horses are quadrupeds," therefore they are animals," or " John is in Paris, therefore John is in France." The other mode of completion, that is completion by finding a subject to the larger term for Minor Premise would in- volve an Illicit Completion. (b). The other class of eases is that in which the pre- dicate is wanting, as " whatever animals are, quadrupeds are" or more likely, "whatever may be predicated of animals may be predicated of quadrupeds." In this case we must find a predicate to the larger term, and make that term and its predicate the Minor Premise, thus, " animals are organic beings subject to disease and death, therefore quadrupeds are " etc., other- wise we have Illicit Completion. (3). In the third place we have the two terms co-ordi- nate and then one member must be negative and the wanting term will be a differentia between them. As " whatever matter is, spirit is not," and we may have " matter is divisible, therefore spirit is not ; " spirit is spontaneous, therefore matter is not," etc. 189. The last form of this kind of comparatives, that with the predicates wanting, is not common in ordinary speech or writing ; but they are not only of use, they are indispensable as means of completing and justifying formulae in both Conditional and Disjunctive Syllogisms. ■ See § 317, § 347, in Sections III and IV, of this Chapter. 190. We may state the principal of Aristotle's dictum in a form to meet both of these classes of cases. COMPARATIVE STLLOOISMS. 95 (1). The subject to the subject of a Universal Propo- sition is subject to its predicate also. (2). 'The predicate to the predicate of a proposition is predicate to its subject also. The first of these forms has been already stated and illustrated, (§ 108.) But they are both obvious from a bare inspection of any series of subordinate terms ex- tending from the individual up to or towards the sum- mum genus, as N, horse, quadruped, animal, etc., the term beloto any one, is below, any one that comes after it, and the term above any one, is above any that comes be- ^191. Aristotle's dictum in the form so often quoted, " Whatever may be predicafted or denied of a class, may be predicated or denied of whatever is contained in that class," is really a comparative proposition. We have in the subject and predicate, or rather antecedent and con- sequent, regarding it as comparative, two terms, " pre- dicate of a class " and " predicate of anything contained in the class," and then we have a third term which im- plies a double use, "whatever," equivalent to "that which," and we have " that may be predicated of any- thing contained in a class which inay be predicated of the class." 193. This proposition we may treat in two ways. In the first place, if we have any simple categorical, we can convert it into a comparative of the kind above stated, by introducing a relative term, mating the terms of the categorical, modals or limiting clauses to th'e term which will be common to both members of the comparative. Thus to take Whatelt's example, "A negro is a man," therefore, " whoever kills a negro kills a man." In this case we have a comparative inference or con- 96 TEXT-BOOK OF LOGIC. elusion, which is certainly legitimate, for it aflSrms of " negro " (which by the premises was contained in the class " man,") only what is declared in the latter mem- ber to have been affirmed, or at least to be affirmable, of the class man in which it is contained. 193. But in the second place, we may take the com- parative thus obtained, as a conclusion, and make it a premise, and supply for the indefinite term " whoever,"' any definite term, for the subject to a minor premise, and then we shall have the same term for subject of the con- clusion with the predicate of the Major Premise for its predicate, thus : Whoever kills a negro kills a man, John kills a negro, therefore, John kills a man. 194. Orj to take another example, and' put the two parts together, we have a Syllogism or Sorites with four propositions. The night is dark, , Whoever walks in the night walks in the dark, John Walks in the night, .". John walks in the dark. 195. As another form we may have two abstract terms, both derived from verbs, the one predicated, of the other, as in an example before me, " Thought is existence." We may replace thfese abstract terms by the verbs from which they were derived, and supply as a nominative, the com- pound relai^ive, " whatever," "whoever," etc., and say, " Whatever thinks exists," for that is but applying to an individual case the doctrine of Aristotle, in the second form in which we gave it, and applying in the second member, as a predicate, a term which in the simple cate- gorical had been made, if not the superior and compre- hending term, at least, a synonym, meaning the same COMPARATIVE STLLOaiSMS. 97 thing as the other ; and in either case the predicate in the simple categorical may be made predicate, or introduced as a modal to the predicate of the comparative. 196. There is still another mode of completing com- paratives, "which though often occurring in practice, I have never seen recognized or explained in any treatise on Logic. Thus, if we say : Those that walk in the dark will stumble. The night is dark, Therefore, those that walk in the night will stumble, we have what all persons will recognize as not only a valid and useful formula, but one that from its nature, must often occur in the application of general principles to practice in the affairs of life. "What we have actually done in completing the syllo- gism in the above case, is to substitute in the modal of a term in the major premise, another word which in the minor is declared to be its subordinate in the order of natural classification. 197. Now by recurring to the law for the change of terms or modals of terms, (§ 131), we have at once the law governing all such cases. The rules, it will be re- membered, when reduced to the form we want, are, (1) Lower terms may replace higher ones in (1) the subject of universal, and (3) the predicate of negative propositions. (2) Higher terms may replace lower ones in (1) the subject of partial proposition and the predicate of affirm- ative ones. Thus, in the proposition, " Those that walk in the dark will stumble," "dark" is part of the modal qf a universal proposition. Hence, if we introduce " night," a lower term, we merely reduce the scope of the subject as we have a right to do. 7 98 TEXT-BOOK OF LOGIC. 198. ComparatiTe propositions are interesting to us as being the origin of all figurative language. We call lan- guage literal when it describes anyobject as it is and im- plies no reality but that which is cognized, or necessarily implied in that which is perceived to exist. But the mind, in that form of m,ental activity which is called im- agination or fancy, is often inclined to go beyond observ- ed realities, and imagine or fancy others, thus creating a world of unrealities, or entia rations. This is in some measure necessary and unavoidable, since we see much that we cannot explain without resort to something that is not seen, which, however, if it were real, would serve to explain what we do see. For example, we see that as soon as the sun appears above the horizon all things are visible and luminous. How is this ? At present we do not know. But the phenomenon is explained by supposing light to be a substance that is emitted from the sun with such astonishing rapidity, and, in such overwhelming abundance that it fills at once the whole hemisphere of the skies. Hence, we speak of light as a substance, of its nature, its reflection, its refraction, its chemical effects etc., etc., as though it were a real substance. 199. And among things that we know, comparisons are constantly made and then transformed into figures of speech. Tins if we say " Washington is the father of his country," or still more briefly in speaking of Washington, omit his name and call him " the father of his country," we imply, and have already made the comparison " As a father to his family, so Washington to his country." 200. If we expand the relation in the first member, we have the " fable," the " parable," or the " allegory," or in modern times "the novel." If we drop one term and say as before, " Washington is the father of his country," we have the simile. If we use one t^rm only as " that fox," CONDITIONAL 8TLL0GI8M3. 99 it is a metaphor, and when an abstract term is thus used in the place of a concrete, as "light" in the example just described, we have the metonymy. SECTION ni. CONDITIONAIi STLLOGISMS. 301. Every object of thought is, and is considered as a cause ; and with one exception, every object is and is con- sidered as an effect also. The exception is the First Cause, the Uncaused Cause. The word cause is, however, used in several senses, and every object considered as an effect has had several causes, that is, several different kinds of cause. (1). There is the efficient cause, that from which effi- ciency proceeds. (2). There are occasional, exciting, or procuring causes which 'set the efficient cause at work, as in the case of an explosion of gunpowder, the gases are the efficient cause, but the spark that ignites the powder is the occasional cause. (3). There is the instrumental cause or means, as the pen with which one writes, the instruments or tools with which one works. (4). There is the material cause, the matter put of which any thing is made, as when we say that iron is the* chief cadse of tools and machinery. The Scholastic writers used to hold that the essentia of a genus are its material cause. (5). There is the formal cause, as the mould which gives shape or form to what is cast in it, and makes the metal peured in to be a plow-beam, a pinion, wheel, etc.. 100 TEXT'BOOK OF LOGIC. etc. The Scholastic writers used to call the differentia of a species its formal cause. (6). There are sometimes conditional or circumstantial causes. These are hardly causes at all, but rather merely antecedent conditions. Thus a man's being alive to-day is hardly a cause of his dying to-morrow or on any subse- quent day, but it' is an indispensable condition. Facts of this kind p,re often spoken of, or written about as causes. (7). Finally there are ■\Yhat are called final causes, which are the object or purpose for Avhich anything is done. Only moral beings can act from final causes, and some such cause enters into the production of all the results of yoluntary action. 202. The existence of a cause of any one of the kinds named, is some proof in the way of demonstration of the reality of the effect which it tends to produce, and the existence of a combination of causes of several kinds may become an absolute proof. But the. investigation of these combinations and their varied forces, depends so much upon a knowledge of the subject matter, and the department of knowledge into which they enter, that no discussion of them except in connection with the scien- tific treatment of the matter itself, could be of any prac- tical value. For the most part, the existence of a cause for an event or fact is regarded as no more than a proba- ble argument in its favor. It serves to account for and explain the existence of the fact or the reality of the .event, rather than to prove it. 203. On the other hand an effect is alwsijs positive proof of a cause. The very word effect implies a thing produced, and of course, therefore a producing cause or agent, that is, an efiBcient cause. This cause may have been a permanent cause, as the earth is a permanent cause of the falling of bodies since it always attracts. It CONDITIONAL SYLLOGISMS. 101 may be only transient, that is, one that acts occasionally only, as powder in exploding, and then the result must haye an occasional cause as well as an efficient one ; and in case the agent were a personal being, there must have been a final cause also. 204. From the study of the nature of any efiect, we are able not only to see that it had a cause, but also some- thing of the nature and properties of the cause. The cause that contrived and made a watch, for example, must have had skill, intelligence, purpose, and must therefore have been an intelligent personal agent, and most likely a human being. The machine that cuts an iron bar at a blow, and in an instant, must have great strength. The object that welds iron or volatilizes gold must have great heat, etc., etc. 205.' Not only is every object in nature connected with some others that precede it as its causes, but the proper- ties of objects, and each one of them how numerous so- ever they are, indicates something of the properties and essential nature of the objects that were its causes. The melting of solids not only implies the action of other nat- ural objects, but it implies also that they were in a heated condition, etc. And every property, condition and fea- ture of the effect ihdicates__ something concerning its cause. 206. In the physical sciences, an invariable antecedent is generally spoken of as the cause of an event.^»&i; in this case there is seldom any distinction between the efficient and the occasional cause ; or rather the two are, for the most part, confounded. But we attach no espec- ial importance to invariable antecedence until we can see some casual relations between the -antecedent and the consequent. And even in the investigations of jN"atural Science, although a recognition of final causes, and the 103 TEXT-BOOK OF LOGIC. argument from them has been much decried ; it is a fact that scientific men are more and more returning to the use of them. It was the design of the Creator that the ox should feed on the grass of the field, therefore the peculiar structure of the teeth, the many-plies, the pro- longed alimentary canal, etc., etc. It was the design that the cat family of animals should feed on flesh and catch their prey by springing upon it, therefore the retractile sharp claws, the canine teeth, the single stomach,, agile frame, Imnf^i '(wiiX. etc., etc. \ 307. But the word "cause" is used in logical discus- sions in. still another sense, it denotes any premise causa cognoscendi or credendi, whereas the causes we have been speaking of are called causcB essendi, those that make a thing to be, and not those that make us believe or know that it is. In this connection, that which is phys- ically an effect, is for the most part logically the cause. That is, the effect is the proof or logical cause of our believing the existence of the physical cause, rather than the reverse. 308. Any Enthymeme, which, as before explained, is a Conclusion with one premise, may be stated conditionally or hypothetically, by making the premise the antecedent or logical cause of the conclusion. Thus A is B because C is B, or conditionally. If C is B, A is B. 309. Regarded in reference to its form alone, therefore, a conditional proposition is merely an Enthymeme stated conditionally, the premise being stated fljst in order^ and constituting what is called the Antecedent, and the con- clusion being stated as the Consequent, the implied or supposed premise being called the Sequence ; the Ante- cedent being the logical cause. 310- A Conditional Syllogism, therefore, differs from an Enthymeme only in the mode of statement. If one CONDITIONAL 8TLL0QI8MS. 103 premise is known and universally assented to, as is often the case, and one wishes to make emphatic the fact that the conclusion cannot be denied'or refused, if the other premise is admitted, he is likely to make that premise the antecedent in a conditional proposition. If A is B, A is C. He will then proceed to show that A is B. Or, in case he wants to refute'any proposition, as A is B, he will select some other proposition, as A is C, which can- not he denied if it be admitted that A is B, and state them as a conditional, thus if A is B, A is 0, and then proceed to show that the proposition A is C, is untrue or absurd, then infer that A is B is untrue, or the truth of the contradictory of A is B. 211. This makes what are called the two ways of com- pleting a conditional Syllogism, (1) by affirming the Antecedent to prove the Consequent. (2). By denying the Consequent to disprove the Antecedent. We may represent this to the eye as follows : If A is B, C is D. A is B, C is not D, .•.C is D, .'.A is not B. The first method, that by affirming the Antecedent, is called the Constructive method, the method by Positidn or the modus ponens ; the other, the method of denying the Consequent, is called; the Destructive method, the method of Amotion or the modus tollens. 21^. !N"ot the argument, however, but only one of the premises is conditional ; the conditional proposition being the Major premise, and a compound of two simple- cate- gorical propositions, of which one of them, the Conse- quent, is asserted to be true on the ground that the other is true. 104 TEXT-BOOK OF LOGIC. We may illustrate these methods by the familiar ex- ample : If John has a feyer, he is sick. John has a fever, therefore, he is sick. Or, in the other method. If John haa a fever, he is sick. But, John is not sick, therefore, he has not a fever. 213. If, however, we affirm the consequent and say, "John is sick," "therefore he has a fever,' we commit . the fallacy, in form called the fallacy of position. That is, -we afSrm the consequent, and therefrom infer the truth of the Antecedent, which is illogical and invalid. Or, if on the other hand, we deny the Antecedent and say, "John has not a fever," and infer, therefore, " he is not sick," we commit the fallacy of "atnotion." The fault is the same, fundamentally, in both cases, John may be sick from other causes than the one assigned; or more generally, as any Conclusion may he proved by more than one Premise, neither does the denial of any one Premise disprove the Conclusion nor does the affirm-' ative of the Conclusion prove any given Premise to be true. 314. Sometimes, however, the Conditional is so stated that the completion of an argument may be in either of the methods, those above characterized as illicit, as well as those that are always valid,' thus, " Only in case God has commanded the observance of the Sabbath, is the use of it for secular purposes a sacrilege, — or, " if God has commanded the observance of the Sabbath, only is it sacrilege to convert it to secular purposes," the word only, showing that the Consequent can have no other Antecedent. In this case there can be no fallacy either CONDITIONAL SYLLOGISMS. . 105 of " position," or " amotion." We may say, (tlie trutli of the assertion is not here under consideration,) " God has n'ot cSmmanded," etc., therefore the secularization of tlie Sabbath is no sacrilege, or " the secalarization is a sacrilege, therefore God has commanded it. 215. As the Major Promise of the Conditional syllo- gism is but an Enthymeme, stated conditionally, we may regard it as an Enthymeme, and complete accordingly, in which case the proposition that is needed to complete the syllogism, is the Sequence of the Conditional. And it is often important to complete the Formula in this way, in order to display the Sequence that is really as- sumed. This Sequence, regarded as a proposition, will sometimes be manifestly untrue, and then as a Sequence it is nothing, or as we say, there is no connection between the Antecedent and'^the Consequent. Thus, a gardener once refused to plant seeds on the ground, as he said : " If we plant them in the new of the moon they will not grow." Here was manifestly an assumption of a Connection 0:1; Sequence, between the state of the moon and the growth of the garden. seeds, a connection which most of us would deny. 216. If there are four terms in the Conditional, the Sequence is double, or we shall be obliged to insert two new propositions. As if A is B, C is D, thus we can complete only by saying. All Cis'A, All A is B, AWBisD, therefore, C is D, _ ' 217. The proposition that was needed in the case of Conditionals of three terms only, and one of them in the case of Conditionals with more than three terms, may be a qomparative judgment, as well as Categorical, 106 TEXT-BOOK OF LOGIC. thus, " if the air is lighter than water, it is lighter than earth." Because " -water is lighter than earth," is in this case obyiously the required Sequence. And again, if vice is Toluntary, virtue is voluntary, because, " "What may be aflBrmed of vice, (in regard to volition), may be affirmed of virtue." 218. In drawing an inference in the destructive meth- od we must note carefully that we are entitled only to the contradictory of the Antecedent, not its contrary. And, in fact, we are liable to the fallacy of illicit process in the constructive method'also. 219. "With three distinct terms there maybe four posi- tions of the terms in relation to one another, thus. If A is^B, B is C. If Ais'B, CisB. If A is B, A is 0. If A is Bi C is A. Now, suppose we have. If A is B, C is B, "We need All C is A for Minor Premise,. then we have All A is B, Air C is A, therefore, All C is B. 220. But if we have. If A is B, B is C, we cannot have for Consequent All B are 0, unless B is an individual term, for we should have an Illicit of the Minor. So, too, with the form. If A is B, C is A, if C is a general term, a universal Consequent will involve either an Illicit of the Minor, or an Undistributed Middle. 321. In the case of the Destructive mode we find that the same sequence as the Constructive method requires, is all that is needed; thus. If A is B, C is B. A is B, C is not B, '.C is B, .".Some A is not B. CONDITIONAL SYLLOGISMS. 107 The Minor Premise required is, All are A, and we have, AH A are B, and No C are B, All C are A, All C are A, . .•.AH C are B, .-. Some A are not B, and no A are B, would be Illicit of the Minor. And yet it is a fallacy that not nnfrequently occurs. If, however, we can have a universal conclusion without Illicit Pro- cess, we are of course, entitled to it. 2^2. What we have thus been speaking of, may be called the obvious Sequence that is, the Sequence that is implied in the formula itself, and can be found by the process indicated. And the Sequence thus found, will be a' general proposition. But there will often be special reasons for the connections that are not stated or inti- mated. In that case we are at liberty to reject the con- ditional, as the basis of reasoning, although there may ■ be a good Sequence between them. Thus, I happen to know that " if John has a letter, it is from his father." No obvious or general Sequence can be found for such an assertion. I cannot, therefore, make it the Major Prem- ise of an Argument, by which to prove to others that the letter is from his father, notwithstanding I should show that he has one. My conditional assertion there- fore, must be regarded as only an assertion, the Sequence to which, as well as the Antecedent, needs proof. 223. In some cases we have what is called a Compound conditional, in which both the Premises are stated Con- ditionally, as, If M is P, and if S is M, S is P, or we may have different terms, as if A is B, and if is D, E is F. If A is B, ) -p, . -p, If C is D, [ ^ ^' ^• In this case all the antecedents must, of course, be af- 108 TEXT-BOOK Oi LOGIC. firmed and proved, or the Consequent is not established as a Conclusion. 224. It is said that the establishment of one of the antecedents, creates a probability of the truth of the Consequent, and these probabilities or " chances," as they are called, are subject to mathematical computation, when they have once been estimated. The only case, however, which I shall refer to here, is that' in which the antece- dents are regarded as only probable, in which case, the consequent is less probable, than any one of the antece- dents, rather than more. In this the Compound condi- tional differs from what is known as the Cumulative Argument, of which I shall speak in the next Section. 225. Thus, for an example, suppose a certain result in a group of chances depends upon the two conditions, (1) a throw of a certain number as a size and (2) upon a certain combination of the pieces when the die is thrown. ISTow the probability of that particular side of the die falling upward is as 1 to 5 against, or 1 in 6, or one-sixth. The probability of the pieces being in the requisite posi- we may call 1 to % against, or one-fourth. The proba- bility of the result is not the-sum of these fractions, five- twelfths, but their product, or one-tiventy-fourtli. 226. Again, we have Continuous Conditionals,, in which the Consequent of the firat Conditional is made the antecedent of the next and so on, as If A is B, A is C, If A is C, A is D, If A is D, A is E, etc. If the Sequence is good in all these cases, we may, of course, cancel out all between the first Antecedent and the last Consequent and have If A is B, A is E, and treat it as if there had been no intervening members. This is vir- tually a Sorites stated conditionally, whereas the simple conditional is an Enthymeme'so stated. 227. From the nature of a Conditional, it follows that DISJUNCTIVE SYLLOGISMS. 109 we may always take iiper contra, or by contraries; thus if we have, If A is B, A is ; it will, of course, be true, also, that if A is not C, A is not B. If, however, one of the members only, as a categorical, is negative, as. If A is not B, A is C, we are to regard the Conditional as a Disjunctive stated conditionally. This will make no difference however, with the reasoning, the method of completing the argument, etc.; for in fact, we are obliged to put Disjunctives into this form in order to test their validity in.reference to their implied matter. 228. We may have of course, a conditional modal in a Categorical syllogism, thus. All M are P, then if A are S S are M. and we shall have of course the same modal in the Conclusion, If A are S .S are P, In this case, however, the reasoning is none the less categorical on account of the modal ; it is not made in any sense con- ditional thereby. SECTION ly, DISJUNCTIVE SYLLOGISMS. ' 229. Wholes are of several kinds, and the relations of parts to their comprehending wholes and to each other are of as many kinds. Thus, a genus is a logical whole, made up of species as parts, and in like manner the spe- cies is made up of individuals as parts. In mathematics a product, is a whole made up of factors; an amount is a whole made xip of several sums by addition ; these are called mathematical or numerical wholes. Logic treats of the relations of parts to logical wholes, and Arithme- tic and Algebra, of the parts to their wholes and to one another in mathematical wholes. 230. But besides these two kinds there are what are 110 TEXT-BOOK OF LOOia called collective wholes, in -which the whole is made up of parts sustaining relations to one another, and to the complex whole, quite different from those already stated. In this kind of wholes, . the whole often has properties which no one of the parts had separately, and it will often happen that properties that may be predicated of each of the parts separately, cannot be predicated of the whole taken together. The union, of parts in these cases is a synthesis, not a mere addition or multiplica- tion. 231. Thus, every chemical compound is of this kind. It has properties which no one of the parts or elements had, and each element loses some of its properties on entering into the combination. So a family, a state, a society, a committee, are collectiye wholes, and much can be said of them that cannot be predicated of any individual of them taken separately. 