COPYRIGHT DEPOSIT » I THE ART OF LOGICAL THINKING OR THE LAWS OF REASONING Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/artoflogicalthinOOatki THE ART OF LOGICAL THINKING OR THE LAWS OF REASONING By WILLIAM WALKER ATKINSON L. N. FOWLER & COMPANY 1, Imperial Arcade, Ludgate Circus London, E. C, EuKland 1909 THE PROGRESS COMPANY CHICAGO. ILL. 6^'^ Copyright 1909 By THE PROGRESS COMPANY Cliicago, 111., U. S. A. 5nj,Aa5 9i.os CONTENTS I. Reasoning 9 II. The Process of Reasoning 17 III. The Concept 25 IV, The Use of Concepts 37 V. Concepts and Images 48 VL Terms 56 VII. The Meaning of Terms 73 VIIL Judgments 82 IX. Propositions 90 X. Immediate Reasoning 99 XI. Inductive Reasoning 107 XII. Reasoning by Induction 116 XIII. Theory and Hypotheses 125 XIV. Making and Testing Hypotheses 132 XV. Deductive Reasoning 144 XVL The Syllogism 156 XVII. Varieties of Syllogisms 167 XVIII. Reasoning by Analogy 179 XIX. FaUacies 186 CHAPTER I. REASONING '* Reasoning^ ^ is defined as: *^The act, process or art of exercising the faculty of rea- son ; the act or f actdty of employing reason in argument; argumentation, ratiocination; rea- soning power ; disputation, discussion, argu- mentation.*^ Stewart says: ^*The word rea- son itself is far from being precise in its mean- ing. In common and popular discourse it de- notes that power by which we distinguish truth from falsehood, and right from wrong, and by which we are enabled to combine means for the attainment of particular ends. ' * By the employment of the reasoning facul- ties of the mind we compare objects presented to the mind as percepts or concepts, taking up the **raw materials'' of thought and weaving them into more complex and elaborate mental fabrics which we call abstract and general ideas of truth, Brooks says : ^ ' It is the think- ing power of the mind ; the faculty which gives us what has been called thought-knowledge, in 10 LoGicAii Thinking distinction from sense-knowledge. It may be regarded as the mental architect among the faculties ; it transforms the material furnished by the senses . . . into new products, and thus builds up the temples of science and phil- osophy. '^ The last-mentioned authority adds: ^^Its products are twofold, ideas and thoughts. An idea is a mental product which when ex- pressed in words does not give a proposition ; a thought is a mental product which embraces the relation of two or more ideas. The ideas of the understanding are of two general classes ; abstract ideas and general ideas. The thoughts are also of two general classes ; those pertaining to contingent truth and those per- taining to necessary truth. In contingent truth, we have facts, or immediate judgments, and general truths including laws and causes, derived from particular facts; in necessary truth we have axioms, or self-evident truths, and the truths derived from them by reason- ing, called theorems/'. In inviting you to consider the processes of reasoning, we are irresistibly reminded of the old story of one of Moliere's plays in which one of the characters expresses surprise on Reasonikg 11 learning that he ^ ' had been talking prose for forty years without knowing it. ' ' As Jevons says in mentioning this : ^ ' Ninety-nine people out of a hundred might be equally surprised on hearing that they had been converting propositions, syllogizing, falling into paralo- gisms, framing hypotheses and making classi- fications with genera and species. If asked whether they were logicians, they would prob- ably answer. No ! They would be partly right ; for I believe that a large number even of edu- cated persons have no clear idea of what logic is. Yet, in a certain way, every one must have been a logician since he began to speak.'' So, in asking you to consider the processes of reasoning we are not assuming that you never have reasoned— on the contrary we are fully aware that you in connection with every other person, have reasoned all your mature life. That is not the question. While every- one reasons, the fact is equally true that the majority of persons reason incorrectly. Many persons reason along lines far from correct and scientific, and suffer therefor and thereby. Some writers have claimed that the majority of persons are incapable of even fairly correct 12 Logical Thinking reasoning, pointing to the absurd ideas enter- tained by the masses of people as a proof of the statement These writers are probably a little radical in their views and statements, but one is often struck with wonder at the evidences of incapacity for interpreting facts and impressions on the part of the general public. The masses of people accept the most absurd ideas as truth, providing they are gravely asserted by some one claiming author- ity. The most illogical ideas are accepted wjithout dispute or examination, providing they are stated solemnly and authoritatively. Particularly in the respective fields of relig- ion and politics do we find this blind accept- ance of illogical ideas by the multitude. Mere assertion by the leaders seems sufficient for the multitude of followers to acquiesce. In order to reason correctly it is not merely necessary to have a good intellect. An athlete may have the proper proportions, good frame- work, and symmetrical muscles, but he can- not expect to oope with others of his kind un- less he has learned to develop those muscles and to use them to the best advantage. And, in the same way, the man who wishes to reason Rbasonikg 13 correctly must develop his intellectual facul- ties and must also learn the art of using them to the best advantage. Otherwise he will w-aste his mental energy and will be placed at a disadvantage when confronted with a trained logician in argument or debate. One who has witnessed a debate or argument be- tween two men equally strong intellectually, one of whom is a trained logician and the other lacking this advantage, will never forget the impression produced upon hitn by the unequal struggle. The conflict is like that of a power- ful wrestler, untrained in the little tricks and turns of the science, in the various principles of applying force in a certain way at a certain time, at a certain place, with a trained and ex- perienced wrestler. Or of a conflict between a muscular giant untrained in the art of box- ing, when confronted with a trained and ex- perienoed exponent of **the manly art.'* The result of any such conflict is assured in ad- vance. Therefore, everyone should refuse to rest content without a knowledge of the art of reasoning correctly, for otherwise he places himself under a heavy handicap in the race for success, and allows others, perhaps less 14 Logical Thinking well-equipped mentally, to have a decided ad- vantage over him. Jevons says in this connection: *^To be a good logician is, however, far more valuable than to be a good athlete ; because logic teaches us to reason well, and reasoning gives us knowledge, and knowledge, as Lord Bacon said, is power. As athletes, men cannot for a moment compare with horses or tigers or monkeys. Yet, with the power of knowledge, men tame horses and shoot tigers and despise monkeys. The weakest framework with the most logical mind will conquer in the end; be- cause it is easy to foresee the future, to cal- culate the result of actions, to avoid mis- takes which might be fatal, and to discover the means of doing things which seemed impos- sible. If such little creatures as ants had bet- ter brains than men, they would either destroy men or make them into slaves. It is true that we cannot use our eyes and ears without geting some kind of knowledge, and the brute animals can do the same. But what gives power is the deeper knowledge called Science. People may see, and hear, and feel all their lives without really learning the na- Reasoning 15 ture of things they see. But reason is the mind's eye, and enables us to see why things are, and when and how events may be made to happen or not to happen. The logician en- deavors to learn exactly what this reason is which makes the power of men. We all, as I have said, must reason well or ill, but logic is the science of reasoning and enables us to dis- tinguish between the good reasoning which leads to truth, and the bad reasoning which every day betrays people into error and mis- fortune. '^ In this volume we hope to be able to point out the methods and principles of correctly using the reasoning faculties of the mind, in a plain, simple manner, devoid of useless tech- nicalities and academic discussion. We shall adhere, in the main, to the principles estab- lished by the best of the authorities of the old school of psychology, blending the same with those advanced by the best authorities of the New Psychology. No attempt to make of this book a school text-book shall be made, for our sole object and aim is to bring this important subject before the general public composed of 16 Logical Thinking people who have neither the time nor inclina- tion to indulge in technical discussion nor academic hair-splitting, but who desire to un- derstand the underlying working principles of the Laws of Reasoning. CHAPTER IL THE PKOCESS OF REASONING k The processes of Eeasoning may be said to comprise four general stages or steps, as follows : L Abstraction, by wMcb is meant the proc- ess of drawing off and setting aside from an object, person or thing, a quality or attribute, and making of it a distinct object of thought. For instance, if I perceive in a lion the quality of strength, and am able to think of this qual- ity abstractly and independently of the animal —if the term strength has an actual mental meaning to me, independent of the lion— then I have abstracted that quality; the thinking thereof is an act of abstraction; and the thought-idea itself is an abstract idea. Some writers hold that these abstract ideas are real- ities, and ^^not mere figments of fancy." As Brooks says : ^ ^ The rose dies, but my idea of its color and fragrance remains." Other au- thorities regard Abstraction as but an act of attention concentrated upon but the particu- 17 18 Logical Thinking lar quality to the exclusion of others, and that the abstract idea has no existence apart from the general idea of the object in which it is included. Sir William Hamilton says: ^^We can rivet our attention on some particular mode of a thing, as its smell, its color, its fig- ure, its size, etc., and abstract it from the oth- ers. This may be called Modal Abstraction. The abstraction we have now been considering is performed on individual objects, and is con- sequently particular. There is nothing neces- sarily connected with generalization in ab- straction ; generalization is indeed dependent on abstraction, which it supposes; but ab- straction does not involve generalization.'' II. Generalization^ by which is meant the process of forming Concepts or General Idea. It acts in the direction of apprehending the common qualities of objects, persons and things, and combining and imiting them into a single notion or conception which will com- prehend and include them all. A General Idea or Concept differs from a particular idea in that it includes within itself the qualities of the particular and other particulars, and ac- cordingly may be applied to any one of these Process of Eeasoning 19 particulars as well as to the general class. For instance, one may have a particular idea of some particular horse, which applies only to that particular horse. He may also have a General Idea of horse, in the generic or class sense, which idea applies not only to the gen- eral class of horse but also to each and every horse which is included in that class. The ex- pression of Generalization or Conception is called a Concept. III. Judgment, by which is meant the proc- ess of comparing two objects, persons or things, one with another, and thus perceiving their agreement or disagreement. Thus we may compare the two concepts horse and ani- mal, and perceiving a certain agreement be- tween them we form the judgment that: *^A horse is an animal ;^^ or comparing horse and cow, and perceiving their disagreement, we form the judgment: ^^A horse is not a cow/^ The expression of a judgment is called a Proposition. IV. Reasoning, by which is meant the process of comparing two objects, persons or things, through their relation to a third object, person or thing. Thus we may reason (a) 20 Logical Thinking thai all mammals are animals; (b) that a horse is a mammal; (c) that, therefore^ a horse is an animal ; the result of the reasoning being the statement that: ^^A horse is an animal. ' ' The most fundamental principle of reasoning, therefore, consists in the compar- ing of two objects of thought through and by means of their relation to a third object. The natural form, of expression of this process of Reasoning is called a Syllogism. It will be seen that these four processes of reasoning necessitate the employment of the processes of Analysis and Synthesis, respect- ively. Analysis means a separating of an object of thought into its constituent parts, qualities or relations. Synthesis means the combining of the qualities, parts or relations of an object of thought into a composite whole. These two processes are found in all processes of Eeasoning. Abstraction is principally analytic ; 6'eneralization or Conception chiefly synthetic; Judgment is either or both analytic or synthetic ; Eeasoning is *^ either a synthesis of particulars in Induction, or an evolution of the particular from the general in Deduc- tion. Process of Reasoning 21 There are two great classes of Reasoning; viz., (1) Inductive Reasoning, or the infer- ence of general truths from particular truths ; and (2) Deductive Reasoning, or the infer- ence of particular truths from general truths. Inductive Reasoning proceeds by discover- ing a general truth from particular truths. For instance, from the particular truths that individual men die we discover the general truth that **A11 men must die;'' or from ob- serving that in all observed instances ice melts at a certain temperature, we may infer that ** All ice melts at a certain temperature.'' Inductive Reasoning proceeds from the known to the unknown. It is essentially a synthetic process. It seeks to discover gen- eral laws from particular facts. Deductive Reasoning proceeds by discover- ing particular truths from general truths. Thus we reason that as all men die, John Smith, being a man, must die ; or, that as all ice melts at a certain temperature, it f oUows that the particular piece of ice under consid- eration will melt at that certain temperature. Deductive Reasoning is therefore seen to be essentially an analytical process. 22 Logical Thinking Mills says of Inductive Eeasoning: ^^The inductive method of the ancients consisted in ascribing the character of general truths to all propositions which are true in all the instances of which we have knowledge. Bacon exposed the insufficiency of this method, and physical investigation has now far outgrown the Ba- conian conception. . . . Induction, then, is that operation by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, induction is the process by which we conclude that what is true of certain in- dividuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times. '^ Eegarding Deductive Eeasoning, a writer says: *^ Deductive Eeasoning is that process of reasoning by which we arrive at the neces- sary consequences, starting from admitted or established premises.^ ^ Brooks says: **The general truths from which we reason to par- ticulars are derived from several distinct sources. Some are intuitive, as the axioms of mathematics or logic. Some of them are Pkocess of Reasoning 23 derived from induction. . . . Some of them are merely hypothetical, as in the in- vestigation of the physical sciences. Many of the hypotheses and theories of the physical sciences are used as general truth for de- ductive reasoning; as the theory of gravita- tion, the theory of light ; etc. Eeasoning from the theory of universal gravitation, Leverrier discovered the position of a new planet in the heavens before it had been discovered by human eyes.'' Halleck points out the interdependence of Inductive and Deductive Eeasoning in the following words: ^*Man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. By induction we ex- amine what seems to us a sufficient number of individual cases. We then conclude that the rest of these cases, which we have not exam- ined, will obey the same general laws. . . . The premise, ^ All cows chew the cud,' was laid down after a certain nrnnber of cows had been examined. If we were to see a cow twenty years hence, we should expect that she chewed her cud. . . . After Induction has classi- 24 LoGiCAii Thinking fied certain phenomena and tlvus given us a major premise, we proceed deductively to ap- ply the inference to any new specimen that can be shown to belong to that class.'' The several steps of Deductive Eeasoning shall now be considered in turn as we proceed. CHAPTER III. THE CONCEPT In considering the process of thinking, we must classify the several steps or stages of thought that we may examine each in detail for the purpose of comprehending them com- bined as a whole. In actual thinking these several steps or stages are not clearly sep- arated in consciousness, so that each stands out clear and distinct from the preceding and succeeding steps or stages, but, on the con- trary, they blend and shade into each other so that it is often difficult to draw a clear di- viding line. The first step or stage in the process of thinking is that which is called a concept. A concept is a mental representation of anything. Prof. Wm. James says: ^^The function by which we mark off, discriminate, draw a line around, and identify a numerically distinct subject of discourse is called concep- tion.^^ There are five stages or steps in each concept, as follows : 25 26 Logical. Thinking I. Presentation. Before a concept may be formed there must first be a presentation of the material from which the concept is to be formed. If we wish to form the concept, animaly we must first have perceived an ani- mal, probably several kinds of animals— horses, dogs, cats, cows, pigs, lions, tigers, etc. We must also have received impressions from the sight of these animals which may be reproduced by the memory— represented to the mind. In order that we may have a full concept of animal we should have perceived every kind of animal, for otherwise there would be some elements of the full concept lacking. Accordingly it is practically impossi- ble to have a full concept of anything. The greater the opportunities for perception the greater will be the opportunity for concep- tion. In other books of this series we have spoken of the value and importance of the at- tention and of clear and full perception. With- out an active employment of the attention, it is impossible to receive a clear perception of anything; and unless the perception has been clear, it is impossible for the mind to form a clear concept of the thing perceived. As Sir The Concept 27 Wm. Hamilton has said: ^^An act of atten- tion, tliat is an act of concentration, seems thus necessary to every exertion of conscious- ness, as a certain contraction of the pupil is requisite to every exertion of vision. • . . Attention, then, is to consciousness what the contraction of the pupil is to sight, or to the eye of the mind what the microscope or tele- scope is to the bodily eye. ... It consti- tutes the half of all intellectual power. ' ' And Sir B. Brodie said: ^^It is attention, much more than in the abstract power of reasoning, which constitutes the vast difference which exists between minds of different individ- uals. ' ' And as Dr. Beattie says : ^ * The force with which anything strikes the mind is gen- erally in proportion to the degree of attention bestowed upon it. ^ ' II. Comparison. Following the stage of Presentation is the stage of Comparison. We separate our general concept of animal into a number of sub-concepts, or concepts of var- ious kinds of animals. We compare the pig with the goat, the cow with the horse, in fact each animal with all other animals known to us. By this process we distinguish the points 28 Logical Thinking of resemblance and the points of difference. We perceive that the wolf resembles the dog to a considerable degree; that it has some points of resemblance to the fox; and a still less distinct resemblance to the bear; also that it differs materially from the horse, the cow or the elephant. We also learn that there are various kinds of wolves, all bearing a great resemblance to each other, and yet hav- ing marked points of difference. The closer we observe the various individuals among the wolves, the more points of difference do we find. The faculty of Comparison evidences itself in inductive reasoning; ability and dis- position to analyze, classify, compare, etc. Fowler says that those in whom it is largely developed ^^Eeason clearly and correctly from conclusions and scientific facts up to the laws which govern them ; discern the known from the unknown; detect error by its incongruity with facts ; have an excellent talent for com- paring, explaining, expounding, criticising, exposing, etc.'' Prof. William James says: **Any personal or practical interest in the results to be obtained by distinguishing, makes one's wits amazingly sharp to detect The Concept 29 differences. And long training and practice in distinguishing has the same effect as per- sonal interest. Bioth of these agencies give to small amounts of objective difference the same effectiveness upon the mind that, under other circumstances, only large ones would make.'' in. Abstraction. Following the stage of Comparison is that of Abstraction. The term ^^Abstraction'' as used in psychology means: ^^The act or process of separating from the numerous qualities inherent in any object, the particular one which we wish to make the sub- ject of observation and reflection. Or, the act of withdrawing the consciousness from a num- ber of objects with a view to concentrate it on some particular one. The negative act of which Attention is the positive. ' ' To abstract is ^ ^ to separate or set apart. ' ' In the process of Abstraction in our consideration