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Necessarily, therefore, it must be, for the most part, a compilation of such views a^ have obtained general acceptance, and can lay but little claim to any high degree of originality. At the same time, I may be permitted to state that some features exist which serve to distinguish this Treatise from its numerous predecessors, and which will, I hope, prove of service to the student by inciting him to examine for himself such theories and principles as come under his notice. Those features to which I more particularly allude, are the reference of all so- called " Immediate Inferences " to the class of syllo- gisms ; the grounds for an extended adoption of Aris- totle's Dictum ; the refutation of the charge that every syllogism involves a petitio prmcipii ; the explication of the inductive theory in Applied Logic ; and, finally, IV PREFACE. the doctrine of classification, by which every detail and branch of Logic is shown to exist in harmonious unison. And as these views are, in a measure, opposed to those contained in works of great repute, I have appended to the body of this Treatise four Articles, wherein are set forth such arguments as I think suffi- cient to justify me in advancing the above-mentioned doctrines. I also deem it advisable to state that it has been my endeavour to give this work as suggestive a character as possible ; and, therefore, although it belongs to a rudi- mentary series, professing to treat only upon the first elements of Logic, I am yet not without hope that it will be found a sufficient introduction to such compre- hensive and elaborate treatises as those of Mr. Mill, Professor De Morgan, and others. But while I have thus been compelled to satisfy myself in many cases with an enunciation rather than with a full investigation of certain doctrines, I still trust that, in the following pages, the student will find all that is really requisite to give him a fair, practical knowledge of Logic. The chapter on Applied Logic is, I am sensible, but a mere sketch. As, however, to do justice to so vast a subject would require a great extension of the present limits, and would thus curtail the utility of this Treatise by enhancing its price, I have contented myself with directing the student's attention to such points as are most important, both in theory and prac- tice. For the same reason, nothing beyond the bare outlines is given of such new doctrines as I have here PREFACE. adopted; all further development of them being de- ferred to a future occasion. I take this opportunity of acknowledging my many and great obligations to those writers upon Logic whose works I have consulted ; and although it may seem invidious to particularise, yet as, for reasons which will be found specified in their proper place, I have expressly referred to Mr. John Stuart Mill, as being the advocate of certain opinions which are com- bated in the following pages, I think it only just that I should here record my admiration for the profound philosophy and great attainments which are so apparent in the writings of that gentleman. S. H. E. London, January, 1865. CONTENTS. INTRODUCTION CHAPTER I. AN INQUIRY INTO THE VARIOUS MEMBERS OP AN ARGUMENT . . 7 CHAPTER II. OF NOTIONS OR TERMS : f 1. Simple-apprehension 14 2. Abstraction of Common -notions 16 3. Predicables, Extension, and Intension .,..,.. 18 4. Division of Common-notions 18 5. Positive, Negative, and Privative Terms 20 6. Definition 21 7. Names and their Divisions 22 8. Opposition of Terms 23 9. Structure of Terms 24 10. Conclusion and Recapitulation 24 CHAPTER III. OF JUDGMENTS OR PROPOSITIONS : 1 . Formation of Judgments . . . . r .... 27 2. Categorical Propositions 28 3. Hypothetical or Conditional Propositions 29 4. Disjunctive or Alternative Propositions 29 5. Quantity of Propositions . 30 6. Quality of Propositions 30 7. Distribution of Terms 31 8. Relation of Terms . 32 CONTENTS. vii Pajre 9. Systematic Classification of Propositions 33 10. Table of Possible Propositions 33 1 1 . Interpretation of the Copula 84 ] 2. On some other Properties of Judgments 35 13. Concluding Remarks 35 CHAPTER IV. OF REASONING OR ARGUMENT SYLLOGISMS: $ 1. Reasoning in General 38 2. Syllogisms Inference 39 3. Opposition 41 4. Conversion 44 5. Coincident Junction 47 6. Mediate Inference formally expressed as such its Divisions 48 7. The Fundamental Law of Mediate Inference 49 8. Of Figure 54 9. Remarks upon the Four Figures 54 10. Of Mood or Mode 57 11. Table of Valid Syllogisms 58 12. Induction and Deduction 61 13. Extension and Intension 64 14. Denomination 66 \5. Syllogistic arrangement of Propositions 60 16. Conditional Syllogisms 6? 17. Disjunctive Syllogisms 72 18. The Dilemma 73 19. Incomplete Syllogisms 75 20. Complex Arguments, or Chains of Reasoning .... 76 21. Recapitulation 80 22. Conclusion 82 CHAPTER V. OP FALLACIES: 1. Applied Logic in general 84 2. Classification of Fallacies 85 3. Formal Fallacies SS 4. Material Fallacies C^uarternio Terminorum 90 5. Material Fallacies Premiss unduly assumed 95 6. Material Fallacies Ignoratio Elenchi Ill 7. Conclusion 115 Viii CONTENTS. CHAPTER VI. Page OF LOGIC AS PRACTICALLY APPLIED: $ 1. Introductory Remarks ... 11? 2. Observation 119 3. Reflection 1. Of Laws and Causes 126 2. Of Induction 331 3. Of Deduction, Hypothesis, and Verification . . . 140 4. Of Analogy 143 5. Of Chance and Probability 345 6. Examples of Reflection a. The Discovery of Neptune 148 b. Kirchhoff's Researches on the Solar Spectrum . 150 4. Conclusion 152 APPENDIX. \ ON JUDGMENTS 155 B. ON THE SO-CALLED IMMEDIATE INFERENCES 159 C. ON THE DICTUM DE OMNI ET NULLO ] 63 D. ON THE SYLLOGISM CONSIDERED AS A Petitio Principii ... 166 Of THB LOGIC. INTRODUCTION. LOGIC may be not inaptly described as the grammar of thought ; that is to say, it reveals and explains the principles according to which our judgments are formed, in much the same manner as grammar analyses the laws which regulate the expression of our thoughts by means of speech. It will, therefore, be seen that Logic is a science of universal extent, inasmuch as wherever any process of reasoning is carried on, there will be found, in full operation, those mental laws which it is the office of Logic to examine and systematise. It does not, however, follow that every person who reasons is a logician, for it is only when a process of judgment is carried on in regular order, and according to the rules derived from a study of the science, that such an appellation could be justly bestowed. And, in like manner, it would be absurd to suppose that there can be no correct reasoning without a good knowledge of Logic; for, in order to perceive the error of such a view, we have only to consider for a moment the mode in which every science is formed. Take, for example, the science of astronomy : the heavenly bodies had been urged through space, by the operation of definite cosmical laws, for ages previous to the discovery of those laws by human philosophers, and it was the very fact of such motions being in progress, which led to the investigation of the principles concerned. B Z INTRODUCTION. Thus, too, with regard to Logic : men had thought and rea- soned according to certain laws, long before Aristotle, by ob- serving and reflecting upon the various judgments which came under his notice, was able to enunciate the great funda- mental truth upon which they were based. It is from con- siderations such as these that we speak of scientific discoveries, and not of scientific inventions ; for tLe latter term can only be applied to some new method of accomplishing a specific object, while the former is always used when we speak of any fresh law or principle, which, previously existing, has been brought to light by the exertions of the philosopher. Like, then, as Newton discovered gravitation, so did Aristotle dis- cover the syllogism ; and, therefore, the notion that the use of the syllogism is merely one method of reasoning, is at once shown to be altogether erroneous. The truth is, that there can be no other process of forming a judgment, since every conceivable example of reasoning may, by the application of certain rules, be reduced to the syllogistic form. From what has now been said, the true value of Logic will be easily discerned, and as its subject is one which lies at the root of all other sciences, its importance can hardly be over- estimated. Its principal use is that it enables us to reason correctly, by furnishing us with various rules and standards wherewith to test the validity of any argument that may be brought before us. And here it is requisite to guard against a very prevalent misconception ; I allude to the idea, that, by means of Logic, one may ascertain the truth or falsehood of any statement. The source of this error is to be found in the supposition that Logic is concerned with the subject of the various statements (technically, propositions) whose relations to each other it investigates ; whereas, in reality, it merely considers their form. Thus, the two propositions, " Water is a fluid," and, " Evil is good," would by a logician be con- sidered as precisely similar, although one of them is false, INTRODUCTION. 3 and the other true. Again, the following argument or syllogism All fluids are poisonous, Water is a fluid ; Therefore Water is poisonous, is perfectly valid and correct, although the conclusion arrived at is false. To render this point quite plain and intelligible, let us adopt the following course : it was above stated that Logic merely considers the form and not the subject (or matter) of propositions ; accordingly, for all logical purposes, we shall not alter the nature of the propositions employed, if we substitute letters for the words we used to express the substances or notions of which we spoke. Thus, instead of " water is a fluid," let us say " A is B," and for " evil is good," let us put " is D : " we then see at once, that in both in- stances we use exactly the same kind of proposition. Again, let us similarly convert the syllogism : we have All A's are B, C is an A; Therefore C is B ; an argument which remains unalterable in form, no matter what ideas are expressed by the letters.* This it is which confers such rigorous accuracy upon all the results and developments of Logic. Indeed, as Professor De Morgan has said, Mathematics and Logic are the two exact sciences. The primary doctrines of chemistry may require alteration as new combinations of the elements are brought to light ; the progressive theories of physiology are modified with every advance of microscopical investigation ; the glorious revelations of astronomy present an ever-changing aspect ; but Logic, like Mathematics, abides, eternal and immutable. The preceding remarks will probably have pointed out to the reader that Logic is concerned with language as distin- * For further information as to form and matter aae page 39 et seq. B 2 INTRODUCTION. guished from the ideas conveyed by the use of words ; but in order that the student may be well grounded in the funda- mental truths of the science before he proceeds to study its details, I shall add some further observations upon this point. Language in its ordinary sense, that is, speech, is useful as a means of communication in two ways : it enables us to minutely describe, or, in other words, to analyse, our various ideas, and it also enables us to convey, by a single sound or sign, the combined impression of many particulars. Take, for example, this description : " I gazed upon her form Transcendent, and upon her face which gleamed Pale through her tears, like some fair statue bathed In the cold moonlight ; and I marked the mute, Sad eloquence of that love-charged heart Which quickly heaved its alabaster veil In trembling fear." Here gradually dawn upon us the many subjects of atten- tion which exist in a single object, and it is only by means of a protracted analysis such as the above, that we are able to convey a complete idea of it. But then, again, we sometimes wish to express the notion of a numerous class of objects, in such a manner that the impression produced may serve for any one of them. Thus, suppose the objects were men, horses, cows, sheep, lions, &c. : we should merely confine our attention to those points in which they resembled each other, and should bestow a name upon this group of qualities, such as '' animal/' by the use of which we might attain the desired end. This process is the reverse of the first, but at the same time is in a measure dependent upon it, for in order to ascer- tain the points of resemblance between various objects, a partial analysis is at all events necessary. Accordingly, Logic takes cognizance of both operations, and investigates the relations which subsist between them and the act of reasoning itself. INTRODUCTION. It has been said above that language enables us to convey by a single sound or sign, the combined impression of many particulars. Now it is our ability to do this, which alone enables us to conduct a process of reasoning ; or otherwise we should find it impossible to judge of the relations between two ideas or objects a condition which is evidently essential to an argument. One of the most curious proofs of this is afforded by deaf-and-dumb persons, who, when they have once been taught to speak by means of their fingers, are observed to use this means of recording their impressions, even when thinking alone. And it has been asserted, that " it will be found by any one who will question a deaf-mute who has been taught language after having grown up, that no such thing as a train of reasoning had ever passed through his mind before he was taught."