333. Now, of all the modes and formulas of reasoning those that depend upon this relation are least understood, and have been least of all reduced to rule. In fact, there are few or no general rules that can be stated and re- duced to formulae. It is probable that a society, a family, etc., made up of christian men, will act in accordance* with the principles of Christianity as they understand it. But we have no way of proving to a certainty, how they will act from a knowledge of their individuality. And it is well known, that in chemistry but very little can be predicted beforehand of the nature of a new compound, from any knowledge we may possess of the nature of the elements. Some things we can know, as for example, if it contains nitrogen, it will be easily re- solved, if it contains carbon it is likely to be combusti- ble, etc., etc. 333. Every object we see or can think or speak of, is DISJUNCTIVE SYLLOGISMS. m part of some collective whole. Every tree is a part of the landscape ; every chair, table and sofa is part of the furniture of the room, the eyes, nose, etc., are parts of tYiQ features or face, every star is part of a constellation, and the constellations themselves are each of them parts of the heavens. 234. But as so little is known of the laws of combina- tion and synthesis in collective wholes, no formulaB or canons can be given for this kind of reasoning. As we have said, however, any species in a genus is a part of the genus, and we may have a form of reasoning based upon this relation, different from those already consid- ered, and known as the Disjunctive syllogism. 335. From the laws of classification and division, stated in a preceding Chapter, it follows that if an indi- " vidual included in any genus is not contained in one of the co-ordinate species, it must be contained in another. Hence, we have the disjunctive assertion. Either n is Ai or n is Aa or, as it is more usual to state it, " n is either A or As " in which n denotes any individual Ai and A2 denotes co- ordinate species. . 236. The Disjunctive Proposition, when used as a part of a Syllogism, is considered the Major Prrmise, and by denying one of the members we establish the other, thus, Either n is Ai or A2 But n is not Ai therefore, n is A2 This is called the Constructive Method, or the modus tollente ponens. 237. Or, if the terms are really co-ordinate and not alternate merely, we may complete by afiflrming one member of the disjunctive, and get for the conclusion, a contradiction of the other, as, 112 TEXT-BOOK OF LOGIC. Either n is Ai or A2 * n is Ai therefore, n is not Aj This is called the modus ponente tollens, or the destruc- tive jnethod. 238. If, however, the terms are not co-ordinate, as Ai and A2 but alternate, this method of completion will be fallacious, since the same individual may be in two or more alternate species, as, " Coleridge was loth a poet and a philosopher." If, therefore, we should say, "he was either a poet or a philosopher," we could not say "he was a poet, and therefore he was not a philosopher." Of course, the n or the subject of the menibers in the above formula, ma)' as well be a species or class as an in- dividual. In this case the predicates Ai and A2 would denote genera instead of species. 239. Or again, we may have the predicate the same in both members, and the subjects different; thus, eitlier Ai is p, or A2 is p. In this ease, Ai and A2 will denote two parts or species, and p a property which must be a differentia of one or the other species, as, " either mind or matter is eternal," either mind or matter is " sponta- neous." 240. The methods of completing, and the limits of their application are the same as in the other forms of the disjunctives. (1). When there are but three terms, one common to both members, and the others different in each, the two are called co-ordinate, and taken together must make up the sum of the divided whole. And this' they can do whether co-ordinate or alternate parts, the only differ- ence being that in the former case no individual can be common to the two, while in the latter case there will be one or more common to both. Henc6, the terms are DISJUNCTIVE SYLLOGISMS. II3 virtually positive and negative in relation to each other. Ai and A2 are the same as A and non-^A. Or if we have two positive terms, as A and B, they are A and non-A, or B and non-B ; A being equivalent to non-B, and B being equivalent to non-A. (2). But we may have more than two co-ordinate terms.' Thus, n is either A, or B, or 0, etc., indefinitely. In this case, any one of them, as A, may be taken for ' positive, and the others together will be its negative, or non-A. And in completing the syllogism, we first deny one member^ and then get for Conclusion the others stated disjunctively, thus, either w is A or B or 0, n is not A,' therefore ra is B or 0. Then again, n is either B or C, t n is not B, therefore n is G. It can make no diflference how many co-ordinate terms there may be. * », 241. This formula is the basis of a method of reasoning sometimes called aiscissio finitimi, which is of great use in some departments of science. Thus in Chemistry, the chemist having a substance to analyze, says virtually, it is either this, that, or the other, naming the four or five groups into which all substances are divided with refer- ence to their chemical composition. He treats it for one group and says as the result, it is not in this, it is not an alkali, for example. He has thereby reduced the number of groups in which it may be found by one. He then tries for another, say acid for example, until he finds that in which it is contained. In this way he saves the • time and labor of testing for each substance in the group 8 114 TEXT-BOOK OF LOGIC. alkali, acid, etc., for.eacli of wbich as much time and labor might be required, and in some cases more would be re- quired for each separately, ,than is needed for the appli- cation of the test that determines the group. 343. It is not necessary nor is it customary to draw out the argument with all the detail and completeness of form that we have described. This, in fact, is seldom done; but the steps that require special consideration are taken, and the rest implied, but omitted, because not re- quiring special attention. If however, there is any un- certainty or question as to the result when it has been obtained, the process is reviewed and the implied steps one after another, are called up for inspection and criti- cism, and no one can be thoroughly master of this meth- od of investigation without understanding the funda- mental laws of the Disjunctive Syllogism. 243. The disjAnctive may always be converted into a comparative, by substituting the contradictory of either one of the members for the antecedent, and using the other for consequent, as, either A is B or C is B. If A is ■not B, C is B, or if is not B, A is B. 244. In this way we may regard them as parts of an Enthymeme, and complete them as already seen, and the premise that is needed will exhibit the contradictory op- position, of the co-ordinates ; as in the above given exam- ple, we should get, all noii-A is C, and all non-C is A. Hence A and together make up the whole. 245. As a formula, the Disjunctive is valid only on condition that all the co-ordinate parts are mentioned, and we have as many members as there are co-ordinate parts. Otherwise the individual n, as in the first uase, might be in the class not mentioned, or as in the second, the term might be a predicate of some other object than those previously denoted by A and B ; that is, it might DISJUNCTIVE StLLOGISMS. II5 be a predicate of part of the indiTiduals contained in one of those species alone, or of some that are contained in each. 246. When this condition, namely, the mention of all of the parts, is not fulfilled and completed, we shall have the fallacy in matter, called non-excluded middle ; that is, if we mention two classes only, when there are three, we omit a third class, a tertium quid, or middle class within which the individual n may be contained. Hence, be- tween any two contradictory propositions, it is customary for logicians to say there is excluded middle ; that is, there can be no proposition expressed in the same terms that will be true while the two expressions are both false. Thus, if I say that "all men are wise," and "some men are not wise," there 'is excluded middle, and one of the propositions must be true. But if we say, "All men are wise," " no men are wise," there is not excluded middle, and the propositions " Some men are wise," and " Some men are not wise," may both be true, while both the universals are false, j^ 247. The Excluded Middle can always be made to ap- jlear in disjunctives by stating them conditionally, and then regarding them as Enthymemes, completing them into Categorical syllogisms. They can be stated condi- tionally by making either member negative, and stating it as the antecedent, thus, " If x is not A, it is B," or " If X is not B, it is A," or again, " If A is not x, B is x," or finally, " If B is not x, A is x" 248. We havQ then four cases, or rather two cases, each of which inay be completed in two ways. (1) If x is not A, X is B, All non-A is B, X is not A, therefore, x is B. 116 TEXT-BOOK OF LOGIC. In this case the required premise is " All non-A (i. e. not A), is B," that is, all of X, the divided whole, which is not in A, is in B. (3) If X is not A, x is B, All non-B is A, X is non-B, therefore, a; is A. ' Here we have, all of X that is not in B is in A, show- ing as before, that A and B must be not only two co-or- dinates, but the only co-ordinatfe parts of X, on which the disjunctive, x is either A or B, is based. (3) If A is not X, B is x, whatever 4- is not, B is, A is not X, therefore B is x. Showing as the case requires, that a; is a property that can be affirmed of whatever is included in the genus X, the divided whole, and is not included in the species or part A. (4) If A is not X, B is x, whatever A is not, B is, B is not X, therefore, A is x. In this case the supplied Premise shows the same re- lation of X. It is a property that is differential between the species A and B, into which the genus X is divided. 249. In some cases, and those not unfrequently occur- ring, the divided whole, or genus itself, will be used as the subject of the members of the Disjunctive, as " All substantial things are either matter or spirit," " All men are Christian or practically heathen," "All money is either paper or coin," etc., etc. 350. In such eases, the minor premise, whether we com- plete in the modus ponente or tollente, must mention the / DISJUNCTIVE SYLLOGISMS. Hi^ 'divided whole, or if not, it assumes it by necessary im- plication ; thus, " These men are not Christians, there- fore," etc. " All substantial things are either matter or spirit," we have " the mind of man is not matter, there- fore," etc., in which case we assume by necessary impli- cation that it is a "substantial thing." 251. What is known as the cumulative argument, or the argument from circumstantial evidence, depends for its force on the relation of parts to a whole. In this case the force of the argument is said to depend upon the concurrence. 253. The Compound Conditional and the Cumulative argument differ in the following points : (1). The Probable argument is used to prove an event or fact which either has not taken place, or which, if it has, is not known to have -taken place." In the Cumula- tive argument, on the other hand, the event or fact is known to have taken place and the Argument is used to prove something concerning one of its causes or ante- cedents. Thus, if a .ship is lost at sea, and one-half of the pas- sengers drowned, and the chances that a certain person was on. board is one to three, or one-fourth, the Prob- ability that he was among the lost is one-eighth. But, in one of the most common cases of the use of the Cum- ulative argument we may suppose that a crime is known to have been committed, and a certain person is suspected. In this case, we collect all the facts or " Circumstances " as they are called, that can be urged as proving or tend- ing to prove his guilt. The event is known, and what we are trying to find is the Agent who caused it. (2). In the second place ; in the Probable Argument the uncertainty attaches to the antecedents if the event b'e future ; whereas, in the Cumulative argument there 118 TEXT-BOOK OF LOGIC. is usually no uncertainty about the antecedents taken • separately, but only about their connection with the event that has occurred. In the case just supposed, one antecedent was indeed certain, the loss of one-half the crew, but the other, whether the person in question was on board is in doubt. In regard to the other example, many of the " circu:mstances " are obvious, and admit of no doubt, and i;he only question is, whether they con- nect the supposed criminal with the act or not. (3). In the Probable argument the antecedents must be all enumerated and taken into the computation of the probability of the event ; but in the Cumulative ar- gument there is no such necessity. In fact the " circum- stances " are seldom, if ever, all stated, and of course, they may be innumerable. (4). Finally ; In the Probable argument, all the ante- cedents must be true or proven, or the consequent will not be proved at all ; and all the force of the others go for nothing if any one of them fails to occur or be ful- filled. Thus, in the example given ; the loss of the ship, were it ever so certain, would not endanger the life of the person in question, provided he was not on board. But, in the Cumulative argument, it will often happen that some one or more of the " circumstances " that we should expect to be connected with the proposition to be proved is not only not proved, but is shown to have been impossible or never to have taken place, and yet the conclusion is regarded as established, nevertheless. 253. The Probable argument, as I have said, may be used to prove past events that are not known to have taken place as well as those that are in the future. So, too, the Cumulative argument, though it is used for the most part with reference to past events, may be used in regard to those that are future. When we know of cei'- majuNcuvE syllogisms. 119, tain causes that are at work, all tending to the same result, we can argue from those causes, their nature and tendencies, to the eflfect which they are likely to produce ; and the argument gains accumulated force from any increase of their numbers instead of being weakened by it. 354. The force of the Cumulative argument depends upon that relation of the parts to a collective whole, whereby it often happens that the whole is more than the sum of the parts, almost realizing Hesiod's paradox, of " a half that is more than its whole." Three sticks that will not either of them stand alone will often stand very firmly if they are bound against each other, and sometimes all the more firmly the greater the weight that presses upon them. 355. The same thing will also often happen in estimat- ing the force of testimony. Thus, suppose two men, notorious liars, should come in and relate a story ; thei-e is no doubt of the fact that they so report, but the con- nection between the statement of either of them and the truth of what one says may be very slight, so that his statement, taken alone, would be worth but little atten- tion, while the concurrence of another man without collusion and as an independent witness, though no more veracious than the first, would make the fact at- tested veiy certain. 356. The following has been suggested as a method of computing the force of the concurrence in arguments of this kind. Estimate the value of each connection of the circumstance with the fact to be proved in a fraction of unity. Take for each fraction its complement in unity, multiply the fractions thus obtained and then subtract that product from unity, and we have a repre- sentative of the resulting force of the concurrence of the 120 TEXT-BOOK OF LOGIC. circumstances in a OumulatiTe argument. Thus, let the probabilities of each be 1-2 and 1-3, the complements in unity will be 1-2 and 2-3 ; their product 2-6, and sub- tracted from unity we should haYC 2-3 as the resulting - probability in this case. The more numerous the cir- cumstances, the greater of course the probability, and the more nearly does it approach certainty by this meth- od of computation. But, in the case of the mere comr pound conditional, as we have already seen, the more numerous the antecedents the less the approach toward certainty. And thus while in the latter case, each new ■ condition weakens the force of the argument; in the cu- mulative argument, on the contrary, each new fact or circuinstance renders it stronger. 257. When the members of a Disjunctive are of the nature of contradictories, so that if either is false the other must be true, and both of them are so related that as Antecedents in a Conditional, they will have the same consequent, the form of the Argument is what is called a Dilemma. -iHschines, in his attack on Demosthenes, puts the statement thus, " Demosthenes did or did not take part in the public rejoicing; If he did, he was inconsistent; if he did not, he is unpatriotic, and in either case un- worthy of our confidence." Or, as we sometimes say, the mail that did this is either a knave or a fool, and, if either, is unfit for his position. 258. The Dilemma, however, is rather a EhetoricaL Figure than a Logical Formula. It is not so much de- signed to prove anything, as to give point and pungency, to what needs no proof. PART III. PRACTICAL. PRACTICAL LOGIC. LANaUAOS AND ABGUMENTATION. 259. It has been sometimes held that Logic is a purely formal science, that it d€a,ls with forms of thought und the formulae of reasoning only, without taking note of the subject matter, or receiving any modifications from it. It is in this respect, say the advocates of this view, like mathematics, which treats of triangles and not of triangular substances, with units, not individuals, with space, not extended objects, with motion, not moving bodies ; and the truths and doctrines which it establishes are in no way affected or modified by the nature or the differentia of the concrete objects or subject matter to which they may be applied. 260. And this view of Logic is certainly true so far as we have already gone in this treatise. The elementary propositions A, B, I and 0, are the same in all their properties and relations, whatever may be the nature of the object denoted by the term that is made subject in the proposition. So likewise, the formulae, the syllogisms whose construction we have considered, are valid, alike for all subjects, whatever may be their nature,"if only they can be brought within the «form of the syllogisms, or stated in its terms. And yet without looking beyond the form, we can never detect a fallacy in Diction, Matter or 1 24 TMXT-B OOK OF LOaia in Method, and without the means of deteqting these, (since we never reason except in the use of words), Log- ic would be of no practical value, even if it could be said to have theoretical certainty. 3M. In proceeding to treat of the practical applica- tion of the formulae and principles already discussed, it must be understood that I can state only the most gen- eral principles, or rather the principles in their most general forms ; since in every department of knowledge there arises the necessity for som« modification of them in their application, in consequence of the nature of the subject matter. 263. I will, however, proceed with such a statement of the general principles of Applied Logic, or the Logic of Proof, as is practicable without going into such a discus- sion of other matter as would make it more proper to call this treatise a cyclopedia of general knowledge, than a Text Book of Logic. 263. But before proceeding to the consideration of the methods of Applied Logic that are determined by the nature of the subject matter and the circumstances under which the formulae are used, we must consider the na- ture and use of language and the fallacies that may arise from the improper, or defective use of it. CHAPTER I. - THE LOGIC OF DICTION. ^ 264. The question has often been proposed and dis- cussed whether we can reason without language? If the question be whether we can reason without usinc/ language it clearly cannot be answered in the negative without excluding from what we designate as " reason- ing " the elementary processes of analysis, abstraction, generalization, &c. If, however, the question be whether we can reason without ^ro^^Mcm^ language, it is sufficient to say perhaps that language is produced by acts of rea- soning, and that probably it would be impossible to per- form those acts without producing some signs or symbols that would represent the things that we are reasoning about. 365. But without entering upon a discussion of this question in either of its phases, it is manifest that lan- guage sustains three relations to our general subject suf- ficiently important to require a discussion of the general subject of the Logic of Language in reference to methods and processes of reasqnii^ ; these relations grow out of the following facts : (1). Without the use of language it is impossible to state or express the mental processes of reasoning so as to make them intelligible or influential upon other minds. 136 TEXT-BOOK 01 LOGIC. {%). The ambiguities of language and the habits in the use of words, the usus loquendi of any dialect, exert a very important influence upon the course of our thoughts and often mislead the mind in its pursuit of truth. (3). Every word and combination of words expresses and represents a fact or state of consciousness, and thus by a process of evolution we can make language itself a means of developing and analyzing these facts and thus find a bridge from the phenomena of consciousness with- in, to the-metaphenomenal facts without — a. sort of tran- scendental Logic. SECTION I WORDS AND SENTENCES. 366. Language consists of separate words joined to- gether by some law of combination so as to denote things in the relations which they appear to sustain to each other. 367. What shall constitute a word is a matter of dialect merely. In Chinese each syllable is a word. In our lan- guage we combine several syllables into a compound word, each syllable, in all probability having been once a separate and distinct word. How far this matter of combination may have gone,.or shall go hereafter, is a matter of no importance to our present purpose. 368. Words are primarily divided into two classes, (1) nouns, denoting things, and (2) all other words, which serve to show the relations, conditions and actionSj of the filings denoted by the nouns. 269. Nouns, may be, in quality, either (1) individual, (3) common, (3) abstract, (4) collective, (5) privative, (6) negative. WOBDS AND SENTENCES. 137 270. Other words, which we may call adjunct words, are, for our present purposes, most conveniently divided into five classes. (1). Adjectives, which qualify nouns, and with a com- mon noun, make a specific term, as " man," "ivhite man" with a proper noun or individual term they limit its scope to some accidental state or mode, as " John Doe (sick^in-bed)." (3). Verbs, which, with the exception of the substan- tive " to be," denote the actions which things are per- forming. (3). Adverbs, which sustain the same relation to verbs that adjectives do to nouns. (4). Prepositions, which always, with perhaps the ex- ception of " of," show the relation between an action and some one of the causes or conditions enumerated in a preceding chapter, as " writes upon paper, with a pen, for the press," etc. (5). Conjunctions which show the relation between parts and wholes, which they do or do not make. If a conjunction be copulative, illative, etc., the parts are de- clared to make the whole. " If disjunctive, exceptive, etc., they are declared not to be united in fact, so as" to make a whole, although such a union is conceivable, and may be made a matter of question. 371. I take- no note here of " participles " since for all present purposes they are the same as mere adjectives. To speak of them as participles ie merely to show their etymological relation to verbs. 373. I take no n'bte of " pronouns " because they are either nouns or adjectives^that is,,personal or relative pronouns which are used instead of nouns themselves, — or adjective pronouns in which case their functions need not be considered separate from that of adjectives or articles. 138 TEXT-BOOK OF LOQIG. 273. Articles I have not included among the distinct parts of speech, since some languages have none. But in fact they are necessary for any well-deyeloped lan- 'guage, and perform a most important part in all culti- vated languages with the exception of the Latin. 274. The use of the Article in English is very pecu- liar. In the Greek Language, and also in the French and German, it may be used with abstract notins, even when not followed by any limiting word or clause, as " the anatomy teaches," etc., " tJie virtue gains _ confi- dence." But in English proper, the article "the" is never used before an abstract noun, except when it is followed by the preposition " of" or a clause beginning with a relative pronoun, as " the pain which we feel," etc. ' 275. This is a very important fact, for it follows from this peculiarity of our language that when we use the article " the " before an abstract noun not thus followed by a limiting clause, we immediately and instinctively oij edify the abstraction and treat it as a concrete sub- stance. Hence has come the belief that what we call " the faculties of the mind " are more substantial than the motions of the body, and we say " the memory " or " the imagination " does so and so. But we never say " ^7«e walking '• or "i5Ae sleeping" does so; we say sim- ply, " walking fatigues us," " sleep, or sleeping refreshes us." 376. It is manifest that words, in order to make a sen- tence that shall be intelligible, must be put together in accordance with the relations, which the things denoted by the nouns in the sentence either (1) appear to sustain or (2) may be supposed to sustain to each other. 