of ani- malsy after having recognized the various points of difference and resemblance between the various species and individuals, we pro- ceed to consider some special quality of ani- mals, and, in doing so, we abstract^ set aside, or separate the particular quality which we 30 Logical Thinking wish to consider. If we wish to consider the size of animals, we abstract the quality of size from the other qualities, and consider animals with reference to size alone. Thus we consider the various degrees of size of the various animals, classifying them accord- ingly. In the same way we may abstract the quality of shape, color or habits, respectively, setting aside this quality for special observa- tion and classification. If we wish to study, examine or consider certain qualities in a thing we abstract that particular quality from the other qualities of the thing; or we abstract the other qualities until nothing is left but the particular quality under consideration. In examining or considering a class or num- ber of things, we first abstract the qualities possessed in common by the class or number of things; and also al)stract or set aside the qualities not comnwn to them. For instance ; in considering classes of ani- mals, we abstract the combined quality of milk-giving and pouch-possessing which is possessed in common by a number of animals ; then we group these several animals in a class which we name the Marsupialiaj of which the The Concept 31 opossum and kangaroo are members. In these animals the young are brought forth in an imperfect condition, undeveloped in size and condition, and are then kept in the pouch and nourished until they are able to care for themselves. Likewise, we may abstract the idea of the placenta^ the appendage which connects the young unborn animal with the mother, and by means of which the foetus is nourished. The animals distinguished by this quality are grouped together as the Placental Mammals. The Placental Mammals are di- vided into various groups, by an Abstraction of qualities or class resemblance or difference, as follows: The Edentata, or toothless creatures, such as the sloths, ant-eaters, arm- adillos, etc. ; the Sirenia, so-named from their fancied resemblance to the fabled^* sirens,'^ among which class are the sea-cows, manatees, dugongs, etc.; the Cetacea, or whale family, which although fish-like in appearance, are really mammals, giving birth to living young which they nourish with breast-milk, among which are the whales, porpoises, dolphins, etc.; the Ungulata, or hoofed animals, such as the horse, the tapir, the rhinoceros, the 32 Logical Thinking swine, the hippopotamus, the camel, the deer, the sheep, the cow, etc. ; the Eyracoidea, hav- ing teeth resembling both the hoofed animals and the gnawing animals, of which the coney or rock-rabbit is the principal example; the Proboscidea, or trunked animals, which fam- ily is represented by the various families of elephants; the Carnivora, or flesh-eaters, represented by various sub-families and species ; the Rodentia, or gnawers ; the Insect- ivora, or insect feeders; the Cheiroptera, or finger-winged; the Lemuroidea, or lemurs, having the general appearance of the monkey, but also the long bushy tail of the fox; the Primates^ including the monkeys, baboons, man-apes, gibbons, gorillas, chimpanzees, orang-outangs and Man. In all of these cases you will see that each class or general family possesses a certain common quality\^]\\Qh. gives it its classifica- tion, and which quality is the subject of the Abstraction in considering the particular group of animals. Further and closer Ab- straction divides these classes into sub- classes; for instance, the family or class of the Carnivora, or flesh-eaters, may be di- The Concept 33 vided by further Abstraction into the classes of seals, bears, weasels, wolves, dogs, lions, tigers, leopards, etc. In this process, we must first make the more general Abstraction of the wolf and similar animals into the dog- family; and the lion, tiger and similar forms into the cat-family. Halleck says of Abstraction : ^ ^ In the proc- ess of Abstraction, we draw our attention away from a mass of confusing details, unim- portant at the time, and attend only to quali- ties common to the class. Abstraction is little else than centering the power of attention on some qualities to the exclusion of others. '' IV. Generalization. Arising from the stage of Abstraction is the stage of General- ization. Generalization is : ^ ' The act or proc- ess of generalizing or making general ; bring- ing several objects agreeing in some point under a common or general name, head or class ; an extending from particulars to gen- erals; reducing or arranging in a genus; bringing a particular fact or series of facts into a relation with a wider circle of facts.'' As Bolingbroke says: *^The mind, therefore, makes its utmost endeavors to generalize its 34 Logical Thinking ideas, beginning early with such as are most familiar and coming in time to those which are less so.'* Under the head of Abstraction we have seen that through Abstraction we may Generalize the various species into the var- ious families, and thus, in turn, into the vari- ous sub-families. Following the same process we may narrow down the sub-families into species composed of various individuals; or into greater and still greater families or groups. Generalization is really the act of Classification, or forming into classes all things having certain qualities or properties in common. The corollary is that all things in a certain generalized class must possess the particular quality or property common to the class. Thus we know that all animals in the class of the Carnivora must eat flesh ; and that all Mammals possess breasts from which they feed their young. As Halleck says: ^*We put all objects having like qualities into a cer- tain genus, or class. When the objects are in that class, we know that certain qualities will have a general application to them alV^ V. Denomination. Following closely upon the step of Generalization or Classification, The Concept 35 is the step of Denomination. By Denomina- tion we mean ^Hhe act of naming or designat- ing by a name.'' A name is the symbol by which we think of a familiar thing without the necessity for making a distinct mental image upon each occasion of thought. Or, it may be considered as akin to a label affixed to a thing. As in the case of the algebraic symbols, a, b, c, X, and 2/, by the use of which we are able to make intricate calculations easily and rapidly, so may we use these word symbols much more readily than we could the lengthy descriptions or even the mental images of the thing sym- bolized. It is much easier for us to think ''horse^^ than it would be to think the full definition of that animal, or to think of it by recalling a mental picture of the horse each time we wished to think of it. Or, it is much better for us to be able to glance at a label on a package or bottle than to examine the con- tents in detail. As Hobbes says: *^A word taken at pleasure to serve for a mark, which may raise in our minds a thought like to some thought we had before, and which being pro- nounced to others, may be to them a sign of what thought the speaker had or had not. 36 Logical Thinking before in his mind.'' Mill says: **A name is a word (or set of words) serving the double purpose of a mark to recall to our- selves the likeness of a former thought and as a sign to make it known to others." Some philosophers regard names as symbols of our ideas of things, rather than of the things themselves; others regard them as symbols of the things themselves. It will be seen that the value of a name depends materially upon the correct meaning and understanding re- garding it possessed by the person using it. CHAPTER IV. THE USE OF CONCEPTS Having observed the several steps or stages of a concept, let ns now consider the use and misuse of the latter. At first glance it would appear difficult to misuse a concept, but a little consideration will show that people very com- monly fall into error regarding their concepts. For instance, a child perceives a horse, a cow or a sheep and hears its elders apply the term ^'ammaV^ to it. This term is perfectly correct, although symbolizing only a very gen- eral classification or generalization. But, the child knowing nothing of the more limited and detailed classification begins to generalize re- garding the animal. To it, accordingly, an ' * animal" is identical with the dog or the cow, the sheep or the horse, as the case may be, and when the term is used the child thinks that all animals are similar to the particular an- imal seen. Later on, when it hears the term ** animal '^ applied to a totally different look- ing creature, it thinks that a mistake has been 37 38 Logical Thinking made and a state of confusion occurs. Or, even when a term is applied within narrower limits, the same trouble occurs. The child may hear the term ^ * dog' ^ applied to a mastiff, and it accordingly forms a concept of dog identical with the qualities and attributes of the mastiff. Later, hearing the same term applied to a toy-terrier, it becomes indignant and cries out that the latter is no ^^dog" but is something entirely different. It is not until the child becomes acquainted with the fact that there are many kinds of creatures in the general category of ^^dog'' that the latter term becomes fully understood and its ap- propriate concept is intelligently formed. Thus we see the importance of the step of Pre- sentation. In the same way the child might imagine that because some particular ^^man^' had red hair and long whiskers, all men were red- haired and long-whiskered. Such a child would always form the concept of **man'' as a creature possessed of the personal qualities just mentioned. As a writer once said, read- ers of current French literature might imag- ine that all Englishmen were short, dumpy, Use of Coitcepts 39 red-cheeked and irascible, and that all Eng- lishwomen had great teeth and enormous feet ; also that readers of English literature might imagine that all Frenchmen were like mon- keys, and all Frenchwomen were sad co- quettes. In the same way many American young people believe that all Englishmen say ^* Don't you know" and all Englishwomen constantly ejaculate: ** Fancy!'* Also that every Englishman wears a monocle. In the same way, the young English person, from reading the cheap novels of his own country, might well form the concept of all Americans as long-legged, chin-whiskered and big-nosed, saying ' ' Waal, I want to know ; " ^ ^ I reckon ; ' ' and ^^Du tell;" while they tilted themselves back in a chair with their feet on the mantel- piece. The concept of a Western man, enter- tained by the average Eastern person who has never traveled further West than Buffalo, is equally amusing. In the same way, we have known Western people who formed a concept of Boston people as partaking of a steady and continuous diet of baked beans and studiously reading Browning and Emerson between these meals. 40 Logical Thinking Halleck says : *^ A certain Norwegian child ten years old had the quality white firmly im- bedded in his concept man. Happening one day to see a negro for the first time, the child refused to call him a man until the negro's other qualities compelled the child to revise his concept and to eliminate whiteness. If that child should ever see an Indian or a Chinaman, the concept would undergo still further revision. A girl of six, reared with an intemperate father and brothers, had the quality of drunkenness firmly fixed in her con- cept of man. A certain boy kept, until the age of eleven, trustworthiness in his concept of man. Another boy, until late in his teens thought that man was a creature who did wrong not from determination but from ignor- ance, that any man would change his course to the right path if he could but understand that he was going wrong. Happening one day to hear of a wealthy man who was neglect- ing to provide comforts for his aged mother in her last sickness, the boy concluded that the man did not know his mother's condition. When he informed the man, the boy was told to mind his own business. The same day he Use of Concepts 41 heard of some politicians who had intention- ally cheated the city in letting a contract and he immediately revised his concept. It must be borne in mind that most of our concepts are subject to change during our entire life; that at first they are made only in a tentative way; that experience may show us, at any time, that they have been erroneously formed, that we have, abstracted too little or too much, made this class too wide or too narrow, or that here a quality must be added or there one taken away/' Let us now consider the mental processes involved in the formation and use of a con- cept. We have first, as we have seen, the presentation of the crude material from which the concept must be formed. Our attention being attracted to or directed toward an ob- ject, we notice its qualities and properties. Then we begin a process of comparison of the object perceived or of our perception of it. We compare the object with other objects or ideas in our mind, noting similarities and dif- ferences and thereby leading towards classifi- cation with similar objects and opposed dis- similar ones. The greater the range of other 42 Logical Thinking objects previously perceived, the greater will be the number of relations established between the new object or idea and others. As we ad- vance in experience and knowledge, the web of related objects and ideas becomes more intricate and complex. The relations attach- ing to the child's concept of horse is very much simpler than the concept of the experi- enced adult. Then we pass on to the step of analysis, in which we separate the qualities of the object and consider them in detail. The act of abstraction is an analytical process. Then we pass on to the step of synthesis, in which we unite the materials gathered by comparison and analysis, and thus form a general idea or concept regarding the object. In this process we combine the various quali- ties discerned by comparison and analysis, and grouping them together as in a bundle, we tie them together with the string of synthesis and thus have a true general conception. Thus from the first general conception of horse as a simple thing, we notice first that the animal has certain qualities lacking in other things and certain others similar to other things; then we analyze the various qualities of the Use of Concepts 43 horse, recognized through comparison, until we have a clear and distinct idea of the vari- ous parts, qualities and properties of the horse; then we synthesize, and joining to- gether these various conceptions of the said qualities, we at last form a clear general con- cept of the horse as he is, with all his qualities. Of course, if we later discover other qualities attached to the horse, we add these to our gen- eral synthesized concept— our concept of horse is enlarged. Of course these various steps in the forma- tion and use of a concept are not realized as distinct acts in the consciousness, for the proc- esses are largely instinctive and subcon- scious, particularly in the case of the ex- perienced individual. The subconscious, or habit mind, usually attends to these details for us, except in instances in which we deliber- ately apply the will to the task, as in cases of close study, in which we take the process from the region of the involuntary and place it in the voluntary category. So closely related and blended are these various steps of the process, that some authorities have disputed vigorously upon the question as to which of 44 Logical Thinking the two steps, comparison or analysis, pre- cedes the other. Some have claimed that an- alysis must precede comparison, else how could one compare without having first anal- yzed the things to be compared. Others hold that comparison must precede analysis, else how conld one note a quality xmless he had his attention drawn to it by its resem- blance to or difference from qualities in other objects. The truth seems to lie between the two ideas, for in some cases there seems to be a perception of some similarity or differ- ence before any analysis or abstraction takes place; while in others there seems to be an analysis or abstraction before comparison is possible. In this book we have followed the arrangement favored by the latest authori- ties, but the question is still an open one to many minds. As we have seen, the general concept once having been formed, the mind proceeds to classify the concept with others having gen- eral qualities in common. And, likewise, it proceeds to generalize from the classification, assuming certain qualities in certain classes. Then we proceed to make still further general- Use of Concepts 45 izations and classifications on an ascending and widening scale, including seeming resem- blances less marked, until finally we embrace the object with other objects in as large a class as possible as well as in as close and limited a sub-class as possible. As Brooks says: *' Generalization is an ascending proc- ess. The broader concept is regarded as higher than the narrower concept ; a concept is considered higher than a percept ; a general idea stands above a particular idea. We thus go up from particulars to generals ; from per- cepts to concepts; from lower concepts to higher concepts. Beginning down with par- ticular objects, we rise from them to the gen- eral idea of their class. Having formed a number of lower classes, we compare them as we did individuals and generalize them into higher classes. We perform the same proc- ess with these higher classes, and thus pro- ceed until we are at last arrested in the high- est class. Being. Having reached the pinna- cle of generalization, we may descend the ladder by reversing the process through which we ascend.^' From this process of generalization, or syn- 46 Logical Thinking thesis, we create from our simple concepts our general concepts. Some of the older au- thorities distinguished between these two classes by terming the former ^^conceptions," and reserving the term ^^ concepts '* for the general concepts. Brooks says of this : * ' The products of generalization are general ideas called concepts. We have already discussed the method of forming conceptions and now consider the nature of the concept itself. . . . A concept is a general idea. It is a general notion which has in it all that is com- mon to its own class. It is a general scheme which embraces all the individuals of the class while it resembles in all respects none of its class. Thus my conception of a quad- ruped has in it all four-footed animals, but it does not correspond in all respects to any par- ticular animals; my conception of a triangle embraces all triangles, but does not agree in details with any particular triangle. The general conception cannot be made to fit ex- actly any particular object, but it teems with many particulars. These points may be il- lustrated with the concepts horse, bird, color, animal, etc.'* Use of Concepts 47 So we may begin to perceive tbe distinction and difference between a concept and a mental image. This distinction, and the fact that a concept cannot be imaged j is generally diffi- cult for the beginner. It is important that one should have a clear and distinct under- standing regarding this point, and so we shall consider it further in the following chapter. CHAPTEE V. CONCEPTS AND IMAGES As we have said, a concept cannot be im- aged—cannot be used as the subject of a mental image. This statement is perplexing to the student who has been accustomed to the idea that every conception of the mind is cap- able of being reproduced in the form of a men- tal image. But the apparently paradoxical statement is seen as quite simple when a little consideration is given to it. For instance, you have a distinct general concept of animal. You know what you mean when you say or think, animal. You recog- nize an animal when you see one and you un- derstand what is meant when another uses the word in conversation. But you cannot form a meipital image of the concept, animal. Why? Because any mental image you might form would be either a picture of some par- ticular animal or else a composite of the quali- ties of several animals. Your concept is too broad and general to allow of a composite 48 Concepts and Images 49 picture of all animals. And, in truth, your concept is not a picture of anything that actu- ally exists in one particular, but an abstract idea embracing the qualities of all animals. It is like the algebraic x—a symbol for some- thing that exists, but not the thing itself. As Brooks says: ^^ A concept cannot be rep- resented by a concrete image. This is evi- dent from its being general rather than parti- cular. If its color, size or shape is fixed by an image, it is no longer general but particular. ' ' And Halleck says: '^It is impossible to image anything without giving that image individual marks. The best mental images are so defi- nite that a picture could be painted from them. A being might come under the class man and have a snub nose, blonde hair, scanty eye- brows, and no scar on his face. The presence of one of these individual peculiarities in the concept man would destroy it. If we form an image of an apple, it must be either of a yellow, red, green, or russet apple, either as large as a pippin or as small as a crab-apple. A boy was asked what he thought of when ^apple^ was mentioned. He replied that he thought of ' a big, dark-red, apple with a bad 50 Logical Thinking spot on one side, near the top.' That boy could image distinctly, but his power of form- ing concepts was still in its infancy. ' ' So we see that while a mental image must picture the particular and individual quali- ties, properties and appearances of some par- ticular unit of a class, a concept can and must contain only the class qualities— thai is, the qualities belonging to the entire class. The general concept is as has been said *^a general idea ... a general notion which has in it all that is common to its own class. ' ' And it follows that a '^ general idea'' of this kind cannot be pictured. A picture must be of some particular thing, while a concept is something above and higher than particular things. We may picture a man^ but we cannot picture Man the concept of the race. A con- cept is not a reproduction of the image of a thing^ but on the contrary is an idea of a class of things. We trust that the student will con- sider this point until he arrives at a clear un- derstanding of the distinction, and the reason thereof. But, while a concept is incapable of being pictured mentally as an image, it is true that Concepts and Images 51 some particular representative of a class may be held in the mind or imagination as an ideal- ized object, as a general representative of the class, when we speak or think of the general term or concept, providing that its real rela- tion to the concept is recognized. These ideal- ized objects, however, are not concepts— they are percepts reproduced by the memory. It is important, however, to all who wish to convey their thought plainly, that they be able to convert their concepts into idealized repre- sentative objects. Otherwise, they tend to be- come too idealistic and abstract for common comprehension. As Halleck well says: *^We should in all cases be ready to translate our concepts, when occasion requires, into the images of those individuals which the concept represents. A concept means nothing except in reference to certain individuals. Without them it could never have had existence and they are entitled to representation. A man who cannot translate his concepts into defi- nite images of the proper objects, is fitted neither to teach, preach, nor practice any pro- fession. . . . There was, not long ago, a man very fond of talking about fruit in the ab- 52 Logical Thinking stract ; but he failed to recognize an individual cranberry when it was placed before him. A humorist remarked that a certain metaphysi- cian had such a love for abstractions, and such an intense dislike for concrete things, as to refuse to eat a concrete peach when placed be- fore him." In the beginning many students are per- plexed regarding the difference between a percept and a concept. The distinction is sim- ple when properly considered. A percept is : * ^ the object of an act of perception ; that which is perceived. ' ' A concept is : ^ ^ a mental rep- resentation." Brooks makes the following distinction : ^ ' A percept is the mental product of a real thing; a concept is a mere idea or no- tion of the common attributes of things. A percept represents some particular object; a concept is not particular, but general. A per- cept can be described by particulars; a con- cept can be described only by generals. The former can usually be represented by an im- age , the latter cannot be imagined, it can only he thought.