* We have hitherto considered Logic purely as a Science, but it is very frequently regarded as an Art, and perhaps it is this mode of viewing it which holds out the strongest in- centive to the student. For it can only be the few who will voluntarily engage in the study of principles which, complete in themselves, give promise of no result beyond that delight which naturally arises from the consideration of organic symmetry and perfection ; the great majority being altogether occupied with the hope of turning their knowledge to some useful purpose. Therefore, in the following pages I shall endeavour to give as practical an effect as possible to the various laws of thought which we shall investigate ; and the student will thus find that Logic, instead of being merely an " ingenious recreation," is in reality a powerful aid to the pro- secution of all other studies. Not that reasoning alone will suffice for the discovery of truth, as to do this an extended observation of facts is indispensable ; but when we have col- lected a sufficient quantity of facts, we shall find that an * Whately's "Logic," p. 13. D INTRODUCTION. acquaintance with Logic will greatly assist us in deducing a correct inference. I now trust that a tolerably clear notion has been gained of the nature and extent of Logic ; and in the next place I shall briefly describe the method of proceeding which I intend to adopt in my explanation of the science. First, then, it will be advisable to select some example of pure reasoning, and, having dissected it, to point out the various members of which it is composed, together with the principles which form, as it were, the framework of the structure. We shall thus obtain a bird's-eye view of the country before us, and we shall be able to advance without doubt or hesitation to the end of our journey. Accordingly, it will next become our duty to examine each branch separately and in detail, which being done, we shall proceed to the consideration of the various combinations formed by these branches, and so at length we shall be enabled to construct, or to analyse at pleasure, any train of argument, however extensive it may be. Here, strictly speaking, the study of Logic as such should terminate ; but in order that the utility of this treatise may be increased, I shall devote a chapter to the discussion of the several fallacies which are of most frequent occurrence, giving such rules for their treat- ment as have been found most effectual. The concluding por- tion of the work will consist of some remarks upon the proper application of Logic, with various illustrative examples. Such is the course which I propose to take, and if the student be not dismayed by the shadowy anticipation of tech- nical difficulties which have no real existence, he will find an ample reward for all his labours. A systematic regulation of his intellect; a probe wherewith to examine the most mysterious doctrines of philosophy ; a wand before whose potent touch the stately fabric of deceit and fraud will dis- appear ; these are but a few of the benefits to be obtained by a study of Logical science. TKM [JJ1TIVER3ITT /> A TREATISE ON LOGIC. CHAPTER I. AN INQU.RY INTO THE VARIOUS MEMBERS OF AN ARGUMENT. IT has already been stated that our first step towards a right understanding of Logic must be a strict examination of some definite argument. Now, as we are not all concerned with the subject of the reasoning, it will be the best plan for us to choose some example which shall present us with the fe west and most simple ideas, so that we may devote our whole at- tention to the reasoning process, and not be led aside by any extraneous matters. Accordingly, let us take for the subject of our investigation, the proof of Euclid's first proposition, which may be thus stated in arguments or syllogisms. 1. The radii of the same circle are ;> *. equal to one another, / ./ \. A and A B are radii of the f> A* ^ E ; same circle BOD; .-. A is equal to A B. -^-LJluX. .-''' 2. The radii of the same circle are equal to one another, B C and A B are radii of the same circle ACE; .-. B C is equal to A B. 3. Things which are equal to the same thing are equal to one another, A C and B C are equal to the same thing (viz. A B) ; /. A is equal to B C. Taking any one of the above syllogisms, we see that it is composed of three statements, among which this relation sub- sists ; that if we admit the truth of the first two, we cannot 8 AN INQUIRY INTO THE avoid admitting the truth of the last. This last statement IB termed the conclusion ; the other two being called the pre- mises. And here the question comes why is it, that, having admitted the premises, we are compelled to admit the conclu- sion ? To answer this we must examine the constitution of each premiss, and ascertain whatever is implied thereby. Thus, in the first of the syllogisms given above, w r e find as a commencement, the following assertion or proposition : " radii of the same circle are equal to one another :" where a certain property, viz., " equality," is asserted, or, in logical language, predicated, of a group or class of objects, viz., " radii of the same circle." That is to say, " equality " is a property common to every individual comprehended in the class. The second proposition is to this effect : " A and A B are radii of the same circle ;" that is, we assert A and A B to be individuals of that very class, concerning which we admitted that " equality " was common to every one of its members. Consequently we are compelled to admit that A and A B possess the property of " equality," and this admission forms the conclusion. Our mode of procedure has therefore been as follows : we first predicate something of a certain class of objects ; we then assert that certain individuals belong to that class ; and lastly, we predicate the same thing of the individuals which we had predicated of the class. Now suppose the syllogism had stood thus : " Radii of the same circle are not equal to one another ; A and A B are radii of the same circle ; therefore A C is not equal to A B :" it would still be perfectly valid, for, having denied that a certain property is enjoyed by a class of objects among which we admit certain individuals to be, we must necessarily deny that those individuals possess the property in question. We thus arrive at this axiom or law : " Whatever is affirmed or denied altogether of any whole, may in like manner be affirmed or denied of any individual part belonging to, or comprehended in, that whole." Aristotle was the first who distinctly enunciated this great truth, and it is commonly known as " Aristotle's Dictum," or the " dictum de omni et nullo" VARIOUS MEMBERS OF AN ARGUMENT. 9 It may at first seem strange that a statement so simple and obvious should be characterised as a great truth ; but a very little reflection will soon convince us that any law which is of universal extent and application, must be the more valuable according as it is the more simple ; and therefore it is with justice that Aristotle is honoured for having enabled us to explain the formation and examine the validity of any argu- ment whatever, in so plain and satisfactory a manner. Another fact also which will appear improbable, is that the dictum may be universally applied ; that is to say, no syllogism can be valid or admissible unless it strictly complies with the require- ments of the dictum, and in a later portion of this work rules will be found by means of w 7 hich it is possible to bring every specimen of reasoning to this test. Indeed, if we would become thoroughly acquainted with the principles of logical science, we must invariably bear in mind the dependence of every train of thought upon the dictum of Aristotle. But it is now time that we should revert again to our example of reasoning, and continue the division of each syllogism into its component parts. We have already seen that a syllogism consists of three propositions divided into the two premises and the conclusion ; we will now examine the propositions themselves more closely. In the statement " radii of the same circle are equal to one another," we see three distinct portions : first, the subject of which we are speaking, and of which something is predicated (that is, asserted or denied) ; secondly, the attribute or condition which is predicated of the subject ; and thirdly, the sign of affirmation or negation. The technical names for these are, the subject, the predicate, and the copula. In the proposition above quoted it will be observed that the whole of the subject is spoken of; for when we say " radii of the same circle," we evidently mean every radius that could possibly be drawn. Accordingly, such a proposition is termed universal, as the predicate is universally applied to every part of the subject. But if we had spoken of a portion only of the subject, and had said " some of the radii of the same circle are equal to one another," we should have what is called a particular proposition inasmuch as the predicate B 3 10 AN INQUIRY INTO THE is affirmed of some particular part of the subject, and not of the whole. Thus we see that propositions may be always divided into universal and particular, and this distribution is said to be made according to quantity. Again, " equality " is predicated affirmatively of " radii of the same circle ;" the sentence is therefore termed an affirma- tive proposition : while if the predicate had been denied of the subject, thus, " radii of the same circle are not equal to one another," it would have been a negative proposition. We have, therefore, another system, by means of which to classify every possible proposition, and this distribution is called a division according to quality. And here we have introduced to our notice a very im- portant branch of Logic, namely, division ; by means of which mental process we may at all times obtain a distinct grasp of any subject which occupies our attention. Indeed, this faculty would seem to be an inherent principle of our nature, for whatever may be the science, an attempt has always been made from the commencement, to properly classify and arrange its various subdivisions ; the best ex- amples of such a course being found in such studies as Natural History, Comparative Anatomy, &c. Accordingly, as Logic instructs us concerning the principles upon which alone a perfect division can be performed, it is an additional proof of the necessity which exists for an intimate acquaintance with that science. We have now glanced quickly, but I trust intelligibly, at the structure of a syllogism and its component propositions. It remains that we should consider the nature of the materials of which the propositions are formed, having already discussed the mode of framing them together. The subject of the first proposition is, " radii of the same circle ;" and in saying this we speak of a class, the individuals of which, though they may differ among themselves in many respects, yet have some features common to all. Thus, one radius of a circle will be unlike its fellows as regards position, but it will be exactly similar with respect to magnitude. So, when speaking of a given circle we mention its " radius," we employ a name that may be applied to any straight line whatever that is VARIOUS MEMBERS OP AN ARGUMENT. 