277. jSTow this is a law that lies below Grammar and Ehetoric ; for a sentence may be so constructed that it will WORDS AND SENTENCES. I39 fulfill every law of Grammar, and of Khetoric too, which nevertheless has no meaning. I ssbj every law of Ehet- oric except that of perspicuity, and here Khetoric is at fault ; for it provides no rule whereby the sentence may be made perspicuous and no criterion by which we can tell why it is so. Campbell in his Ehetoric gives the following example ; "All the voices of the celestial joy- fulness, qualiiy, commix and harmonize in the fire which was from eternity in the good quality." No one, as the author remarks, can say that this is not true, for the simple reason that he does not know what it means. And it must be confessed that much of what has hith- erto been considered Metaphysics, is of precisely this character. 278. With the description above given of the function of the adjunctive parts of speech, all that is required to make sentences intelligible is a compliance with these .four rules. EuLE 1. In categorical propositions where the verb used is simply " is," or its plural " are, " the predicate must be either, (a) a synonym of the subject. (5) an adjective denoting some quality that does or may be understood to belong to the" subject as " snow is cold ;" " paper is white," etc. (c) some common noun that denotes a class in which the subject is, or may be supposed to be contained, as "horses are quadrupeds;" eagles are birds;" "whales are mammals." 279. If the adjective denotes a property that does be- long to the noun, or a rtoun-predicate denotes a class that does include the subject, the proposition is both intelli- gible and true ; if not, it is intelligible but false, as " snow is warm ; " " horses are birds." And even the proposition 9 130 TEXT-BOOK OF LOGIC. that is false when taken literally, may be true figuratively. Snow may be warm compared with something else; "horses" maybe called " birds," in reference to their beauty of form, or their speed of motion. Rule 3. If the verb be any other than the verb "to be," the grammatical noniinative must be a concrete term to denote the agent that does, or may be conceived to perform, the action. 380. We are so much accustomed to the departure from this rule, by metonymy, that we shall hardly bf pre- pared to admit it without some of the considerations that follow below. But of course we cannot conceive of any action without something that acts, and that something whatever it may be, will be. denoted by a concrete term if denoted or spoken of at all ; or rather whatever term is used to denote it becomes de facto concrete. BuLE 3. If the verb be ti'ansitive, denoting not only a state of action, but actual causation, either producing, perceiving, or changing something, the word which de- notes the grammatical object must be a concrete term. 281. This also results from the nature of the act deno- ted ; thus, " to eat " is a verb of this kind, and in order that the act may be performed there must be something that is eaten, and that thing must be a substantial reali- ty, or the act cannot take place, or be conceived to take place. 383. Many verbs, however, are active intransitive, as "to walk, " "to run," and they require no objective case after them. Many of -them will take none, except as they are followed by a preposition between them and the noun, as " to walk on the floor, with a cane," etc. Many such words, however, will take after them an abstract noun de- noting the action itself; thus we may say either "to strike the ground," denoting the object struck, or- "to strike a WORDS AND SENTENCES. 131 blow," the objective in this case denoting no object, and is only a more emphatic way of stating the matter than the simple verb withont the noun. EuLB 4. The fourth rule is, that conjunctions connect- ing words, must connect only those that are of the same quality ; that is, if one be abstract, the others must be sa, too ; if one be concrete, the others must be concrete, also. 283. This is obvious from the definition of the func- tion' of conjunctions given above. We can conceive of any concrete objects being grouped together to make a collective whole ; we can conceive of almost ^ny proper- ties being contained in the same object. But the man who should say that " water," for example, is composed of oxygen, hydrogen and fluidity would violate our rule Md cause us to look up in astonishment, wondering what he could mean. -284. These rules apply to simple and* compound sen- tences only. When a sentence is complex, or rather when it has a complex term, that is, a term that consists of more than one word, we must remember that, («) Adjectives limit the sentence so as to apply to either some species of the. class, or some special state or mode of the individuals; and thus a proposition, which would be doubtful or only partially true without the limitation, becomes true with it. (i) The noun following a preposition, unless it be the preposition " of," iau6t be concrete, if it is to denote any- thing that is to be considered as a cause, material, instru- ment, etc. Otherwise, the preposition and the abstract noun are virtually an adverb, as " with speed " is the same as " speedily," " in haste," " hastily," etc. The preposition "of," however, stands between two nouns, rather than between a noun and a verb, and the 132 TEXT-BOOK OF LOGIC "twQ nouns may be replaced by a single complex term, by making the one that follows the preposition an ad- jective qualifying the one before it, as "horses of wood," " wooden horses," " goddess bornof the sea," " sea-born goddess," etc. (c) An adverb limits the scope of the verb, as the ad- jective does that of the noun, and in fact may always be transferred to the subject of the proposition, and become an adjective, as " John walks with speed," " John (with speed, or speedy at the time), is walking." In this case, the adjective so obtained, can denote only an accidental property or mode of the subject. 285. Language used in accordance with the above rules and conditions may be considered literal or didactic, (all other is figurative or poetic), and if it describes things as they are, it is true, if not, it is intelligible, though un- true. But if used in violation of any one of these rules it becomes in itself unintelligible, and neither true nor false ; and the only way to educe any meaning or make it intelligible is to treat the language as figurative, and substitute for it its logical equivalent. This may be done in one of two ways. (1) When .we have an abstract term, by way of meton- ymy, and a concrete term is demanded, we can always convert the term into its logical equivalent, by taking for the abstract noun its proper adjective, and placing after it any noun that that adjective may qualify ; thus, " ti;ade enriches men," " men trading, or by trading, en- rich themselves." " Food satisfies hunger," " food satis- fies men hungry," or "hungry men." In this case, we might as well say " animals," since " hunger " can be predicated of animals as well as of men." And it should be always borne in mind that it is safest to take the most general term that the adjective can be predicated WOBDS AND SENTENCES. 133 of; since whatever is true of the genus, is always true of , the species, but not. the converse. In many cases, however, when the abstract noun fol- lows the verb, it is best to consider it'a part of the verb, or substitute another verb that expresses the same thing without requiring, the aid of a noun, as " exhausts the strength ; " this is equivalent to ." enfeebles," but is more forcible rhetorically, and we might say, " medicine strength-exhausts," or " takes away strength." "We are, however, so much accustomed to these metony- mies that we understand those that all are accustomed to without the process I have been speaking of; and in fact scarcely regard them as figurative es'pressions at all. But the moment we meet with a new and unfamiliar one, we pause, and often, after the'best we can do, find ourselves at a loss to comprehend what the author intended to say. And in our effort to comprehend, we objectify abstrac- tions, mythologize a meaning to the word, and imagine or fancy something corresponding to it. (2) In case "the expression is a metaphor or simile, it arises as we have seen, from a comparison, and is, for the most part, if not* always, designed to describe an effect when the cause, and the modus operandi, either or both of them are unknown. In this case, we are simply to re- turn to the full statement of the comparative proposition in which the figure originated. Thus, to take a familiar example, " light comes from the sun at the rate of twelve millions of miles per min- ute." This, of course, objectifies " light " and makes it a substantial thing that can "come" and "go," etc. But all that is really known, and all that can be held to be fairly proved by the observed phenomena in the case, is that the effect is the same as if '" light " were a sub- stance that moved from the sun to the earth in the time 134 TMXT-B OOKOFLO GIC. .or at the rate aboye specified ; or, in a more formal state- ment, "the effect (which is seen) is to the cause (whatever that may be) as a substance (heat) coming at the rate, etc., to the earth." In this last case we get a result which is intelligible and true ; because it describes an observed fact, (the illu- mination of the earth,) with whatever of attendant cir- cumstances had been noticed at the time. But it says nothing, for. the observer knows nothing, of the nature of heat, whether it be a substance emanating, an undu- lation in an imponderable ether, or a mere " mode of molecular motion." 28G. Under-the former rule, the one in regard to met- onymies, we get a proposition that is always intelligible, but not always true. The proposition will always have lost much if not all of its . beauty and rhetorical force. ' Thus, if we transform " God is love," into " God is lov- ing," we have . all of the truth that there was in the exposita, but the force is gone. The proposition, how- ever, often becomes absurd the moment we have substi- tuted the logical equivalent for the abstract term. Thus a certain writer, in order to explain, and as a means of explaining the origin of material objects says, " suppose two simple activities meet, and at the place of meeting resist each other, they produce a third thing, etc." Now for " two simple activities " put, as by the rule " two sim- ple acting bodies," " two simple bodies in action," and we have the manifest absurdity of attempting to account for the origin of the first body by supposing two before it to produce it. FALLACIES IN DICTION. 135 SECTION n. falijAcibs in diction. 287. A Fallacy is any formula or other statement which has the appearance of an argument without the validity of o-ne ; and so we call both the fact by reason of which it lacks concluding force, and the formula itself, by the same name, a Fallacy, as when we say,' "his whole argument is a fallacy," or when we speak of the fallacy of one's argument. 288. Fallacies are divided primarily into two classes, Logical Fallacies and Extra Logical Fallacies. Those are called Logical Fallacies which offend against any of the rules" that are considered as coming properly within the province of Logic, and are sub-divided into two sub-classes, Fallacies in form and 'Fallacies in diction. The Extra Logical Fallacies are also sub-divided into two sub-classes. Fallacies in Matter or material Fal- lacies, and Fallacies in Method. Hence, we have four species of Fallacies, Fallacies in Form, Fallacies in Diction, Fallacies in Matter, and Fal- lacies in Method. 289. A Fallacy is said to be in form when it is apparent from the form of the syllogism merely, without consid- ing or knowing what is the meaning of the terms. Of this kind are most of those we have already spoken of, as Undistributed Middle, Illicit Process, etc. 290. A Fallacy is said to be in diction when the lan- guage used is such that it appears to express and repre- sent the formula though it does not. Of these we have had no example discussed thus far. But I shall enumer- ate six in the following pages, namely: Figurative Lan- 136 TEXT-BOOK OF LOGIC. guage, Many Assertions, Ambiguous Middle, Variation of Condition, Division and Composition, Substance and Accident. 391. A Fallacy is said to be in matter when one of the premises is untrue, and this may extend to either the premises that are asserted, or to those that are implied as in Enthymenaes, etc. And of tijis kind there may be five, " N"on vera pro vera, Non causa pro causa, Metabasis, No sequence, and Non-excluded Middle." 292. A Fallacy is said to be in method when the speaker or writer assumes what he ought to prove, or adduces arguments which are perfectly good, but do not prove what is required or what he claims for them as a Conclu- sion. 293. Most modern writers of note give no list, classifl- ■ cation or account of the Fallacies, on account, perhaps, of the incompleteness of the list hitherto, and the want of clearness and satisfactoriness in the classifications that have been made. Perhaps an account of them is not necessary to the completeness of a treatise on Logic, ' but it would certainly be of great practical value, as all will confess, if a complete enumeration and a satisfactory classification and explanation of them could be given- We need not only to know the way to truth, but we are better prepared fo^its successful pursuit, when we have had the principal, if not all the sources of error pointed out to us. On a subsequent page, (§ 519, Note,) I have appended a classified list of the Fallacies. 294. I give in the first place, the list of Fallacies as. they are presented in the Scholastic writers, taking the one I give from Aldrich. These writers speak of them as of two kinds. Fallacies in dictione and extra dictionem.. And I give the list, not because I think it of much value, but, (for the reason I have very often introduced techni- FALLACIES IN DICTION. 137 cal terms,) because they occur in writings where educated men will meet with them and feel the need of some ex- planation of their meaning. 295. In dictione are six. (1) Equivocation, (2) Am- pMbolia, (3) Composition, (4) Division, (5) Accent, (6) Figure of Speech.. The example of equivocation given as an illustration is, " the dog is an animal, Sirius (the dog star) is a dog," the equivocation being in the word " dog." Amphibolia consists in an uncertainty in the grammatical construc- tion of a word, as for example, the antecedent of a pro- noun or the subject of a verb. Composition and Division I shall explain more fully below. Accent is the mislead- ing the mind of the hearer by placing the emphasis in a sentence upon the wrong word, as in the well-known ex- ample, " Do you ride to town to-day ?" It may be made to have six meanings as we accent one or another of its words. Figure of Speech is rather form of expression, as when one infers from the form of the word " musa " which is feminine, that "poeta " is feminine also, because they both terminate in the letter " a." 296. Extra dictionem (1) Accidents, (2) a Dicto se- cundum quid ad dictum simpliciter, {3) Ignoratio Elen- chi, (4) A non causa pro causa, of which there are two varieties, a non vera causa and a non tali causa, (5) Con- sequences, (6) Petitio Principii, (7) Plurimum Interro- gationum. 297. Accidents and Quid I shall explain more fully below, as my sixth in diction. Ignoratio Elenchi and Petitio Principii, I shall also explain as Eallacies in Method. A non causa I shall explain as a Fallacy in Method ; it is simply the assertion or the assumption of a premise, which, because it is not true, is not a logical cause of the conclusion. A non tale I shall treat as a 138 ■ TEXT-BOOK OB LOQia Fallacy in diction, and call it the Fallacy of Variation ; the Fallacy of Consequences is in fact, any Fallacy in Form. And Plurimum Interrogationum, I shall treat as the second Fallacy in diction, calling it rather the Fal- lacy of many Assertions, than the Fallacy of many questions. 398. Of the Fallacies in Form I shall say no more ; ' they have all been described in the foregoing pages when we were discussing the forms themselves. When they occur we have simply a non sequitur.; the Conclusion may be true as a proposition, but it does not follow from, and its truth is not proved by the Premises. 399. Fallacies in Diction' I have defined in general. They are Fallacies in the statement of a syllogifim where- by it appears to fulfill all the requirements of the form- ula and yet does not. In case of a Fallacy of this kind the conclusion may be said to follow joer fallaciam, hot truly or validly, but by a Fallacy, .300. We know or detect a Fallacy in Diction only by considering the meaning of the words used. And we find that one or more words in the syllogism must be taken in different senses or with different limitations in the different parts of the syllogism in order that the propositions whether Premise or Conclusion in which it ' occurs, may be assented to. Thus, if a man should say, " feathers are light," we should not think of disputing him. And if afterwards he should say, "light is neces- sary to color," we certainly should, not dispute him. But if he go on and infer that therefore " feathers are necessary to color," we should hesitate, and on looking back we might find that his Syllogism was faultless in form, each Premise true,' but in order that the Premises may be assented to as true it is necessary to understand the word "light " to mean different things in each. FALLACIES IN DICTION. 139 301. Heiice, I draw two practical inferences of great value. , ^. . , .. (I). A Fallacy in Diction is more likely to occur where one person is reasoning by supplying one Premise of his own, from a Premise laid down by another person, than if he were stating both Premises himself and as his own. Hence most of these Fallacies occur when but one Premise is prominently stated. (3). No one can safely use as a Premise any proposi- tion that he does not comprehend, and of course any one must be able to explain the inference or conclusion he draws, otherwise he has no security, and we have no guarantee against a Fallacy in Diction. In etery science there are technical terms that have meanings peculiar to their use in that science, to such an extent that if one uses them who does not know their scientific meaning, he is pretty sure to make false applications of them, or what is the same thing and leads to the same result, makes false deductions from propositions in which they occur when used by him as Premises. 302. (1). Of the Fallacies in Diction the first that I mention is the Fallacy of Figurative Speech. This is in fact like the old Figura Dictionis, and yet it is not the same. What I mean by it is the Fallacy of taking what is figurative in one Premise as though it were liter- al in the other. Thus we veiy commonly say " light comes from the sun." But whatever comes must be a substantial reality capable of separate existence. This latter is but the common sense of mankind and is in accordance with the strictest analysis of the word "comes." Hence, most people believe from such ex- pressions that light, heat, etc., are substantial. 303. I have said that every figurative expression is a suggestio falsi, suggests something false and it is the 140 TEXT-BOOK OF LOGIC. ' province or function of the Fallacy I am now speaking of to bring out tHis that is false; and to hold or afi&rm it .as an inference from the figurative expression. 304. (3). Many Assertions; the ancients call this a Fallacy of Many Questions. The example they gave was something lite this : •" Have you left off tippling ?" If the respondent answered in the afiBrmative he admit- ted thereby that he had been in the habit of tippling or drinking to excess. But if he should answer in the neg- ative he. would admit that he still continued the habit. But if we put the sam« thing into the form of an asser- tion, we have a doul|«e assertion. " Such a one has left off the habit of drinking," asserts the two facts that he once had the habit and that he now has it not. 305. When St. Paul says, " after the manner which they call heresy, so worship I the God of my fathers," we can readily imagine some one had said, 'fie has joined the Christian heresy." Now suppose for the sake of the truth that was in the- assertion "he has joined the Christians," St. Paul had allowed the statement to pass, and some one had" quoted it for the other assertion, " Christianity is a heresy," and used St. Paul as an au- thority to prove the assertion, we should have the Fallacy of Many Assertions. 306. In fact, there is scarcely a proposition possible that does not make or imply two assertions. If I say, " This is a pen," I assert (1) that it is^ — that it exists aa something, and (2) that it is a pen, either of which may be untrue. I may be mistaken, and suppose there is something when there is not, or I may suppose it to be a pen when it is something else. 307. The Fallacy under discussion, therefore, can occur when, of the two propositions implied, one is true, and the other is false ; so that what is false will be admitted - FALLACIES IB DICTION. 141 for the sake of the one that is true, and then the propo- sition will be reasoned from for the sake of the one that is false. 308. (3). Amiiguous Middle as it is usually called, or, as it is better understood, ambiguous terms. Any term is said to be ambiguous, when it is used to denote two or more different things, or in two or more different senses. And there is scarcely a word that is not so used ; as any one can see by turning to his dic- tionary. 309. When words are so used, they are, for all the pur- poses of Logic, the same as two words, and if the thought were so expressed, we should have at once and obviously the Fallacy in form of " Many Terms." As an example the one already used is as good as any that occurs to me. Light comes from the siin. Feathers are light. Therefore, Feathers come from the sun. 310. E"o one would assent to both the Major and Mi- nor Premises, if he were required to understand the word " light " in the same sense in both. But accepting it in different senses we can assent to both of ^hem as true, and yet the inference or conclusion is false. 311. (4). Variation of Conditions. This is substan- tially the same as the scholastic writers meant by Nan tale, pro tali; that is, the object denoted by one of the terms, though the same in substance, is not such in' its quantity, condition, etc., when spoken of in one Premise as it is when taken into the other. 313. Vai-iations may be of three kinds at least: quan- tity, time. and condition. (1) In quantity, as in the following example : 143 TEXT-BOOK OF LOGIC. . Money will buy whatever is for sale. A two-shilling piece is money. Therefore, A two-shilling piece will buy- whatever is for sale. Here the fallacy is two obvious to need exposition. (2). In time, Whatever is. in the zenith is always overhead. The sun is in the zenith. Therefore, The sun is always over head. This is faultless in form, but it implies a difference in the time contemplated. (3). For a Variation of Condition, we have the follow- ing: We eat what we buy in the market. But we buy raw meat in the market. Therefore, We eat raw meat. - Sometimes the act denoted by the verb itself makes a change in the condition of the subject. Thus, on the 14th of June Eichard Roe married a wife ; but on that day Rachel Roe was not a wife, therefore, Richard Roe did not marry Rachel Roe. But " he married a maid and she made him a wife." 313. (5) Division and Composition. This is the result of using a term as a collective term in one Premise, and then as a general term in the other, or,'possibly in the conclusion. As an example : The Romans conquered Carthage. Cicero was a Roman. Therefore, Cicero conquered Carthage. Here it is manifest that we must understand the Rom- ans collectively in the Major Premise; while, of course, it is used as a general term in the Minor. Otherwise the Premises would not be assented to as true. 3li. This form of the fallacy is called Division, because FALLACIES IN DICTION. 143 we use the Middle term first as a colleotive term, and then as. a general term. But in case we use the Middle term first as a general term or distributively, and after- wards as a collective term, or collectively, the Fallacy is said to' be one of Composition. Thus : Three and five are two numbers. Eight is three and five. Therefore. Eight is two nunibers. Or again: " The miracles of Christ would fill more books than the world could contain. But the things related by the Evangelists are miracles of Christ. Therefore, The things related by the Evangelists fill more books than the world could contain." Here "The mirades of Christ" must: be taken collec- tively in the Major Premise, else the proposition would not be drSsented to as true. But in the Minor Premise the term is used as general, being made the predicate of an affirmative proposition. Hence the fallacy of Division. 315. The difference between general an^ collective terms has already been somewhat discussed ; but it may be well to recall it. Whatever may be predicated of a general term may be predicated, and is in fact predicated distributively, that is of each individual contained in the class. And conversely, whatever may be predicated of all the individuals of any class, may be predicated of the class as a common prop- erty. But in regard to collective wholes neither of these propositions are true. Take, for example, a family, we may say " it is a divine institution, . it is the union of parents, children, etc." But we could not say either of these things of any single member of the family. Again we may say of each member that he is a " biped," and a 144 \ TEXT-BOOK OF LOGIC. "vertebrate mammal," etc., neither of which could be said of the family. 316. We have some terms that are always collective, as church, army, 'congress, etc. But any general term may be used collectively, when used as the subject of a propo- sition. And our only criterion by which to determine the question whether a term be so used or not, is to consider from the nature of what is predicated of the subject whether it can de affirmed of the individuals comprising the class separately and individually or not. Thus in the example given, " the Eomans conquered Carthage," the act is one tfeat requires their combined activity. No one of them did it alone. Hence the word is used collective- ly. But in another example "the Eomans spoke the Latin language," we see that the word must be under- stood as used generally, since the act ascribed to them is an individual act ; each one of them must have done it for himself. 317. (6) The last class of Fallacies in Diction are the Fallacies of Substance and Accident. Whatevey exists at all, must exist (1) as a suistanct, with certain essential properties that can never be destroy- ed without destroying its individuality and making it to be something else, called by a different name and belong- ing to a different species. And (2) it must exist in some particular mode, at some particular time or place; that is in some congeries of accidental properties, or circumstan- ces which not only can be changed, but which are con- stantly and continually changing. 