^ ^ Thus one is able to image the percept of a particular horse which has been perceived; but he is unable to image correctly Concepts and Images 53 tlie concept of horse as a class or generic term. In connection with this distinction between perception and conception, we may as well consider the subject of apperception, a term favored by many modern psychologists, al- though others steadfastly decline to recognize its necessity or meaning and refuse to employ it. Apperception may be defined as: ^^per- ception accompanied by comprehension ; per- ception accompanied by recognition." The thing perceived is held to be comprehended or recognized— that is, perceived in a new sense, by reason of certain previously acquired ideas in the mind. Halleck explains it as: ^Hhe perception of things in relation to the ideas which we already possess.'^ It follows that all individuals possessed of equally active or- gans of perception, and equally actit^e atten- tion, will perceive the same thing in the same way and in the same degree. But the apper- ception of each individual will differ and vary according to his previous experience and training, temperament and taste, habit and custom. For instance, the familiar story of the boy who climbed a tree and watched the passers-by, noting their comments. The first 54 Logical Thinking passer-by noticing the tree, says aloud : ' ' That would make a good stick of timber/* ^^Good morning, Mr. Carpenter,*' said the boy. The next man said: *^That tree has fine bark.'* ^^Good morning, Mr. Tanner,'* said the boy. Another said, ^^I bet there's a squirrel *s nest up in that tree.** *^Good morning, Mr. Hunter, * ' said the boy. The woman sees in a bird something pretty and ^^ cunning.*' The hunter sees in it some- thing to kill. The ornithologist sees it as something of a certain genus and species, and perhaps also as something appropriate for his collection. The farmer perceives it to be something destructive of either insects or crops. A thief sees a jail as something to be dreaded ; an ordinary citizen, something use- ful for confining objectionable people; a po- liceman, something in the line of his busi- ness. And so on, the apperception differing upon the previous experience of the indi- vidual. In the same way the scientist sees in an animal or rock many qualities of which the ordinary person is ignorant. Our training, experience, prejudices, etc., affect our apper- ception. Concepts and Images 55 And so, we see that in a measure our con- cepts are determined not only by our simple perceptions, but also materially by our apper- ceptions. We conceive things not only as they are apparent to our senses, but also as colored and influenced by our previous impressions and ideas. For this reason we find widely varying concepts of the same things among different individuals. Only an absolute ndnd could form an absolute concept. CHAPTER VI. TERMS In logic the words concept and term are practically identical, but in the popular usage of the terms there is a distinct difference. This difference is warranted, if we depart from the theoretical phase of logic, for the word con- cept really denotes an idea in the mind, while the word term really denotes a word or name of an idea or concept— the symbol of the latter. In a previous chapter we have seen that De- nomination, or ^ ' the act of naming or designat- ing by a name'' is the final step or stage in forming a concept. And it is a fact that the majority of the words in the languages of civilized people denote general ideas or con- cepts. As Brooks says : ^ ^ To give each indi- vidual or particular idea a name peculiar to it- self would be impracticable and indeed impos- sible; the mind would soon become over- whelmed with its burden of names. Nearly all the ordinary words of our language are gen- eral rather than particular. The individuals 56 Tebms 57 distinguished by particular names, excepting persons and places, are comparatively few. Most objects are named only by common nouns ; nearly all of our verbs express general actions ; our adjectives denote common quali- ties, and our adverbs designate classes of ac- tions and qualities. There are very few words in the language, besides the names of persons and places, that do not express general ideas. ' ' In logic the word term is employed to denote any word or words which constitute a concept. The word concept is employed strictly in the sense of a subject of thought, without refer- ence to the words symbolizing it. The con'- cept, or subject of thought, is the important element or fact and the term denoting it is merely a convenient symbol of expression. It must be remembered that a term does not necessarily consists of but a single word, for often many words are employed to denote the concept, sometimes even an entire clause or phrase being found necessary for the current term. For the purpose of the consideration of the subjects to be treated upon in this book, we may agree that: A term is the outward 58 Logical Thinkii^g symbol of a concept; and that: The concept is the idea expressed by the term. There are three general parts or phases of Deductive Logic, namely: Terms, Proposi- tions and Syllogisms. Therefore, in consider- ing Terms we are entering into a considera- tion of the first phase of Deductive Logic. Un- less we have a correct understanding of Terms, we cannot expect to understand the succeeding stages of Deductive Eeasoning. As Jevons says: *^When we join terms to- gether we make a Proposition; when we join Propositions together, we make an argument or piece of reasoning. . . . We should generally get nothing but nonsense if we were to put together any terms and any proposi- tions and to suppose that we were reasoning. To produce a good argument we must be care- ful to obey certain rules, which it is the pur- pose of Logic to make known. But, in order to understand the matter perfectly, we ought first to learn exactly what a term is, and how many hinds of terms there may be; we have next to learn the nature of a proposition and the different kinds of propositions. After- wards we shall learn how one proposition may Terms 59 by reasoning be drawn from other proposi- tions in the kind of argument called the syllogism.'^ Now, having seen that terms are the out- ward symbols or expression of concepts, and are the names of things which we join to- gether in a proposition, let us proceed to con- sider the different kinds of terms, following the classifications adopted by the authorities. A term may contain any number of nouns, substantive or adjective or it may contain but a single noun. Thus in, *^ Tigers are fero- cious," the first term is the single substantive * ^tigers;'' the second term is the single ad- jective *^ ferocious." And in the proposition, ^^The King of England is the Emperor of India," there are two terms, each composed of two nouns, ^'King of England" being the first term and ^* Emperor of India" being the second term. The proposition, ^ ' The library of the British Museum is the greatest collec- tion of books in the world," contains fifteen words but only two terms ; the first term being **The library of the British Museum," in which are two substantives, one adjective, two definite articles and one preposition ; the sec- 60 Logical Thinking ond term being, ^41ie greatest collection of books in the world, " which contains three sub- stantives, one adjective, two articles, and two prepositions. The above illustration is sup- plied by Jevons, who adds: ^^A logical term, then, may consist of any number of nouns, substantive or adjective, with the articles, prepositions and conjunctions required to join them together; still it is only one term if it points out, or makes us think of a single ob- ject, or collection, or class of objects.^ ^ (A substantive, is : ^^the part of speech which ex- presses something that e:^sts, either material or immaterial. '0 The first classification of terms divides them into two general classes, vi^., (1) Singu- lar Terms; and (2) General Terms. A Singular Term is a-Mmi denoting a single object, person or thing. Although denoting only a single object, person or thing, it may be composed of several words ; or it may be composed of but one word as in the case of a proper name, etc. The following are Singular Terms, because they are terms denoting but a single object, person or thing: *^ Europe ; Min- nesota ; Socrates ; Shakespeare ; the first man ; Terms 61 the highest good ; the first cause ; the King of England; the British Museum; the Commis- sioner of Public Works ; the main street of the City of New York." It will be noted that in all of the examples given, the Singular Term denotes a particular something, a specific thing, a something of which there is but one, and that one possesses particularity and indi- viduality. As Hyslop says : ' ' Oneness of kind is not the only or distinctive feature of Singu- lar Terms, but individuality, or singularity, as representing a concrete individual whole." A General Term is a term which applies, in the same sense, to each and every individual object, person or thing in a number of objects, persons or things of the same kind, or to the entire class composed of such objects persons or things of the same kind. For instance, ^ ' horse ; man ; biped ; mammal ; trees ; figures ; grain of sand ; matter," etc. Hyslop says, re- garding General Terms: ^^In these instances the terms denote more than one object, and apply to all of the same kind. Their meaning is important in the interpretation of what are called universal propositions." Another general classification of Terms di- 62 Logical Thinking vides them into two respective classes, as fol- lows: (1) Collective Terms; and (2) Distribu- tive Terms. Hyslop says of this classifica- tion : ^ ^ This division is based upon the distinc- tion between aggregate wholes of the same kind and class terms. It partly coincides with the division into Singular and General Terms, the latter always being distributive.'' A Collective Term is one which denotes an aggregate or collected whole of objects, per- sons or things of the same or similar kind, which collective whole is considered as an indi- vidual, although composed of a totality of sep- arate individual objects, persons or things. Thus the following terms: ^^ regiment; con- gregation ; army ; family ; crowd ; nation ; com- pany ; battalion ; class ; congress ; parliament ; convention;" etc. are Collective Terms, be- cause they denote collective, aggregate or composite wholes, considered as an individual. A Distributive Term is a term which denotes each and every individual object, person or thing in a given class. For example, are the terms: *^man; quadruped; biped; mammal; book; diamond; tree.'' As Hyslop says: ^^ General terms are always distributive." Teems 63 Also: ^^It is important also to keep clear the distinction between class wholes and collective wholes. . . . They are often confused so as to call a term denoting a class a Collective Term.'* Another general classification of Terms divides them into the following two respect- ive classes; (1) Concrete Terms; and (2) Ab- stract Terms. A Concrete Term is a term denoting either a definite object, person or thing which is sub- ject to perception and experience, and may be considered as actually existent concretely, as for instance: horse; man; mountain; dol- lar; knife; table; etc., or else an attribute thought of and used solely as an attribute, as for instance: *^ beautiful, wise, noble, virtu- ous, good,'' etc. An Abstract Term is a term denoting the at- tribute, quality or property considered as apart from the object, person or thing and as having an abstract existence, as for instance : ^^ beauty; wisdom; nobility; goodness; vir- tue," etc. As we have seen elsewhere, these qualities have no real existence in themselves, but are known and thought of only in connec- 64 Logical Thinking tion with concrete objects, persons and things. Thus we cannot know ^^ Beauty," but may know beautiful things; we cannot know ^^ Vir- tue," but we may know virtuous people, etc. An attribute or quality is concrete when ex- pressed as an adjective; and abstract when expressed as a noun; as for instance, ^^beauti- ful" and *^ beauty," respectively, or ^^ virtu- ous ' ' and ^ ' virtue, ' ' respectively. The distinc- tion may be summed up as follows: A Con- crete Term is the name of a thing or of a qual- ity of a thing expressed as an adjective and as merely a quality ; while an Abstract Term is the name of a quality of a thing, expressed as a noun and as a ^Hhing^^ in itself. Certain terms may be used as either Con- crete Terms or as Abstract Terms, and cer- tain authorities have seen fit to classify them as Mixed Terms, as for instance the terms: ^ ^ government ; religion; philosophy;" etc. Another general classification of Terms di- vides them into two respective classes as fol- lows: (1) Positive Terms; and (2) Negative Termis. A Positive Term is a term which denotes its own qualities, as for instance: ^^good, human. Teems 65 large, square, black, strong," etc. These terms indicate the presence of the quality de- noted by the term itself. A Negative Term is a term denoting the ab- sence of a quality, as for instance: ^^ inhuman, inorganic, unwell, unpleasant, non-conduc- ive, '^ etc. These terms deny the presence of certain qualities, rather than asserting the presence of an opposite quality. They are es- sentially negative in nature and in form. Jevons says : ^^ We may usually know a Nega- tive Term by its beginning with one of the little syllables un-, in-, a-, an-, non-, or by its ending with -less. ' ' Hyslop says : ^ ' The usual symbols of Negative Terms are in, un, less, diSy a, or an, anti, mis, and sometimes de, and tiotj and not.'' Jevons adds: ^^If the English language were a perfect one, every term ought to have a Negative Term exactly correspond- ing to it, so that all adjectives and nouns would be in pairs. Just as convenient has its negative inconvenient; metallic, non-metallic; logical, illogical; and so on; so blue should have its negative, non-blue; literary, non- literary; paper, non-paper. But many of these Negative Terms would be seldom or 66 Logical Thinking never used, and if we happen to want them, we can make them for the occasion by putting not-, or non-, before the Positive Term. Ac- cordingly, we find in the dictionary only those Negative Terms which are much employed.'* The last named authority also says: ^ ' Sometimes the same word may seem to have two or even more distinct negatives. There is much difference between undressed and not- dressed, that is *not in evening dress.' Both seem to be negatives of ^dressed,' but this is because the word has two distinct meanings." Some authorities insist upon closer and fur- ther classification, as for instance, in the case of what they call a Privative Term, denoting the absence of qualities once possessed by the object, person or thing, as : *^deaf, dead, blind, dark," etc. Hyslop says that these terms ^^are Positive in form and Negative in matter or meaning." Also in the case of what they call a N ego-positive Term, denoting ^Hhe presence of a positive quality expressed in a negative manner," as : disagreeable, inhuman^ invaluable, etc. These last mentioned classes however are regarded by some as the result of ** carrying too far" the tendency toward Terms 67 classification, and the two general classes, Positive and Negative, are thought sufficient for the purpose of the general student. The same objection applies to a classification oc- casionally made i. e., that which is called an Infinitated Term, denoting a term the intent of which is to place in a distinct category every object, person or thing other than that expressed in the corresponding Positive Term. The intent of the term is to place the positive idea in one class, and all else into a separate one. Examples of this class of terms are found in: ^^not-I, not-animal, not- tree, un- moral," etc. Hyslop says of these terms: *^They are not always, if ever, recognized as rhetorically elegant, but are valuable often to make clear the really negative, or infimta- tively negative nature of the idea in mind. ' ' Another general classification of Terms di- vides them into two respective classes, as fol- lows: (1) Absolute Terms; and (2) Kelative Terms. An Absolute Term is a term denoting the presence of qualities intrinsic to the object, and not depending upon any relation to any other object, as for instance: ^^man; book; 68 Logical THiisrKi:tsrG horse; gun;'' etc. These terms may he re- lated to many other terms, but are not neces- sarily related to any other. A Relative Term is a term denoting certain necessary relations to other terms, as for in- stance: ^'father; son; mother; daughter; teacher ; pupil ; master ; servant ; ' ' etc. Thus it is impossible to think of ^^ child'' except in relation to ^* parent," or vice versa. The one term implies the existence of its related term. Hyslop says of the above classification: ^^Kelative Terms suggest the thought of other individuals with the relation involved as a part of the term's meaning, while Absolute Terms suggest only the qualities in the sub- ject without a relation to others being neces- sarily involved." Some authorities also classify terms as higher and lower; also as hroad and narrow. This classification is meant to indicate the content and extent of the term. For instance, when we classify, we begin with the individ- uals which we then group into a small class. These classes we then group into a larger class, according to their resemblances. These larger classes then go to form a part of still Teems 69 larger classes, and so on. As these classes advance they form broader terms; and as we retreat from the general class into the less general and more particular, the term becomes narrower. By some, the broader term which includes the narrower is called the higher term,, and the narrower are called the lower terms. Thus animal would be a higher and broader term than dog, cat or tiger because it includes the latter. Brooks says: ^^ Since a concept is formed by the union of the common attributes of individuals, it thus embraces both attributes and individuals. The attri- butes of a concept constitute what is called its content; the individuals it embraces consti- tute its extent.'^ Accordingly, the feature of including ob- jects in a concept or term is called its exten- sion; while the feature of including attributes or qualities is called its intension. It follows as a natural consequence that the greater the extension of a term, the less its intension; the greater its intension, the less its extension. We will understand this more clearly when we consider that the more individuals contained in a term, the fewer common properties or 70 Logical Thinking qualities it can contain ; and the more common properties, the fewer individuals. As Brooks says: ^^The concept man has more extension than poet, orator or statesman, since it em- braces more individuals; and less intension, since we must lay aside the distinctive attri- butes of poet, orator and statesman in order to unite them in a common class man.'