11 drawn from the centre to the circumference. Such a word is called by logicians, a common-name or common-term, because, as just stated, it is enjoyed in common by a multi- tude of objects. But if we proceed to the subject of the second proposition, we are met by terms which differ entirely from the preceding, viz., " AC and A B," the names given to individual radii. These of course can only be applied to a single object, and are consequently known as singular- terms, thus serving to distinguish the various members of a common-term. Let us here pause for a moment to consider the results at which we have now arrived, and let us fully comprehend the purport of common and singular terms. We see that a common -term when applied to an object, merely indicates that it possesses certain properties which are shared in like manner b;y all the other constituents of a specified group. It is, therefore, evident that such a term or name belongs in reality not to an individual, but to a definite combina- tion of qualities which are found in it. And the mode in which a common-term is obtained, is by comparing a number of separate objects, observing the points wherein they agree, combining these points of agreement into one idea, and then giving this combination a name, so that at any future time we may be able to recall the idea without having the trouble to go through the same operations again. Thus, for ex- ample, men observed the properties of many natural bodies, and finding that a certain number refused more or less to alter their volume or shape, the name of solidity was con- ferred upon this property ; and, accordingly, whenever we hear the term " solid " applied to anything, we at once know that the body spoken of will resist a change either as to volume or shape. This process of combining various pro- perties into one idea is called abstraction, and is the reverse of that previously described, namely division ; for while the latter is al ogether occupied in discovering the points of difference between various notions, the former exclusively deals with the points of resemblance. A singular -term is on the contrary employed to designate individuals instead of classes, and therefore is a mere arbi- 12 AN INQUIRY INTO THE trary sign which conveys the notion of one single object. Such are all names of persons, rivers, cities, &c., and even common-terms may be converted into singular-terms by the employment of the demonstrative pronouns, as " this book," " that house," &c. &c. There is yet another distinction of the members of a pro- position, which it will be needful to notice. We have hitherto spoken of the subject and predicate together with the copula ; now the two former are called the terms, as when a proposi- tion is expressed in logical order they will form its respective boundaries or terminations, the copula occupying an interme- diate position. Of these terms it will be observed that there are three in each syllogism ; two forming the subject and predicate of the conclusion, while the other is confined to the premises, in both of which it occurs. From these positions it is, that the names of the respective terms are derived ; thus, the pre- dicate of the conclusion is called the major-term, the sub- ject of the conclusion is known as the minor-term, and the remaining term is characterised as being the middle-term. These names, too, are used to distinguish the premises, for that proposition which contains the major-term is called the major premiss, while the other, for a similar reason, is styled the minor premiss. We are now in a condition to perceive clearly the full force of the train of reasoning which we chose in the first place as the subject of our analysis. In the first syllogism, we see that a middle -term, " radii of the same circle," is chosen, with which are respectively compared the major-term, " mutual equality," and the minor term, " A and A B ;" the result of this comparison being, that a certain relation, viz., " mutual equality," may be predicated of A C and A B. In the second syllogism, we have precisely the same major and middle terms, but a different minor-term, which, however, is found to bear a similar relation towards " mutual equality," as did the other minor, "AC and A B." The object then sought to be at- tained, is to show the equality of certain portions of the two minor-terms, and this is done by employing a fresh middle- term to serve as a means of connecting the idea of " equality " VARIOUS MEMBERS OF AN ARGUMENT. 13 with the notion u A C and B 0." This middle-term is " things which are equal to the same thing," and when it has been properly applied, as in the third syllogism, we attain the de- sired result, viz., "AC and B are equal to one another," or " A is equal to B 0." Finally, let us recapitulate the information which we have acquired from our rapid survey of the extent of Logic. We .find that it will be necessary to investigate, first the subject of notions or terms ; next, the comparison of terms, or pro- positions ; and finally, the deducing a conclusion from the juxtaposition of two propositions, or in other words, the nature and construction of syllogisms. Necessarily this preliminary chapter has been somewhat discursive, and has but briefly sketched the more salient prin- ciples and branches of Logic. This glimpse of the path before him, however, as stated in the Introduction, will pro- bably prove of great assistance to the student, for he will now proceed to a more detailed examination of the science, with a good notion of what he may expect to meet ; a course which is surely preferable to that too often followed, whereby the learner is introduced at once to tedious technicalities, without the slightest idea as to where he will find himself at the end of his study. 14 CHAPTER II. OP NOTIONS OR TERMS. THE student is now about to descend into the plain, and to enter upon that road whose various windings and ultimate end he has recently sun 'eyed from an eminence. Conse- quently he will for awhile lose sight of the goal, but as he is in a great measure acquainted with the general features of his course, he will not be dismayed if the path should not immediately appear to tend in the desired direction. And here I may mention that at first we shall proceed through a region abounding in hard names ; but as the principal technicalities of the science have been already introduced, together with the principles upon which they are based, no difficulty will, I apprehend, be experienced in conquering what might otherwise prove a rather formidable array. Our immediate subject is, of course, notions or terms ; for we must obviously possess a certain number of ideas (logically, terms), before it would be possible for us to make any attempt whatever at a train of thought or reasoning. Accordingly, it might be considered necessary that I should in the first place examine the question as to whether ideas are coeval with the mind itself, or whether they are the results of ex- perience : but, were I to do this, I should quit the domains of Logic for those of metaphysics. Suffice it, therefore, if I describe the manner in which we obtain certainly many of our ideas, and possibly all. 1. Simple -apprehension. Yv r hen any object is presented to the mind, and the atten- tion is directed to it, a certain mental impression is produced, unintelligible indeed as to its nature, but the result of which OF NOTIONS OR TERMS. 15 is that the object is recognised when again observed. That is to say, an idea is formed in the mind of that combination of properties and appearances which revealed itself to the senses upon inspection. Such an idea is termed an intuition, or singular -representation, and evidently can only refer to an individual object. It is also necessary for purposes of inter- communication, that names should be given to these several intuitions, and these names are called singular -terms ; such, for example, are, " London, France, Charles, Bucephalus." Now it is evident that if a separate personal name were to be bestowed upon each object, great confusion would result ; and as in the majority of cases it is by no means essential that, when speaking of an object, reference should be made to some particular individual, it would speedily be found necessary to assign certain class-names, under which a number of similar objects might be grouped. This, accordingly, is done in the following manner. Suppose a great many individual books had come under our notice, and we wished to be able to recall at pleasure the general idea produced by any one of them, without, however, mentioning it by name. In the first place we should com- pare several together, and ascertain the points in which they resembled, and differed from each other ; thus, we should perceive that some were illustrated and others not ; that one related to biography, another to history, and a third to mathe- matics ; that there were many gradations of size and bulk ; that they were bound in various styles; but also that every one of them agreed in possessing certain definite propertiers. These properties we should then proceed to abstract or separate from those qualities wherein the volumes differed ; and, combining the former into one idea, we should be able to conceive of a class of things, each member of which would contain in itself all those marks or attributes which we had selected as essential to the idea in question. Finally, we should apply some name, in the present case '* book," to the class thus imagined, and in this manner we should ac- complish the object with which we had set out. The process which has here been described is that of ab- straction ; it will be seen to consist of five steps, viz., com- 16 OF NOTIONS OR TERMS. parison, or placing several objects together in order to judge of their resemblance ; reflection, by which we decide upon the properties in which they agreo or differ ; abstraction, which enables us to form the points of resemblance into one idea complete in itself; generalisation, or the conception of a class whose members shall each contain (inter alia) this com- pound idea; and denomination, by means of which we im- pose a name for the purpose of recalling to our remembrance both the class and the idea ; the names thus imposed, being known as common terms ; e.g., " sea, river, mountain." Into these two classes, then, viz., singular and common re- presentations, may all our notions be divided ; and as that action of the mind which merely consists of forming an idea is termed simple-apprehension, so it is said to be incomplex- apprehension when we receive a notion of individuals with- out observing any relation between them, or complex -appre- hension, when we perceive the existence of a class. 