318. Some nouns denote substances in their simplest mode or form, or rather regardless of mode or form, as "iron," "air," etc., etc., but others denote them as in some particular mode or form, as " wind," which is " air in motion." Or again we may have "water-' as the sub- FALLACIES IN DICTION. 145 stantial thing and then have "sea," " river," " lake," "rain," " fog," etc., etc., as modes of water. 319. Hence a,ll nonns, except these substantive nouns, are equivalent to a noun and an adjective, as " wind," " air in motion," " river," running water." And even " water'* might be regarded as " oxygen and hydrogen in a certain state of combination." 320. A noun always denotes its object by all the prop- erties that are essential to the object. There are, how- ever, certain properties which, although in reference tg the object they are quite accidental, do become, never- theless, quite essential to the proposition in which the word occurs. "With these it will be understood, accepted and assented to as true, while without such limitations, it would be likely to be misunderstood, and pretty sure to be contradicted and rejected altogether. 321. But a modification or modal which is essential to one proposition, becomes useless or mischievous when the same subject is used in another proposition, and with a different predicate ; and vice versa, that which is acciden- tal in one, will be regarded as essential in another. 322. Hence, when-a modification or modal is intro- duced into a Premise which is accidental there, and so brought into the conclusion as to be regarded as essential, we have that variety of the Fallacy under consideration which is called Fallacia Accidentis, or fallacy of acci- dents. 323. But on the other hand, if we make what was es- sential in the premise, accidental in the conclusion, or treat it as such, we have the other form of this fallacy, as it has been called, A dicta secundum quid ad dictum sim- pliciter, or simply, and for brevety's sake, we may call it the fallacy of Quid. Thus, if I should say that Mr. Jones is a good shoe- 10 146 TEXT-BOOK OF LOGIC. maker, I imply that he is a man, for he must be that to be a shoemaker; that is, shoemaker is a shoemaking man. If now, using this as a premise, I infer and assert that he is a " good man," I have treated the adjectiye, " shoemaking," which was what I had chiefly in mind, when I asserted or assented to the premise, as accidental. If now I drop it out of the conclusion, and make the other adjectiye, "good," qualify the substance " man," rather than " shoemaking," as it had before done, we have one form of Fallacy under consideration. 334. This fallacy is yery likely to occur in the use of adjectives which may be understood to qualify either the substantial thing or the mode implied in the word used to denote it. Thus, if I speak of a man as "my old friend," it may be a matter of doubt whether I mean to imply that the man is old, or only that the friendship is old, though the man may be young. If, however, the adjective is understood by, the person that utters it to to qualify one, and is taken by him who heard it to qual- ify the other, we have one or the other of the forms of the fallacy of Substance and Accidents, as the case may happen to be. 335. This fallacy is especially likely to occur in reason- ing from comparisons ; since comparisons are always made secundum quid, with reference to' some one point of resemblance or analogy, and the moment we begin to extend one beyond that point, we begin to take it as dic- tum simpliciter, as if the resemblance extended to other points than the one intended, or possibly as constituting complete identity. Thus, I not long since heard a clergy- man arguing from the declaration, " That same Jesus shall so come in like manner as ye have seen him go in- to Heaven," that Christ would come again in visible form to abide on earth. I could not help raising the FALLACIES IN DICTION. 147 question whetlier he was not mistaking the point of re- semblance intended, and committing the fallacy of quid. In the following'example the fallacy is manifest. Nebu- chadnezzar ate grass like an ox, the ox eats grass stand- ing on all fours, with horns and hoofs, therefore Nebu- chadnezzar must haTe had horns and hoofs during his estrangement. 326. This Fallacy, fallacia accidentis, often occurs in those mental processes that precede the utterance of a Proposition and when, of course, no Premises are giyen on account of which we can regard it as a conclusion. Thus a few years ago a friend happened in town where there had been a religious service on a day in the week, Friday. He remarked on the fact, " I see you have pray- ers on Fridays." It was true in fact, but we had had the service not because it was Friday, the Fridaywess, if I may use such an expression, being purely accidental. The essential thing was that it was St. Peter's day. It was St. Peters day essentially and Friday by accident that year. Again four or five of the first Presidents of the United States went out of oflJce at the age of sixty-six. And yet they did not go out of office because they were sixty-six years old; it was because their tenn of office, four years, had expired. But, if, in view of these facts, one should say that " the Presidents go out of office at the age of sixty-six," he would be committing the Fallacy of Accidents, even though he should not state the Prem- ise from which the inference was made. 327. If then, into any proposition, we introduce an adjective when it is not necessary as a limitation to the scope of the proposition, the man who reasons from it as though the adjective were necessary, commits the Fallacy of Accidents; and if we omit an adjective when it was necessary as a limitation, the man who reasons from the 148 TEXT-BOOK OF LOGIC. proposition as though no such limitation had been nec- essary, will commit the Fallacy of Quid — or Substance. 338. I think the foregoing will be found to be a com- plete list and account of the Fallacies in Diction. It will often happen, however, that one will be in doubt to which class to refer what is obviously a Fallacy in Diction of some kind. In a general sense they may all be said to be Fallacies of Ambiguous Middle, since in them all, the middle term is used in a different sense in the two Prem- ises. Yet strictly, it is not ambiguity in -all the cases ;' since ambiguity consists in denoting one thing in dhe Premise, and another thing in the other. But in the Hon tale or variation, it is the same thing, differing only in quantity, time and place. In Division and Composition it is the same individuals considered in one Premise as a class or genus only, and in the other as a collective whole, and in the Fallacy of Substance and Accidents, it is the same thing that is denoted by the term in both proposi- ■ tions, but in one the statement is made in reference to its substance or essential properties only, and in the other in reference to something which if not accidental to the substance or thing itself, is at least accidental to the prop- osition that is affirmed. 339. However, it is sufficient for all the purposes of criticism, to refer them to any one of the classes, since they are each of them, and all alike fatal to the reasoning. The only object of the classification at all, is to show the precise nature of the Fallacy, and to assist in making it manifest as such ; the calling it by a name will have no effect, except as the name is understood to indicate the nature of the fault, and this it can do only when properly applied and when used in the presence of those who understand it. CHAPTER II. » THU LOOIC OFPBOOF. 330. There is one important sense in whicli all reason- ing may be considered as belonging to two classes, or of two kinds. Mathematical and Logical, (although logical , reasoning in the broadest sense in which the term is used, includes mathematical). A third kind is sometimes spoken of, as Moral reasoning, which however, is not so much reasoning, in any, proper sense of the word, as per- suasion. It consists rather, of an appeal to the Con- science and Moral Feelings of man, than in any effort to convince him of a truth. When men speak, as they sometimes do, of historical reasoning, etc., they mean logical reasoning concerning historical facts. 331. In the Physical Sciences the principal inquiries are after laws and causes. Hence Induction and Elimin- ation are the two principal processes, the parts of Logic most in use, and these are processes in which Fallacies in Form or in Diction are not likely to occur; and in which moreoTef, no general rules and principles can be of much use; such rules and principles, so- far as these Sciences are concerned, are intuitive and self evident ; the great difficulty is in the exercise of insight, in dis- criminating the essential, from the really accidental properties of objects, and in discerning between real 150 TMXTrBOOK OF LOGIC. causes and mere attending circumstances and unimpor- tant conditions. And in this, no general rules or for- mulsB can be of much use. The seeing of the eye must precede the use of optical instruments, and "without that, they are of no use. 332. In mathematical reasoning we" deal with units, or objects, considered merely as existing or possible and be- ing therefore numiers. When several of them are com- bined, they are considered as making up geometrical objects, having size and form also, as the line, the surface, the solid, etc. In this kind of reasoning, the reasoning cannot be based upon the nature or properties of its ob- jects — units having no properties — and the chief inipor- tance of the discussion attaches to the process or formula of reasoning, as addition, subtraction, involution, evolu- , tion, transposition, transformation, etc. Fallacies in Form or in Diction can scarcely occur ; and in fact they never occur except when the mathematician attempts to pass from the domain of mathematics to ontology, and speaks of the nature and reality of the things denoted by his symbols, as for example, " zero," " infinite," etc. Hence no one doubts the utility and necessity of Mathematics. At every stage, it is explaining to him steps and processes that he knew not before, and enabling him to do things of the greatest importance that he could not do before, and could never have done without the knowledge thus gained. Nobody doubts the utility of Mathematics. 833. In logical reasoning, on the other hand, we deal with individuals, and not mere units, with objects having properties and having therefore an individuality, or iden- tity, resmblances, analogies, contrarieties, etc., and on these properties the reasoning is based. In this kind of reasoning, the formulae and processes are important in- deed, but yet they are very subordinate in importance to TEE LOGIC OF PROOF. 151 tlie primary acts of insight and sagacity on ■which the, reasoning depends and which all reasoning presupposes. ' In Logic we find indeed, a scientific explanation and vin- dication of what we have been accustomed to do and what we can do without a knowledge of theoretical Logic, and moreover, we find an explanation of, and a warning against the possible dangers aiid fallacies'; but we do not learn to do any one thing that we could not do, and had not been accustomed to do, after a fashion, before we had taken the trouble to study the science of reasoning. We learn only to do the things more intelligently and with greater security against error. But after all that our study of the science can do for us, the great practical difficulty remains and recurs on every occasion in which we are called upon to exercise our reasoning faculties, the difficuly and necessity of discriminating and discuss- ing the nature of the objects about which we are to reas- on- and the method of reasoning applicable to the case. Hence many doubt the , use and necessity of Logic as a science. 334. Again : in the application of Mathematics we are forced at every step to recall our rules and formulee, to think of them, and thus we retain them in mind and are constantly impressed with their importance, an impor- tance which constitutes an in^spensible necessity for them. No man, for example, can make a simple calcu- lation, compute the smallest sum in his business transac- tions, without recalling his multiplication table, and remembering that three times three are nine, three times four are twelve, ~etc. Hence all believe that the Multi- plication table is a good thing, and that Mathematics is a practical thing, and necessary as a part of one's educa- tion. As already said, in Mathematics, although the reasoning can be stated in, or reduced to, some one of 152 TEXT-BOOK OF LOGIC. the Formulse given above, there is little or no danger of ■ Fallacies either in Form or in Diction. This is owing entirely to the nature of the subject matter of the reason- ing. And as a general rule there is no class of persons who are less likely to think well of, and appreciate the Science of Logic as a science of reasoning than mere Mathematicians. 335. In logical reasoning, on the other hand, one ia constantly drawing inferences- and conclusions without remembering, or even having ever distinctly considered that a term that may be predicated of a class, may be predicated of each individual in the class ; or that the predicates of any subject may be predicated partially of each other. Hence people are constantly making mis- takes in their reasoning, without knowing or suspecting it ; and they attribute the differences in opinion which are the consequences of such mistakes, to toy thing but the right cause. They do not see the use of Logic ; have never studied it, or derived any benefit from the study (that they are aware of) if they have, and as they get along well enough, in their own estimation, without such ^ study, they regard it as useless. 336. So they say ; and yet there is not one of them, nor a sincere and earnest student, or practitioner in any department of knowledge, who does not feel and ex- press often, in diverse ways, the need for a fuller exposi- tion and a better understand of the principles of what is really Logic, as applied to his special department. These men, however, seldom call that which they want. Logic. The mathematician, is of course, profoundly im- pressed with the importance of his science, and. yet Mathematics itself, that is pure Mathematics is nothing but logic — the logic of number and form. The great popularity and the high estimate placed on Mill's Trea- THE LOGIC OF FROOF. 153 tise of Logic, have not been to any extent the result of its completeness as an exposition of all that is included in the term Logic, but rather for the care and attention ■which was given in developing the Logic of the meth- ods of scientific investigation in the domain of physi- cal Science. And in all the modern efforts in Meta- physics and Theology, the discussion of questions of ■what is purely Logic applied to their several subject matters, forms a large and conspicuous element, not to say the chief or only one of importance. And any book in -whatever department of knowledge, that rises to the dignity of a scientific, treatise at all, is, and of necessity must be, largely occupied -with the logic or principles, methods and formulae of reasoning, applicable to the subject matter treated of and the ends aimed at in the undertaking. 337. If ho^wever, we consider the Logic of Proof or applied Logic in its most general principles it runs so nearly into Khetoric that it is difficult to preserve the just boundary between them. I think, ho-wever, that Whatelt's distinction,* for ■which, ho"wever, he cites CiCEBO as authority, is the just and proper one ; " the business of Logic is to judge of the force of arguments; that of Ehetoric is to find and use them." In Ehetoric •we aim at conviction, in order thuf we may persuade, and sometimes it ■will happen that the author aims to per- suade ■without caring ■whether he convinces or not. Hence he must al^ways take into account the feelings of his audience, both towards himself and his subject. He must also consider their intellectual state, not only in reference to the amount of intelligence they possess and the knowledge they may happen to have of the subject Bhetoric, Part I, Chapter n, § L 154 TEXT-BOOK 01 LOGIC. , he proposes to discuss, but also and chiefly with refer- ence to any prepossessions they may haye in its favor, or any prejudices they may he laboring under against it. 338. But in Logic we take no notice of such things ; we look only at the nature and intrinsic force of the ar- guments. And for an ultimate result, that is all that requires to be considered; for mere states of feeling, prepossessions and prejudices will soon pass away ; while the substantial force of an argument will remain the same forever. And of course, it is that, that will finally prevail. SECTION I. THE CEBTAINIY OP PBOPOSITIONS. 339. We shall have occasion to use several terms, as "presumption," "probability," "certainty," etc. It may be well to say a few more words about them before proceeding any farther. 340. "A Presumption," as has been explained is merely such a preoccupation of the minds of those addressed in favor of any proposition as to make it necessary to as- sume the burden of proving the contrary. This is gen- erally best done by the three steps, one or all of them as the occasion may requirp. (1). Show how the error came to be believed or ac- cepted as truth. , ' (3). Adduce probable arguments, that is, facts that will account for that being true which we wish to prove to be true. (§ 202.) (3). Positive arguments— facts that show that it is true. (§203.) CEBTAINTY OF PROPOSITIONS. I55 341. "A Probability" is merely the capability of being proved. We sbbw this in the lowest degree whenever, and by whatever means we show that the proposition is not absurd or self-contradictory. But also, and far bet- ter, and in a higher degree, when we show by reasoning from cause to effect, a priori in the physical sense, that there is some reason for believing it, some adequate cause for its being true, and thus create a presumption in its favor. 343. When we establish "a high degree of probability," as it is called, or show that there is a balance of proba- bilities in favor of any proposition, we create what is called a " moral certainty." It is called a " moral cer- tainty," because of the ethical doctrine that in all cases where such a probability is all that we can have, and im- portant consequences depend upon our acting upon the the proposition as true, it is the duty of man so to act. What seems most probable is regarded as obligatory in such cases. Hence the term " moral certainty." 343. Again when we have established a general law or truth, by any of the processes of Observation, Average or Induction, we have for it what is called a physical certainty. In reference to future events it is only a very high degree of moral certainty. Since whatever is to occur, is pretty sure to occur in accordance with the general laws and uniform rules of nature and experience. If, however, the event be in the . past, this form of cer- tainty comes to be what we call historic certainty, and of course, may be of all degrees, from the merest pre- sumption up towards that absolute certainty that can come from demonstration alone. 344. And then finally we have what is called ahsolute certainty. This, in its strictest sense, can come from demonstration alone. ISo mere observ*ation or testimony 156 TEXl-BOOK OF LOGIC. can produce it ; since after all there will be the possi- bility of (1) false perception in consequence of some ab- normal condition or exercise of the organs of sense and perception, and (3) mistaking the results of imagination far those of perception — a mistake, which as psychology teaches, is more frequently made than is generally sup- posed. 345. But in the case of absolute certainty, there can be no exception, and the proposition must be true in all places, and at all timess and under all circumstances. 346. The conflict oi facts or alleged facts with such pro- positions, or rather propositions for which such a cer- tainty is claimed, is always a serious one. It becomes dia- mond cut diamond. Of course,if the alleged fact ie a fact, it will refute the demonstration, and show either that (1) the process has been faulty, or (2) and what is more likely, that one or the other of the Premises with which we started was untrue. 347. The grounds of certainty are commonly regarded as three. (1) Sufficient Cause, (3) Excluded Middle,' (3) Identity and Contradiction. 348. Sufi&cient Cause is in fact anything that produces a feeling of certainty with regard to the conclusion, and that certainty may be either moral, physical or absolute certainty ; although, for the most part, we speak of that which produces the two former only as a sufBcient cause. 349. But in the last analysis sufficient cause is found to consist in one or the other of two things : Observa- tion or Testimony. 350. The grounds of probability are numerous. In a strict and technical sense, any proposition is probable which is susceptible of proof ; that is, any proposition that may be true under any circumstances and at any time onplace. It is more common, however, to speak of CERTAINTY OF PBOPOSITIONS. 157 such propositions as possible rather than prohable. But in this sense, any proposition does not involve a contradic- tion in terms is in itself probable, however unlikely to be true. 351. Or, again, any proposition is to be regarded as probable, in the sense of being more likely to be true than otherwise, which is generally accepted as true, or which has been held by the persons most likely to be in- formed on the subject. I shall, however, treat of the arguments and means by which a proposition may be made or shown to be prob- able in a separate section below, Section VII of this Chapter. 353. The principle of Excluded Middle has already been explained (^ 246). On it rests the criticism of all of what is called indirect reasoning or proof; and the re- lations of Propositions one to another as coming under this rule have been explained (§ 90). If there is really Excluded Middle between contradictories, when one is proved to be true the other is proved by that process and on the principle of Excluded Middle to be false. We may, however, just as well extend the application of this prin- ciple to all cases of immediatCi, inference coming under the rules laid down in § 90, etc. 353. Strictly speaking, there can be Excluded Middle only when there are but two propositions, and they must be so related that the subject will Ije the same in both — the one universal and the other partial-^and the predi- cate of the one will be a positive term, and that of the other the same term used negatively. As All S are P, Some S are non-P, or No S are P, (All S are non-P), Some S are P. 354. But the principle extends to the relation of three or more propositions, as well as to that between two only, 158 TEXT-BOOK OF LOGia vrhen the co-ordinate terms are really co-ordinate parts of any whole (§ 343-347). Thus let n denote any indi- vidual in a genus, and the genus be X, and divided inl^o co-ordinate species A, B, C, D. We can, of course, rep- resent these as two, A denoting one and non-A the other, and non-A will he equivalent to B, C and D ; Or, if we use B, then non-B will be A, and D. 355. Thus the principle of Excluded Middle extends to any Disjunctive Proposition, however numerous its parts may be, provided the co-ordinate terms denote co- ordinate species and enumerate them all. This last is, of course, an essential condition ; otherwise, the indi- vidual n may be in the species not enumerated or men- tioned. 356. The Principle of Identity and^ Contradiction is usually spoken of as one principle. The principle when stated explicitly is as follows : (1) Any proposition that is absolutely true can be reduced to a form in which the subject and predicate will be the same as S is S. (3) A^y proposition that is false absolutely can be reduced to a form in which the subject and predicate will be some one word as the* subject, and the same term in its negative form as predicate, as S is non-S, or S is not S. The method of reducing propositions to these forms I shall discuss in the next Section. 357. Indirect proof or disproof consists in establishing a proposition by sh straight line Jet fall from any point out of a given line 168 TEXT-BOOK OF LOGIC. perpendicular to that line' is the shortest distance be- tween that point and the line, we begin by supposing some other line to be shorter than the given line and then proceed to show that the other (supposed) shorter line is not shorter nor even so short as itself. 379. This method of verbal demonstration may &,lso be used with great advantage in metaphyisics. In case we have an abstract term where sense and the logic of language requires a concrete one>(§ 278-383) we have of course a figurative where w;e ought to have a didactic proposition. Taken literally, it is unintelligi- ble, and can be understood, at all only by objectifying the mere properties and modes of things, thus making them as substantial as the things themselves. But when thus understood the propositions are untrue, and we have committed the fallacy of Figura dictionis the mo- ment we proceed upon them as true. 380. If now, instead of this, we replace the abstract term by its logical equivalent found according to the rule laid down in (§ 385, 1) we shall have the true mean- ing of the. passage. This substitution of the logical equivalent for the abstract term may indeed make-the proposition senseless or even a contradiction in terms. But, if so, it is no worse than it was before. 381. Again, we may apply this method of verbal dem- onstration to propositions considered as expressing and representing facts or states of consciousness, and thus make it a means of developing and displaying all that is implied in them. Thus, suppose the question be as to the nature of the objects in the external world. Whether .they are substantial realities, as most men believe, or the mere "shadows of ideas," as some philosophers have held, or mere "subjective, in the mind. itself like the ob- jects of a dream," as has been thought by others. We IDENTITY AND CONTBADIGTION. 169 ■have the proposition, "I see these- objects," "I see this paper." But by Rule 3 (§ 280) the grammatical object of a transitive verb must be a concrete term ; the word " paper " must, therefore, denote a substantial thing, and the paper itself is an objective substantial reality. If not, the word paper is abstract, and it does not denote a thing ; it denotes no-thing — nothing. Hence we have, " I see nothing." But, " to see nothing," is " not to see," and the act of perception does not take place — percep- tion is not perception. Hence it is as certain that the ob- jects we see are substantial realities and external to our- selves as that the acts which we denote by the word per- ception ever take place. In this way we may have a Transcendental Logic . which, beginning with the facts of consciousness, will develope and demonstrate from them all that is implied in them, and thus give us, as I think, the principles and . doctrines of Metaphysics — or, Ontology — in a form that will make them as intelligible as the facts of Natural Science and as certain as the truths of Mathematics. SECTION ni INDIVIDTIAIi PEOPOSmONS. 