*^ In the same way the general term animal is quite extended for it includes a large number of in- dividual varieties of very different and varied characteristics and qualities ; as for instance, the lion, camel, dog, oyster, elephant, snail, worm, snake, etc. Accordingly its intension must be small for it can include only the qual- ities common to all animals, which are very few indeed. The definition of the term shows how small is its intension, as: ^^ Animal. An organic being, rising above a vegetable in va- rious respects, especially in possessing sensi- bility, will and the power of voluntary mo- tion.^' Another narrows the intension still further when he defines animal as: *^a crea- ture which possesses, or has possessed, life.'' Halleck says: ^^ Animal is very narrow in in- tension, very broad in extension. There are Terms 71 few qualities common to all animals, but there is a vast number of animals. To give the full meaning of the term in extension, we should have to name every animal, from the micro- scopic infuoria to the tiger, from the angle- worm to the whale. When we decrease the extension to one species of animal, horse, the individuals are fewer, the qualities more numerous. ' ' The importance of forming clear and dis- tinct concepts and of grouping, classifying and generalizing these into larger and broader concepts and terms is recognized by all au- thorities and is generally regarded as form- ing the real basis of all constructive thought. As Brooks says: ^^Generalization lies at the basis of language : only as man can form gen- eral conceptions is it possible for him to form a language. . . . Nearly all the ordinary words in our language are general rather than particular. . . • This power of generali- zation lies also at the basis of science. Had we no power of forming general ideas, each particular object would be a study by itself, and we should thus never pacs beyond the very alphabet of knowledge. Judgments, ex- 72 Logical Thinking cept in the simplest form, would be impossi- ble ; and it is difficult to see how even the sim- plest form of the syllogism oould be con- structed. No general conclusion could be drawn from particulars, nor particular con- clusions from generals; and thus neither in- ductive nor deductive reasoning would be pos- sible. The classifications of science could not be made; and knowledge would end at the very threshold of science* ^^ CHAPTER VII. THE MEANING OF TERMb Every term has its meaning, or content, as some authorities prefer to call it. The word or words of which the term is composed are merely vocal sounds, serving as a symbol for the real meaning of the term, which meaning exists only in the mind of the person under- standing it. To one not understanding the meaning of the term, the latter is but as a meaningless sound, but to one understanding it the sound awakens mental associations and representation and thus serves its purpose as a symbol of thought. Each concrete general term has two mearir- ings, (1) the actual concrete thing, person or object to which the term is applied; and (2) the qualities, attributes or properties of those objects, persons or things in consequence of which the term is applied. For instance, in the case of the concrete term hook, the first meaning consists of the general idea of the thing which we think of as a booh, and the sec- 73 74 Logical Thinking ond meaning consists of the various qualities which go to make that thing a book, as the printed pages, the binding, the form, the cover, etc. Not only is that particular thing a book, but every other thing having the same or similar properties also must be a book. And so, whenever I call a thing a book it must possess the said qualities. And, whenever I combine the ideas of these qualities in thought, I must think of a book. As Jevons says: ^*In reality, every ordinary general term has a double meaning: it means the things to which it is applied, . • . it also means, in a totally different way, the qualities and peculiarities implied as being in the things. Logicians say that the number of things to which a term applies is the extension of the term ; while the number of qualities or peculiarities implied is the intension.^ ^ The extension and intension of terms has been referred to in the previous chapter. The general classification of the degrees of exten- sion of a general term is expressed by the two terms, Genus and Species, respectively. The classification of the character of the intension Meaning of Terms 75 of a term is expressed by the term, Difference, Property and Accident^ respectively. Genus is a term indicating; *^a class of ob- jects containing several species; a class more extensive than a species ; a universal which is predicable of several things of different species. '^ Species is a term denoting: **a smaller class of objects than a genus, and of two or more of which a genus is composed; a predicable that expresses the whole essence of its sub- ject in so far as any common term can express it.'' An authority says : ^ ^ The names species and genus are merely relative and the same com- mon term may, in one case, be the species which is predicated of an individual, and in another case the individual of which a species is predicated. Thus the individual, George, belongs to the logical species Man, while Man is an individual of the logical species Animal. ' ' Jevons says: *^It is desirable to have names by which to show that one class is contained in another, and accordingly we call the class wHch is divided into two or more smaller ones, the genus, and the smaller ones into which it is 76 Logical Thinking divided, the species/^ Animal is a genus of which man is a species ; while man^ in turn, is a genus of which Caucasian is a species ; and Caucasian, in turn, becomes a 5'e7^l^5 of which Socrates becomes a species. The student must avoid confusing the logical meaning of ^ the terms genus and species with the use of the same terms in Natural History. Each class is a ^^ genus' ^ to the class helow it in ex- tension; and each class is a ^^ species'' to the class above it in extension. At the lowest ex- treme of the scale we reach what is called the infima species, which cannot be further sub- divided, as for instance *^ Socrates ''—this lowest species must always be an individual object, person or thing. At the highest ex- treme of the scale we reach what is summum genus, or highest genus, which is never a spe^ cies of anything, for there is no class higher than it^ as for instance, ^* being, existence, real- ity, truth, the absolute, the infinite, the ulti- mate,'' etc. Hyslop says: ^*In reality there is but one summum genus, while there may be an indefinite number of infimae species. All intermediate terms between these extremes are sometimes called subalterns, as being Meaning of Terms 77 either genera or species, according to the re- lation in which they are viewed." Passing on to the classification of the char- acter of the intension of terms, we find : Difference, a term denoting: ^^The mark or marks by which the species is distinguished from the rest of the genus ; the specific char- acteristic.'^ Thus the color of the skin is a difference between the Negro and the Cau- casian; the number of feet the difference be- tween the biped and the quadruped ; the form and shape of leaves the difference between the oak and the elm trees, etc. Hyslop says: *^ Whatever distinguishes one object from an- other can be called the differentia. It is some characteristic in addition to the common qual- ities and determines the species or individual under the genus. ' ' Property, a term denoting: **A peculiar quality of anything ; that which is inherent in or naturally essential to anything." Thus a property is a distinguishing mark of a class. Thus black skin is a property of the Negro race ; four feet a property of quadrupeds ; a certain form of leaf a property of the oak tree. 78 Logical Thinking Thus a difference between two species may be a property of one of the species. Accident^ a term denoting: *^Any quality or circumstance which may or may not belong to a class, accidentally as it were ; or, whatever does not really constitute an essential part of an object, person or thing. ' ^ As, for instance, the redness of a rose, for a rose might part with its redness and still be a rose— the color is the accident of the rose. Or, a brick may be white and still be a brick, although the ma- jority of bricks are red— the redness or white- ness of the brick are its accidents and not its essential properties. Whately says: ^^Acci- dents in Logic are of two kinds— separable and inseparable. If walking be the accident of a particular man, it is a separable one, for he would not cease to be that man though he stood still ; while, on the contrary, if Spaniard is the accident connected with him, it is an in- separable one, since he never can cease to be, ethnologically considered, what he was born.'* Arising from the classification of the mean- ing or content of terms, we find the process termed ^^ Definition.'' Definition is a term denoting: ^'An expla- Meaning of Terms 79 nation of a word or term. ' * In Logic the term is used to denote the process of analysis in which the properties and differences of a term are clearly stated. There are of course sev- eral kinds of definitions. For instance, there is what is called a Real Definition, which Whately defines as: *^A definition which ex- plains the nature of the thing by a particular name.'' There is also what is called a Physi- cal Definition, which is: *^A definition made by enumerating such parts as are actually separable, such as the hull, masts, etc., of a ship.'' Also a Logical Definition, which is: '^A definition consisting of the genus and the difference. Thus if a planet be defined as *a wandering star,' star is the genus, and wan- dering points out the difference between a planet and an ordinary star." An Accidental Definition is: ^*A definition of the accidental qualities of a thing." An Essential Definition is: **a definition of the essential properties and differences of an object, person or thing." Crabbe discriminates between a Definition and an Explanation, as follows : ^* A definition is correct or precise; an explanation is gen- eral or ample. The definition of a word de- 80 Logical Thinking fines or limits the extent of its signification; it is the rule for the scholar in the use of any word ; the explanation of a word may include both definition and illustration; the former admits of no more words than will include the leading features in the meaning of any term; the latter admits of an unlimited scope for diffuseness on the part of the explainer. '^ Hyslop gives the following excellent expla- nation of the Logical Definition^ which as he states is the proper meaning of the term in Logic. He states: *^The rules which regulate Logical Defini- tion are as follows : 1. A definition should state the essential attributes of the species defined. 2. A definition must not contain the name of word defined. Otherwise the definition is called a circiilus in definiendo. 3. The definition must be exactly equiva- lent to the species defined. 4. A definition should not be expressed in obscure, figurative, or ambiguous language. 5. A definition must not be negative when it can be affirmative. '' A correct definition necessarily requires the Meaning of Terms 81 manifestation of the two respective processes of Analysis and Synthesis. Analysis is a term denoting: ^^The separa- tion of anything into its constituent elements, qualities, properties and attributes." It is seen at once that in order to correctly define an object, person or thing, it is first necessary to analyze the latter in order to perceive its essential and accidental properties or differ- ences. Unless the qualities, properties and attributes are clearly and fully perceived, we cannot properly define the object itself. Synthesis is a term denoting: ^^The act of joining or putting two or more things to- gether ; in Logic : the method by composition, in opposition to the method of resolution or analysis.'^ In stating a definition we must necessarily join together the various essential qualities, properties and attributes, which we have discovered by the process of analysis; and the synthesized combination, considered as a whole, is the definition of the object ex- pressed by the term. CHAPTEE VIIL JUDGMENTS The first step in the process of reasoning is that of Conception or the forming of Con- cepts. The second step is that of Judgment, or the process of perceiving the agreement or disagreement of two conceptions. Judgment in Logic is defined as : ^ ^ The com- paring together in the mind of two notions, concepts or ideas, which are the objects of apprehension, whether complex or incomplex, and pronouncing that they agree or disagree with each other, or that one of them belongs or does not belong to the other. Judgment is therefore aflfirmative or negative.'' When we have in our mind two concepts, we are likely to compare them one with the other, and to thus arrive at a conclusion re- garding their agreement or disagreement. This process of comparison and decision is what, in Logic, is called Judgment. In every act of Judgment there must be at least two concepts to be examined and com- 82 Derived Judgments 83 pared. This comparison must lead to a Judg- ment regarding their agreement or disagree- ment. For instance, we have the two con- cepts, horse and animal. We examine and compare the two concepts, and find that there is an agreement between them. We find that the concept horse is included in the higher concept of amimal and therefore, we assert that: ^^The horse is an animal/^ This is a statement of agreement and is, therefore, a Positive Judgment. We then compare the concepts horse and cow and find a disagree- ment between them, which we express in the statement of the Judgment that: ^^The horse is not a cow.'' This Judgment, stating a dis- agreement is what is called a Negative Judgment. In the above illustration of the comparison between the concepts horse and animal we find that the second concept animal is broader than the first, horse, so broad in fact that it in- cludes the latter. The terms are not equal, for we cannot say, in truth, that ^^ an animal is the horse." We may, however, include a part of the broader conception with the narrower and say : ^ ^ some animals are horses. ' ' Sometimes 84 Logical Thinking both concepts are of equal rank, as when we state that: ^^Man is a rational animal." In the process of Judgment there is always the necessity of the choice between the Posi- tive and the Negative. When we compare the concepts horse and animal, we must of neces- sity decide either that the horse is an animal, or else that it is not an animal. The importance of the process of Judgment is ably stated by Halleck, as follows: ^^Were isolated concepts possible, they would be of very little use. Isolated facts are of no more service than unspun wool. We might have a concept of a certain class of three-leaved ivy, as we might also of poisons. Unless judg- ment linked these two concepts and decided that this species of ivy is poisonous, we might take hold of it and be poisoned. We might have a concept of bread and also one of meat, fruit and vegetables. If we also had a concept of food, unrelated to these, we should starve to death, for we should not think of them as foods. A vessel, supposing itself to be far out at sea, signaled another vessel that the crew were dying of thirst. That crew certainly had a concept of drinkable things Judgments 85 and also of water. To the surprise of the first, the second vessel signaled back, ^Draw from the sea and drink. You are at the mouth of the Amazon.' The thirsty crew had not joined the concept drinkable to the concept of water over the ship's side. A man having taken an overdose of laudanum, his wife lost much valuahle time in sending out for anti- dotes, because certain of her concepts had not been connected by judgment. She had good concepts of coffee and of mustard; she also knew that an antidote to opium was needed ; but she had never linked these concepts and judged that coffee and mustard were anti- dotes to opium. The moment she formed that judgment she was a wiser woman for her knowledge was related and usable. . . . Judgment is the power revolutionizing the world. The revolution is slow because na- ture's forces are so complex, so hard to be re- duced to their simplest forms and so disguised and neutralized by the presence of other forces. . . • Fortunately judgment is ever silently working and comparing things that, to past ages, have seemed dissimilar; and it is continually abstracting and leaving out of 86 Logical. Thinking the field of view those qualities which have simply served to obscure the point at issue. '^ Judgment may be both analytic or synthetic in its processes ; and it may be neither. When we compare a narrow concept with a broader one, as a part with a whole, the process is syn- thetic or an act of combination. When we compare a part of a concept with another con- cept, the process is analytic When we com- pare concepts equal in rank or extent, the process is neither synthetic nor analytic. Thus in the statement that : ^ ^ A horse is an animal, ' ' the judgment is synthetic; in the statement that: *^some animals are horses,'' the judg- ment is analytic; in the statement that: ^^a man is a rational animal," the judgment is neither analytic nor synthetic. Brooks says: ^^In one sense all judgments are synthetic. A judgment consists of the union of two ideas and this uniting is a process of synthesis. This, however, is a superficial view of the process. Such a synthesis is a mere mechanical synthesis; below this is a thought-process which is sometimes analytic, sometimes synthetic and sometimes neither analytic nor synthetic.'' Judgments 87 The same authority states: ^^The act of mind described is what is known as logical judgment. Strictly speaking, however, every intelligent act of the mind is accompanied with a judgment. To know is to discriminate and, therefore, to judge. Every sensation or cog- nition involves a knowledge and so a judg- ment that it exists. The mind cannot think at all without judging; to think is to judge. Even in forming the notions which judgment compares, the mind judges. Every notion or concept implies a previous act of judgment to form it: in forming a concept, we compare the common attributes before we unite them ; and comparison is judgment. It is thus true that * Every concept is a contracted judgment; every judgment an expanded concept.' This kind of judgment, by which we affirm the existence of states of consciousness, discrimi- nate qualities, distinguish percepts and form concepts, is called primitive or psychological m judgment/^ In Logical Judgment there are two aspects ; i. e., Judgment by Extension and Judgment by Intension. When we compare the two con- cepts horse and animal we find that the con- 88 Logical. Thin^king cept horse is contained in the concept animal and the judgment that ''a horse is an anirmiV' may be considered as a Judgment by Exten- sion. In the same comparison we see that the concept horse contains the quality of animal- ity, and in attributing this quality to the horse ^ we may also say ^^the horse is an animal/^ which judgment may be considered as a Judg- ment by Intension. Brooks says: ^^Both views of Judgment are correct ; the mind may reach its judgment either by extension or by intension. The method by extension is usually the more natural.'' When a Judgment is expressed in words it is called a Proposition. There is some con- fusion regarding the two terms, some holding that a Judgment and a proposition are identi- cal, and that the term ^^proposition" may be properly used to indicate the judgment itself. But the authorities who seek for clearness of expression and thought now generally hold that : 'M Proposition is a Judgment expressed in words/ ^ In the next chapter, in which we consider Propositions, we shall enter into a more extended consideration of the subject of Judgments as expressed in Propositions, Judgments 89 which consideration we omit at this point in order to avoid repetition. Jnst as the re- spective subjects of Concepts and Terms nec- essarily blend into each other, so do the re- spective subjects of Judgments and Propo- sitions. In each case, too, there is the ele- ment of the mental process on the one hand and the verbal expression of it on the other hand. It will be well to keep this fact in mind. CHAPTER IX. PROPOSITIONS We have seen that the first step of Deduct- ive Reasoning is that which we call Concepts. The second step is that which we call Propositions. In Logic, a Proposition is: ^' A sentence, or part of a sentence, affirming or denying a con- nection between the terms ; limited to express assertions rather than extended to questions and commands.