2. Abstraction of Common-notions The faculty of abstraction is possibly the most active and powerful with which the human mind is endowed ; far from remaining quiescent when it has succeeded in forming a common -notion (or conception as distinguished from intuition) by the comparison of separate individuals, it instantly pro- ceeds to repeat the process on a larger scale. This is done by treating a number of classes as so many individuals, and then when their points of resemblance have been noted and combined into one idea forming a higher class, which will include amongst its members all the former classes. Nor need we stop even here, for it is evident that no limit exists to the number of repetitions of such a proceeding, unless indeed there be a limit to the exercise of imagination itself. Now r every science arranges the subjects upon which it treats, in a perfectly similar manner, this being based upon the results of abstraction : accordingly, logicians have devised a certain scheme of names for this system, which we shall now explain. OF NOTIONS OR TERMS. 17 A single object is called an individual, and comprehends within itself two distinct sets of marks or attributes ; these are; first, that combination of qualities which we abstracted to form the idea of a class, and, secondly, such attributes as remain. Each of the former is termed a property, whilst the latter are called accidents or differences ; the class of which the individual is a member being known as a species. This species, which is merely composed of individuals, is culled the lowest or infima species, and the next higher class, being founded upon a consideration of infima species, is termed a genus : the latter name, however, is only applied when we contrast the higher class with the lower, for in the next stage of our conceptions we come to a yet wider genus, of which the previous genus is only a species. Thus we go on until we arrive at the most comprehensive class of all, which is accordingly named the highest or summum genus, and this, of course, can never be a species, for there is no higher class to include it. Every other genus is called a sifoaltern genus, being alternately a species and a genus. An example of the above method of arrangement may be given as follows : Individual .... Iron. Intima species . . . Metal. SuDaitern genus . . Elementary substance. -. Summum genus . . Matter. Accordingly, we can say that iron is a kind of metal ; that a metal is a species of elementary substance ; that an elemen- tary substance is a genus of which metals are a species, or that an elementary substance is a species of matter. It is, of course, quite clear that the precise details of the system, such as the question of what are to be considered as individuals, or where abstraction is to cease, must be left to the arbitrary regulations of each science : the only point here insisted upon being the fact that this system is employed in every pursuit which engages the human mind, thus showing decisively that thought proceeds according to certain fixed laws ; which laws it is the province of Logic to explain. 18 OF NOTIONS OR TERMS. 3. Predicables, Extension, and Intension. We have already stated that "predication" is the affirming or denying one thing of another; thus, when I say "A is B," I am said to predicate B affirmatively of A, but were I to state that " A is not B," I should predicate B negatively of A. Now those notions or terms which may be predicated affirmatively of others are called "predicables" and must neces- sarily include a greater number of objects than the subjects of which they are predicated.* Thus, a species may always be predicated of an individual, or a genus of a species ; and there- fore, in accordance with the above-given example, we may say " iron is a metal," or " metals are elementary substances," but not " metals are iron," or " elementary substances are metals." It will here be seen that in legitimate propositions, the subject contains within itself not only the whole of the marks or attributes which collectively form the predicate, but also an additional series of qualities. For instance, " iron " con- tains the common-notion of a " metal," together with those peculiar marks which enable us to distinguish it from other metals : accordingly, there is a greater number of marks or attributes in the subject than in the predicate, and this kind of comprehensiveness is called the intension of a term. But, on the other hand, we see that the predicate embraces a much larger number of objects than the subject, as a "metal" not only includes everything that is " iron," but multitudes of other things besides, such as " gold, silver," &c. ; and this species of capacity is known as the extension of a term. Con- sequently, a term used in extension comprises only the specific properties of a body ; and as it is, therefore, more general and less distinctive, it may always be predicated of a term used in intension, which consists both of properties and of accidents.f 4:. Division of a Common -notion. If we are desirous of completely understanding any sub- ject, it is very necessary for us to examine it closely, and the * Here, of course, I allude to common-terms, for a singular-term can never bo predicated of anything but itself; e.g., we can say * ; John is John," but not " a man (i.e., every man) is John." f See page 17. OF NOTIONS OR TERMS. 19 mental process by which we perform this is what I shall now consider. It is, in logical language, termed division, and consists in viewing every general idea as composed of two main sections, viz., the several members or parts of the idea, and the tie which connects them together. We then place the various parts in regular symmetrical order, such as is best adapted to their mode of union, and thus we are enabled to study each object separately, both as regards its own indi- vidual features, and its relations to the other members of the system. Now the " tie " or " mode of union " which has been here alluded to, is altogether arbitrary, and depends upon the purpose which w r e have in view when entering upon the study of any subject. Take, for example, the science of natural history : Aristotle, looking upon the blood as the grand basis of the phenomena of life, divided all animals into two great classes, one possessing colourless and the other red blood, which done, he proceeded to describe the individuals forming these classes ; Cuvier, on the contrary, adopted the bony skeleton as his guide in the arrangement of the various forms of life ; while Rymer Jones, Vogt, and Siebold have respectively chosen the nervous system, the phenomena of development, and the relative complexity of organisation, as keys wherewith to unlock the vast storehouse of nature. But when we have in this manner set apart some portion of the subject as a general principle to which we must con- stantly adhere, it becomes necessary to separate the subject into as many parts as may be convenient. This is done by observing the marks in which one group or class of objects differs from another, and thus dividing the whole of the sub- ject into a certain number of genera : each of these genera is then examined and similarly divided into lower genera ; and BO we go on until we can no longer discover any smaller groups in a class, but are compelled to enumerate the indi- viduals of which it consists. Thus we arrive at a regular system of summum genus, subaltern genera, infima species, and individuals. In order, however, that this process may be properly per- formed, logicians have laid down the following rules : 20 OF NOTIONS OR TERMS. 1. The whole subject must be divided : that is to say, the various parts taken together must exactly equal the genus divided. 2. The division must be conducted according to some single, definite principle. 3. The parts must be quite distinct ; no two containing any common object. Thus, if we were studying architecture, and wished to ob- tain a correct idea of the class of objects which are termed buildings, we must discuss the whole of the subject, and not confine our attention to a few species, such as palaces and temples only. And then when commencing the division, we must proceed according to some settled principle, such as, for instance, " application," consistently with which we should form the different species of " private-dwelling-houses," " factories," " warehouses," " churches," &c., and therefore no confusion would result, for the third rule given above would remain uninfringed. But if we were to pursue a different plan, and to divide buildings indiscriminately into " palaces," " Doric," " Gothic," " prisons," &c., we should violate both of the latter rules, having employed two principles of division, viz., " style" and " application," in consequence of which the various classes would be intermingled, and no true division would be per- formed ; for it is evident that some palaces might be Doric and others Gothic, &c. This error is termed cross -division, and is one of the most frequent sources of confusion and per- plexity in discussion and argument. 5. Positive, Negative, and Privative Terms. In order to test a division as to whether it be perfect, logi- cians are accustomed to take each part separately, and ex- amine the possibility of dividing the whole subject into positive and privative portions with reference to the selected part. Thus, suppose the subject " man " be divided according to the principle of " colour :" we should have the four species of" white-men," "black-men," "red-men," and "yellow-men." We tli en see that it is possible to also divide " man " into the two ideas or conceptions of " whitemen " and "non-whitemen," for black, red, and yellow may all be described as non-white. OF NOTIONS OR TERMS. 21 In the same manner " man " may be divided into " black " and "non -black," "red" and "non-red," "yellow" and " non- yellow," and so at length we see that none of the classes in- termingle with each other. The term " white-men " is called positive, because it denotes that a certain view (white) is taken of the object (men), while the term " non-whitemen " is said to be privative, in conse- quence of its implying that such a view might be, and yet is not taken. If, on the other hand, it were impossible to form a certain notion of a subject, the term which implies this, such as, for instance, a " non-white negro," would be styled negative. 6. Definition. In the process of logical division it is evidently necessary that we should employ some means of precisely determining, first, the full extent of the subject to be divided, and then the respective capacities of the various parts or species : this we are enabled to do by the use of definitions, that is, certain expressions which describe an object or notion in such a manner that we are enabled to distinguish it from all others. Now the act of forming these expressions is termed the process of definition, and consists in an enumeration of the various attributes composing a notion. As a notion, how- ever, may be either singular or common, we are obliged to use two kinds of definition, one of which, accidental definition, is applied to individuals, and consists of the specific name together with the accidents ; while the other, essential -defini- tion, being applied to classes, consists of the generic name, together with the specific difference. Thus, the Thames might be defined as " a river which flows through London," where " a river " is the name of the species, and " flowing through London " the accident which distinguishes the Thames from other rivers. Again, we may define light as " a species of motion affecting the optic nerves in such and such a manner," the genus being " motion," and " affecting the optic nerves" the difference which distinguishes light from other species of motion. This latter kind of definition, consisting of the genus and 22 OF NOTIONS OR TERMS. specific difference, is also termed logical-definition, in opposi- tion to physical -definition, which enumerates such parts of the object as are actually separable : e.g., the boiler, mechanism. &c., of a steam-engine. Some writers also include physical- definitions under the head of essential-definitions. Various rules have from time to time been given by logicians for the purpose of securing correct definitions, and may be summed up as follows. 