383. I have remarked that Logic is responsible for the process of reasoning alone, and not at all for the truth of any proposition that is introduced and used as a Prem- ise, Hence, though the reasoning may be entirely and perfectly correct and faultless in all respects, the conclu- sion can have no more certainty, than the Premises, and ■will in fact have only less than either of the Premises taken separately, if in fact both of them have any de- 170 TEXT-B OOK OF LOOia gree of uncertainty ; that is, unless one of them is an absohite truth, the nature of the uncertainty is precisely the same as that which we have considered and discussed in the case of Compound Conditionals. (§ 333.) 383. Hence, it becomes inlportant to loot into the methods by which the various kinds of propositions may be proved, and to consider the nature and extent of uncertainty, insepa'rable from each class of them res- pectively. 884. Any proposition that we may have occasion to prove, will be either (1) Individual, (3) Partial, (3) Gen- eral or (4) UniversaL An individual proposition affirms something, of one object only; a, general proposition af- firms its predicate of a class, with the possibility, if not the fact, of exceptions, and a universal proposition af- firms its predicate with no possibility of exceptions. 385. Partial propositions are to be treated as virtually several individual propositions combined into one, with- out making a class, by giving their differentia ; thus, if we speak of " some men," the " some men " may be Englishmen, they may be poets or anything else, but our proposition does not give them a specific name, it uses the general name " men " partially, and every man, every part of the genus not less than two nor more than all, minus one, may be included. 386. An individual proposition relates to an individual object; that object may be denoted by a proper noun, or by any common noun used in the singular number, with an article or demonstrative pronoun, pointing it out, aS "the men," "this man." 387. An individual proposition may affirm the exis- tence of the object simply, or its existence in some par- ticular mode ; thus, if I say " space exists," I affirm its substantial existence alone, or its existence substanti&l- INDIVIDUAL PROPOSITIONS. 17I iter. But if I say " it surroands all things," I afflnii its existence in a particular mode, the mode of surround- ing, etc. Hence, anything and everything that we can aflBrm of an object except existence alone, implies and affirms existence in some mode or " modaliter " as well as substantially. 388. An object can be known or proved to exist only as it is known or proved to exist in some particular mode ; for any property or action we may ascribe to it, or that may be implied in the name we denote itby, con- stitutes such a mode. • 389. An individual proposition asserting either the existence of any object or any mode of it may be proved in either of three ways. (1). direct observation, (2). reasoning from effect to cause. (3). reasoning from cause to effect. 390. But a proposition asserting some property of an object without asserting or assuming, the reality or exis- tence of the object, may be proved by demonstration from the nature of the object. Thus suppose I demon- strate the length of one side of a triangle from the length of the other two sides and their included angle. I make no use of the fact of the existence of such a triangle, I do not imply its existence. In fact, the tri- angle does not exist, and is no fact at all. Triangular objects may exist, but their existence or reality makes no part of the basis or ground on Which the demonstration proceeds. And the conclusion is virtually no more than a hypothesis, so far as the reality of the object is con- "cerned. It asserts the conditions under which the tri- angle or rather the triangular object, must exist, if it exists at all. But this method of proof gives us no means of demonstrating the existence of the object itself. 172 T&XT-BOOK OF LOQia Hence we limit ourselves in this Section to a considera- tion of the three methods of proof already indicated. 391. We may know an object as either (1) an object, (3) as a cause, or (3) as an effect. (1). If we know that a thing exists by observation we know it as an object, and by its properties, and we can, of course, predicate of it any one or all of those proper- ties by which it is observed. (2). If we know it as a cause, we know it by reasoning from some observed effect. We know it, moreover, as in the act or mode of causation, and as possessing the pro- perties by which it can be the cause of such' an effect. (3). If we know it as the effect of an operation or process, or we know it as the effect or- result of observed causes, which are known to be in operation. We know from the nature of, the causes and their mode of opera- tion, something of the nature of the effect they will produce, and this nature is a mode of the effect itself. 392. Hence we never know or can prove that a thing or object exists without knowing something more than the mere fact of its existence. We always know something about it, some of its properties and modes, something of its nature. 393. I have said that there are but three ways of knowing or proving the existence of an object. Of the former of these three ways, observation including sense- perception and consciousness, we have examples and illustrations in every act of perception that takes place. We perceive the object, and of course, can predicate of it what we perceive it to be. We give it a name which may be at first an individual or proper name, and then on seeing another object like it, we give to it the same name ; the individual term becomes generalized, and is a common noun, and thus it comes to pass that but very INDIVIDUAL PBOFOSITIONS. 173 few of the objects of knowledge, of which we have occa- sion to speak, have proper or individual naines. Moun- tains, Eivers, Continents, States, Towns, persons; and a few of the other objects that we have most frequent oc- casion to speak of, as a pet dog, horse, etc., have proper names. But with regard to other objects, when we wish . to individualize them in speaking of them, we are obliged to use some descriptive' article, pronoun or phrase, ascribing to them some inseparable accident. 394. Of the second kind we have examples in the dis- covery of the planet Neptune, by means of a perturba- tion in the motion of the planet next to it in the order of exteriority. The astronomer, Leverrier, knew the perturbation as an effect, and from the study of it came to know that there was another body or mass of matter, in a certain direction and at a certain distance, etc. The existence of the supposed agents, heat, light, electricity, rests upon this kind of cognition. What they are in themselves we do not know. We only know What they do. We know them — if at all — only as causes of certain observed effects. 395. What may be thus proved to exist as a cause need not be the efficient cause as described in the preceding classification of causes (§ 201). It may be a cause in any one of the senses there given, efficient, occasional, instrumental, material, formal, or final, according to the nature of the effect and as its nature and condition de- mand. 396. And so, too, we may reason from an effect to a " condition," th^t is the condition in which something else is now existing or has existed, at some preceding time. Thus, the fact that a man died on Wednesday, for example, is proof that he was alive on the day pre- cedingy though his being alive on . that day was not a 174 TEXT-BOOK OS LOGIC. cause, in any recognized sense of the word cause, of his dying the next day. 397. A real cause, causa vera, must always be denoted by & positive term, but a condition will be depoted by an abstract term ; and not only so, but the abstract term will denote only a separable accident. 398. In the third place there are certain processes which are supposed to produqe, or to have, as results, objects of which we know nothing except what is indi- cated to us by the process. Thus we speak of the results of addition, subtraction, multiplication, division, etc., as " amounts," " remainders," " products," " quotients," etc, The words " substance" and " space" are of this kind. We suppose all the properties of an object to be with- drawn or taken from it and call ijjiat which remains or would remain, if i» fact anything would remain of it, if such a process were at all possible, " substance." Or, if an object have form and solidity, we suppose it anni- hilated and call that which would remain where it was — " space." 399. Then we have sometimes a combination of the last two methods called reasoning from a " sign." A si^n is always an effect, and will be an object in a certain state. We reason from it as an effect to its cause and then from that cause to another effect, which, in con- sequence of that activity by which it produced the first effect, it must have produced the other also. Thus, if the mercury in the thermometer stands at a certain degree below freezing point, for example, it, as an effect, proves that as a cause the air is below freezing also. But if the air is at that temperature it must have frozen the water, the ground, or other substances, ac- cording to the circumstances, although the freezing of the water and the sinking of the mercury in the ther- INDIVIDUAL PBOPOSITIONS. 175 mometer were in no recognized sense of the words re- lated as cause and effect to each pther. They are both effects of a -cause common to them both, and they are signs of each other, so that the one could not be pro- duced without the production of the other. 400. But the " causes " and the " effects," alike, from which we reason,must hare been observed as facts. Hence the two last named methods of proving individual prop- ositions rest upon and pre-suppose the first and the first is observation, external and by sense-perception, or inter- nal and by consciousness. And the observations which other persons make can always be made available to us by the intervention of Testimony. 401. In Observation, whether by sense-perception or consciousness, the only thing thdt is absolutely true is the fact or state of consciouness. I say, "I see a pen." This implies more than a fact of consciousness. It im- plies that there is a pen that is seen. This is an infer- ence from the consciousness of seeing it; and the possi- bility of abnormal activity of the organs, of mistaking the object, etc., etc, must all be taken into account, for even in hallucination and dreams there is the conscious- ness of the mental act or state which we call perceiying. - 403. Testimony is based on observation, and is there- fore accessory and subsidiary to the first only, of these methods of cognition. It is the substitution of obser- vations made by other persons for our own personal ob- servation. 403. In this case, the value of the testimony is comr monly held to depend on the following conditions : (1). The opportunity to make the observation, to see, hear, etc., what is testified to. (3). Honesty, or disposition to tell the truth concern- ing what was observed. 176 TEXT-BOOK OF LOGIC. (3). Sagacity in discriminating the observed fact from any theory concerning it, or any play of fancy or imagi- nation while in the act of perceiving it. (4). Freedom from prejudice in one direction or another that may operate upon the memory of what was observed or dispose one to exaggeration. 404. What I have thus spoken of, it will be carefully noted, is positive testimony to an affirmative proposition, as when one says S is P. 405. But we have two other cases, (1) affirmation of a negative proposition, or what is logicallv the same, the denial of an affirmative proposition, as when I affirm that S is not P, or I deny that S is P, and (3) what is called " negative testimony," that is, the omission to mention the subject at all. 406. It is commonly held that positive testimony to an affirmative proposition is of more force than affirmative testimony to a negative. ' This is correct as a general rule. The reason for this doctrine is to be found in the psychology of the cases. Such an affirmation implies the act of observation and also a distinct recollection of it. The affirmation of a negative also implies an act of observation and a' recollection of that act. But it also implies something more ; it implies thought and reason- ing at the time, noticing the absence of that, the presence of which is denied. Thus, suppose two witnesses, each testifying to having seen a man on a certain occasion, the one says he had a glove on his right hand, and the other says he had not. JSTow the witness who says that he had the glove on, is, on the whole, and in' general, the most ' likely to be right. He saiv the glove, the other man did not see it ; but his not seeing it may have been the result of inattention on his part,, as well as the absence of the glove. INDIVIDUAL PROPOSITIONS. I77 407. In such cases, however, a good deal depends upon "the peculiarities of each case. If in the case just sup- posed there was anything to make the absence of the glove remarkable, apd contrary to expectation, then the man who gives the negative testimony,, is doubtless to be regarded as the most reliable witness m this case ; that is, he is less likely to be mistaken than the other person, who expecting that there was a glove, may have imagin- ed its presence without seeing it at the time and now thinks he saw it. 408. It may therefore be laid down as a better state- ment of the law in the case, that, other things being equal, that testimony is to be preferred which affirms a state of facts which was in itself least expected and therefore most likely to attract attention and fix itself in memory. If, however, the state of facts was so contrary to expectation and the common experience of mankind as to be consid- ered improbable, a question will always arise as to the veracity of the witness, as well as to the probability of his having been mistaken at the time. 409. In the other case, we have what is sometimes called negative testimony. It is rather the absence of testimony, the total failure to mention or speak of that which is the subject of inquiry. ' 410. Thus, I believe that in all the writings in the Scrip- tures, there is no mention of the fact that St. Paul ever undressed himself in order to go to bed at night. , And yet in this case the absence is really no proof that the Apostle did not conform to what is otherwise known to have been the general custom of his age and nation. 411. But suppose the matter in question had been some- thing unusual, contrary to what is known to have been the custom of the age, the omission to speak of it if it had occurred, or its mention if it had not, would certainly 12 178 TEXT-BOOK OF LOGIC. require to be accounted for, and "would therefore be of some value as testimony. In all historic narrations, thousands of little details that always occur, are not men- tioned, "^hile, whatever, is unusual, whether by its occur- rence or its omission, is likely to be mentioned and is in fact just the kind of incident that makes the staple of history. 413. And for this reason an incidental mention of a fact is often of more value than a direct or even an em^ phatic assertion of it. The incidental allusion to a fact implies that it was generally known and universally be- lieved, while an express or emphatic assertion implies that the matter asserted was either so little known, so improbable in its character, or, perhaps, so extensively denied, as to be in need of additional te'stimony. Thus, St. Paul asks " Have we not power to lead about a * * * wife as well as * * * Cephas ?" Now in this the Apos- tle does not assert that Cephas (who is supposed to have been Peter) had a wife, but he implies it and alludes to the fact as if it were well known and undisputed. Or when a Greek historian, Thucydides, speaks of a certain city as being near to the place where Xerxes dug the canal across the island .of Euboea, his testimony to the fact of such a canal having been cut there, is regarded'as stronger than if he had expressly affirmed it. 413. Hume's sophism, that " nothing can be proved by testimony which is more improbable than the falsity of testimony," has enough of truth in it to make it pungent as an antithesis and enough of error to make it danger- ous as a maxim. Nothing can, of course, be proved by the testimony of any one witness which is more improb- able than it is that he should be wrong in his testimony, whether from intentional falsehood or unavoidable mis- take. But that nothing, that is more improbable than PARTIAL PROPOSITIONS. 170 the falsity of any one testimony or source of proof, can be proved by the combined and concurrent force of tes- timony of various kinds and from various sources, is a proposition that will not be assented to. for a moment by any one who knows its meaning or import. A' fact ma^ be proved in this way with a force of conclusion that is greater than that of even a mathematical demonstration. So true is this, that any fact that is so proved, will be held to and acted upon, notwithstanding any amount of reasoning or demonstration that may be brought to bear against it. SECTION IV. PABTIAL PBOPOSITIONS. 414. Partial propositions are of two kinds in refere to the grpund on which they are affirmed, although thtx . is nothing to indicate this difference in their form. 415. In the first place they are but an aggregation of several individual propositions. We see one man that has red hair, then another that has red hair, and so on until we say, as the result of our observation, that " Some men have red hair." And we thus, virtually express a doubt, or at least some measure of uncertainty whether the proposition would 'be true if it were made general. There is usually something in the nature of the predicate that gives rise to such a doubt. 416. -But in the other case, the partial proposition is the result of the conversion by limitation of a general or universal proposition, as "All A are B, therefore, some B are A." In this case, generalization, whether by induc- tion or othei-wise, must have occurred between the obser- 180 TEXT-BOOK OF LOGIC. vations on which the individual proposition rested and •the partial proposition, as well as. the conversion which preceded it. And the partial proposition has, therefore, the same measure of certainty and of uncertainty, or of doubt also, as belonged to the general proposition — the exposita-^from which it was derived. ' 417. What I have to say of partial propositions in this place relates to t'hose of the first named class. They are like individual propositions in respect to the ways in which they can be proved. We are ob^ed to prove the predicate of each individual separately. But in fact, the proof of a predicate of any one individual object makes its afiBrmation of others in the same natural species prob- able. If once a man has been born without hands it is probable that others have been born into the world with that form of monstrosity also. If once in the experience of man, a stone has been known to fall from the atmos- phere^^a meteorite — it is probable that more than one has so fallen. 418.- But again it will sometimes happen that we can prove a partial proposition when the predicate cannot be proved to a certainty of any one individual. Thus, in the dusk of evening, we may have, from observation, abundant proof that there are some men standing on a distant eminence, when our means of knowledge or proof would not enable us to name one single individual who was there. In the same way, we may be able to demonstrate from the nature of perception, etc., the proposition that " Some of the objects we think we see around us are real," while it would be impossible to prove with like certainty the reality of any one particu- lar object as against the possibility of a false perception, or hallucination. 419. Hence, in some cases, the certainty of the truth PARTIAL PROPOSITIONS. 181 of a partial proposition will be greater than that which pertains to any one of the individual propositions that are subsumed under it. This resuls; from. the nature of our method of proof and from the uncertainty that at- taches to each particular act of observation. And the amount of certainty may be regarded as a probability, ' coming under the formula given for computing the forcfe of the elements in a cumulative argument, (§ 256).' Thfe uncertainty will be an improbability of the truth, or probability of the falsity of the proposition, which will diminish towards zero under the formula for computing the form of mere probable arguments, (§ 323): that is, the probability of the same mistake, occurring . in repeated instances under different circumstances must be a dim- inishing probability, and as it diminishes, the certainty of the result of the observation increases towards an ab- solute certainty. 420. There is, of course, always some measure of un- certainty or doubt in regard to the truth of any individ- ual proposition. If it rests on observation, there is the possibility of false-perception, hallucination, etc., which becomes greater just in proportion to the improbability of the event itself. If it rests on testimony, there is of course, therefore, an additional possibility of error in this source or means of proof. If upon demonstration — either (1) from effect to cause, or (2) from cause to effect — ^there is always an element of, uncertainty. in the falli- bility of human insight in detecting this relation. ■ 421. Now when this uncertainty arises from any one caiise and" pfertains ■ to several' propositions, it of course effects them all alike — whatever may be the method of their proof. But in such cases, it must be known — ^that is we must know — precisely what it is or we cannot know that it is common to all the propositions asserted on the 183 TEXT-BOOK OF LOGIC. ground of proof affected by it. Thus, if a man lias a defect in his eye-sight — color-blindness, for example — this cause of uncertainty in anything that he may assert concerning color. will effect all such assertions alike. If one be an opium eater, the effect of this drug on the. mental operations is such that it gives a like uncertainty to any and all the assertions such a person may make. So, too, the imperfegtions of any instrument — thermometer, weighing-scales, measuring rod, barometer, etc.-^will af- fect equally and alike any statement of a result obtained by the use of such instruments ; and the uncertainty does not decrease with any increase in the number of observa- tions. The ratio of the certainty to the uncertainty, or of the probability to the improbability, will be a con- stant quantity whatever may be the number of pro|)Osi- tions that jnay be affected by the cause of the uncertain- ty. If it be one to ten in one proposition, it will be ten to a hundred in ten propositions. 433. But when the cause of uncertainty is not com- mon to them all, but is peculiar to each, whatever it may be, the combined uncertainty is less in two propo- sitions than in either of them taken by itself; and so on decreasing with ,the number of cases. This, of course, supposes that there was no motive to mistate, no inten- tional misrepresentation of. facts. It becomes really a case of cpncurrence of testimony. The fact of the truth of a statement is always in and of itself a sufficient ex- planation of the agreement of the witnesses testifying to it. . But the agreement, when the statement is untrue, becomes a phenomenon to be accounted for. Collusion and intentional falsification is the first explanation that is likely to occur to the mind. But when this is found to have been impossible, another explanation must be sought, and unless some satisfactory explanation is found, GENEBAL PROPOSITIONS. 183 the improbability of any other explanation than the reality of the event asserted increases with the number of witnesses, assertions or circumstances until it becomes so great that the certainty is regarded as absolute. It is even practically greater than demonstration. 423. This remark, however, cannot be extended to gen- eral propositions. Thus, from the nature of the argu- ment in favor of miracles, for example, it is more certain that some miracles have been wrought than it can be that any particular miracle was wrought. And yet it is less certain that all the events that are claimed as mi- raculous ever occurred than that any particular miracle was wrought. It is more certain that some of the ob- jects we see are real than that any one of them is so, and yet less certain that they are all, without exception, real, with no false perception and no hallucination, than that any particular one of them, even the least certain is a reality. SECTION V. GENEKAl PBOPOSITIONS. 424. A general proposition always implies a course of reasoning, and so, in one sense, is the staitement of a matter of opinion, which, however, is often regarded a^ a matter of fact — a, general fact. 425. As the subject of such a proposition is always general, the individuals comprehended in the class will be of two kinds, examples and exceptions — the one con- foi-ming to the rule and the other not. Thus, " mam- mals live on land," this is the rule. But whales are mam- mals, and yet they live in the water ; hence, they are an exception to the rule. 184 TEXl-BOOK OF LOGIC. 436. Exceptions and-Examples must, of course, belong to the same natural class, as " mammals " in the abova example. And when the exceptions become very nu-- merous the rule is of but yery little value as a rule ; and. if the exceptions should become more numerous than the examples, the rule would be reversed, and its con- trary — not its contradictory — would be the rule. 437. The maxim, " exceptio prolat regulam," is true only as we understand the " exceptio " to refer to the act of noting an individual as an exception. For, if the rule were not otherwise than the exception, the contra- riety or departure from it would not. be noticed. 438. General propositions are formed by Induction. In Deduction the Major Premise — that which is regard- ed as such — is, more comprehensive than the conclusion. Hence, in such formulae we reason from the general to the particular or individual. For example, let us take the letters of the Alphabet in this order : A, B, 0, etc., and representing a series of subordinate classes, A being infima species and Z the summnm genus, and we have A are B, B are C; are D, therefore, A are D. It is ob- vious that while the subject of the conclusion is the low- est in the series of ahy that is used in' the formula, the predicate of the conclusion is the highest. This is the order of Deduction. ' 439. But in the inverse order called Induction, we be- gin with the individual object and have for the subject of our conclusion a term denoting a class and therefore much more comprehensive than the term we start with. 439. Induction, strictly speaking, is a word that de- notes merely t|ie process of bringing in the facts or in- dividual objects to enable us to generalize a conclusion, that is, to enlarge the sphere of the class of which we I afiirm a predicate. If, for example we say, " this horse GENERAL PROPOSITIONS. 