^' Hyslop defines a Propo- sition as: ^^any affirmation or denial of an agreement between two conceptions.'' Examples of Propositions are found in the following sentences: **The rose is a flower;'' *^a horse is an animal;" *^ Chicago is a city;" all of which are affirmations of agreement be- tween the two terms involved; also in: *^A horse is not a zebra;" '^ pinks are not roses ;" *^the whale is not a fish;" etc., which are denials of agreement between the terms. The Parts of a Proposition are: (1) the Subject, or that of which something is af- 90 Pbopositions 91 firmed or denied; (2) the Predicate, or the something which is affirmed or denied regard- ing the Subject; and (3) the Copula, or the verb serving as a link between the Subject and the Predicate. In the Proposition: ^^Man is an animal/' the term man is the Subject ; the term an ani- mal is the Predicate ; and the word is, is the Copula. The Copula is always some form of the verb to he, in the present tense indicative, in an affirmative Proposition; and the same with the negative particle affixed, in a nega- tive Proposition. The Copula is not always directly expressed by the word is or is not, etc., but is instead expressed in some phrase w3iich implies them. For instance, we say ' ^ he runs,'' which implies ^^he is running." In the same way, it may appear at times as if the Predicate was missing, as in: *^God is," by which is meant ^ ^ Grod is existing. ' ' In some cases, the Proposition is inverted, the Predi- cate appearing first in order, and the Subject last, as in: ^'Blessed are the peacemakers;" or ^^ Strong is Truth." In such cases judg- ment must be used in determining the matter, 92 Logical Thinking in accordance with the character and meaning of the terms. An Affirmative Proposition is one in which the Predicate is affirmed to agree with the Subject. A Negative Proposition is one in which the agreement of the Predicate and Subject is denied. Examples of both of these classes have been given in this chapter. Another classification of Propositions di- vides them in three classes, as follows (1) Categorical; (2) Hypothetical; (3) Dis- junctive. A Categorical Proposition is one in which the affirmation or denial is made without reservation or qualification, as for instance: ^^Man is an animal ;'' ^Hhe rose is a flower,'^ etc. The fact asserted may not be true, but the statement is made positively as a state- ment of reality. A Hypothetical Proposition is one in which the affirmation or denial is made to depend upon certain conditions, circumstances or sup-, positions, as for instance: ^^If the water is boiling-hot, it will scald;" or **if the powder be damp, it will not explode,'' etc. Jevons says: ^^Hypothetical Propositions may gen- Propositions 93 erally be recognized by containing the little word ^if;^ but it is doubtful whether they really differ much from the ordinary proposi- tions. . . . We may easily say that * boil- ing waiter will scald/ and ^damp gunpowder will not explode, ' thus avoiding the use of the word 4f/ '' A Disjunctive Proposition is one ^^ implying or asserting an alternative," and usually con- taining the conjunction *^or,'' sometimes to- gether with ^ ^ either, "as for instance : ' ^ Light- ning is sheet or forked;" ^^ Arches are either round or pointed ; " ^ * Angles are either obtuse, right angled or acute." Another classification of Propositions di- vides them in two classes as follows: (1) Uni- versal; (2) Particular. A Universal Proposition is one in which the whole quantity of the Subject is involved in the assertion or denial of the Predicate. For instance: *^A11 men are liars," by which is affirmed that all of the entire race of men are in the category of liars, not some men but all the men that are in existence. In the same way the Proposition : ^^No men are immortal" is Universal, for it is a universal denial. 94 Logical Tnii^KiNG A Particular Proposition is one in which the affirmation or denial of the Predicate involves only a part or portion of the whole of the Sub- ject, as for instance: ''Some men are athe- ists," or ''Some women are not vain," in which cases the affirmation or denial does not involve all or the whole of the Subject. Other examples are: ^^A few men," etc.; ^^many people," etc.; "certain books," etc.; "most people," etc. Hyslop says : ' ' The signs of the Universal Proposition, when formally expressed, are all, every, each, any, and ivhole or words with equivalent import. The signs of Particular Propositions are also certain adjectives of quantity, such as some, certain, a few, many, most or such others as denote at least a part of a class. The subject of the Distribution of Terms in Propositions is considered very important by Logicians, and as Hyslop says : ' ' has much im- portance in determining the legitimacy, or at least the intelligibility, of our reasoning and the assurance that it will be accepted by others." Some authorities favor the term, ** Qualification of the Terms of Propositions," Pbopositions 95 but the established usage favors the term ** Distribution/* The definition of the Logical term, ^^Dis- tribution/* is: ^^The distinguishing of a uni- versal whole into its several kinds of species ; the employment of a term to its fullest extent; the application of a term to its fullest extent, so as to include all significations or applica- tions." A Term of a Proposition is distrib- uted when it is employed in its fullest sense ; that is to say, when it is employed so as to ap- ply to each and every object^ person or thing included under it. Thus in the proposition, ^^ AH horses are animals," the term horses is distributed; and in the proposition, ^^Some horses are thoroughbreds," the term horses is not distributed. Both of these examples re- late to the distribution of the subject of the proposition. But the predicate of a proposi- tion also may or may not be distributed. For instance, in the proposition, ^^All horses are animals," the predicate, animals, is not dis- tributed, that is, not used in its fullest sense, for all animals are not horses— \hQve are some animals which are not horses and, therefore, the predicate, animals, not being used in its 96 Logical Thinking fullest sense is said to be ^^not distributed.^' The proposition really means : ^ ^ All horses are some animals/' There is however another point to be re- membered in the consideration of Distribution of Terms of Propositions, which Brooks ex- presses as follows: ^^Distribution generally shows itself in the form of the expression, but sometimes it may be determined by the thought. Thus if we say, ^Men are mortal,' we mean all men, and the term men is distrib- uted. But if we say ^ Books are necessary to a library,' we mean, not *all books' but *some books. ' The test of distribution is whether the term applies to ^each and every/ Thus when we say *men are mortal,' it is true of each and every man that he is mortal." The Rules of Distribution of the Terms of Proposition are as follows : 1. All universals distribute the subject. 2. All particulars do not distribute the subject. 3. All negatives distribute the predicate. 4. All affirmatives do not distribute the predicate. The above rules are based upon logical rea- Propositions 97 soning. The reason for the first two rules is quite obvious, for when the subject is univer- sal, it follows that the whole subject is ir.- volved; when the subject is particular it fol- lows that only a part of the subject is involved. In the case of the third rule, it will be seen that in every negative proposition the whole of the predicate must be denied the subject, as for instance, when we say : ^ ^ Some animals are not horses^ ' ' the whole class of horses is cut off from the subject, and is thus distributed. In the case of the fourth rule, we may readily see that in the affirmative proposition the whole of the predicate is not denied the subject, as for instance, when we say that: ^^ Horses are animals," we do not mean that horses are all the animals, but that they are merely a part or portion of the class animal—therefore, the predicate, animals, is not distributed. In addition to the forms of Propositions given there is another class of Propositions known as Definitive or Substitutive Proposi- tions, in which the Subject and the Predicate are exactly alike in extent and rank. For in- stance, in the proposition, ^^A triangle is a polygon of three sides'^ the two terms are in- 98 Logical Thinking terchangeable ; tliat is, may be substituted for each other. Hence the term ^^ substitutive/^ The term *^ definitive '^ arises from the fact that the respective terms of this kind of a proposition necessarily define each other. All logical definitions are expressed in this last mentioned form of proposition, for in such cases the subject and the predicate are pre- cisely equal to each other. CHAPTER X. IMMEDIATE REASONING In the process of Judgment we must com- pare two concepts and ascertain their agree- ment of disagreement. In the process of Eeasoning we follow a similar method and compare two judgments, the result of such comparison being the deduction of a third judgment. The simplest form of reasoning is that known as Immediate Eeasoning, by which is meant^the deduction of one proposition from another which implies it. Some have defined it as: ^^ reasoning without a middle term/^ In this form of reasoning only one proposition is required for the premise, and from that premise the conclusion is deduced directly and without the necessity of comparison with any other term of proposition. The two principal methods employed in this form of Reasoning are; (1) Opposition; (2) Conversion. Opposition exists between propositions hav- : 99 100 Logical Thinking ing tlie same subject and predicate, but differ- ing in quality or quantity, or both^ The Laws of Opposition are as follows : L (1) If the universal is true, the particu- lar is true. (2) If the particular is false, the universal is false. (3) If the universal is false, nothing follows. (4) If the particular is true, nothing follows. II. (1) If one of two contraries is true, the other is false. (2) If one of two contra- ries is false, nothing can be inferred. (3) Contraries are never both true, but both may be false. III. (1) If one of two sub-contraries is false, the other is true. (2) If one of two sub- contraries is true, nothing can be inferred con- cerning the other. (3) Sub-contraries can never be both false, but both may be true. IV. (1) If one of two contradictories is true, the other is false. (2) If one of two con- tradictories is false, the other is true. (3) Contradictories can never be both true or both false, but always one is true and the other is false. In order to comprehend the above laws, the student should familiarize himself with the Immediate Eeasoning 101 following arrangement, adopted by logicians as a convenience: Propositions Universal J^"^^*^^^ (^> Negative (E) AjBfirmative (I) Negative (0) Particular Examples of the above : Universal Affirma- tive (A): ^^AU men are mortal;" Universal Negative (E) : ^^No man is mortal;" ^^Par- ticular Affirmative (I): *'Some men are mortal;" Particular Negative (0): ^^Some men are not mortal." The following examples of abstract prop- ositions are often used by logicians as tend- ing toward a clearer conception than ex- amples such as given above : (A) ^^AUAisB," (I) ^^SomeAisB." (E) ^^No A is B.'' (0) ^^SomeAisnotB." These four forms of propositions bear cer- tain logical relations to each other, as follows : A and E are styled contraries. I and are sub-contraries; A and I and also E and are 102 Logical Thinking called subalterns; A and and also I and E are styled contradictories. A close study of these relations, and the symbols expressing them, is necessary for a clear comprehension of the Laws of Opposi- tion stated a little further back, as well as the principles of Conversion which we shall men- tion a little further on. The following chart, called the Square of Opposition, is also em- ployed by logicians to illustrate the relations between the four classes of propositions : Conversion is the process of immediate reasoning by which we infer from a given proposition another proposition^ having the Immediate Reasoning 103 predicate of the original for its subject, and the subject of the original for its predicate ; or stated in a few words: Conversion is the transposition of the subject and predicate of a proposition. As Brooks states it : ^ * Proposi- tions or judgments are converted when the subject and predicate change places in such a manner that the resulting judgment is an in- ference from the given judgment.'' The new proposition, resulting from the operation or Conversion, is called the Converse; the orig- inal proposition is called the Convertend. The Law of Conversion is that: ^*No term must be distributed in the Converse that is not distributed in the Convertend." This arises from the obvious fact that nothing should be afl&rmed in the derived proposition than there is in the original proposition. There are three kinds of Conversion; viz: (1) Simple Conversion; (2) Conversion by Limitation; (3) Conversion by Contraposi- tion. In Simple Conversion there is no change in either quality or quantity. In Conversion hy Limitation the quality is changed from uni- versal to particular. In Conversion by Nega- 104 Logical Thinking tion the quality is changed but not the quan- tity. Referring to the classification tables and symbols given in the preceding pages of this chapter, we may now proceed to consider the application of these methods of Conver- sion to each of the four kinds of propositions ; as follows : The Universal Affirmative (symbol A) proposition is converted by Limitation, or by a change of quality from universal to particu- lar. The predicate not being ^^distributed'' in the convertend, we must not distribute it in the converse by saying ^^all/^ Thus in this case we must convert the proposition, *^all men are mortaP' (A), into ^^some mortals are men" (I). The Universal Negative (symbol E) is con- verted by Simple Conversion, in which there is no change in either quality or quantity. For since both terms of *^E'' are distributed, they may both be distributed in the converse with- out violating the law of conversion. Thus '^No man is mortal'' is converted into: *'Na mortals are men." ^^E" is converted into The Particular Affirmative (symbol I) is Immediate Reasoning 105 also converted by Simple Conversion in which there is no change in either quality or quan- tity. For since neither term is distributed in *^I/' neither term may be distributed in the converse, and the latter must remain ^^I/' For instance; the proposition: **Some men are mortal" is converted into the proposition, **Some mortals are men." The Particular Negative (symbol 0) is con- verted by Conversion by Negation, in which the quality is changed but not the quantity. Thus in converting the proposition: ^*Some men are not mortal," we must not say ^^some mortals are not men," for in so doing we would distribute men in the predicate, where it is not distributed in the convertend. Avoid- iug this, we transfer the negative particle from the copula to the predicate so that the conver- tend becomes ^*I" which is converted by Simple Conversion. Thus we transfer ^ ^ Some men are not mortal ' ' into * ^ Some men are not- mortal" from which we easily convert (by simple Conversion) the proposition: **Some not-mortals are men." It will be well for students, at this point, to consider the three following Fundamental 106 Logical Thiistkii^g Laws of Thought as laid down by the authori- ties, which are as follows: The Law of Identity ^ which states that: ^^The same quality or thing is always the same quality or thing, no matter how different the conditions in which it occurs.'' The Law of Contradiction, which states that: *^No thing can at the same time and place both be and not be.'' The Law of Excluded Middle, which states that: ^^ Everything must either be or not be; there is no other alternative or middle course." Of these laws. Prof. Jevons, a noted author- ity, says : ' ' Students are seldom able to see at first their full meaning and importance. All arguments may be explained when these self- evident laws are granted; and it is not too much to say that the whole of logic will be plain to those who will constantly use these laws as the key." CHAPTER XI. INDUCTIVE BEASONING Inductive Eeasoning, as we have said, is the process of discovering general truth from particular truths, or inferring general laws from particular facts. Thus, from the experi- ence of the individual and the race regarding the particular truth that each and every man under observation has been observed to die sooner or later, it is inferred that all men die, and hence, the induction of the general truth that ^^AU men must die,'' Or, as from ex- perience we know that the various kinds of metals expand when subjected to heat, we in- fer thsit all metals are subject to this law, and that consequently we may arrive by inductive reasoning at the conclusion that: **A11 metals expand when subjected to heat.'' It will be noticed that the conclusion arrived at in this way by Inductive Reasoning forms the funda- mental premise in the process of Deductive Eeasoning. As we have seen elsewhere, the two processes. Inductive and Deductive Rea- 107 108 Logical Thinking soning, respectively are interdependent— restr ing upon one another. Jevons says of Inductive Eeasoning: *^In Deductive Eeasoning we inquire bow we may gather the truth contained in some proposi- tions called Premises, and put into another proposition called the Conclusion. We have not yet undertaken to find out how we can learn what propositions really are true, but only what propositions are true when other ones are true. All the acts of reasoning yet con- sidered would be called deductive becmise we deduce, or lead doivn the. truth from premises to conclusion. It is an exceedingly important thing to understand deductive inference cor- rectly, but it might seem to be still more im- portant to understand inductive inference, by which we gather the truth of general proposi- tions from facts observed as happening in the world around us.'' Halleck says: **Man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. By induc- tion we examine what seems to us a suiB&cient number of individual cases. We then con- clude that the rest of these cases, which we Inductive Reasoning 109 have not examined, will obey the same general law. . . . Only after general laws have been laid down, after objects have been classi- fied, after major premises have been formed, can deduction be employed. ' ' Strange as may now appear, it is a fact that until a comparatively recent period in the history of man, it was held by philosophers that the only way to arrive at all knowledge was by means of Deductive Eeasoning, by the use of the Syllogism. The influence of Aris- totle was great and men preferred to pursue artificial and complicated methods of Deduct- ive Reasoning, rather than to reach the truth by obtaining the facts from Nature herself, at first hand, and then inferring general prin- ciple from the facts so gathered. The rise of modern scientific methods of reasoning, along the lines of Inductive Inference, dates from about 1225-1300. Roger Bacon was one of the first to teach that we must arrive at scientific truth by a process of observation and experi- mentation on the natural objects to be found on all sides. He made many discoveries by following this process. He was ably seconded by Galileo who lived some three hundred 110 Logical. Thinking years later, and who also taught that many great general truths might be gained by care- ful observation and intelligent inference. Lord Francis Bacon, who lived about the same time as Galileo, presented in his Novum Or- ganum many excellent observations and facts regarding the process of Inductive Eeasoning and scientific thought. As Jevons says: *^ In- ductive logic inquires by what manner of rea- soning we can gather the laws of nature from the facts and events observed. Such reason- ing is called induction, or inductive inquiry, and, as it has actually been practiced by all the great discoverers in science, it consists in four steps.'' The Four Steps in Inductive Reasoning, as stated by Jevons, are as follows : First /S^e^?.— Preliminary observation. Second Step.— The making of hypotheses.^ Third /Siep.— Deductive reasoning. Fourth /S'^e^^.— Verification. It will be seen that the process of Inductive Eeasoning is essentially a synthetic process, because it operates in the direction of combin- ing and uniting particular facts or truths into general truths or laws which comprehend, Inductive Reasoning 111 embrace and include them all. As Brooks &ays: ^^The particular facts are united by the mind into the general law ; the general law em- braces the particular facts and binds them together into a unity of principle and thought. Induction is thus a process of thought from the parts to the whole— a synthetic process. '^ It will also be seen that the process of Induct- ive Reasoning is essentially an ascending process, because it ascends from particular facts to general laws; particular truths to universal truths ; from the lower to the higher, the narrower to the broader, the smaller to the greater. Brooks says of Inductive Reasoning : ^ ' The relation of induction to deduction will be clearly seen. Induction and Deduction are the converse, the opposites of each other. De- duction derives a particular truth from a general truth; Induction derives a general truth from particular truths. This antithesis appears in every particular. Deduction goes from generals to particulars ; Induction goes from particulars to generals. Deduction is an analytic process ; Induction is a synthetic process. Deduction is a descending process— 112 LoGiCAii Thinking it goes from the higher truth to the lower truth; Induction is an ascending process— it goes from the lower truth to the higher. They differ also in that Deduction may be applied to necessary truths, while Induction is mainly restricted to contingent truths.'^ Hyslop says : ^ ' There have been several ways of de- fining this process. It has been usual to con- trast it with Deduction. Now, deduction is often said to be reasoning from general to par- ticular truths, from the containing to the con- tained truth, or from cause to effect. Induc- tion, therefore, by contrast is defined as rea- soning from the particular to the general, from the contained to the containing, or from effect to cause. Sometimes induction is said to be reasoning from the known to the un- known. This would make deduction, by con- trast, reasoning from the unknown to the known, which is absurd. The former ways of representing it are much the better. But there is still a better way of comparing them. Deduction is reasoning in which the conclusion is contained in the premises. This is a ground for its certitude and we commit a fallacy when- ever we go beyond the premises as shown by Inductive Eeasoning 113 the laws of the distribution of terms. In con- trast with this, then, we may call inductive reasoning the process by which we go beyond the premises in the conclusion. . . . The process here is to start from given facts and to infer some other probable facts more gen- eral or connected with them. In this we see the process of going beyond the premises. There are, of course, certain conditions which regulate the legitimacy of the procedure, just as there are conditions determining deduction. They are that the conclusion shall represent the same general kind as the premises, with a possibility of accidental differences. But it goes beyond the premises in so far as known facts are concerned.