1. The definition must be of exactly the same extent as the object defined : that is to say, it must not be of too narrow or too wide an application. Thus, to define "gravity" as " a force which attracts bodies to the earth " would be too narrow, as not including the celestial attractions, and being only applicable to terrestrial gravity : to define it as " a force which attracts one body to another," would be too wide, in consequence of its including magnetic attraction, &c. 2. The definition must not contain anything beyond what is absolutely essential to the subject. For instance, it would be incorrect to say that a " man" is "an animal endowed with the faculty of speech and with life" as it might then be supposed that the existence of an animal with speech, but lifeless, was possible. 3. The definition must be plainer than its subject, and must not be a repetition of the same term : e.g., the explana- tion that " a metal " is " a metallic substance," would be no definition at all, while to assert that it is " a product of Plutonic action " is equally unsatisfactory. 7. Names and their Divisions. We have already seen that when an idea or conception is gained of any object or class of objects, some name is imme- diately attached to it, for the purpose of recalling the impres- sion at any future time. It now remains to describe the various species into which these names are divided for logical purposes. 1. Making a division according to logical quality, we find that all names or terms may be divided into positive, privative, and negative, which have been described above. Positive terms, however, are also called definite t from their distinctly OF NOTIONS OR TERMS. 23 defining an object ; while for the reverse reason privative and negative terms are styled indefinite. 2. Names, as regards the method of using them, are either univocal, equivocal, or analogous ; that is to say, some have only one meaning, such as " book," "sofa ;" others have several meanings, such as " light," which signifies either the contrary of " heavy," or a physical force ; while others, again, are ex- tended from one object to another in consequence of some similarity thus, " tongue " may be applied either to the body or to a piece of land. 3. Viewed as to their mutual dependence, terms are absolute or relative. The former appellation is bestowed upon those terms which are considered by themselves as a whole ; the latter belongs to those which form part of a more complex idea. For example, the term " man " would be absolute ; while plaintiff would be relative, as being a portion only of the idea plaintiff-and-defendant. It will therefore be seen that relative terms exist in pairs, and cannot be applied to the same object, as then they would be what is called opposite, to distinguish them from compatible terms, as those are named which may be so applied. Correlatives is a name given to each pair of relative terms, and implies their mutual connection. 4. Terms are either concrete or abstract, according as they imply a notion together with the object furnishing the notion, 01 the notion by itself. Thus " fluid " is a concrete, "fluidity'' an abstract term. Also when the terms employed are common terms, or the names of classes, a further distinction will be observed. Take, for example, the concrete term "fluid;" it is evident that there is here implied a substance possessing certain attributes ; ac- cordingly, such a term is called attributive, or connotativc, because it connotes some attributes together with the object. Again, the abstract term " fluidity " is, in like manner, named absolute, or non-connotative, from its merely denoting ail attribute and nothing beyond. 8. Opposition of Terms. There is said to be a contradiction in terms, or two terms 24: OF NOTIONS OR TERMS. are said to be in contradictory opposition to one another, when the only difference between them consists in the respective presence and absence of a negative particle ; this difference enabling us to apply them universally. Thus, everything must be either "living" or "not living," "red" or "not red," &c. When, however, two terms differing as to the same idea cannot be both applied to the same object, and yet there are some objects to which neither can be applied, such terms are said to be in contrary opposition to one another : e.g., a man is not at the same time " walking " and " running," but a tree does neither, 9. Structure of Terms. An idea or term is expressed by a word or words ; thus, 14 man," " horse," " steam-engine," " the Emperor of Russia/' and such words as can be used alone to represent a term, are called categorematic ; while all others are denominated syn- categorematic. Sometimes, however, we meet with a single word apparently filling the place of a term, but for which it is necessary to substitute some other expression before its fnll import is conveyed. Take, for example, the sentence " He loves ;" this, if reduced to logical form, would be " He is a person who loves." 10. Conclusion and Recapitulation. \Ve have now reached the end of our investigation into the first great division of Logic, and before we proceed any further, it will be well for us to cast a brief glance backwards, and fully comprehend the connection which exists between the subjects just discussed, and those to come. The course, then, of our investigations has been first to analyse the method in which we gain and record the im- pressions or ideas produced by the various objects which attract our attention : iD doing this we found that all our ideas are either of individuals or of classes, the former being the result of incomplex-apprehension, the latter of complex-apprehension, which consists of the five processes of comparison, reflection, abstraction, generalisation, and deno- OF NOTIONS OR TERMS. 25 miiiation. In the next place we examined the mode of arranging and classifying our ideas by the abstraction and division of conceptions (common-notions) : this led us to per- ceive that the subject of a proposition embraces more marks or attributes than the predicate, while the predicate compre- hends a greater number of objects ; that is to say, the subject has the greater intension, the predicate the greater exten- sion. We then showed how a logical division might be tested by the use of positive and privative terms, which done, it became our duty to describe the process of definition, and to explain the various rules which have been laid down for the purpose of securing correct results. Finally, we enu- merated the divisions of the various names which have been bestowed upon ideas, and concluded by noticing the opposi- tion and structure of terms. It will of course be understood that in order to form an idea, it is not necessary that a tangible, corporeal object should be presented to the senses, for we have many notions to which there exists no corresponding reality : such, for ex- ample, are our ideas of justice, honesty, &c. In fact it may be said that no common-notion whatever has any existence out of our own minds ; the conception of "man'' for instance being merely that of a combination of marks or attributes which are never found separately by themselves, but are always united to other objects. Thus it is certainly true that the idea " man " has no isolated existence, but still it cannot be denied to exist, simply because it does so in conjunction \yith something else. This question, here touched upon, is the celebrated bone of contention between the schools of the nominalists and the realists, the former following Abelard, and denying that common-notions (or universals) are anything more than mere names, while the latter, under the guidance of Plato, strongly affirmed the reality of their existence. The days of the schoolmen was the time when this controversy grew most warm, and such was the importance attached to the subject, that kings and popes did not scruple to exert their utmost power in the attempt to secure the triumph of the sect which they respectively patronised. But this by the way. 26 OF NOTION L OR TERMS. Now when the mind has once become supplied with ideas, it is enabled to reflect, the result of which is the formation of certain judgments. These judgments, when formally stated, are termed in logical language propositions; and, accordingly, the subject of our next chapter will be an examination of their origin and nature. CHAPTER III. OP JUDGMENTS OR PROPOSITIONS. 1. Formation of Judgments. Judgment is the act of determining by comparison whether one idea is or is not included within another ; that is to say, it ascertains whether an individual belongs to a certain species, or a species to some genus. Archbishop Thomson has defined it as " an attempt to reduce to unity two cogni- tions." He says, "When one decides that * Socrates is wise/ it is that hereafter one may, by combining the two notions, think of ' the wise Socrates.' " Now it is by no means evident that the two cognitions are here attempted to be reduced to unity, for no person would surely expect to render them so inseparable, that whenever the idea of " wisdom " presented itself to his mind it should be invariably accompanied by the notion of " Socrates." In fact the judgment that " Socrates is wise/' is merely an assertion that " Socrates belongs to the class or species of wise men," or " Socrates possesses wisdom," thus enabling us to fix his place more exactly in our system of ideas.* Accordingly, it will be seen that judgment is the result of that mental faculty which so strongly impels us to classify and arrange the various notions with which our senses provide us, so that we may the more clearly comprehend the various dependencies and relations by which they are connected to- gether into one harmonious whole. We have already con- sidered three portions of this faculty, viz., abstraction, division, and definition ; it now remains to consider judgment, without which none of these processes could be conducted. * For further information upon this point, see Appendix A. o2 28 OF JUDGMENTS OR PROPOSITIONS. And here it might well be asked whether, if the formation of common-notions is the result of judgment, a judgment also in its turn is not the result of reasoning for we have already seen that the conclusion of a syllogism is a judgment or pro- position. This question, however, belonging as it does to metaphysics, cannot be satisfactorily answered in the present place ; and, therefore, I shall at once proceed to discuss the nature and proximate origin of propositions, without minutely investigating their remote ancestry. 2. Categorical Propositions. A categorical judgment or proposition is an assertion that one idea agrees or disagrees with another, and consists of three parts the subject or idea under examination ; the predicate, or idea to which the subject is referred ; and the copula, which determines the relation between them. Thus, in the proposition " lions are animals," the subject is " lions," and is connected to the predicate " animals," by the copula " are," which implies that " lions " form a species of the genus " animal." This judgment results from our having compared the two ideas with a view to ascertain whether the attributes of " animal " were contained in " lion." The subject and predicate of a proposition, may of course be infinitely varied, since there is no limit to the number of ideas ; but the copula always remains the same, being either " is," or " is not," or their equivalents. And here it may be remarked that the word " is " signifies, when employed in a proposition, the identicality of the subject and predicate, such identicality being, however, limited by the form of the propo- sition. The subject and predicate are also called the terms of the proposition, as they form its boundaries or terminations. Categorical propositions are divided into pure and modal the former being cases where the subject is directly asserted to agree or disagree with the predicate ; the latter where the subject is said to agree or disagree with the predicate in some particular manner. For instance, " The sea is rough ;" " He addressed the people ;" are both pure, but "The sea is terribly rough ;" " He addressed the people good humouredly ;" are modal. This distinction is, however, of no use for logical pur- OF JUDGMENTS OR PROPOSITIONS^ poses, since we may always treat modal propositions as being pure, by simply attaching the mode to either the subject or the predicate : thus, in the example above given, " terribly rough " must be taken for the predicate. 