185 is a ruminant," our assertion is less general or compre- hensive than if we say " horses," or " all horses " are " ruminant," and still less general than if we say " all hoofed animals are ruminant ;" that is, while the predi- cate remains the same, the subject becomes larger in its comprehension as it includes more individuals. 431. In all cases of pure demonstration, we generalize at once, because in demonstration, we never introduce any merely accidental matter. Thus if we prove thatthe angles of one triangle are equal to two right angles, we instantly and immediately affirm that in all triangles the sum of the angles is equal, etc. ; simply because we had been reasoning upon the nature of a triangle and had not taken into the scope of our argument anything that is • peculiar to any one class of them. In demonstration however, we deal with things in the abstract, as the ex- pression is, that is, we speak of them and consider them in reference to their essential nature, and regardless of those properties which make up their actual and varying conditions ; therefore, whatsis true of one must be true of all its species" at all times in all places, and under all conditions and circumstances.. Hence, such truths are called absolute truths. 432. But the moment we come to deal with and rea- son about things in the concrete as they exist, and as we observe them in nature before we can reason by demon- stration concerning them, we must distinguish between the essential and the accidental properties. This We do partly by an immediate insight into their nature ; but for the most part we must. make comparisons and exam- ine objects in various relations. And we thus find that what is to be regarded as essential in one relation, is only accidental in another. Thus, take iron as an ^example, its weight is the only thing that is essential, if we use it 186 TEXT-BOOK OP LO&IC. merely for its weight as ballast in a ship. Its form is essential if we use it for cannon shot. Its ductility is essential if we use it for wire ; its susceptibility to mag- netism if we would maKe it into needles for a Survey- or's compass. 433. Induction is, spoken of as the method by which we establish or discover, and discover that we may es- tablish, what are called the general laws or principles of Nature. The methods of induction depend so much up- on the peculiarities of the subject matter with which the process is concerned, that all the general principles that fall within the province of Logic, are very .general and can be very easily and briefly stated. But they are at the same time so general, that any such statement, of them can have but very little practical value. 434. Induction depends upon the following first prin- ciples in the law of classification, and the relation of objects one to another. (1). Any property that may be ascribed to more than one individiml object, and is not a separable accident merely, it is a common property; (2). Any common property that may be ascribed to several objects in any one class, may be ascribed to some and just as many objects in any higher class up io, and including the summum genus- (3). Any property that may be ascribed to several in- dividuals in a class, may be made the differentia of the class, and thus the basis of a classification. (4). Any property that may be made a differentia is also a formal property, (a formal cause in the Scholastic use of terms), and implies some other property, as a mo- dal or final cause, which may therefore be ascribed to the class of jvhich the. formal property is differentia. 435. It .will be observed that in the above stated rules, I GENEBAL PROPOSITIONS. 187 tlie words '■ property that may be ascribed to," are equiv- alent to " a term that may be predicated of," used in the discussion of the deductive formula ; since whenever a property may be ascribed to anything, the term denoting that property may be aflBrmed or predicated of the term denoting that object, used as the subject of a proposi- tion. 436. The first three of these rules need no illustration or proof, the last, how€ver,^may be better for a word. We have already seen in our remarks on demonsj;ration, that any one property in an object always implies some other property inhering- in the same object. Thus ex- tension implies divisibility, etc. In like manner any property in an object implies some other, both in (1) its other moods and separable accidents, and (3) in its rela- tions to other thiftgs. Thus eating is a separable acci- dent of an animal, since it is not always eating, bvit the kind of food and manner of eating depend upon the form of its mouth, the structure of its digestive appara- tus, etc. And these last are inseparable and common properties in the constitution of the animal ; they are such, moreover, as to indicate to the experienced obser- ver what is the kind of food and mode of eating which they occasion ; they stand in the relation of cause and efiect to it. 437. When, therefore we can discern any such property in one object, we can make \k the differentia of a species, and may at once and on that ground, affirm the modal property of the species thus made, as a class. 438. In the process of arriving at such generalizationSj however, there are several intermediate steps, which have indeed been variously stated and explained, and which »may, perhaps, be best described as follows : (1). In the first place we group objects together in a 188 TEXT-BOOK OS LOGIC. natural classificatin based upon the more obvious prop- erties that are essential to the individuals. (2). We next find that some less obvious property, mode of life, or action,-pertains to some one of the individuals in one of these classes. (3). We then examine others of the class and find the same property to be true of them, and then finally : (4). We infer that it is true of all the individuals in the class. 439. Take as an illustration. After having observed the resemblance between certain animals, which we call cows, for example, we see that one of them, after clipping the grass for her morning's meal, retires to a shady place and raises what she has swallowed, and chews or masticates anew. We find on examination that others of the same species do the same thing in all-its essential features. The question may then arise whether the females alone do this, or whether the males of the same species " chew the cud" also. Having found that they do, we next inves- tigate to see if other animals of other natural species, as sheep, camels, etc., do so likewise. And we proceed in this way until we group together several species into a class, whose distinguishing trait is that they " chew the cud," and call them " ruminants," and then say " that all ruminants chew the cud." This is, of course, a defini- tion. But as we proceed we find other properties com- mon to all ruminants, and accompanying the mode denot- ed by the word "ruminating," such as' structure of teeth, stomach, intestinal canal, hoofs, e^.,. etc., go that after induction has been completed, we feel safe in prediciating any one of these properties or modes, of any animal or class of animals which we have found to possess any other of them. * And this is all there is of the general or logical princi- QENERAZ PROPOSITIONS. 189 pies of induction that can be explained except as in each science we explain the details of the application of the method by reference to and in connection with the dis- cussion of the" nature of the subject to which we are to apply our method. 440. In most cases we find these properties connected as cause and effect under some of the different senses of the word. In many cases, however, we can go no farther by our induction, than merely to affirm a general fact. Thus, it is a general fact that all resinous bodies (so far as yet known), have certain electrical properties. No reason, however, has yet been discovered, or can now be assigned, why resins should thus affect other bodies when they are electrically excited. We see no connection of cause and effect between,the natural peculiarities of resins and the electric effects they produce, no such connection, for example, as we see between the structure of the stom- ach and rumination in the ruminants, or between teeth and the carnivorous habits of the camivora. 441. Now,, undoubtedly, any process of induction may be stated as an Enthymeme with the Minor Premise stated in detail, thus : a is P, 5is P, c is P, therefore, S, (which is the class of which a b and e are individuals,) are P, the prosyllogism in the parenthesis being always assumed, though not often expressly stated. But it mallifestly assumes.the not-expressed Major Prem- ise, " what is true of the individuals' a, b, c, etc., (which have been examined,) is true of all the rest of the class," though they have not been examined. 442. But on what ground can we make this assertion ? Or what right have we to assume this Major Premise ? 190 TEXT-B OK OF LO GIG. Manifestly on the ground of some insight into the con- nection, as of cause and effect, between the property which we make the differentia of the class, and P, the property or mode which we affirm of them in the con- clusion ; otherwise our conclusion could have no mpre than a vague and uncertain probability based on the an- alogy or resemblance of the objects actually examined. 443. It is very important for the completeness and clearness of scientific discussion that the classification should be based, upon those properties, as differentia; of species, that are the most central and controlling in the organization, means and habits of life, those which are the causes that determine and necessitate the rest. Hence, in order to attain this stage of science, there have been frequent changes in the classifications and nomenclature in all of the natural sciences, chemistry, mineralogy, bot- any, 'zoology, etc., etc., each successive founder of a new system aiming to introduce a nomenclature in which the names, classes and species should be to the greatest^ ex- tent possible, indicative and suggestive of the nature and habits of the individuals it denotes. 444. It is .obvious from the nature of the method of proving general propositions, that no person can prove a general proposition who has not proved the truth of some one, at least, of the individual propositions com- ing, under it. Thus, no one can prove, or have any right to assert that " Whales are mammals," for example, who ■cannot show in regard to some particular whale that it is a mammal. A knowledge of individuals "necessarily jirecedes the assent to general propositions in the order of knowledge. Of course, one may take a general proposition on authority, without such knowledge of individual cases. This, however, is mere belief, and not knowledge. » GENERAL FEO-PUSITIONS. 191 445. This rule, however, does not always apply to par- , tial propositions. For example, I may see in the dusk of evening that there are some men on a distant hill, without being able to name or identify any one person so as to say that he was there. 446. Besides induction, we have another process, ^wr- age, by which we arrive at general facts. The result of an average differs from a generalization not only in, the process but also in the character of the proposition ob- tained. The proposition will not be true (precisely) of each of the individuals and need not be true of any of them. Thus, suppose one takes note of the weight of the mercury in a barometer for some hundreds of times, at all hours of the day, and in all kinds of temperature and of weather, and divides the sum by the number of observations, he gets the average height, which gives him a datum on which to estimate the weight of the atmos- phere, the height of the place above the sea level, etc. It is, however, barely possible, though not at all likely, that tlie instrument may not have been observed at that exact height at any one time of observation. Nevertheless, the facts thus obtained are often of the utmost import- ance in science and in the practical affairs of life. 447. Average is also a method of approacMng a fact which is often available when no exact observation can be made. Suppose, for example, a mariner at sea wishes to take an observation o;f the sun or some star, and the vessel rocks so that he can get no exact observation. He can take several, and thus, by an average of them, make the errors neutralize and counteract each other, until the result will be a very close aproximation to the exact fact, " possibly the exact fact itself. 448. It is, in fact, seldom the case that important ob- servations can be taken without some liability to ferror. TEXT-BOOK OF LOGIC. 192 which must be provided for and guarded against in this way. There is usually some excitement of the nerves themselves, there is some error in the instruments, etc., that needs to be guarded against. Even the varying size of the pupil of the eye of the observer, has been found to be a cause of difference in the reported results of ob- servations in some of the more delicate of the efforts to obtain exact'data for astronomical calculations. And for all these sources of error, average is the best remedy that has been yet provided. SECTION VI. ttNIVBESAI; PBOPOSITIONS. 449. A universal proposition differs from an individ- ual proposition in that while the latter affirms a predi- cate of only one object, that is an object that is logicqMy an individual, though physically complex, and made up of parts ; the former affirms its predicate of a class gf individuals ; and it differs from a ^ewera^ proposition in. that while to a general proposition there may be excep- tions, the universal proposition, if it be universal in its nature and not from mere accident, can admit of no ex- ceptions. 450. A univei'sal proposition can be proved in three ways only, (1) by demonstration a jBrioW from the nature of the subject matter, (2) by actual inspection of the in- dividuals included within the scope of the assertion, as when I say that " All the pennies in my hand were coined' in a given year," I can know this only by inspecting them all; (3) by authority. 451. The first kind may be called Universal a priori, and may include any number of individuals ; the second GENERAL FR0P.08ITI0NS. 193 Universal aposteriori, and can include only the observed individuals ; the third are Uniwrsal iy authority, and can include only the cases expressly named, or precisely described in the act that makes the proposition true. 453. Authority in the sense here used, is different from testimony, and creates or produces the truth which it as- serts or declares, as when the Creator pronounced all the seventh days holy, the command or declaration made them so, and impressed upon them a character which they had not per se, or in themselves. 454. In demonstration or reasoning from the nature of the subject, no particular form is used, and any and all valid forms may be used : and all the reasoning can be reduced to the formulse that have been considered. But demonstration is always first in the order of time, and must enter in, as a part of all reasoning; and all reason- ing, as well as, the proof of the rules and formulae of reasoning, must be proved and established by it. 455. Demonstration is, as we have said, called analyti- cal reasoning, because it reasons from the nature of the subject by means of analysis.' 456. Analysis is' of three kinds (two of which we have already explained) namely, (1) Physical, (3) Logical (3) Mathematical. Physical analysis resolves a compound into its component parts, as in Chemistry. Logical an- alysis resolves the conception of an object into the ;^rop- erties of the object itself. Mathematical analysis consists in making such changes in the form of an equation as that any one of the terms may be made the first member, and the others, constituting the second, will show its nature and value. 457. The word demonstration, in its niost general use, is applied also to the three diiferent processes, according to the three different .kinds of analysis. 13 194 TEXT-BOOK OF ZOGIO. (1) Physical Demonstration, as in Chemistry and Anatomy. In Chemistry, the demonstration consists in showing by analysis (Chemical analysis), the elementary parts of which any compound is composed ; the laws of this method of reasoning Chemistry itself explains. It tells us how we may separate a compound, so as to find its components, and how to. find and identify and weigh them after the analysis. In Anatomy, the process is rather division than analysis — or, to use the technical expression, it is dissection. Division separates the parts without changing them. But in analysis, the parts ex- hibit properties and qualities that were not obvious be- fore. (3). Mathematical 'Demonstvsbtion. This is of two kinds, (1) Algebraic. (3) Geometric. In the first we resolve the equations into parts called terms — connected by cer- tain algebraic signs. Algebra teache^ how we may change these terms without afiecting the value of the equation. And with each change in the form of the equa- tion, some new truth that was implied in it — although not obvious before — becomes obvious, as though it were the only one for which the equation was designed. In the second case or Geometric Demonstration, which is really one form of Logical Demonstration, we begin with the line and angle, etc., and end in proving a prop- erty of the line or angle. (3) But that which is more especially called demon- stration, is Logical Demonstration. In this, as I have said, we reason from the nature of the thing — that is, its essential properties. And before there can be either physical or mathematical demonstration, there must have been some acts pf logical demonstration. Mathematics, for example begins with axioms and definitions. Chemistry assumes both, if it does not expressly state ihem. It has GENERAL PBOPOSITIONS. 195 its definitions of its elementary substances ; and the two axioms at least : (1) that in analysis and synthesis we neither create nor destroy any particle of matter, and(Si) that when any two substances that have been together without chemical action^upon each for any length of time, begin to act, there is proof of the influence of some other agent acting upon them. 458. Demonstration may have for its starting point, either (1) a fact, or (2) a definition, or as it is more com- monly expressed a conception. 459. A mathematical demonstration is one that be- gins, not with a thing or an object, but with a concep- tion — an abstraction — an objectified abstraction, as are all of the so-called objects of mathematics, number, form lines, angles, etc. N"o such things exist as objects. A line, for example, that has. length without breadth is an impossibility. 'And all siich demonstrations end in prey- ing only a possible property or a necessary condition. Thus, when we prove in terms that " Any one side of a tliangle is less than the sum of the other two sides," we do not necessarily know or believe that there is any thing that is triangular in form actually in existence. And all that we prove is that, if there is any such thing in ex- istence, it must be true, from the very nature of things, that any one side will be less than the sum of the length of the other two. 460. But a" demonstration may begin with a fact or an object, and prove from it the existence of some other fact or object. The object must be one that has been observed, and it must be regarded as either cause or effect. Of this we have had examples' and illustrations already. (§§ 392, 394) 461. In reasoning from facts, we begin with an analy^ sis which is for the most part assumed as having been 196 TEXT-SOOK OF LO&ia made, rather than formally and expressly made as a part of the argument. And that which we first prove is the existence of some other object or fact. But for reasons already assigned, the reasoning that proves the existence of the object or the reality of the fact, proves also some- thing more than its existence; it proves something con- cerning some of its properties, modes, attributes, and, if the argument be from effect to cause, it proves also some of the laws under which it acts. 462. Demonstration is made possible by the fact that there is no one property or object of thought that does not imply another. Thus, the straightness of a line im- plies its shortestness although it is not the same thing-; the extension of a body implies its divisibility, etc. Hence any property that is used as the differentia in a definition implies some other property which is not affirmed in the definition, and that, some other property, and so on. This relation of properties is, however, a matter of in- sight. It cannot be demonstrated any mote than we can demonstrate by reasoning, the color of a rose. 463. As the properties which we ascribe to an object in its definition are obtained by an analysis, a definition is called an analytical proposition. But those which we affirm on the ground that they are implied by the defini- tion, are called synthetic propositions. When, however, a proposition is proved by an appeal to facts rather than by demonstration a priori, it is an a posteriori proposi- tion. Analytic propositions and propositions that are synthetic a priori constitute what is called necessary matter while a posteriori propositions constitute what is called contingent matter. * 464. Demonstration, therefore, can admit into its sphere only a priori propositions, propositions in necessary mat- ter, either analytic or synthetic a priori. Or, in other QEtlEBALPmPOSlTIO'NS. 197 words, it can deal only witli the essential properties of things. In mathematics it deals with their form and their uumher ; in all other departments, with whatever constitutes or may be assumed as constituting their es- sential nature. 465. Hence, if the demonstration be good, the fact — ^if it be a fact and is proved — can admit of no doubt or suc- cessful contradiction; and ifit.be a general proposition it must be universal also, and can admit of no exceptions. It must be absolutely true, true for all times and places, and under all circumstances. * It will be seen and felt to be true by all intelligent beings just so soon as they com- prehend the reasoning by which it is demonstrated. 466. The certainty of demonstration depends in the last analysis on the principles of Identity and Contradiction. 467. I have spoken of three ways of effecting a dem- onstration or proving, the truth of a universal proposi- tion, as distinguished from a mere general proposition. And I have said that there are but the three. This, how- . ever, is contrary to the common opinion, and many there ■ are who hold to the inductive method — or proof by facts — as constituting the only reliable method of establisning universal truths, "especially iSi the department of physi- cal and social science. 468. Df my doctrine, however, several demonstrations may be given. Thus, suppose we have the terms x'' -\-x -|- 41, and expand it into a series, then making x succes- sively equal to 0, we have 41, « 1, « « 1 -f- 1 + 41, = 43, « 3, « « 4 -j- 2 -i- 41, = 47, « 3, « " 9 4- 3 -i- 41, = 53, « 4, « « 16 -I- 4 -i- 41, = 61, and so on; the result will be in each case & prime num- 198 TEXT-BOOK 01 , LOQIO. ber for some forty or fifty times, and then for a few times the number will not be prime. 469. But again, we have a more general form. Every fact is the product of causes, which, considered as pro' ducing "the effect by motion or change, are called ^'forces." Not only is every object that we observe considered as an object, or substantially, a product or an effect, but more- over, each state of the object is, in like manner, the re* suit of the forces that have been at work upon it, and so not only, a sign and an indication of their character, but it is also a measure of the intensity and direction of their resultant. If the forces are constant, the line will be a straight one, and of course, any two points will de- termine the direction or law. But the fCrces may be of any varying intensity. 470. We may illustrate this by supposing a man sit- ting in his buggy, and riding in a certain direction, say westward. If now, he fixes his attention on any point in the rim of one of the wheels of his vehicle, it will appear to him to move, by turns, in all directions — how forward, then downward, then backward and then up- wards again. And if, instead of revolving several times a second, it revolved but otce in his life time, he could collect any number of facts, make any number of observa- tions to prove that that particular object in the rim of his wheel, say a nail-head, was moving in any one of all possible directions that lie in the plain of the wheel's motion, and none of them, perhaps, would indicate, that the wheel itself was moving westward or that the gener- al tendency of the nail was in that direction. 471. To illustrate the case still further, we know that water increases in specific gravity as it cools from' 312 degrees down. Now between 212 degrees and' 40 degrees, for example, we may have any number of observationsj OENEBAL PROFOBITIONS. 199 all tending to prove the general lav, that as water be- comes colder it grows more dense. But at 39.5 degrees, we find a point of inflection, so to call it ; for below that temperature, water grows less dense with loss of tempera- ture. 473. So in Political Economy, we find in a great num- ber of stages in society, that wealth increases faster than population. Prom this we might infer as Carey, Smith, and others have done, a universal law that wealth in- creases faster than population. But in other stages, un- doubtedly, wealth decreases, hence other writers, as Mal- thus, Eicardo, and the English writers generally, have inferred that the law is, that property decreases with the increase of population, (that is, in proportion to num- bers), and that the cases where it increases in proportion to numbers are exceptions to the general rule. But in both cases and in all cases, if we can recur to the forces that produce the change, and ascertain their nature and the law of their action, we can find what is the law of change, and shall probably find that to that law, when fairly known and accurately stated, there are no excep- tions ; the existence of recognized exceptions being in all cases,. as I think, the proof of inadequate statements; statements that are inadequate because of imperfect com- prehension and inaccurate generalization. SECTION vn. PEOBABIiE PEOPOSITIONS. 