-' The following example may give you a clearer idea of the processes of Inductive Eeasoning : First Step. Preliminary Observation. Ex- ample: We notice that all the particular magnets which have come under our observa- tion attract iron. Our mental record of the phenomena may be stated as: '^ A, B, C, D, E, F, Gr, etc., and also X, Y, and Z, all of which 114 Logical Thinking are magnets, in all observed instances, and at all observed times, attract iron/^ Second Step. The Making of Hypotheses. Example : Upon the basis of the observations and experiments, as above stated, and apply- ing the axiom of Inductive Eeasoning, that: *'What is true of the many, is true of the whole, ' ' we feel justified in forming a hypothe- sis or inference of a general law or truth, ap- plying the facts of the particulars to the gen- eral, whole or universal, thus: ^^All magnets attract iron. ' ' Third Step. Deductive Reasoning. Exam- ple : Picking up a magnet regarding which we have had no experience and upon which we have made no experiments, we reason by the syllogism, as follows: (1) All magnets attract iron; (2) This thing is a magnet; therefore (3) This thing will attract iron. In this we apply the axiom of Deductive Eeasoning: ^^ Whatever is true of the whole is true of the parts.'* Fourth Step. Verification. Example: We then proceed to test the hypothesis upon the particular magnet, so as to ascertain whether or not it agrees with the particular facts. If Inductive Reasoning 115 the magnet does not attract iron we know that either our hypothesis is wrong and that some magnets do not attract iron; or else that our judgment regarding that particular ^^ thing" being a magnet is at fault and that it is not a magnet. In either case, further examina- tion, observation and experiment is necessary. In case the particular magnet does attract iron, we feel that we have verified our hypothe- sis and our judgment. CHAPTEE XII. KEASONING BY INDUCTION- The term ^^ Induction," in its logical usage, is defined as follows: '' (a) The process of in- vestigating and collecting facts; and (b) the deducing of an inference froinl these facts; also (c) sometimes loosely used in the sense of an inference from observed facts." Mill says: ^^ Induction ^ then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individ- uals of a class, is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times. ' ' The Basis of Induction is the axiom that : ^^What is true of the many is true of the whole.^^ Esser, a well known authority, states this axiom in rather more complicated form, as follows: ^'That which belongs or does not 116 Reasoning by Induction 117 belong to nuany things of tlie same Mnd, be- longs or does not belong to all things of the same kind.'' This basic axiom of Induction rests upon the conviction that Nature's laws and mani- festations are regular, orderly and uniform. If we assume that Nature does not manifest these qualities, then the axiom must fall, and all inductive reason must be fallacious. As Brooks well says: ^^ Induction has been com- pared to a ladder upon which we ascend from facts to laws. This ladder cannot stand un- less it has something to rest upon; and this something is our faith in the constancy of Na- ture 's laws. ' ' Some authorities have held that this perception of the uniformity of Nature's laws is in the nature of an intuitive truth, or an inherent law of our intelligence. Others hold that it is in itself an inductive truth, arrived at by experience and observation at a very early age. We are held to have noticed the uniformity in natural phenomena, and alm'ost instinctively infer that this uniformity is con- tinuous and universal. The authorities assume the existence of two kinds of Induction, namely: (1) Perfect In- 118 Logical Thinking duction; and (2) Imperfect Induction. Other, but similar, terms are employed by different authorities to designate these two classes. Perfect Induction necessitates a knowledge of all the particulars forming a class; that is, all the individual objects, persons, things or facts comprising a class must be known and enumerated in this form of Induction. For instance, if we hnew positively all of Brown ^s children, and that their names were John, Peter, Mark, Luke, Charles, William, Mary and Susan, respectively; and that each and every one of them were freckled and had red hair ; then, in that case, instead of simply gen- eralizing and stating that: ^^John, Peter, Mark, Luke, Charles, William, Mary and Susan, who are all of Brown's children, are freckled and have red hair,'' we would save words, and state the inductive conclusion: ^^All Brown's children are freckled and have red hair. ' ' It will be noticed that in this case we include in the process only what is stated in the premise itself , and we do not extend our inductive process beyond the actual data upon which it is based. This form of Induction is sometimes called *^ Logical Induction," be- Eeasoning by Induction 119 cause the inference is a logical necessity, with- out the possibility of error or exception. By some authorities it is held not to be Induction at all, in the strict sense, but little more than a simplified form of enumeration. In actual practice it is seldom available, for it is almost impossible for us to know all the particulars in inferring a general law or truth. In view of this difficulty, we fall back upon the more practical form of induction known as : Imperfect Induction, or as it is sometimes called ^^ Practical Induction,'' by which is meant the inductive process of reasoning in which we assume that the particulars or facts actually known to us correctly represent those which are not actually known, and hence the whole class to which they belong. In this process it will be seen that the conclusion ex- tends beyond the data upon which it is based. In this form of Induction we must actually employ the principle of the axiom: ^'What is true of the many is true of the whole''— that is, must assume it to be a fact, not because we know it by actual experience, but because we infer it from the axiom which also agrees with past experience. The conclusion arrived at 120 LoGicAii Thii^king may not always be true in its fullest sense, as in the case of the conclusion of Perfect Induc- tion, but is the result of an inference based upon a principle which gives us a reasonable right to assume its truth in absence of better knowledge. In considering the actual steps in the proc- ess of Inductive Eeasoning we can do no bet- ter than to follow the classification of Jevons, mentioned in the preceding chapter, the same being simple and readily compre- hended, and therefore preferable in this case to the more technical classification favored by some other authorities. Let us now consider these four steps. First Step. Preliminary observation. It follows that without the experience of oneself or of others in the direction of observing and remembering particular facts, objects, per- sons and things, we cannot hope to acquire the preliminary facts for the generalization and inductive inference necessary in Induct- ive Eeasoning. It is necessary for us to form a variety of clear Concepts or ideas of facts, objects, persons and things, before we may hope to generalize from these particulars. In Reasonikg by Induction 121. the chapters of this book devoted to the con- sideration of Concepts, we may see the funda- mental importance of the formation and ac- quirement of correct Concepts. Concepts are the fundamental material for correct reason- ing. In order to produce a perfect finished product, we must have perfect materials, and a sufficient quantity of them. The greater the knowledge one possesses of the facts and ob- jects of the outside world, the better able is he to reason therefrom. Concepts are the raw material which must feed the machinery of reasoning, and from which the final product of perfected thought is produced. As Hal- leck says: ^' There must first be a presentar tion of materials. Suppose that we wish to form the concept fruit. We must first per- ceive the different kinds of fruit— cherry, pear, quince, plum, currant, apple, fig, orange, etc. Before we can take the next step, we must be able to form distinct and accurate images of the various kinds of fruit If the concept is to be absolutely accurate, not one kind of fruit must be overlooked. Practically this is impossible ; but many kinds should be examined. Where perception is inaccurate 122 Logical Thinking and stinted, the products of thought cannot be trustworthy. No building is firm if reared on insecure foundations.'' In the process of Preliminary Observation, we find that there are two ways of obtaining a knowledge of the facts and things around us. These two ways are as follows : I. By Simple Observation, or the percep- tion of the happenings which are manifested without our interference. In this, way we perceive the motion of the tides; the move- nient of the planets; the phenomena of the weather; the passing of animals, etc. II. By the Observation of Experiment^ or the perception of happenings in which we in- terfere with things and then observe the re- sult. An experiment is: *^A trial, proof, or test of anything ; an act, operation, or process designed to discover some unknown truth, principle or effect, or to test some received or reputed truth or principle." Hobbes says : ^^To have had many experiments is what we call experience. ' ' Jevons says : ^ ' Experi- mentation is observation with something more ; namely, regulation of the things whose behavior is to be observed. The advantages Reasoning by Induction 123 of experiment over mere observation are of two kinds. In the first place, we shall gener- ally know much more certainly and accurately with what we are dealing, when we make ex- periments than when we simply observe nat- ural events. ... It is a further advan- tage of artificial experiments, that they en- able us to discover entirely new substances and to learn their properties. ... It would be a mistake to suppose that the mak- ing of an experiment is inductive reasoning, and gives us without further trouble the laws of nature. Experiments only give us the facts upon which we may afterward reason. . . . Experiments then merely give facts, and it is only by careful reasoning that we can learn when the same facts will be observed again. The general rule is that the same causes will produce the same effects. Whatever happens in one case will happen in all like cases, pro- vided that they are really like, and not merely apparently so. . . . When we have by re- peated experiments tried the effect which all the surrounding things might have on the re- sult, we can then reason with much confidence as to similar results in similar circumstances. 124 Logical Thinking . . . In order that we may, from our obser- vations and experiments, learn the law of na- ture and become able to foresee the future, we must perform the process of generalization. To generalize is to draw a general law from particular cases, and to infer that what we see to be true of a few things is true of the whole genus or class to which these things belong. It requires much judgment and skill to gener- alize correctly, because everything depends upon the number and character of the in- stances about which we reason.'* Having seen that the first step in Inductive Eeasoning is Preliminary Observation, let us now consider the next steps in which we may see what we do with the facts and ideas which we have acquired by this Observation and Experiment. CHAPTER XIII. ^ ' THEOEY AND HYPOTHESES Following Jevons' classification, we find that the Second Step in Inductive Reasoning is that called ^^The Making of Hypotheses.'' A Hypothesis is: ^^A supposition, proposi- tion or principle assumed or taken for granted in order to draw a conclusion or inference in proof of the point or question ; a proposition assumed or taken for granted, though not proved, for the purpose of deducing proof of a point in question." It will be seen that a Hypothesis is merely held to be possibly or probably true, and not certainly true; it is in the nature of a working assumption, whose truth must be tested by observed facts. The assmnption may apply either to .the cause of things, or to the laws which govern things. Akin to a hypothesis, and by many people confused in meaning with the latter, is what is called a Theory. A Theory is : ^^ A verified hypothesis ; a hy- pothesis which has been established as, ap- 125 126 Logical. Thinking parently, the true one/' An authority says ^^ Theory is a stronger word than hypotJiesis. A theory is founded on principles which have been established on independent evidence. A hypothesis merely assumes the operation of a cause which would account for the phenom- ena, but has not evidence that such cause was actually at work. Metaphysically, a theory is nothing but a hypothesis supported by a large amount of probable evidence.'' Brooks says: ^^When a hypothesis is shown to explain all the facts that are known, these facts being varied and extensive, it is said to be verified, and becomes a theory. Thus we have the theory of universal gravitation, the Copernican theory of the solar system, the undulatory theory of light, etc., all of which were originally mere hypotheses. This is the manner in which the term is usually em- ployed in the inductive philosophy; though it must be admitted that it is not always used in this striot sense. Discarded hypotheses are often referred to as theories; and that which is actually a theory is sometimes called a hypothesis." The steps by which we build up a hypothe- Theory and Hypotheses 127 sis are numerous and varied. In the first place we may erect a hypothesis by the methods of what we have described as Perfect Induction, or Logical Induction. In this case we proceed by simiple generalization or simple enumeration. The example of the freckled, red-haired children of Brown, mentioned in a previous chapter, explains this method. It re- quires the examination and knowledge of every object or fact of which the statement or hypothesis is made. Hamilton states that it is the only induction which is absolutely necessitated by the laws of thought. It does not extend further than the plane of experience. It is akin to mathematical reasoning. Far more important is the process by which hypotheses are erected by means of inferences from Imperfect Induction, by which we reason from the known to the unknown, transcend- ing experience, and making true inductive inferences from the axiom of Inductive E6a- soning. This process involves the subject of Causes. Jevons says : * ^ The cause of an event is that antecedent, or set of antecedents, from which the event always follows. People often make much difficulty about understanding 128 Logical Thinking what the cause of an event means, bnt it really means nothing beyond the things that must exist before in order that the event shall hap-- pen afterward/^ Causes are often obscure and dilBficult to determine. The following five difficulties are likely to arise : I. The cause may be out of our experience, and is therefore not to be un- derstood; 11. Causes often act conjointly, so that it is difficult to discover the one pre- dominant cause by reason of its associated causes ; III. Often the presence of a counter- acting, or modifying cause may confuse us; IV. Often a certain effect may be caused by either of several possible causes; V. That which appears as a cause of a certain effect may be but a co-effect of an original cause. Mill formulated several tests for ascertain- ing the causal agency in particular cases, in view of the above-stated difficulties. These tests are as follows: (1) The Method of Agreement; (2) The Method of Difference; (3) The Method of Eesidues; and (4) the Method of Concomitant Variations. The fol- lowing definitions of these various tests are given by Atwater as follows : Theoby and Hypotheses 129 Method of Agreement: ^^If, whenever a given object or agency is present without counteracting forces, a given effect is pro- duced, there is a strong evidence that the ob- ject or agency is the cause of the effect." Method of Difference: "li, when the sup- posed cause is present the effect is present, and when the supposed cause is absent the effect is wanting, there being in neither case any other agents present to effect the result, we may reasonably infer that the supposed cause is the real one." Method of Residue : ^^ When in any phenom- ena we find a result remaining after the effects of all known causes are estimated, we may attribute it to a residual agent not yet reckoned. ' ' Method of Concomitant Variations : ^ ^ When a variation in a given antecedent is accom- panied by a variation of a given consequent, they are in some mianner related as cause and effect." Atwater adds: ^^ Whenever either of these criteria is found free from conflicting evi- dence, and especially when several of them concur, the evidence is clear that the cases ob- 130 Logical Thinking served are fair representatives of the whole class, and warrant a valid inductive conclu- sion/^ Jevons gives us the following valuable rules: L ^^ Whenever we can alter the quantity of the things experimented on, we can apply a rule for discovering which are causes and which are effects, as follows : We must vary the quantity of one thing, making it at one time greater and at another time less, and if we observe any other thing which varies just at the same times, it will in all probability be an effect. ' ' II. ^^ When things vary regularly and fre- quently, there is a simple rule, by following which we can judge whether changes are con- nected together as causes and effects, as fol- lows : Those things which change in exactly equal times are in all likelihood connected to- gether/' III. ^^It is very difficult to explain how it is that we can ever reason from one thing to a class of things by generalization, when we ccmnot he sure that the things resemble each other in the important points. . . . Upon Theory and Hypotheses 131 what grounds do we argue ? We have to get a general law from particular facts. This can only be done by going through all the steps of inductive reasoning. Having made certain observations, we must frame hypothe- ses as to the circumstances, or laws from which they proceed. Then we must reason deductively; and after verifying the deduc- tions in as many cases as possible, we shall know how far we can trust similar deductions concerning future events. ... It is diffi- cult to judge when we may, and when we may not, safely infer from some things to others in this simple way, without making a complete theory of the matter. The only rule that can be given to assist us is that if things resemble each other in a few properties only, we must observe many insta/nces before inferring that these properties will always be joined to- gether in other cases.' ^ CHAPTER XIV. MAKING AND TESTING HYPOTHESES The older philosopliers and logicians were often at a loss how to reasonably account for the origin of hypotheses. It will be seen, after giving the matter a little thought, that the actual formation of the hypothesis is more than a mere grouping together or synthesis of facts or ideas— there is another mental process which actually evolves the hypothesis or theory— which gives a possible reason. What is this mental process ? Let us consider the matter. Brooks well says : ' ' The hypoth- eses of science originate in what is called an- ticipation. They are not the result of a mere synthesis of facts, for no combination of facts can give the law or cause. We do not see the law ; we see the facts and the mind thinks the law. By the power of anticipation, the mind often leaps from a few facts to the cause which produces themi or the law which governs them. Many hypotheses were but a happy in- tuition of the mind. They were the result of 132 Testing Hypotheses 133 what La Place calls ^a great guess,' or what Plato so beautifully designates as ^a sacred suspicion of truth/ The forming of hypoth- eses requires a suggestive mind, a lively fancy, a philosophic imagination, that catches a glimpse of the idea through the form, or sees the law standing behind the fact. ' ' The student of The New Psychology sees in the mental operation of the forming of the hypothesis— ^^ the mind thinking the law"— but an instance of the operation of the activi- ties of the Subconscious Mind, or even the Superconscious Mind. (See the volume on the Subconscious Mind in this series.) Not only does this hypothesis give the explanation which the old psychology has failed to do, but it agrees with the ideas of others on the subject as stated in the above quotation from Brooks ; and moreover agrees with many re- corded instances of the formation of great hypotheses. Sir Wmf. Hamilton discovered the very important mathematical law of qua- ternions while walking one day in the Dublin Observatory. He had pondered long on the subject, but without result. But, finally, on that eventful day he suddenly ^^felt the gal- 134 Logical Thinking vanic circle of thought" close, and the result was the realization of the fundamental mathe- matical relations of the problem. Berthelot, the founder of Synthetic Chemistry, has testi- fied that the celebrated experiments which led to his remarkable discoveries were seldom the result of carefully followed lines of con- scious thought or pure reasoning processes; but, instead, came to him ^^of their own ac- cord,'^ so to speak, ^^as from a clear sky.'^ In these and many other similar instances, the mental operation was undoubtedly purely subjective and subconscious. Dr. Hudson has claimed that the ^^ Subjective Mind" can- not reason inductively, and that its opera- tions are purely and distinctly deductive, but the testimony of many eminent scientists, in- ventors and philosophers is directly to the contrary. In this connection the following quotation from Thomson is interesting: *^The system of anatomy which has immortalized the name of Oken is the consequence of a flash of an- ticipation which glanced through his mind when he picked up in a chance walk the skull of a deer, bleached and disintegrated by the Testing Hypotheses 135 weather, and exclaimed after a glance, ^It is part of a vertebral colnnrn ! ' When Newton saw the apple fall, the anticipatory question flashed through his mind, ^Why do not the heavenly bodies fall like this apple ?