3. Hypothetical or Conditional Propositions. All judgments are not formed by a comparison of existing notions, for it is possible to decide upon the mutual relation of two assumed conditions of things. Accordingly, we meet with a class of propositions termed hypothetical, or conditional, whose assertions are subject to a certain condition : of this kind are such sentences as the following " If the results of geological science are trustworthy, the earth has existed for countless ages." " If you do this well, you shall be rewarded." Hypothetical propositions are not, however, to be considered as different in nature from categoricals, for both species of judgment result from precisely the same operation of the mind. This will be clearly seen if we examine one of the instances given above, and ascertain what it is that we really assert. Taking the first example, it is evident that we decide nothing as to the results of geological science, or as to the earth, but we say that the assuming those results to be trust- worthy would necessitate our granting the earth to be of the age stated. This judgment, then, may be expressed as follows, viz., " The case or supposition of the results of geolo- gical science being trustworthy, is a case or supposition of the earth having existed for countless ages" where the subject, copula, and predicate of a categorical proposition will be at once recognised. 4:. Disjunctive or Alternative Propositions. There is yet another form which our judgments may assume, this being the statement of some alternative, such as, " Either Tyndall is wrong, or mechanical force produces heat ;" which, accordingly, is known as a disjunctive or alter- native proposition. To show its harmony with the forms already discussed, we have only to remark that it may be converted at will into a hypothetical, as, " If Tyndall is not 30 OF JUDGMENTS OR PROPOSITIONS. wrong, mechanical force produces heat ;" or into a categori- cal, thus : k< The case of Tyndall being wrong, and the case of mechanical force producing heat, are all the cases possible." As regards hypothetical and disjunctives considered apart from categoricals, we shall have more to say when we come to discuss the treatment of arguments where they occur ; at present, however, we are concerned altogether with pure cate- goricals, having shown that all propositions whatever may be regarded as such. 5, Quantity of Propositions. As we have no ideas beyond those of individuals and of classes, our judgments must always be concerning intuitions (singular-notions), or conceptions (common-notions). Now a singular-notion being indivisible, we must invariably treat of the whole of it ; but as regards common-notions, we are able to discuss either a part or the whole. This distinction has enabled logicians to divide all propositions according to quantity ; that is to say, according to the extent of their subjects : and, therefore, whenever the subject is a singular- notion, as, " John is rich," or the whole of a common-notion, as, " All metals are conductors of heat," the proposition is called universal ; but if only part of a common -notion be employed for a subject, as, "Some metals are lighter than water," then it is termed particular. 6. Quality of Propositions. Another division of propositions is according to the signi- fication of the copula, which is termed the quality of a judg- ment, and as this must be either affirmation or negation (' is " or " is not "), so propositions are styled affirmative or negative, according as they respectively express the agree- ment or disagreement of subject and predicate. Thus, " The whale is a mammifer " is an affirmative proposition ; while " No alloy of ammonium is stable " is negative. It must here be remarked that a negative sign may occur in a proposition, and yet not belong to the copula ; in such a case the proposition is affirmative. Take, for example, this OF JUDGMENTS OR PROPOSITIONS. 31 judgment, "Not to accept the offer is great folly," and we see that the " non-acceptance " and " great folly " are declared to agree with each other. 7. Distribution of Terms. Whenever in a judgment a term is used in its full sense that is to say, as comprehending every single object that it could possibly include it is said to be distributed: accord- ingly, every universal proposition distributes its subject, but particulars do not. When, however, we examine into the distribution or non-distribution of the predicate, we find that this depends not on the quantity, but upon the quality of the proposition. Thus in negative judgments it will be seen that the whole of the predicate is declared to disagree with the subject ; as, for instance, in the following proposition, " No negro kingdom is civilised," where the entire idea of " civili- sation " is pronounced to be incompatible with the idea of " negro kingdoms." But in affirmative judgments the case is different, as we can only infer from the form of the expression, that a, part of the predicate is implied. Thus, knowing that one portion of the genus "animal" is composed of "horses," or in other words, that the attributes forming the idea of " animal " is to be found in every horse, we can say correctly that " horses are animals." Here, then, the predicate is not distributed. Consequently, we arrive at these two rules : 1. The subject is distributed in universal, but not in particular propositions. 2. The predicate is distributed in negative, but not in affirmative propositions. The latter rule is, however, subject to three exceptions ; first, when in an affirmative proposition the predicate is a singular notion and is consequently distributed, for we can- not think of a part only of an intuition ; secondly, when some expression is employed which indicates that the whole of the common-notion forming the predicate is compared with the subject. Thus, in both of the propositions, " Davy was the discoverer of potassium," and " These fragments are all that 32 OF JUDGMENTS OR PROPOSITIONS. remain," the predicate is distributed. The third exception is to bo found in negative propositions, where the predicate is qualified in such a manner as to indicate that part only of its signification is employed. This will be observed in such sentences as " Steam-engines are not some machines ;" " No men are some created beings;" which import respectively that some machines are not steam-engines, and that some created beings are not men. These latter propositions are termed partial-negatives, those to which the rule applies being styled total-negatives. 8. Relation of Terms. We have already stated that judgment is the act of deter- mining by comparison, whether one idea is or is not included within another. In doing this we find some cases where the notions are of equal extent, such as the various intuitions produced by the same object under different circumstances, or those conceptions which comprise the same individuals. This fact we express in the form of the proposition, which consequently indicates that it is the result as it were of two judgments, the one having ascertained that the subject of thought belonged to a certain class, while the other deter- mined that it was co-extensive with the class. Such propo- sitions are those mentioned above as constituting exceptions to the rule which declares that no affirmative proposition dis- tributes the predicate. Now in consequence of this relation, it follows that we may indifferently affirm the predicate of the subject, or the subject of the predicate. Thus it matters not whether we say " Davy was the discoverer of potassium," or " The discoverer of potassium was Davy ;" or again, whether we say, " These fragments are all (the fragments) that remain," or " All the fragments that remain are these (fragments)." Accordingly, such propositions are termed substitutive, from our being able to employ subject and predicate as substitutes for each other. All other affirmative propositions have their predicates non-dietributed, and merely import that these may be attri- buted to, and not substituted for, the subjects. On this account thev are stvled attributive. OP JUDGMENTS OR PROPOSITIONS. 3? 9. Systematic Classification of Propositions. Having now given a full description of the various divisions and subdivisions of propositions, it will be well to give a short summary of the system. This is best done by the use of a " scheme," as follows : Propositions regarded logically, i.e. with reference to their form, are divided according to 1 1 Quantity, Quality, into into I 1 1 1 ! Universal. Particular. Affirmative : these being sub- divided as regards the relative extent of subject and predicate, into i Negative : these being sub- divided as regards the distribution or non-distribution of the predicate, into i .1 i Substitutive. Attributive. 1 ! Total. Partial 10. Table of Possible Propositions. We see by the above scheme, that propositions are of four great classes, affirm ative-substitutive, affirmative -attri- butive, total -negative, and partial-negative. Each of these may be again subdivided into universal and particular, so that altogether there are eight possible kinds of judgment or predication. The names of these propositions, however, being too long and cumbersome for constant repetition, logicians have adopted certain letters to serve as symbols for these names, and in the following table will be found a list of all possible propositions, together with their respective symbols, and illustrative judgments ; the subject and predicate in each being represented by the letters X and Y. c3 34 OF JUDGMENTS OR PROPOSITIONS. Name. Example. Symbol. Univ. Affirm. Substi. All X is all Y. * U. Univ. Affirm. Attrib. All X is some Y. A. Univ. Total Neg. No X is Y. E. Univ. Partial Neg. No X is some Y. rj. Part. Affirm. Substi. Some X is all Y. Y. Part. Affirm. Attrib. Some X is some Y. I. Part. Total Neg. Some X is no Y. O. Part. Partial Neg. Some X is not some Y. w . In this table there are two propositions which, as being of little practical importance, we may leave out of our future consideration. I allude to those whose symbols are rj arid u ; the reason of their inutility being as follows. When we say " no men are some animals " (rj), we mean " some animals are not men " (0), which latter, being a much more forcible and convenient mode of expression, is usually adopted. Also when we say " some men are not some animals " (w), the power of negation is still less, for there is nothing to prevent us saying at the same time " some men are some animals." Accordingly, I shall confine my future remarks to the six kinds of judgment, U, A, E, Y, I, and 0, and when the student is able to treat arguments involving these, he will find very little difficulty in disposing of those rare cases in which r) and w may occur. 