472. We make a proposition probable in contingent matter by (1) showing a sufficient cau^, which will consist for the most part, in mere physical matter, the phenomena of the inanimate world, in showing an efS.- 200 TEXT-BOOK OF LOQIO. cient and an occasional cause, with the proper conditions ; and in moral matter the actions of rationtil beings and moral agents, final cause, as motiye, takes the place of occasional cause in physical matter, or (2) by showing an analogous case, by showing, that is, that something like it has occurred. Thus we render the Christian mir- acles probable by showing that the Creator has interposed from time to time, in the geological ages to introduce new species of plants and animals, and establish new orders of things. 474. The Argument from Analogy iei often used with a good deal of rhetorical effect. Its real logical force, however, is much less. In fact, the word "analogy " is used somewhat vaguely and indefinitely, so that it is difl&cult to say precisely what its force is without know- ing something beforehand of what is meant by it. 476. It is not uncommon. to have an argument which is entirely of the nature of an Induction, though some- what incomplete, and less conclusive than Induction usually is, spoken of as Analogy. When the argument or inference is based on the resemblance of objects one to another, it has the nature of an Induction. Whereas Analogy has been defined to be " a resemblance of -ratios," as has already been said. 476. There are no two objects within the range of our thought, that do not resemble each other in some res- pect. But this similarity is not usually called resem- blance unless it be in some obvious or conspicuous prop- erty. Hence, objects and events are said to resemble each other when they are obviously or strikingly alike. Such a resemblance, however, can hardly be regarded as the basis of an argument in itself considered. We must look deeper into the matter before we can make any such use of it. BROS ABLE PROPOSITIONS. 201 477. Ev.ery substantial object whether matter or mind is always a true cause — causa vera, though not always acting as a cause — causa causans. And moreover, it is a cause in different relations — and productiye of differ- ent classes of effects by, or in consequence of its proper- ties; each property being connected with a class of effects that are peculiar to itself. Thus, this piece of paper as a hard substance, will produce certain effects that it could not produce if it were soft ; as white it will produce other effects that it could not produce if it were of any other color, and so of the rest. Now by these properties hardness, color, etc., etc., objects resem- ble each other. 478. But in reference to their mode of operation in producing their effects they are " analogous ;" that is the ratio or relation of any one to its appropriate .effect is the same as that of any other of them to its appropri- ate effect. Hence resemblance always implies analogy ; resemblance of objects in their color for example, implies analogy in their relations to other objects, in so far as those objects are affected by their color. So, again, the seeds of different plants always resemble one another in some of those properties in consequence of which they are seeds. , And it is in consequence of those properties that they act as germs that grow into plants. Hence, also they are analagous — the relations of any one to the tree or plant that grows from it being the same as that of any other totha tree or plant that "grows from it. 479. In the same way also the seed of a plant, and the egg or ovum of an animal have some points of resem- blance in the essentia of tie proximate genus to which they both'belong. And they are analogous too — the re- lation of the seed to the plant being the same as that of the ovum to the animal. 203 TEXT-BOOK OF LOOIO. 480. And finally there may be an observed analogy "where there is no obvious resemblance that ■would lead us to expect it ; that is, in cases where we do not know what it is in either of the objects that occasions the change or transformation. Thus, there is an analogy between the passage of an insect through the chrysalis state and the change of a tad-pole into the frog, though we could hardly reason from the one to the other, or point out the resemblance on which it is based. 481. If we know beforehand that the relation or ratio between any two pairs of terms respectively is the same and one relation is already known, we can, of course, aflQrm it of the other pair as a conclusion on the ground of the one that is known. Or if both are unknown, and one is more easily ascertained than the other, we can as- certain that by observation, and afiQrm the other as an inference or conclusion. 483. But in most cases, when what is called the Argu- ment from Analogy is resorted to, the thing that is un- known is the identity of the relations, and the effort is to prove from the resemblance of the two objects which are different in the two membfets, that they have a third term common to both members, with an identity of re-* lation between each one of them and the common third term. Thus, in Butler's famous argument for Revealed Eeligion and especially for the doctrine of the immor- tality of the soul, he argues from the resemblance be* tween the chrysalis state of the worm, and the fuller de- velopment of life in the butterfly to the future life of man. , 483. And yet it seems to me that his Argument is val- uable only as it is one step in ah Induction to show that as a general law of Nature, nothing perishes ; it may undergo changes, and great changes, but through all of PROBABLE PROPOSITIONS. 203 them it comes out a reality, cHanged to some higher form, but not*aiinihilated. 484. Analogy, however, is of great rhetorical force in removing what is sometimes called " the antecedent im- prohability" of an event or a fact which one wishes to prove real. It shows that things like the one in ques- tion have occurred ; or, at least, that something as strange .and improbable has occurred, and thereby secures atten- tion to the Positive Arguments, and prepares the mind to give them the influence that is justly their due. 485. But even in this case the talue of the argument is founded on the resemblance of the two facts or events, and is in so far an Induction, or rather oj the nature of an Induction, and comes short of it in precisely that which gives to Induction its concluding force. 486. rhere is also a method of establishing a very high degree of probability, a degree that is sometimes claimed as demonstrating absolute truth, called by Whatelt '"^Progressive Approach." It is of -the nature of demon- stration by means of ratios of variation, when the exact condition of one or both variables cannot be, or has not Ijeen realized. The ordinary attempt to prove the first law of motion is of this kind. The law is this : " If a body be in motion without any resisting force, it will continue to move forever." The argument is : " If we roll a ball, for instance, on a sand-bank, then on a car* peted floor, and then on a marble slab, we find that 'the length of the time during which it continues to roll, will increase, as the resisting obstacles are diminished. Hence, If resistance could be reduced to zero, the time of con- tinuing to move would become infinite, or the ball would continue to move forever." But we cannot remove all the resisting force, nor can we wait to see whether it would move quite so long as the terms of the proposition 204 TEXT.B OOKOF LO QIC. contemplate — "foreyer" — nor, finally, can -we find the exact differential co-efficient so as to be able to demon- strate the exact value of- either of the variables from any assumed value of the other. The law can, however, doubtless be proved by demonstration a priori irom the nature of matter as inert. 487. "Whatblt gives another example, in the case of the argument for the existence of God. He says that " All men, even the lowest in the scale of intelligence, have some ideas of something supernatural, and as we ascend from the lowest stage up to the highest yet at- tained in any community, we find this idea approaching towards- an adequate conception of a One Supreme Being, who is the Creator and Moral Governor of the Universe. Hence, as a state of perfect intelligence is that alone in which the prevalent opinions of nlen will be all true and adequate, we may assume that the doc- trine concerning God, which it is. thus shown will then prevail, is- the true one, and the one that ought now to be accepted as a matter of belief, and acted upon by faith as a means of moral culture and intellectual proT gress." 488. The results obtained by these processes, although they may be true — absolutely true^-are not, however, shown by the processes to be more than probable, highly probable — having only that degree of probability, which, as it is sufficient for action in most cases, and is all that from the nature of the case we can have, has been called moral certainty. But no absolute law can be proved in this way, or by any of the methods of induction and average, as has been shown in the preceding section (§ 467). Still, less therefore, of course, can any form of mere probable argument establish anything that can be properly regarded as an absolute certainty. PROBABLE PROPOSITIONS. 305 489. It will sometimes happen tliat we can create a presumption in *faTor of any fact or event by showing that such things are reported or believed to have occur- red elsewhere, although the argument is not at all in the nature of analogy. Thus, if we had but .one exaipple of the falling of meteorolites, it is doubtful if the reality of the meteorolite in that one case could be effectually established. But if we show that such things have oc- 'curred occasionally, or, at least, that such things have been reported and believed to have occurred, we render the aflBrmation of the occuri'ence of one in any particu- lar case — probable — that is the assertion of its occur- rence will, by this means, be made to be regarded as pos- sible, and so we gain attention to the arguments that may be adduced in its favor, which might otherwise , fail to receive attention. The popular belief in the possi- bility of anything is often practically the most effective part of the proof of its reality. 490. But, in order to make any event seem probable and to remove any antecedent improbability that there may be, we may show (1). By analogy, that such things have occurred. (3). That the circumstances and conditions of things were such that it might have occurred ; and (3). That there were causes of one kin^ or other that could have produced it. 491. Among the causes there must always be an effi- cient cause which is sufficient for the effect, " causa suffi- ciens f and in physical matter an occasional or exciting cause; but in moral matter a final cause or motive takes the place of an occasional cause and is, in fact, the occa- sional cause. 492. But, without first establishing the probability of an event by one or all of these means, it is doubtful if 306 TEXT-BOOK OF LOGIC. any amount of positive argument will produce convic- tion except indeed in those cases in ■v\jjhich the antece- dent probability of the event is already admitted before we begin our argument. SECTION vm. EXTBA LOGIOAl FAIXAOIES. 493. The Extra Logical Fallacies are of two kinds, those that are in the Matter, and those that are in the Method. 494. Fallacies in Matter consist in Premises, whether assTlmed or expressly stated, that are either (1) untrue or (3) irrelevant. 495. If a proposition introduced or assumed by neces- sary implication is merely untrue, it is said to be a " Non vera pro vera," something not true, taken and used as truth. 496. Of course, any Conclusion drawn from such a premise can derive no degree of certainty from the reason- ing into which the untruth has entered, as though it were true. Aristotle has strangely enough devoted three chapters of his Prior Analytics, (Book II, chapters 2d, 3d and 4th) tQ a discussion of the cases in which we may have Conclusions that are true from Premises that are confessedly false. 497. It is indeed true that a Premise may be false and the conclusion true. But the conclusion is not proved by any such inference. There may be no Fallacy in Form or in Diction, but if one Premise is false no truthfulness or certainty can be derived for the conclusion from that source. Aristotle's examples (one of" them) is as fol- lows: EXTRA LOGICAL FALLACIES. 201 Every stone is an animal : Every man is a stone : Therefore, Every man is an animal. The conclusion is true enough while both Premises are false. 498. But suppose we change 'the Major Premise, and say " Every stone is a quadruped," and we should have in Conclusion every man is a quadruped. It seems manifest that this father of Logic could not have had any very clear and satisfactory comprehension of the nature of reasoning, or he would not have treated this part of his subject as he has done. 499. As there is no limit to error it would be possible to prove anything to be true if by any possible or con- ceivable formula we could prove a proposition to be true by means of one that is false — except, of course, in that indirect method in which we first prove that what we had assumed as true, is false, and then infer from this proved falsity, the truth of its contradictory. But as truth is one, we are limited by it in the assumptions we can make in regard to any object of thought. " This paper is white," is the only assertion I can make in regard to it with a predicate belonging to the category of color. To say that it is black, or red, or green, etc., are assertions which would, each and all of them, be untrue, if the owe, " it is white," is true. But the untrue assertions may be as numerous as the predicates denoting colors or shades of colors — minus one. 500. The next form of the Fallacies in Matter is the Non causa pro causa. This differs from the last one named in that the prop- osition affirmed in this case is true, but irrelevant. That is^ it is no Premise to the Conclusion we wish to prove. The old example, " There is a comet, therefore there will 308 TEXI-BOOK OF LOGIC. be a famine," is a case of physical cause. The comet is no cause (physical) of a famine, and therefore, no proof (cause logical) of a coming famine. So if one, in at- tempting to prove that the vertical angles made by two straight lines crossing each other, are equal, should be- gin by asserting that a straight line is the shortest dis- tance between two points, the proposition would be true enough, but of no use as a means of proving that the opposite vertical angles are equal. 501. It should be understood that any argument when drawn out at full length, ^nd completed by supplying all the suppressed or omitted Premises, would be a Sorites of the form, AisB BisC isD etc., etc. That is, a series of propositions in which, whatever may be their quality, or logical quantity, each term would ap- pear in two consecutive propositions, and each proposi- tion, besides furnishing one term for that which is next to follow, must also contain one that was used in the proposition that preceded it. The only exception to this is the Conclusion, which furnishes no new term, and is made up of one that was contained in the premise last stated, and another in that which was first stated. And if we find on reducing th"e argument to this formula, and completing it, any Premise that does not work into some such series under this law it is a Non causa. 503. Metabasis. I have introduced this term borrowed from Aristotle, to denote the Fallacy of applying reason- ing which is correct, and Conclusions which are true, of one object or subject matter, to another by way of resem- blance or analogy, when no such analogy or resemblance EXTRA LOGICAL BALLACIES. 309 exists. I think we have an example of this fallacy in the arguments of those, who deny the freedom of the human will, on the ground that, it is alleged, its (Jhoice must be determined by the strongest motives, or by the prepon- derance of motives, and in the direction of their resultant. This is true of motion in physical science. But the mind is essentially unlike natural objects in respect to action and motion, whereas the objection to the freedom of tlie will and the arguments against it, are based on the as- sumption that they are alike. 503. In fact a large share of what has passed current in psychology and metaphysics, is but a metabasis of the most violent kind. It objectifies abstractions, as "facul- ties," " ideas," etc., an^ proceeds to talk of their origin, jiature, functions and laws, as though they were realities as substantial as the limbs and tissues of the body. Nor are we without examples of the same fallacy in the at- tempts at theoretical explanation of the facts in physical science. Heat, light, gravity, etc., are objectified and then we reason about them as though they were measu- rable, if not "ponderable," substances. 604. So, too, when Cabanis said " the brain secretes thought as the liver secretes bile," if he meant the "as" to denote a resemblance of mode and not as an equiva- lent to "as surely as," he committed a metabasis; for thought and bile being very unlike in their nature, their secretion cannot be alike, even if thought can be said to be " secreted " at all. 505. No Sequence ; this is akin to, if it is not the same as what is sometimes spoken of as the Fallacy of Post hoc, ergo propter hoc, " after this, therefore on account of this'' although this expression is much more frequently used in reference to physical sequences. All Conditional judgments or propositions, as we have 14 310 TEXT-BOOK OF LO&JO. se.en, assume a logical Sequence between the Antecedent and the Consequent. "Wherever there is no such Se- quence, we have the Fallacy in Matter that I am now speaking of. The true method of detecting and expos- ing this fallacy, is to regard the Conditional as an Bnthy- meme and complete it into a syllogism as has already been described. (§§ 220, 226) 506. lion excluded middle. This has . been described. (§ 352). A Disjunctive must state all the parts or con- ditions. As between the conclusion and the Premise of an Enthymeme, as we have seen, there can be no middle proposition in which we can rest while we admit the Premise and deny the Conclusion. But if the disjunctive result from an actual division, the parts whether co-or- dinate or alternate, may be ever so numerous, as the case may require or inclination may lead us. But how many soever they are, they must all be mentioned, and there will be one member of the disjunctive Major Premise for each part, which will of course form a term in each part. Otherwise there will not be an Excluded Middle. 507. Thus, in discussing the question of the unity of the origin of the human race, it is customary to say, or rather assume, that " the present diversity owes its origin either to climatic influences or a diversity in the origin, of the various races." But manifestly we may have a tertium quid, a third supposition without referring to miraculous, interposition, of which the above Disjunctive takes no notice as among the possible causes of the phe- nomena to be accounted for, namely, the origin of a black skin for example, in some mere lusus naturm, some monstrosity, like that of Albinism, and then its per- petuation by the well known laws of the transmission of the congenital peculiarities of the parents to their offspring. EXTRA LOGICAL FALLACIES. 311 508. Of Fallacies in Method, I have named but two, Petitio Principii and Ignoratio Elenchi, or in English -we may designate them as " Begging the Question," and " Mistaking the Issue or Proof." 509. The simplest form of any complete argument re- quires two Premises in order to a Conclusion. But for the mosf part, one of these Premises is already admitted,, and needs no argument to enforce it, does not even need in many cases to be so much as explicitly stated, whereas the other is doubted, dissented from or denied. And it is seen and admitted that if that Premise is proved, the Conclusion will follow, and no farther objection will be made. Hence the Premise which the audience or the reader doubt and require to have proved, is for them, a question, and is therefore " the question." If now the advocate should take this Premise for granted, and go on to prove the other and claim assent to the Conclusion on the ground of the proofs he had adduced, his hearers would accuse him of having "begged the question ; " of having assumed without proof, and perhaps without so much as effort at proof, the only thing they ever doubted in the Premises. 510. Sometimes this Fallacy runs into a special form called "reasoning in a circle," curriculum nefas. In this case a proposition is first used as a Premise for the purpose of proving another as a Conclusion, and this Conclusion is used as a Premise to prove that from which as a Premise, it had been deduced. Thus, for example, it is asserted that " the gravity of bodies is in exact propor- tion to their quantity of matter." But how will you determine or measure " their quantity of matter " ? By weight ? Then the assertion becomes " their gravity is in . proportion to their gravity," or "their weight is in pro- portion to their weight." Will you determine it by the 312 TEXT-BOOK OF LOOIO. particles ? But how do you know how many particles a mass contains ? We have no way of counting them or computing them. It is then said " that the number of" particles yaries with, or is in proportion to, the weight or gravity." Hence we' have the gravity of a mass is equal to its quantity of matter. Its quantity of matter varies with the niimber of its particles. The number of its particles varies with its weight. But its weight is equal to its gravity. 511. Ignoratio EUnchi means literally, Mistaking the Proof. It supposes a certain proposition to be proved as a Conclusion and then the introduction • of arguments, which are perfectly good and conclusive for the proof of some other proposition perhaps, but have no bearing upon, or tendency to prove the one before the advocate, and which the occasion requires him to prove. An illus- tration is commonly cited from Thucydides. Oleon had argued that it yt&BJust for the Athenians to put the Mitylenians to death for their treachery. Diodatus, in reply, said that that was not the question. No one doubted that it was just to put them to death, the only question before the Assembly was, whether under the circumstances, it would be expedient to do so. 512. There is, moreover, another form of fallacy in Jtlethod, which however, so far as I know, had not a,t- tracted the attention of the ancient writers on the subject, but which so exactly comes under the meaning of this name, — Mistaking the Proof — that I will venture to in- clude it in this class. It consists in using one mode of proof when an9ther and a different one is demanded by the nature of the case. Thus if one should attempt to prove a proposition in mathematics by either "induction" or "testimony," the proof would not be what is required. METHODS OF REFUTATION. 213 For at most, the latter, testimony, would establish only a "probaile opinion " and the other could prove the prop- osition to be generally true indeed, but not absolutely true with no possibility of exceptions. 513. Or in the other direction, if x)ne should attempt to prove a proposition in contingent matter by a demon- stration, he could establish or prove only a possibility, or at most, an antecedent probability. It was the great fault of the Scholastic Philosophy which prevailed be- fore the time of Bav ^^ ■ j < _ ■"•"■' 8. All unrighteous persons are justly offensive to those that are around them ; but none that are justly offensive to those that are around them can enter Heaven, therefore, no urujghteous person can enter Heaven. 9. No contract to do what is wrong can have any binding force. But all contracts to do what is wrong are used as excuses to the con- ^ science by those who do wrong, therefore, some things that are used r- as excuses by those that do wrong have no binding force. >i 10. All metals are dug out of the earth ; coal is dug out of the earth, therefore, coal is a metal. 11. Some of the animals that live in the sea are six-legged ; but . all six-legged aniTnalg are insects, therefore, some insects hve in the sea. 12. Whatever opposes human progress is an uimecessary evil ; some of the usages of the past oppose human progress, therefore, some of the usages of the past are unnecessary evils. 13. All indulgence is unfavorable to mental vigor ; but some in- du^ences are deemed innocent, therefore, some things deemed inno- cent are unfevorable to mental vigor. ' 14. No wrong may be done that good may come of it ; but what- ever isjione that..good may come of it, "is done from a good motive, therefore, some things done from good motives are, nevertheless, wrong. Y 238 TEXT-BOOK OF LOGIC. 15. No mere triek deserves success ; but some things deserving ■ success are done from disinterested motives, therefore, some of the things done from disinterested motives are not mere tricks. 16. Those who endure evils merely because they caimot escape them are no true heroes. Some of those who have been reckoned martyrs, endured only because they could not escape their sufferings, therefore, some that have been reckoned martyrs are no true heroes. 17. No man of enlightened mind Can oppose the education of the people ; but some ecclesiastics do oppose the education of the people, therefore, some ecclesiastics are not of enlightened minds. 18. No candid man will be influenced by prejudice ; but some can- did ,men err in judgment, therefore, some who err in judgment are not influenced by prejudice. 19. All the fixed stars shine with their own Ught. Some of the heavenly bodies do pot shine with their own Hght, therefore, some of . the heavenly bodies are not fixed stars. 20. Some fictitious compositions are not injurious. But all ficti- tious compositions affirm what is not true, therefore, some composi- tions that affirm, what is not true, are not, nevertheless, injurious. 21. Some things allowed by the law are, nevertheless, dishonest. All the things that are allowed by the law, however, may be done with impunity, therefore, some dishonest things may be done with impunity. 22. Air is essential to the support of vegetable life ; but the light of the sun is not air, therefore, the light of the sun is not necessary to vegetable Ufe. 23. No discontented persons are happy ; but the popr are not al- ways discontented, therefore, the poor are not always unhappy. 24. Some recreations are necessary to the the preservation of health and spirits. All recreations, however, are liable to be carried to ex- .cess and • be abused ; so that some things liable to abuse are never- theless necessary for man. 25. Any one who is candid will refrain from condemning a book without reading it: some Reviewers do not refain from this; there- fore some Reviewers are not candid. 