^ In neither case had accident any important share; Newton and Oken were prepared by the deepest previous study to seize upon the unimportant fact odff ered to them, and to show how important it might become; and if the apple and the deer-skull had been wanting, some other falling body, or some other skull, would have touched the string so ready to vibrate. But in each case there was a great step of anticipation; Oken thought he saw a type of the whole skeleton in a single verte- bra, while Newton conceived at once that the whole universe was full of bodies tending to fall. • . . The discovery of Groethe, which did for the vegetable kingdom what Oken did for the animal, that the parts of a plant are to be regarded as metamorphosed leaves, is an apparent exception to the necessity of disciple for invention^ since it was the dis- covery of a poet in a region to which he seemed to have paid no especial or laborious 136 Logical Thinkikg attention. But Goethe was himself most anx- ious to rest the basis of this discovery upon his observation rather than his imagination, and doubtless with good reason. ... As with other great discoveries, hints had been given already, though not pursued, both of Goethe's and Oken's principles. Goethe left his to be followed up by others, and but for his great fame, perhaps his name would never have been connected with it. Oken had amassed all the materials necessary for the establishment of his theory; he was able at once to discover and conquer the new terri- tory.'' It must not be supposed, however, that all hypotheses flashing into the field of conscious- ness from the Subconsciousness, are neces- sarily true or correct. On the contrary many of them are incorrect, or at least only partially correct. The Subconsciousness is not infal- lible or omniscient— it merely produces re- sults according to the material furnished it. But even these faulty hypotheses are often of value in the later formation of a correct one. As "Whewell says: ^^To try wrong guesses is with miost persons the only way to hit upon Testing Hypotheses 137 right ones." Kepler is said to have erected at least twenty hypotheses regarding the shape of the earth's orbit before he finally evolved the correct one. As Brooks says: ^ ' Even incorrect hypotheses may be of use in scientific research, since they may lead to more correct suppositions. The supposition of the circular motions of the heavenly bodies around the earth as a center, which lead to the conception of epicycles, etc., and at last to the true theory is an illustration of this. So the ^theory of phlogiston' in chemistry, made many facts intelligible, before the true one of ^oxidation' superseded it. And so, as Thom- son says, ^^with the theory that ^Nature ab- hors a vacuum,' which served to bring to- gether so many cognate facts not previously considered as related. Even an incorrect conception of this kind has its place in science, so long as it is applicable to the facts; when facts occur which it cannot explain, we either correct it or replace it with a new one. The pathway of science, some one remarks, is strewn with the remains of discarded hypoth- eses." Halleck says regarding the danger of hasty 138 Logical Thinking infereiice: ^^Men moist constantly employ im- perfect induction in order to advance ; but great dangers attend inductive inferences made from too narrow experience. A child has experience with one or two dogs at his home. Because of their gentleness, he argues that all dogs are gentle. He does not, per- haps, find out the contrary until he has been severely bitten. His induction was too hasty. He had not tested a sufficiently large number of dogs to form such a conclusion. From one or two experiences with a large crop in a cer- tain latitude, a farmer may argue that the crop will generally be profitable, whereas it may not again prove so for years. A man may have trusted a number of people and found them honest. He concludes that people as a rule are honest, trusts a certain dishon- est man, and is ruined. The older people grow, the more cautious they generally be- come in forming inductive conclusions. Many instances are noted and compared; but even the wisest sometimes make mistakes. It once was a generally accepted fact that all swans were white. Nobody had ever seen a dark swan, and the inference that all swans were Testing Hypotheses 139 white was regarded as certainly true. Black swans were, however, found in Australia.'' Brooks says regarding the probability of hypotheses: ^^The probability of a hypoth- esis is in proportion to the number of facts and phenomena it will explain. The larger the number of facts and phenomena that it will satisfactorily account for, the greater our faith in the correctness of our supposition. ... If there is more than one hypoth- esis in respect to the facts under considera- tion, that one which accounts for the greatest number of facts is the most probable. . . . In order to verify a hypothesis it must be shown that it will account for all the facts and phenomiena. If these facts are numerous and varied, and the subject is so thoroughly investigated that it is quite cer- tain that no important class of facts has been overlooked, the supposition is regarded as true, and the hypothesis is said to be verified. Thus the hypothesis of the ^ daily rotation' of the earth on its axis to account for the succes- sion of day and night is accepted as absolutely true. This is the view taken by Dr. Whewell and many other thinkers in respect to the 140 Logical Thinking verification of a hypothesis. Some writers, however, as Mill and his school, maintain that in order to verify a hypothesis, we must show not only that it explains all the facts and phenomena, but that there is no other possi- ble hypothesis which will account for them. . . . The former view of verification is regarded as the correct one. By the latter view, it is evident that a hypothesis could never be verified. ' ' Jevons says: '^In the fourth step (verifica- tion), we proceed to compare these deductions with the facts already collected, or when nec- essary and practicable, we make new obser- vations and plan new experiments, so as to find out whether the hypothesis agrees with nature. If we meet with several distinct dis- agreements between our deductions and our observations, it will become likely that the hypothesis is wrong, and we must then invent a new one. In order to produce agreement it will sometimes be enough to change the hy- pothesis in a small degree. When we get hold of a hypothesis which seems to give results agreeing with a few facts, we must not at once assume that it is certainly correct We Testiitg Hypotheses 141 must go on making other deductions from it under various circumstances, and, whenever it is possible, we ought to verify these re- sults, that is, compare them with facts ob- served through the senses. When a hypothe- sis is shown in this way to be true in a great many of its results, especially when it en- ables us to predict what we should never otherwise have believed or discovered, it be- comes certain that the hypothesis itself is a true one. . . . Sometimes it will happen that two or even three quite different hypothe- ses all seem to agree with certain facts, so that we are puzzled which to select. . . . When there are thus two hypotheses, one as good as the other, we need to discover some fact or thing which will agree with one hypothesis and not with the other, because this imme- diately enables us to decide that the former hypothesis is true and the latter false." In the above statements regarding the verification of hypotheses we see references made to the testing of the latter upon the '^ facts" of the case. These facts may be either the observed phenomena or facts appar- ent to the perception, or else facts obtained 142 Logical Thinking by deductive reasoning. The latter may be said to be facts which are held to be true if the hypothesis be true. Thus if we erect the hy- pothesis that ^^AU men are mortal/' we may reason deductively that it will follow that each and every thing that is a man must die sooner or later. Then we test our hypotheses upon each and every man whom we may sub- ject to observation and experiment. If we find a single man who does not die, then the test disproves our hypotheses ; if on the con- trary all men (the ^^ facts'' in the case) prove to be mortal, then is our hypotheses proven or established. The deductive reasoning in this case is as follows: ''If so-and-so is true re- garding such-and-such a class ; and if this particular thing belongs to that class ; then it will follow that so-and-so is true regarding this particular thing." This argument is ex- pressed in what is called a Hypothetical Proposition (see Chapter IX), the considera- tion of which forms a part of the general sub- ject of Deductive Eeasoning. Therefore as Jevons has said, '^Deductive Reasoning is the Third Step in Inductive Reasoning, and pre- cedes Verification", which we have already Testing Hypotheses 143 considered. Halleck says: ^^ After Induction has classified certain phenomena and thus given us a major premise, we may proceed deductively to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made major premise. . . . Deduc- tion takes that as a fact, making no inquiry about its truth. . . . Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed. ^^ In view of the above facts, we shall now proceed to a consideration of that great class of Reasoning known under the term— Deduc- tive Reasoning. CHAPTER XV. DEDUCTIVE EEASONING We have seen that there are two great classes of reasoning, known respectively, as (1) Inductive Reasoning, or the discovery of general truth from particular truths ; and (2) Deductive Reasoning, or the discovery of par- ticular truths from general truths. As we have said. Deductive Reasoning is the process of discovering particular truths from a general truth. Thus from the gen- eral truth embodied in the proposition ^^All horses are animals,'' when it is considered in connection with the secondary proposition that ^^ Dobbin is a horse,'' we are able to de- duce the particular truth that: ^^ Dobbin is an animal." Or, in the following case we deduce a particular truth from a general truth, as follows: ^^All mushrooms are good to eat ; this fungus is a mushroom ; therefore, this fungus is good to eat. ' ' A deductive argu- ment is expressed in a deductive syllogism. Jevons says regarding the last stated il- 144 Deductive Eeasoning 145 lustration: ''Here are three sentences which state three different facts; but when we know the two first facts, we learn or gather the third fact from the other two. When we thus learn one fact from other facts, we infer or reason, and we do this in the mind. Seasoning thus enables us to ascertain the nature of a thing without actual trial. If we always needed to taste a thing before we could know whether it was good to eat or not, cases of poisoning would be alarmingly frequent. But the appearance and peculiarities of a mushroom may be safely learned by the eye or the nose, and reasoning upon this informa- tion and the fact already well known, that mushrooms are good to eat, we arrive with- out any danger or trouble at the conclusion that the particular fungus before us is good to eat. To reason, then, is to get some knowl- edge from other knowledge.^ ^ The student will recognize that Deductive Eeasoning is essentially an analytic process, because it operates in the direction of analyz- ing a universal or general truth into its par- ticulars—into the particular parts which are included within it— and asserting of them that 146 Logical Thinking **what is true of the general is true of the particnlar.'^ Thus in the general truth that **A11 men are mortal/^ we see included the particular truth that *^ John Smith is mortaP' —John Smith having been discovered to be a man. We deduce the particular truth about John Smith from the general truth about ^*all men. ^ * We analyze * ^ all men ' ' and find John Smith to be one of its particular parts. Therefore, *^ Deduction is an inference from the whole to its parts; that is, an analytic process. '^ The student will also recognize that Deduc- tive Eeasoning is essentially a\ descending process, because it operates in the direction of a descent from the universal to the particu- lar; from the higher to the lower; fronn the broader to the narrower. As Brooks says: ^* Deduction descends from higher truths to lower truths, from laws to facts, from causes to phenomena, etc. Given the law, we can by deduction descend to the facts that fall under the law, even if we have never before seen the facts ; and so from the cause we may pass down to observed and even unknown phenomena.'' Deductive Reasoning 147 The general truths which are used as the basis of Deductive Reasoning are discovered in several ways. The majority arise from In- ductive Reasoning, based upon experience, observation and experiment. For instance in the examples given above, we could not truth- fully assert our belief that: ^^AU horses are animals'' unless we had previously studied both the horse and animals in general. Nor without this study could we state that ^^ Dob- bin is a horse. '^ Nor could we, vdthout pre- vious study, experience and experiment truth- fully assert that: ^^AU miushrooms are good to eat;" or that *^this fungus is a mush- room;" and that ^ therefore, this fungus is good to eat. ' ' Even as it is, we must be sure that the fungus really is a mushroom, else we run a risk of poisoning ourselves. General truths of this kind are not intuitive, by any means, but are based upon our own experi- ence or the experience of others. There is a class of general truths which are called intuitive by some authorities. Halleck says of these: ^^Some psychologists claim that we have knowledge obtained neither through induction nor deduction; that we 148 Logical Thinking recognize certain truths the moment we per- ceive certain objects, without any process of inference. Under the head of intuitive knowl- edge are classified such cases as the follow- ing: We perceive an object and immediately know that it is a time relation, as existing now and then. We are said to have an intuitive concept of time. When we are told that the whole is greater than a part ; that things equal to the same thing are equal to each other ; that a straight line cannot enclose space, we imme- diately, or intuitively, recognize the truth of these statements. Attempts at proof do not make us feel surer of their truth. . . . We say that it is self-evident, or that we know the fact intuitively. The axioms of mathe- matics and logic are said to be intuitive.'' Another class of authorities, however, deny the nature of intuitive knowledge of truth, or intuitive truths. They claun that all our ideas arise from sensation and reflection, and that what we call ^ intuition" is merely the result of sensation and reflection reproduced by memory or heredity. They hold that the in- tuitions of animals and men are simply the representation of experiences of the race, or Deductive Reasoning 149 individual, arising from the impressions stored away in the subconsciousness of the individual. Halleck states regarding this: ^^This school likens intuition to instinct. It grants that the young duck knows water in- stinctively, plunges into it, and swims without learning. These psychologists believe that there was a time when this was not the case with the progenitors of the duck. They had to gain this knowledge slowly through ex- perience. Those that learned the proper aquatic lesson survived and transmitted this knowledge through a modified structure, to their progeny. Those that failed in the les- son perished in the struggle for existence. . . . This school claims that the in/tui- tion of cause and effect arose in the same way. Generations of human beings have seen the cause invariably joined to the effect; hence, through inseparable association came the recognition of their necessary sequence. The tendency to regard all phenomena in these relations was with steadily increasing force transmitted by the laws of heredity to pos- terity, until the recognition of the relation- ship has become an intuition. ^^ 150 Logical Thinking Another class of general truths is merely hypothetical. Hypothetical means *^ Found- ed on or including a hypothesis or supposi- tion; assumed or taken for granted, though not proved, for the purpose of deducing proofs of a point in question.'^ The hypothe- ses and theories of physical science are used as general truths for deductive reasoning. Hypothetical general truths are in the nature of premises assumed in order to proceed with the process of Deductive Eeasoning, and without which such reasoning would be im- possible. They are, however, as a rule not mere assumptions, but are rather in the na- ture of assumptions rendered plausible by experience, experiment and Inductive Eeason- ing. The Law of Gravitation may be con- sidered hypothetical, and yet it is the result of Inductive Eeasoning based upon a vast multitude of facts and phenomena. The Primary Basis of Dedv^ctive Reasoning may be said to rest upon the logical axiom, which has come down to us from the ancients, and which is stated as follows: ^^ Whatever is true of the whole is true of its parts/ ^ Or, as later authorities have expressed it: ^* What- Deductive Eeasoning 151 ever is true of the general is true of the par- ticular.'? This axiom is the basis upon which we build our Deductive Reasoning. It fur- nishes us with the validity of the deductive inference or argument. If we are challenged for proof of the statement that ' ' This fungus is good to eat/' we are able to answer that we are justified in making the statement by the self-evident proposition, or axiom, that ^* Whatever is true of the general is true of the particular. ' ' If the general ' ^ mushroom ' ' is good to eat, then the particular, ^^this fun- gus'' being a mushroom, must also be good to eat. All horses (general) being animals, then according to the axiom, Dobbin (partic- ular horse) must also be an animal. This axiom has been stated in various terms other than those stated above. For instance : '^Whatever may be affirmed or denied of the whole, may be denied or affirmed of the parts;'* which form is evidently derived from that used by Hamilton who said : ^ * What belongs, or does not belong, to the containing whole, belongs or does not belong, to each of the contained parts." Aristotle formulated his celebrated Dictum as follows: ''What- 152 Logical Thinking ever can be predicated affirmatively or nega- tively of any class or term distributed, can be predicated in like manner of all and singular the classes or individuals contained under it.'^ There is another form of Deductive Eea- soning, that is a form based upon another ax- iom than that of: ^^ Whatever is true of the whole is true of the parts. '^ This form of reasoning is sometimes called Mathematical Eeasoning, because it is the form of reasoning employed in mathematics. Its axiom is stated as follows: *^ Things which are equal to the same thing, are equal to one another/' It will be seen that this is the principle em- ployed in mathematics. Thus: ^^x equals y; and y equals 5; therefore, x equals 5.