11. Interpretation of the Copula. The copula, as already stated ( 2), signifies a certain identically of the subject and predicate. This identically, however, may be considered from several points of view, ac- cording to the purpose we have in hand. Thus, if we were engaged in determining the intension of the notion " fluids," i.e. in ascertaining what were its marks or attributes, and we were to form this judgment, "All fluids are compressible," we should mean that fluids were contained in the class of com- pressible substances, in virtue of one of their attributes being compressibility. But if we were chiefly desirous to fix the relative extent of the terms, i.e. to determine their extension, we should only care to imply by the above expression that the class of compressible substances included amongst other things the class of fluids. OF JUDGMENTS OR PROPOSITIONS. 35 It will, however, be observed that these are not two different meanings of the proposition, but merely two different modes of regarding the same meaning. Another method of interpreting the copula, or connection between subject and predicate, has been suggested. This consists in viewing the judgment as regards its denomination, i.e. in considering it as implying that the predicate may be given as a name to each of the objects contained in the subject. The example stated above, if interpreted in this manner, would be held to imply that the name " compres- sible " might be given to every fluid. 12. On some other Properties of Judgments. It is impossible for us to form a complete idea of any object, as we are unable ever to ascertain the whole of its various marks or attributes. Accordingly, we observe continually some new feature, and this it is which causes us to make so many fresh judgments. At the same time there always exists a certain set of marks which are almost inseparably connected in our minds with respective ideas; so that it is scarcely possible to recall these ideas without at the same time recall- ing those attributes. Take, for example, the case of material bodies ; we cannot think of any, without also thinking of shape and extension, two properties of matter. Upon these considerations, metaphysicians, and after them, logicians, are occasionally accustomed to consider judgments with reference to their bearing upon our knowledge of the subject. If they increase our information, such as those which result from our discovery of some new attribute, they are termed ampliative. If they add nothing to what we really know 7 , they are called explicative when they are in a measure explanatory of the subject by predicating some- closely-connected attribute; or tautologous, when the predicate is identical with the subject, such as, " A man's a man." 13. Concluding Remarks. In the present chapter we have taken the subject of "judgments," for logical investigation, and the result of our studies may be summarised as fellows. 3fi OF JUDGMENTS OR PROPOSITIONS. Judgment is the act of determining the agreement or dis- agreement of two notions, and when its result is expressed in words, it forms a sentence which is termed a proposition. Propositions may be stated categorically, such as " A is B," or " A is probably B," the former being pure, the latter modal : hypothetically, such as " if A is B, C is D :" or disjunctively, such as " either A is B, or C is D." All propositions may, however, be reduced at pleasure to a pure categorical form. Accordingly, in a systematic account of judgments, reference is made exclusively to pure categoricals, concerning which there are four great doctrines. The first is of quantity, and divides all propositions into universal or particular, according to the respective extent of their subjects. The second is of quality, and divides all propositions into affirmative or nega- tive, according to the import of their copulae. The third is of distribution, and determines in what cases the various terms are employed as wholes or parts, i.e., whether they are distributed or non-distributed. The fourth is of relation, and arranges all propositions according to the extent of their predicates ; affirmatives being divided into substitutives and attributives, and negatives into total and partial. From this classification it results that there are eight different kinds of propositions, each being for the convenience of logicians distinguished by an arbitrary symbol. Two, however, of these species may be dispensed with as being of little prac- tical importance ; and, therefore, only the remaining six need be dwelt upon in future. Judgments may also be viewed as regards the significance of their import, which varies with the method of interpretation. Thus, they may be considered with reference to their intension, or attributes of the subject; extension or relative capacity of the predicate ; denomina- tion, or applying the predicate as a name to each member of the subject ; or, finally, with reference to their bearing upon our knowledge, according to which they are ampliative, or informing ; explicative, or explanatory ; tautologous, or useless. We are, therefore, now in a position to enter upon the in- vestigation of a most important and interesting topic the formation of new judgments from a consideration of some OF JUDGMENTS OR PROPOSITIONS. S already existent. This process, termed reasoning, is as it were, the very climax of logical science, and illustrates the use of our preceding reflections upon terms and judgments. Its study is, however, far from being difficult when orderly arranged, and is calculated to induce the most pleasing emo- tions in the mind of any person who has attentively pursued it, and has observed the singular simplicity and harmony with which the mind works. In fact, we have already had some remarkable instances of this, for we have discovered that the vast, nay infinite world of ideas than which nothing can be more varied and diverse may be referred to a few simple processes of the intellect, and may be grouped together into a system of surprising lucidity. The same thing occurs with our innumerable judgments, which, though outwardly dissimilar and confused, are found to be all constructed on the same plan, and to be capable of arrangement in orderly sequence and regularity. Accordingly, to him who zealously strives after a complete understanding of these facts, there accrues an elevation of the mind such as cannot otherwise be attained. That grand principle of systematic grouping which underlies all his capacities of acquiring knowledge, is roused into vigorous and healthy exercise ; his powers of observation, or rather, his capabilities of impression by outward objects, are greatly increased ; and, while he is charmed by the stately vista of theoretical truth which reveals itself before him, he is at the same time conscious that his toils have not been unfruitful in practical results. CHAPTER IV. OF REASONING OR ARGUMENT. SYLLOGISMS. 1. Reasoning in General. THE desire of the mind for knowledge admits of no satiety : vast though its acquisitions may be, the pursuit is in nowise slackened ; and the regions of infinity itself oft yield rich spoils to some aspiring intellect, which, thirsting for new worlds to conquer, has striven to investigate the most mys- terious recesses of the universe. This fact is proclaimed in every page of the world's history : the speculations of the philosopher, the actions of the statesman, the harmonious breathings of the poet, all alike bear witness that the watch- word " progress " is stamped indelibly upon the human mind. If, then, we consider that in our souls- there is implanted a faculty which irresistibly carries us forward to the acquire- ment of new truths, we shall not be surprised when we discover that there are also implanted certain natural laws, which serve to control and guide that faculty in the manner best adapted for the attainment of its ends. Accordingly, since these laws exist, and are the same in all minds, it results that the method of acquirirfg knowledge is identical in every case. Now, information may be obtained in three different ways : by the presentment to our minds of the various objects of thought, thus inducing the formation of ideas ; by the com- parison of ideas, which enables us to make judgments ; and by the comparison of judgments for the purpose of arriving at some new truth. The two former of these processes have hitherto engaged our attention exclusively ; we have there- fore now to investigate the latter, which, of all the mind's OF REASONING OR ARGUMENT. SYLLOGISMS. 39 actions, challenges our observation in the most marked manner. Beasonmg, then, consists in arriving at some new truth, from a consideration of other truths already established. These truths it is evident may be expressed in numberless ways, as also may the truth to be inferred ; but whenever an act of reasoning is put into words, it will always be found possible to separate it into two portions, one expressing some admitted truths, the other some truth resulting from them. Thus the mere arrangement of the argument (as an act of reasoning when expressed in words is termed) matters nothing with regard to the principles involved ; and, conse- quently, in spite of these principles being, as above stated, universal, we everywhere find that reasoning is expressed in whatever manner may be suggested by the circumstances of the case. This it is, which has led to such erroneous opinions as to the true office and nature of Logic ; men, distinguished in other respects for their prodigious intellectual power (e.g. Locke), having imagined that because Logic alters the loose, popular arrangement of arguments, into a form better adapted for elucidating the principles concerned, it therefore is oc- cupied in teaching some particular method of reasoning, the laws of which are different to those employed by such as have not studied the science. 2. Syllogisms. Inference. From the preceding remarks it will have been gathered that before entering upon a logical investigation of any act of reasoning, it is necessary that this should be expressed in a certain regular form. Such forms are termed syllogisms, and are so constructed as to show the validity of the argument, without any reference to its matter, i.e., to the subjects of which it treats : that is to say, the mere manner of expression is such that the new truth, or conclusion, is at once seen to be legitimately deduced from the truths already granted, viz., the premises. The act of thus deducing the conclusion from the premises is termed inference, and consists in ascertaining the full pur- port of the premises. Thus, ascertaining that chlorine is a OF REASONING OR ARGUMENT. gas, and knowing that all gases are elastic, I infer, or conclude that chlorine is elastic. If expressed in logical form, the argument would run thus : " All gases are elastic ; chlorine Is a gas ; therefore chlorine is elastic." It is not, however, always the case that we commence our reflections with the premises, for we frequently first consider the conclusion, under the guise of a question or problem. For instance, suppose in the above case that we wished to know whether chlorine was elastic or not : we might ascertain the truth by examining the substance ; and, finding it to be a gas, we should be certain that it was elastic, as previous investiga- tions had decided that all gases were so. Here we see that there are two terms, " chlorine," and " elastic," the agreement or disagreement of which, we were enabled to decide upon by finding some third term, " gas," wherewith they might be respectively compared. This third term is called the middle term, and is the very essence of the syllogism ; the inference connected with it being accordingly termed syllogistic, or mediate inference. We now arrive at a somewhat interesting question, viz., whether there can be any kind of reasoning other than mediate inference ; that is to say, can we from one judgment or truth only, directly infer some other ? Some writers have contended that such a thing is possible, and have accordingly described a species of reasoning which they term immediate inference. Others have denied the possibility of this, and assert that in the examples adduced by their opponents, there is no inference or reasoning whatever. Now the truth would appear to be that the disputed cases are in reality certain examples of mediate inference, which possess such strongly marked peculiarities as to distinguish them from all other instances of reasoning, and to lead to the belief that the laws upon which they are constructed differ from those of the regular syllogism. It will, therefore, be well to consider these arguments apart from the great bulk of reasonings, more especially as owing to the above mentioned views being adopted, logicians have devised rules for the treatment of such cases, to which rules both parties agree. The arguments themselves may be SYLLOGISMS. classed under three great heads or doctrines, viz., opposition, conversion, and coincident junction : these I shall now pro- ceed to investigate, showing in each case the real nature of the argument. 