26. Sensualists wish to enjoy perpetual gratification without sati- ety. But this is impossible; therefore the sei^ualist desires what can never be attained. APPENDIX. 229 27. Liljeralit y is a means of making others happy. But it is not a means of making one's self Keh; therefore making one's self rich does not always make others happy. 28. ssrfee_ls a legitimate mode of exposing the failings of others. But the calling others by iE-names is not satire; therefore it is no legitimate mode of exposing their failings. 29. No one is free who is enslaved by his appetites. The sensu- alist is enslaved by his appetites; therefore no sensuaJist is free. ^ 30. No one is rich who has not enough. No miser has enough; therefore no miser is rich. 31. Some men like strong drink. Yet strong drink ruins them ; therefore some men love what ruins them. 32. It is a difficult task to restrain all inordinate desires. To con- form to the precepts of Scripture implies a restraint of all inordinate desires; therefore it is a difficult task to conform to the precepts of Scripture. 33. AH amiable men merit the esteem and respect of their fellow • men. And certainly all who aim only to do good to their fellow men, deserve to be esteemed and respected on that account; hence all who are striving to do good to others are amiable men. 34. A man who deliberately devotes himself to a life of sensuality is deserving of strong reprobation. But those do not delibera,tely devote themselves to a life of sensuality who are hurried into excess by the impulse of the passions; such therefore as are hurried into excess by the impulse of the passions jare not deserving of strong reprobation. 35. Things are soon ready in a well reordered house. Mine is a weU ordered house; therefore things are soon ready in it. 36. Things are soon ready in a well ordered house. Things are never soon ready in my house; therefore mine is not a well ordered house. 37. Things are soon ready in a well ordered house. My house is not a well ordered house; therefore things are never soon ready in it. 38. Some effectual check to the progress of seditious publications is absolutely essential to the safety of our country. The total abo- • lition of the art of printing would prove such a check; therefore the art of printing should be totallyraboUshed. 39. Every hen comes from an egg. But every egg copies from a hen; therefore every egg comes from and egg. 230 TEXT-BOOK OF LOGIC. ^ 40. SomemHlie heathen aluthors deserve' credit. But all heathen authors relate prodigies; therefore prodigies deserve credit. y 41. Tyranny is an unnecessary restraint upon human liberty, The English government imposes no unnecessary restraint upon the lib- erty of its subjects; therefore the English governmeht is no tyranny. 42. All that glitters is not gold. Tinsel glitters; therefore it is not , gold. ' ( 43. No trifling business will enrich those that engage in it. Speculation is no trifling business; therefore speculation will enrich all who are engaged in it. 44. No cat has two tails. Every cat has one tail more than no oat; therefore every cat has three tails. 45. All truly great men are generous and n»ble in their disposition. There are, however, few men that are truly great; hence mdst men are not generous and noble in their disposition. 46. That man is independent of the caprices of Fortune who places his chief happiness in moral and'intellectual excellence. A true phil- osopher is independent of the caprices of Fortune; therefore a true philosopher places his chief happiness in moral and intellectual excellence. ^ 47. None but whites are civilized. The Hindoos are not white; therefore the Hindoos are not civilized. 48. None but whites are civilized. The ancient Germans were whites; therefore they were civiUzed. 49. None but civilized people are white. The Gauls were white; therefore they were civihzed. ^50. Only patriotism can save a nation. But political sagacity is /not patriotism ; therefore political sagacity cannot save a nation. ^ 51. All the Helots were slaves, and all the Athenians were free; /tberefore no Athenians were Helots. ■S^ 52. AH acts of Congress require the signature of the President. ' But joint resolutions are not "acts" of .Congress; therefore they do not require the signature of the President. ^ 53., Meat and drink are necessaries of life. The revenues of Vit- ' elius were spent on meat and drink ;''theref ore they were spent on the necessaries of life. 54. Persons that have been accustomed to freedom ^can never be happy in a state of servitude. The American slaves have never been accustomed to freedom; therefore they are liappy in their servitude. APPENDIX. 331. , 55. A tariff on imported goods will raise the price of the article to \ the consTimer, whether imported or of domestic^maiiufaotare. But a tariff is a means of protecting domestic industry; therefore the pro- tection of domestic induiatiy raises the price of the articles we con- ^ sume. ^ 56. The ancient astrologers spoke of Mars and Jupiter and Saturn. ' But Mars, Jupiter, etc., are planets; therefore the ancient astrolqgefs spoke of the planets. i 57. Gold and silver are precious metals. And gold and silver liavfe ' always been used as money; therefore the precious metals have alwiaiyft been used as money. \c " ' 58. Animals and vegetables are the only organic bpdiete.' ^pongek , are not animal and vegefeble; therefore sponges are not organic- bodies. 59. Agriculture and manufactures create wealth. But trade is neither agriculture nor manufactures; tllerefore trade does not create wealtiL 60. The study of Mathematics is essential ito a complete educa- tion, because it produces a habit of close and oonstaiit reasoning. 61. Fianiliarity is productive of contempt, inasmuch as it occa- sions a needless exposure of private failings. 62. Man needs the restraints of law, since he is naturally selfish; and is, moreover, subject to desires and passions which have no limit or power of restraint in themselves. 63. Wilkes was a favorite with the populace. He who is a favor- ite with the populace must Understand how to manage them; he ' who understands how to manage tiiem, must be well acquainted with their character; he Who is well acquainted with their character, must hold them in contempt; therefore "Wilkes must have held the populace iu contempt. 64. The child tit Themistocles governed his niother; she govenied her husband; he governed Athens; Athens, Greece; and Greece, the woiid; therefore the child of Theinistocles governed the world. 65. A wise man is never surprised because he is never disappointed ; and he is never disappointed, because he forms no expectations that are not placed upon the most certain basis. 66. Whoever receives the stolen goods from a thief, becomes thereby partaker of his guilt. John is a tJiief ; therefore whoever receives the stolen goods flx>m him becomes partaker of his guilt. X. ,S32 TEXl.B OOE OTLO QIC. ' 67. . Of two evils the less is to be preferred; therefore since ooca- sional turbulence is a less evil than a rigid despotism, it is to be preferred. 68. Jupiter was the son of Saturn; therefore the son of Jupiter was the grandson of Saturn. 69. Discord is a greater vice than intemperancej since discord al- ways implicates more than one person in its guilt. 70. Capitalists will use their money in giving employment to labor, only on condition that they can make money by doing so; and titey can make money by it only on condition they can sell the commod- ities that are produced by the labor; and they can sell these com- modities only on condition there are people able to buy them; and the people vrill be able to buy, only on condition that their own labor is sufficiently productive to leave them in possession of means to. buy with, after paying for those other things that must be , provided for first. Hence, it is not the an^ount of capital that is employed in trade,. but the productiveness of labor, that will determine the amount of trade in any community. j^^^ 71. That which excites a passion always precedes it. Insultvcx- cites anger; therefore it always precedes anger. 72. All our conceptions of existence are one kind or another of thought; therefore existence is thought. 73. If fire may be separated from flint, a property may be sepaT rated from its subject. But fire cannot be separated from ftint; therefore a property cannot be separated from its subject -74. If hatred and malice are contrary to the Divine law, they ought to be avoided. That they are so no one can deny; therefore they should be avoided. ■ 75 . If the penal laws against the Papists were enforced, they would be oppressed and wronged. But those laws are not enforced, and therefore they have nothing to complain of in the way of oppression or persecution. 76. If testimony to miracles is to be admitted, the miracles claimed for Mahomet are to be admitted. But as the narrative of those mir- acles is not to be Admitted, no testimony to miracles is to be ad- mitted. ■^ S . 77. If the exercise of war in defence of one's country were sinful, "it would have been forbidden in the Scripture, either expressly or by impUoation. But it is not so forbidden; therefore we may safely in- fer that defensive .wars are not sinful. APPENDIX. 233 78. If the fourth commandment is obligatory, we are indeed bound to set apart one day in seven. But no one supposes now that that commandment is obhgatory; hence there is no obligation to keep one day any more sacred than another. 79. The adoration of images is forbidden to Christians if the Mo- -saic law was designed, not for Israelites alone, but for all men. It was, however, designed for IsraeHtes alone; hence the adoration of images is not forbidden to Christians. 80. A wise lawgiver must either recognize the rewards and pun- ishments of a future state, or he must be able to appeal to a Provi- dence dispensing them in this life. Moses did not do the former, and therefore he must have done the latter. 81. The virtues are either passions, faculties, or habits. But they are not passions, for passions do not depend on previous determina-. tion; and they are not faculties, for faculties are possessed by nature; the virtues, therefore, are habits acquired by voluntary exertion and eflfort. 82. The early assignment of the Epistle to the Hebrews to St. Paul as its author, must have been either from its being really his, or from its professing to be his and containing his name. But it makes no claim to being his. Consequently, nothing but a knowl- edge of the fact that he wrote it could have led the early Christians to attribute it to him. 83. If every objection that can be urged would justify a chajige of estabUshed laws, no laws could reasonably be maintained. But some laws can be reasonably maintained ; therefore, no objection that can be urged will justify a change in estabUshed laws. 84. If any complete theory could be framed to expla,in the estab- lishment of Christianity by human causes, such a theory would have been propounded before this time. But no such theory has been proposed ; therefore, we may conclude that no such theory can be devised. 85. If a man is ignorant he should consult others as a means of VnalHTig up his deficiency in knowledge. If he is wise, yet two heads for counsel are better than one ; therefore, in all important matters one should take counsel with others. 86^ If one is superior to others he should be polite and gentle in his manners towards them, as a matter of Christian compassion and magnanimous condescension. If he is among equals he should be civil and courteous, since such a demeanor is as much their right 334 tmxt-hook of logic. from Mm as his right from them. And if he is among his superiors, he should show himseK courteous and civil, as being due to those having authority over us for the good of the whole. In any case, therefore, we are bound by the most sacred obligations to be civil and considerate of the feelings of others. 87. If the Government provides for these debts by imposition, it will become odious to the people and perish. If it does not provide for them, it wiU be overthrown by the most dangerous of all parties, I mean extensive discontent of the moneyed interest, 88. If I am under the chastening hand of God, and if there is no unrighteousness in Him, it must be that I am punished for my in- iquity. , 89. If expiatory sacrifices were divinely appointed before fhe - Mosaic law, they must have been expiatory not of ceremonial sin (for there could be- none then), but of moral sin. If so, the Levitical sac- rifices must have had no less eflBcacy. In that case 'the atonements under the Mosaic law would have ' made the comers thereunto per- fect, as pertaining to the conscience.' But this they could notac- oompUsh. Henoe we infer that expiatory sacrifices could not have been appointed before the Mosaic law. 90. If transportation is not felt as a severe punishment, it is in it- self iU-suited to the prevention of crime : if it is so felt, much of its severity is wasted, from its taking place at too great a distance to af- fect the feeUngs, or even come to the knowledge, of most of those whom it is designed to deter ; but one or other of these must be the case : therefore, transportation is not calculated to answer the pur- pose of preventing crime. 91 . When the observance of the first day of the week, as a reHgious festival in commemoration of Christ's resurrection, was first intro- duced, it must have been a novelty : when it was a novelty, it must have attracted notice : when it attracted notice, it would lead to in- quiry respecting the truth of the resurrection : when it led to this inquiry, it must have exposed the story-as an imposture, supposing it not attested by living witnesses : therefore when the observance of the first day of the week, &c., was first introduced, it must have ex- posed as an imposture the story of the resurrection, supposing it not attested by living witnesses. 92. If the prophecies of the Old Testament had been written with- out knqwledge of the events of the time of Christ, they could not correspond with them exactly ; and if they had been forged by Chris- APPENDIX. 235 tians, they would not be preserved and acknowledged by the Jews : they are preserved and acknowledged by the Jews, and they corres- pond exactly with the events of the time of Christ ; therefore, they were neither written without knowledge of these events, nor were forged by Christians. 93. Now "if Christ be preached that He rose from the dead, how say some among you that there is no resiirrection from the dead ? But if there be no resurrection of the dead then is Christ not risen ; and if Christ is not risen then is our preaching vain, and your fiiith is also vain. Yea, and we are found felse witnesses against Grod, because we have testified of God that He raised up Christ whom he raised not up, if so be that the dead rise not. For if the dead rise not, then is not Christ raised ; and if Christ be not raised your faith is vain, ye are yet in your sins. Then they also which are fallen asleep in Christ are perished. ESAMPIiES IN DrOHON. 94. The end of a true soldier's life is the welfare of his country : but death is ih& end of a soldier's life ; therefore, his death is requisite to the safety and welfore of his coontry. 95. Time is sufScient far all things : a day in summer is time ; there- fore, a single summar'^ day is sofScieut for all things. 96. The fish inclosed in the net were an indiscriminate mixture of all kinds ; those that wesre set aside and saved as valuable, were fish that had been inclosed in the net ; therefor^ fish of all kinds were set aside and saved as valuable. 97. No man can possess the powei to perform am impossibility. But a miracle is an impossibility ; therefore, no man can work a miracle. ,98. This team is used every day in the week. B^nt Sunday is a day in the week ; thexefore, this team is used on Sunday. 99. To kill a man is a crime. A hurglstr breaking into ft house is a man ; therefore, to kiH a burglao: wheiu breaking into your house, is a crime. J.0O. The prindples of justice are variable : the appointments of na- ture are invariable : therefore, the principles of justice are no ap- pointment of nature^ 336 TEXT-BOOK OF LOGIO. 101. Labor will overcome all obstacles ; agriculture is labor, there- fore, agriculture will overcome all obstacles. 102. A story is not to be believed, the reporters of which give contra- dictory accounts of it ; the story of the life and exploits of Bonaparte is of this description : therefore, it is not to be believed. 103. Nothing which is of less frequent occurrence than the falsity of testimony, can be fairly established by testimony ; any extraordin- ary and unusual fact is a thing of less frequent occurrence than the falsity of testimony (that being very common) : therefore, no extra- ordinary and unusual fact can be fairly estabhshed by testimony. 104. Testimony is a kind of evidence which is very likely to be false ; the evidence on which most men believe that there are pyra- mids in Egypt is testimony : therefore, the evidence on which most men believe that there are pyramids in Egypt is very likely to be false. 105. God made our first parents ; but our first parents were sinners, therefore, God made sinners. 106. He who cannot possibly act otherwise than he does, has neither merit nor demerit in his action. A. liberal and benevolent man in relieving the sufferings of the poor cannot do otherwise than relieve them : therefore, there is no merit in his actions. 107. Madame De Stael says that genius is of no sex : but Madame De Stael was a genius ; therefore, she was of no sex. {\'^'\'^' 108. Whatever intoxicates is forbidden by the principles of morality . But wine, cider and ale intoxicate ; therefore; their Tise is forbidden by the principles of morahty. 109. Every poor clergyman is deserving of the gratitude and sym- pathy of aU good men for the sacrifices he is. making in the cause of reUgiou and morality. But every clergyman who entirely neglects his duty is a poor clergyman ; therefore, every clergyman entirely neg- lecting his duty is deserving of the gratitude and sympathy of aU goodmen. '--.^-■, ",, ^^, CN^ vv.cX .■- CA.v.^ 110. A young lady that receives-^fts and other tokens of affection from a married man is disgraced thereby. Her father is a married man ; therefore, the young lady that leceives gifts, etc., &om her father is disgraced. N^sifa^^.j.-C-^— ■ -«!^ 0,piVv.cl^ . ' 111. Christ died for sinners only ; but all that are now or ever will Jje in heaven are among those for whom Christ died ; therefore, those now in heaven or hereafter to be there are sinners. APPENDIX. 237 112. The water that falls on the mountains and hills, either runs down the sides or soaks into the ground and forms subterranean res- ervoirs and then appearing as springs and forming brooks and riv- ulets, finds its way to larger streams and then into the ocean. But the water that falls on the mountains and hill-tops is for the most part snow and ice ; therefore, that Which forms the rivers and runs into the ocean is for the most part snow and ice. 113. The cause of evil is itself an evil. But that Chiistiaiiity has caused much evU in the shape of wars, opjttession, imposture, fanat- icism and persecution cannot be denied. 114. "Property is a creation of law." Horses are property ; there- fore, horses are a creation of law. 115. He who has a confirmed habit of any kind of action, exercises no self-denial in the practice of that action : a good man has a con- firmed habit of virtue ; therefore, he'Swho exercises self-denial in the practice of virtue is not a good man. 116. He is the greatest lover of any one who seeks that person's greatest good : a virtuous man seeks the greatest good for himself ; therefore, a virtuous man is' the greatest lover of himself. V^ 117. A building is not a nuisance ; but a pig-pen is a building, there- ' ' fore, a pig-pen is not a nuisance. 118. A protective tariff is a measure designed to promote the in- terests of domestic industry : the advocates of free trade oppose a protective tariff ; therefore, the advocates of free trade oppose the. interests of domestic economy. 119. Theft is a crime : theft was encouraged by the laws of Sparta ; therefore, the laws of Sparta encouraged crime. 120. No evil should be allowed that good may come of it. But all punishment is an evil ; therefore, no punishment should be allowed. 121. Repentance is a 'good thing. But no persons have so much repentance as the wicked ; therefore, none have so much good as the y/ioked. 122. He who bears armS at the command of the magistrate does what is lawful for a Christian. The Svriss in the French service, and the British in the American service bore arms at the command of the magistrate ; therefore, they were doing only what was lawful for a ChristiaJi to do. -123.- He who caUs you a man speaks the truth ; but he that call* you a knave calls you a, man ;- therefore, he who calls you a knave speaks the truth. 238 TEXT-BOOK OF LOGIC. 124. All the material objects within the reach of the earth's attrac- tion tend downwards towards the earth . But smoke is a material object; therefore smoke tends downwards. 125. Washington, Adams, Jefferson and Madison went out of the office at the age of sixty-six. But Washington, Adams, etc. , were Presidents of the United States ;„therefore the Presidents ol the Uni- ted States go out of office at the age' of sixty-six. 126. These are all good men and true and have been so pronounced by the court every one of them. But of these men some are known to be profane swearers, others are occasionally intoxicated, one or two Uve in adulteiy, and one at least has been engaged in rebellion against his country; therefore it is possible for men to be profane, intemperate, hcentious or even rebels and yet be good and true men. 127. A monopoly of the sugar-refining business is beneficial to sugar-refiners; and of the corn-trade to corn-growers; and of the silk-manufacture to silk-weavers ; etc ., etc . ; and thus each class of men are benefitted by some restrictions. Now all these classes of men make up the whole community; therefore a system of restric- tions is beneficial to the community. 128. I cut this cane from an orange tree in Florida. But what I cut in Florida was a mere rough crooked branch of a tree; therefore this cane is but a rough, crooked stick . 129. What we wear upon our backs once grew upon the backs of sheep. But mere unspun and unwashed wool is all that grows up- on the backs of sheep; therefore what we are wearing is merely unspun wool. 130. No man ever died on Thursday who was not aUye the preced- ing Wednesday; therefore their living on Wednesday was the cause of their dying on the Thursday following. No man should hve through Wednesday; it is dangerous. 131. Animal food may be entirely dispensed with (as is shown by the practice of the Brahmins and of some monks) ; and vegetable food may be entirely dispensed with (as is plain from the example of the Esquimaux and others). But all food consists of animal food and vegetable food; therefore all food may be dispensed with. 132. The Eepubhcans as a general thing advocate a Protective Tariff. But a Protective Tariff is inseparable from high prices: there- fore the Bepublican party are in favor of high prices. APPENDIX. 239 133. The Demporats are in favor of Free Trade. But Free Trade reduces the wages of labor and increases the inequality between the rich and the poor; therefore the Democrats are in favor of increasing the difference between the rich and poor, making the rich richer and the poor poorer. 134. The papers say that insurgents against the Turkish govern- ment are Cretans. But " the Cretans are always liars;" therefore the papers say that the insurgents etc., are liars. 135. Grovemment is of divine institution. But the government is either a monarchy, an oligarchy or' a democracy; therefore either monarchy, oligarchy or democracy must be of divine institution and all other forms are contrary to the Divine Will. 136. Wine vdll intoxicate those that drink it. But Christians in the sacrament of the Lord's Supper drink wine; therefore Christians in practicing the Communion drink what will intoxicate them. 137. Love makes every sacrifice easy. A man's affection for him- self is love; therefore a man's affection for himself or self-love makes all sacrifices easy. 138. Monarchists (of this class) claim for kings a divine right to rule. But kings in ruling commit many crimes and outrages; there- fore such monarchists claim for kings, a divine right to do wrong. 139. Whatever is deposited at the bottom of lakes, seas etc., is soft mud. Limestone was deposited at the bottom of the sea; therefore limestone is mere soft mud. 140. Baron Rothschild was made a peer of England because he was rich. He became rich by lending money on interest; Kothschild was created a baron therefore for no other reason than that he had loaned money upon interest successfully. 141. The Constitution of the United States says that " the Senate shall have the sole power to try all impeachments." The tribunal that tried Andrew Johnson, however, was not "the Senate," butthe " High Court of Impeachment;" consequently the trial of Johnson was not in accordance with the Constitution of the United States. 142. St. Paul says " If I yet pleased men I should not be Jihe ser- vant of Christ." Wherefore regarding St. Paul as an inspired au- thority we may infer that whoever pleases men or is popular with his fellow-men and in his own age and community is not a true and accepted servant of Christ. 143. The Bible teaches that servants shall obey their masters in all 340 TEXT-BOOK -OF LOGIO. things, sincerely and from the heart not with mere eye service as meu-pleasers. And this is equivalent to telling them to do whatever their masters direct or command them to do. But in some cases the masters direct th^r servants to commit crimes and do very wicked things ; therefore the Bible teaches the servants in these cases to com- mit crimes etc. 44. The Constitution of the United States protects every citizen of the United States in those rights of person and property which the State in which he may happen to live secures to him by its laws. But the laws of some of the States secure to certain of its citizens the complete enslavement of one class of its population; therefore the Constitution of the United States protects the institution 6i sla- very and guarantees to the slaveholder his rights of property in his . slaves. 145. In the winter of 1867 Congress passed a law regulating the land and naval forces of United States which the President disap- proved and vetoed. It was, however, passed over his veto and sub- sequently issued as an 6rder to the officers of thearmy and navy, the order being endorsed by the President with the usual word " ap- proved." Afterwards on the trial of his impeachment counsel argued from this that he had "approved " tte law and was therefore estopped by his own act from afterwards treating it as unconstitu- tional. ,. ' ''