^' Or stated in logical terms: ^^A equals B; B equals C; therefore, A equals C' Thus it is seen that this form of reasoning, as well as the ordinary form of Deductive Eeasoning, is strictly mediate, that is, made through the medium of a third thing, or ' ' two things being compared through their relation to a third.'' Brooks states: "The real reason for the certainty of mathematical reasoning may be stated as follows: First, its ideas are defi- Deductive Reasoning 153 nite, necessary, and exact conceptions of quantity. Second, its definitions, as the de- scription of these ideas are necessary, exact, and indisputable truths. Third, the axioms from which we derive conclusions by compari- son are all self-evident and necessary truths. Comparing these exact ideas by the necessary laws of inference, the result must be abso- lutely true. Or, stated in another way, using these definitions and axioms as the premises of a syllogism, the conclusion follows inevi- tably. There is no place or opportunity for error to creep in to mar or vitiate our derived truths. '^ In conclusion, we wish to call your atten- tion ' to a passage from Jevons which is worthy of consideration and recollection. Jevons says : ' ^ There is a simple rule which will enable us to test the truth of a great many arguments, even of many which do not come under any of the rules commonly given in books on logic. This rule is that whatever is true of one term is true of any term which is stated to he the same in meaning as that term. In other words, we may always substitute one term for another if we know that they refer to 154 Logical Thinking exactly the same thing. There is no doubt that a horse is some animal, and therefore the head of a horse is the head of some animal. This argmnent cannot be brought under the rules of the syllogism, because it contains four distinct logical terms in two proposi- tions; namely, horse, some animal; head of horse, head of some animal. But it easily comes under the rule which I have given, be- cause we have simply to put ' some animal' in- stead of ^a horse'. A great many arguments may be explained in this way. Gold is a metal ; therefore a piece of gold is a piece of metal. A negro is a fellow creature; there- fore, he who strikes a negro, strikes a fellow creature." The same eminent authority says: ^^When we examine carefully enough the way in which we reason, it will be found in every case to consist in putting one thing or term in place of another, to which we know it to have an exact resemblance in some respect. We use the likeness as a kind of bridge, which leads us from a knowledge of one thing to a knowledge of another ; thus the true principle of reason- ing may he called the substitution of similars, Deductive Reasoning 155 or the passing from like to like. We infer the character of one thing from the character of something which acts as a go-between, or third term. When we are certain there is an exact likeness, our inference is certain; when we only believe that there probably is, or guess that there is, then our inferences are only probable, not certain/^ CHAPTEE XVI. THE SYLLOGISM The third and highest phase or step in reasoning— the step which follows after those styled Conception and Judgment— is gener- ally known by the general term ^ ' Reasoning, ' ' which term, however, is used to include the two precedent steps as well as the final step itself. This step or process consists of the comparing of two objects, persons or things, through their relation to a third object, per- son or thing. As, for instance, we reason (a) that all mammals are animals; (b) that a horse is a mammal; and (c) that, therefore, a horse is an animal. The most fundamental principle of this step or reasoning consists in the comparing of two objects of thought through and by means of their relation to a third object. The natural form of expression of this process of reasoning is called a ^* Syllo- gism. '^ The process of reasoning which gives rise to the expression of the argument in the form 156 The Syllogism 157 of a Syllogism must be understood if one wishes to form a clear conception of the Syllo- gism. The process itself is very simple when plainly stated, although the beginner is some- times puzzled by the complicated definitions and statements of the authorities. Let us sup- pose that we have three objects, A, B and C, respectively. We wish to compare C and B, but fail to establish a relation between them at first. We however are able to establish a relation between A and B ; and between C and A. We thus have the two propositions (1) ^^A equals B; and (2) C equals A'\ The next step is that of inferring that ' ^ if A equals B, and C equals A, then it must follow, logic- ally, that C equals B/^ This process is that of indirect or mediate comparison, rather than immediate. C and B are not compared directly or immediately, but indirectly and through the medium of A. A is thus said to mediate between B and C. This process of reasoning embraces three ideas or objects of thought, in their expres- sion of propositions. It comprises the funda- mental or elemental form of reasoning. As Brooks says : ^ ^ The simplest movement of the 158 Logical Thinking reasoning process is the comparing of two objects through their relation to a third/* The result of this process is an argument ex- pressed in what is called a Syllogism. Whate- ly says that: *^A Syllogism is an argument expressed in strict logical form so that its conclusiveness is manifest from the structure of the expression alone, without any regard to the meaning of the terms/' Brooks says: **A11 reasoning can be and naturally is ex- pressed in the form of the syllogism. It ap- plies to both inductive and deductive reason- ing, and is the form in which these processes are presented. Its importance as an instru- mient of thought requires that it receive spe- cial notice.'* In order that the nature and use of the Syllogism may be clearly understood, we can do no better than to at once present for your consideration the well-known ^^Kules of the Syllogism,'' an understanding of which carries with it a perfect comprehension of the Syllogism itself. The Eules of the Syllogism state that in order for a Syllogism to be a perfect Syllo- gism, it is necessary : The Syllogism 159 I. That there should be three, and no more than three, Propositions. These three prop- ositions are: (1) the Conclusion, or thing to be proved; and (2 and 3) the Premises, or the means of proving the Conclusion, and which are called the Major Premise and Minor Pre- mise, respectively. We may understand this more clearly if we will examdne the following example : Major Premise: ^^Man is mortal; (or ^^A isB^O- Minor Premise : ^ ^ Socrates is a man ; " (or ^^CisA'O. Therefore: Conclusion: ^^ Socrates is mortal" (or **C isB'O It will be seen that the above Syllogism, whether expressed in words or symbols, is logically valid, because the conclusion must logically follow the premises. And, in this case, the premises being true, it must follow that the conclusion is true. Whately says: * ' A Syllogism is said to be valid when the con- clusion logically follows from the premises; if the conclusion does not so follow, the Syllo- gism is invalid and constitutes a Fallacy, if the error deceives the reasoner himself; but 160 Logical Thinking if it is advanced with the idea of deceiving others it constitutes a Sophism/^ The reason for Eule I is that only three propositions— a Major Premise, a Minor Premise, and a Conclusion— are needed to form a Syllogism, If we have more than three propositions, then we must have more than two premises from which to draw one conclusion. The presence of more than two premises would result in the formation of two or more Syllogisms, or else in the failure to form a Syllogism. II. That there should be three and no more than three Terms. These Terms are (1) The Predicate of the Conclusion; (2) the Subject of the Conclusion; and (3) the Middle Term which must occur in both premises, being the connecting link in bringing the two other Terms together in the Conclusion. The Predicate of the Conclusion is called the Major Term, because it is the greatest in extension compared with its fellow terms. The Subject of the Conclusion is called the Minor Term because it is the smallest in ex- tension compared with its fellow terms. The Major and Minor Terms are called the Eoo- The Syllogism 161 tremes. The Middle Term operates between the two Extremes. The Major Term and the Middle Term must appear in the Major Premise. The Minor Term and the Middle Term must appear in the Minor Premise. The Minor Term and the Major Term must appear in the Conclusion. Thus we see that The Major Term must be the Predicate of the Conclusion; the Minor Term the Subject of the Conclusion; the Mid- dle Term may be the Subject or Predicate of either of the premises, but must always be found once in both premises. The following example will show this ar- rangement more clearly : In the Syllogism: *^Man is mortal; Socra- tes is a man; therefore Socrates is mortal," we have the following arrangement: ^^ Mor- tal," the Major Term; ^^ Socrates," the Minor Term; and ''Man," the Middle Term; as follows : Major Premise: ^^Man" {middle term) is mortal (major term). Minor Premise: ''Socrates" {minor term) is a man {major term). ^^ 162,, Logical Thinking Conclusion: ^^ Socrates" (minor term) is mortal (major term). [ Tke reason for the rule that there shall be *^only three^^ terms is that reasoning consists in comparing two terms with each other through the medium of a third term. There must he three terms; if there are more than three terms, we form two syllogisms instead of one. III. That one premise, at least, must he affirmative. This, because ^'from two nega- tive propositions nothing can be inferred." A negative proposition asserts that two things differ, and if we have two propositions so as- serting difference, we can infer nothing from them. If our Syllogism stated that: (1) **Man is not mortal;" and (2) that *^ Socra- tes is not a man;" we could formi no Conclu- sion, either that Socrates was or was not mor- tal. There would be no logical connection between the two premises, and therefore no Conclusion could be deduced therefrom. Therefore, at least one premise must be af- firmative. IV. If one premise is negative, the conclu- sion must he negative. This because ^^if one The Syllogism 163 term agrees and another disagrees with a third term, they must disagree with each other/' Thus if our Syllogism stated that: (1) ^^Manisw^ mortal; "and (2) that:^^Soc- rates is a man;'' we must announce the Nega- tive Conclusion that: (3) *^ Socrates is not mortal." V. That the Middle Term must he distrib- uted; (that is, taken universally) in at least one premise. This ^* because, otherwise, the Major Term may be compared with one part of the Middle Term, and the Minor Term with another part of the latter ; and there will be actually no coromon Middle Term, and conse- quently no common ground for an inference. ' ' The violation of this rule causes what is com- monly known as ^^The Undistributed Mid- dle," a celebrated Fallacy condemned by the logicians. In the Syllogism mentioned as an example in this chapter, the proposition ^^Man is mortal," really means '^ All men," that is, Man in his universal sense. Literally the prop- osition is ^^ Air men are mortal," from which it is seen that Socrates being '^a man" (or some of all men) must partake of the quality of the universal Man. If the Syllogism, in- 1 164 Logical Thi^s-king stead, read: ''Some' men are mortal," it woiild not follow that Socrates must be mortal — fre might or might not be so. Another form of this fallacy is shown in the statement that (1) "White is a color; (2) Black is a color; hence (3) Black must be White. The two pre- mises really mean ^^ White is some color; Black is some color; and not that either is ' ' all colors. ' ' Another example is : ^ ^ Men are bipeds; birds are bipeds; hence, men are birds.'' In this example ^^ bipeds'' is not dis- tributed as "all bipeds" but is simply not-dis- tributed as "some bipeds." These syllo- gisms, therefore, not being according to rule, must fail. They are not true syllogisms, and constitute fallacies. To be "distributed^^' the Middle Term must be the Subject of a Universal Proposition, or the Predicate of a Negative Proposition; to be " undistributed' ' it must be the Subject of a Particular Proposition, or the Predicate of an Affirmative Proposition. (See chapter on Propositions.) VI. That an extreme, if undistributed in a Premise, may not be distributed in the Con- clusion. This because it would be illogical and The Syllogism 165 unreasonable to assert more in the conclusion than we find in the premises. It would be most illogical to argue that: (1) ^^AU horses are animals; (2) no man is a horse; there- fore (3) no man is an animal. '^ The conclu- s.ion would be invalid, because the term ani- mal is distributed in the conclusion, (being the predicate of a negative proposition) while it is not distributed in the premise (being the predicate of an affirmative proposition). As we have said before, any Syllogism which violates any of the above six syllogisms is invalid and a fallacy. There are two additional rules which may be called derivative. Any syllogism which violates either of these two derivative rules, also violates one or more of the first six rules as given above in detail. The Two Derivative Rules of the Syllogism are as follows : Vn. That one Premise at least must he Universal. This because ^^from two particu- lar premises no conclusion can be drawn.'' VIII. That if one premise is Particular, the Conclusion must he particular also. This be- 166 Logical Thinking cause only a universal conclusion can be drawn from two universal premises. The principles involved in these two Deri- vative Eules may be tested by stating Syllo- gisms violating them. They contain the es- sence of the other rules, and every syllogism which breaks them will be found to also break one or more of the other rules given. CHAPTEE XVII. VARIETIES OF SYLLOGISMS The authorities in Logic hold that with the four kinds of propositions grouped in every possible order of arrangement, it is possible to form nineteen different kinds of valid argu- ments, which are called the nineteen moods of the syllogism. These are classified by di- vision into what are called the four figures, each of which figures may be known by the po- sition of the middle term in the premises. Lo- gicians have arranged elaborate and curious tables constructed to show what kinds of prop- ositions when joined in a particular order of arrangement will make sound and valid syllo- gisms. We shall not set forth these tables here, as they are too technical for a popular presentation of the subject before us, and be- cause they are not necessary to the student who will thoroughly familiarize himself with the above stated Laws of the Syllogism and who will therefore be able to determine in 167 168 Logical Thinking every case whether any given argument is a correct syllogism, or otherwise. In many instances of ordinary thought and expression the complete syllogistic form is omitted, or not stated at full length. It is com- mon usage to omit one premise of a syllogism, in ordinary expression, the missing premise being inferred by the speaker and hearer. A syllogism with one premise unexpressed is sometimes called an Enthymene, the term meaning ^4n the mind.'' For instance, the following: *^We are a free people, therefore we are happy," the major premise ^^All free people are happy'' being omitted or unex- pressed. Also in ^^ Poets are imaginative, therefore Byron was imaginative," the minor premise ^ ' Byron was a poet ' ' is omitted or un- expressed. Jevons says regarding this phase of the subject : ^ ' Thus in the Sermon on the Mount, the verses known as the Beatitudes consist each of one premise and a conclusion, and the conclusion is put first. ^Blessed are the merciful: for they shall obtain mercy.' The subject and the predicate of the conclu- sion are here inverted, so that the proposition is really ^ The merciful are blessed. ' It is ev- Varieties of Syllogisms 169 idently understood that ^AU who shall obtain mercy are blessed, ' so that the syllogism, when stated at full length, becomes: ^All who shall obtain mercy are blessed ; All who are merci- ful shall obtain mercy ; Therefore, all who are merciful are blessed/ This is a perfectly good syllogism." Whenever we find any of the words: ^^fee- cause^ for, therefore, since/' or similar terms, we may know that there is an argument, and usually a syllogism. We have seen that there are three special kinds of Propositions, namely, (1) Categori- cal Propositions, or propositions in which the affirmation or denial is made without reser- vation or qualification; (2) Hypothetical Propositions, in which the affirmation or de- nial is made to depend upon certain condi- tions, circumstances, or suppositions; and (3) Disjunctive Propositions, in which is im- plied or asserted an alternative. The forms of reasoning based upon these three several classes of propositions bear the same names as the latter. And, accordingly the respective syllogisms expressing these forms of reasoning also bear the class name or 170 Logical Thinking term. Tlras, a Categorical Syllogism is one containing only categorical propositions; a Hypothetical Syllogism is one containing one or more hypothetical propositions ; a Disjunc- tive Syllogismi is one containing a disjunctive proposition in the major premise. Categorical Syllogisms, which are far more common than the other two kinds, have been considered in the previous chapter, and the majority of the examples of syllogisms given in this book are of this kind. In a Categorical Syllogism the statement or denial is made pos- itively, and without reservation or qualifica- tion, and the reasoning thereupon partakes of the same positive character. In propositions or syllogisms of this kind it is asserted or as- sumed that the premise is true and correct, and, if the reasoning be logically correct it must follow that the conclusion is correct, and the new proposition springing therefrom must likewise be Categorical in its nature. Hypothetical Syllogisms, on the contrary, have as one or more of their premises a hypo- thetical proposition which affirms or asserts something provided, or *4f," something else be true. Hyslop says of this : ' ' Often we wish Varieties of Syllogisms 171 first to bring out, if only conditionally, the truth upon which a proposition rests, so as to see if the connection between this conclusion and the major premise be admitted. The whole question will then depend upon the matter of treating the minor premise. This has the ad- vantage of getting the major premise admit- ted without the formal procedure of proof, and the minor premise is usually more easily proved than the major. Consequently, one is made to see more clearly the force of the ar- gument or reasoning by removing the ques- tion of the material truth of the major premise and concentrating attention upon the relation between the conclusion and its conditions, so that we know clearly what we have first to deny if we do not wish to accept it. ' ' By joining a hypothetical proposition with an ordinary proposition we create a Hypo- thetical Proposition. For instance: ''// York contains a cathedral it is a city; York does contain a cathedral; therefore, York is a city.'' Or: ^^If dogs have four feet, they are quadrupeds; dogs do have four feet; there- fore dogs are quadrupeds." The Hypotheti- cal Syllogism may be either affirmative or 172 Logical Thinking negative ; that is, its hypothetical proposition may either hypothetically affirm or hypothet- ieally deny. The part of the premise of a Hy- pothetical Syllogism which conditions or ques- tions (and which usually contains the little word * 4f ^ is called the Antecedent. The ma- jor premise is the one usually thus condition- ed. The other part of the conditioned propo- sition, and which part states what will happen or is true under the conditional circumstances, is called the Consequent. Thus, in one of the above examples : ^ * If dogs have four f eet ^ ' is the Antecedent; and the remainder of the proposition: *^they are quadrupeds'^ is the Consequent. The Antecedent is indicated by the presence of some conditional term as : if, supposing^ granted that, provided that, al- though, had, were, etc., the general sense and meaning of such terms being that of the little word '^i/.'' The Consequent has no special indicating term. Jevons gives the following clear and simple Rules regarding the Hypothetical Syllogism : I. * ^ If the Antecedent be aflSrmed, the con- sequent may be affirmed. If the Consequent be denied, the Antecedent may be denied.'* Varieties of Syllogisms ; 173 IL ^^ Avoid the fallacy of afl&rming the consequent, or denying the antecedent. This is a fallacy because of the fact that the condi- tional statement made in the major premise may not he the only one determining the con- sequenf The following is an example of '^Affirming the Consequent:" ^'If it is rain- ing, the sky is overclouded; the sky is over- clouded; therefore, it is raining. '^ In truth, the sky may be overclouded, and still it may not be raining. The fallacy is still more ap- parent when expressed in symbols, as follows: ''If A is B, C is D ; C i5 D ; therefore, A is B.'^ The fallacy of denying the Antecedent is shown by the following example: ''If Ea- dium were cheap it would be useful ; Radium is not cheap ; therefore Radium is not useful. ' ' Or, expressed in symbols : "If A. is B, C is D ; A is not B ; therefore C is not D." In truth Radium may be useful although n<5t cheap. Jevons gives the following examples of these fallacies: ^^If a man is a good teacher, he thoroughly understands his subject ; but John Jones thoroughly understands his subject; therefore, he is a good teacher." Also, ^^If snow is mixed with salt it melts ; the snow on 174 Logical Thinking the ground is not mixed with salt; therefore it does not melt/' Jevons says: *^To affirm the consequent and then to infer that we can affirm the ante- cedent, is as bad as breaking the third rule of the syllogism, and allowing an undistributed middle term. . . . To deny the antece- dent is really to break the fourth rule of the syllogism, and to take a term as distributed in the conclusion which was not so in the pre- mises/' Hypothetical Syllogisms miay usually be easily reduced to or converted into Gategori- cal Syllogisms. As Jevons says : * * In reality, hypothetical propositions and syllogisms are not different from those which we have more fully considered. It is all a matter of the con- venience of stating the propositions.*^ For in- stance, instead of saying: *^If Eadium were cheap, it would be useful," we may say ' ^ Cheap Radium would be useful ; " or instead of saying : ^ ' If glass is thin, it breaks easily, ' ' we may say ^^Thin glass breaks easily." Hy- slop gives the following Rule for Conversion in such cases : ^ * Regard the antecedent of the hypothetical proposition as the subject of the Varieties of Syllogisms 175 categorical, and the consequent of the hypo- thetical proposition as the predicate of the categorical. In some cases this change is a very simple one; in others it can be effected only by a circumlocution. '' The third class of syllogisms, known as The Disjunctive 8yllogism\y is the exception to the law which holds that all good syllogisms must fit in and come under the Eules of the Syllo- gism, as stated in the preceding chapter. Not only does it refuse to obey these Eules, but it fails to resemble the ordinary syllogism in many ways. As Jevons says: ^^It would be a great mistake to suppose that all good logi- cal arguments must obey the rules of the syl- logism, which we have been considering. Only those arguments which connect two terms to- gether by means of a middle term;, and are therefore syllogisms, need obey these rules. A great many of the arguments which we daily use are of this nature ; but there are a great many other kinds of arguments, some of which have never been understood by logicians until recent years. One important kind of ar- gument is known as the Disjunctive Syllo- gism, though it does not obey the rules of the 176 Logical Thinking syllogism, or in any way resemble syllo- gisms/^ The Disjunctive Syllogisml is one having a disjunctive proposition in its major premise. The disjunctive proposition also appears in the conclusion when the disjunction in the ma- jor premise happens to contain more than two terms. A disjunctive proposition, we have seen, is one which possesses alternative predi- cates for the subject in which the conjunction *^or^^ (sometimes accompanied by ^^ either^') appears. As for instance : ^ ^ Lightning is sheet or forked ;'' or, ^^ Arches are either round or pointed;'^ or, ^^ Angles are either obtuse, or right angled, or acute. ' ' The different things joined together by ^^or'' are called Alterna-