3. Opposition. The relation which exists between any two propositions differing in form, but identical in matter, is termed opposi- tion. Thus, the judgments "All fishes swim," and " No fishes swim," agree as regards their matter, i.e., their subjects and predicates are respectively formed by the same notions ; but they differ with respect to form, one being A, or universal- affirmative-attributive, while the other is E, or universal -total - negative : they are accordingly said to be opposed. And here it should be remarked, that in order for opposition to exist, the respective subjects and predicates must, in both propositions, be considered with reference to the same ideas, time, and circumstances. Thus, I might say, " This man is happy," and " This man is not happy," with perfect truth, providing I were alluding to his condition at separate times ; but otherwise, the judgments would be opposed to each other. The doctrine of opposition is based upon an examination of the various forms of propositions, and declares the natural laws which regulate their mutual relations. Take, for ex- ample, a proposition in E, " No metals are vaporisable." On analysing this, we arrive at the following results: that the proposition asserts the total exclusion of the class " metals " from the class of " vaporisable substances;" that since from the nature of things we know there must always be either a total exclusion, or partial inclusion at least of one class in another accordingly, if the proposition be true, any judgment which asserted an inclusion (even if only partial) of " metals" within " vaporisable substances," would be false ; while if the proposi- tion were not true, a judgment of partial inclusion, at any rate, must be correct. The rule, then, that we should deduce from such an examination would be, " Either E or I must be true ;" this, when required for formal use, being converted into ita equivalent categorical propositions, " The case of E being false, is a case of I being true ;" and "the case of I being false, 4:2 OF REASONING OR ARGUMENT. is a case of E being true." Taking the example given above, we have for the complete syllogism, The case of E being false is a case of I being true, The present is a case of E (" no metals are vaporisable ") being false ; /. The present is a case of I (" Some metals are vaporis- able ") being true. In logical language, when we assert the truth of any pro- position, we are said to posit it ; when we deny its truth, we remove it. Consequently the above rule is thus technically expressed, " From the position of E we may infer the removal of I ; from the removal of E we may infer the position of I -, and, in both cases, vice versa" The relation thus declared to subsist between E and I, is called contradictory-opposition, and E and I are termed the contradictories of each other. I have now I trust shown, once for all, that the inference which obtains in cases of opposition, is mediate, and may be regularly expressed in the syllogistic form. I shall, therefore, in recounting the remaining kinds of opposition, merely give the usual logical rules for the position and removal of propo- sitions, without discussing their bases, as the student will be able to do this for himself, by following the method of proce- dure adopted above.* There are four kinds of opposition : contradictor) 7 , contrary, subaltern, and subcontrary. Contradictory opposition exists only between E and I, although those writers who do not recognise U and Y, describe it as also existing between A and 0. The rule of this oppo- sition is, " The position of a judgment infers the removal of its contradictory ; the removal of a judgment infers the position of its contradictory." It has been fully explained above. Contrary opposition exists between those pairs of judgments which may be false together, but cannot at the same time be true. These are A and E, A and U, A and 0, A and Y, U and Y, U and 0, E and U, and E and Y. The rule is, 'The position of a judgment infers the removal of its con- trary." Nothing, however, follows from the removal of a judgment. Thus, " All whales are warm-blooded," and " Somo * For further remarks upon this subject see Appendix B. SYLLOGISMS. 43 whales are not warm-blooded," are contraries (A and 0) : if we admit the former, we must deny the latter, but if we deny the latter, we are in doubt whether to say, " All whales are all the warm-blooded (things) " (U), or, " All whales are (some) warm-blooded " (A). Subaltern opposition exists between certain pairs of judg- ments which may be true or false together, viz., A and I, U and I, Y and I, E and 0, and Y and 0. In these cases, that judgment which has most distribution in its terms is called the subatiernant, its opposite being styled the subal- ternate. Thus I is subalternate to A, U, and Y, while is so to E and Y. The rule here is that, " The position of the subalternant infers the position of the subalternate." Subcontrary opposition exists between I and 0, which may be true, but cannot be false together ; accordingly, the rule in this case is, " The removal of a judgment infers the position of its subcontrary." Y and have been termed subcontraries by Dr. Thomson, but they would rather appear to come under the head of subaltern opposition, where it will be ob- served that I have placed them. It is proper to remark here that the word opposition does not in logical language imply an incongruity of two judgments, for we have just seen that there are some cases where opposed propositions may both be true at the same time ; it is merely a name given to a certain relation existing between the various forms of judgments, such relation differentiating as the forms themselves differentiate. Therefore, when Sir William Hamilton states* that " there is no opposition between sub- contraries," and that to say so " is a mistake," he appears to have been misled by grafting the ordinary sense of the word ;< opposition " upon its logical signification ; for at a short distance previously we find him declaring opposition to be a relation existing between two judgments which are " opposed or conflictive" It is, however, somewhat strange that he should omit to take any notice of subaltern opposition as such, and content himself with merely mentioning it as a relation oil subordination. He, it will thus be seen, admits of only two kinds of opposition contradiction and contrariety. * " Lectures on Logic," vol. i. p. 261. 4"i OF REASONING OR ARGUMENT. It is generally the practice in logical works to give a figure or " scheme " of opposition ; and, as this plan is useful in many respects, I subjoin the following, which shows at a glance the relations that have been described above as exist- ing between the various forms of propositions. (All X is all Y) U - Contrary - Y (Some X is all Y) > ^L CO (All X is some Y) A/ Subaltern - 1 (Some X is some Y) /f (No X is Y) E - Subaltern - O (Some X is not Y) V "3 1 (All X is all Y) U Contrary Y (Some X is all Y) 4-. Conversion. Conversion is the technical name applied to the operation of forming one judgment from another in such a manner that the subject and predicate of the original proposition (the con- vertend) shall be respectively the predicate and subject of the new one (the converse). Thus, " Some men of great imagina- tion are all the good poets," is said to be the converse of " All good poets are men of great imagination." Now it is evident that a process of inference takes place here :* let us, therefore, inquire into its nature. The import of our first judgment is that the class of " good poets " is included, amongst other things, in the class * See Appendix B. SYLLOGISMS. 45 of " men of great imagination ;" and as we know from the natural laws of extension that when one thing is included in another, a part of the object including is equal to the whole of the object included, we therefore see that in the present case it will be allowable to predicate the entire class of good poets," of " some men of great imagination." Accord- ingly, we frame a general judgment which may be applicable to all cases, and which runs thus, " A case of A is the case of the same subject and predicate being reversed and thrown into the form of Y." The syllogism, then, will be as follows : A case of A is a case of Y containing the same terms as A, but reversed in position, The present case (" all good poets," &c.) is a case of A ; /. The present case is a case of " some men of great imagination are all good poets." The general practice, however, with regard to conversion is the same as that pursued in reference to opposition : instead of framing a syllogism every time we wish to convert a pro- position, we employ certain rules which enable us to perform the operation in a more speedy manner. These rules are : 1. The quality of the converse must be the same as that of the convertend. 2. No terms must be distributed in the converse, but such as are distributed in the convertend. If the above rules be adhered to, no difficulty need be ex- perienced in converting any proposition whatever ; but as a means of facilitating the process still more, the following table will be found useful. U may be converted into U A Y E , E Y I o , o A I One peculiarity of this table will be at once noticed by the student : I allude to the employment of the form rj. This is necessitated by the consideration that if we follow the rules 4.G OF REASONING OR ARGUMENT. just given, we can only convert into r? ; it is, ho7> r ever, a conversion which is never likely to be made, for, as stated in a former part of this work (p. 34), is " a much more forcible and convenient mode of expression" than ?/. The above method of conversion may be termed simple- conversion, although this name is usually limited to the con- version of E and I ; that of A being called conversion per accidens, or by limitation, in consequence of a particular pro- position being educed from a universal ; while is treated as inconvertible.* There is another process which is sometimes considered as a species of conversion, and which may well be examined in the present place. It is variously termed conversion by equipollence, by contraposition, by negation,^ by double nega- tion,"^ and immediate inference by means of privative concep- tions ; the name which I shall employ will be privative-con- version, as this both indicates the nature of the process, and is harmoniously opposed to the term simple conversion. The modus operandi of privative-conversion consists in changing the quality of the convertend, and altering its predicate into a corresponding positive or privative concep- tion, according as the case may be. The reasoning pro- cess which forms the foundation of the doctrine is as follows. Take some proposition in A, as, " All intellectual men are amiable," and let us think what it is that we know about its terms : the judgment itself makes us aware that " intellectual men " are in the class of " amiable men," but gives us no further information regarding the latter class ; we know, how- ever,^" that it is possible to form a conception which shall in- clude every man not comprised under " amiable men," and that then we may deny the latter of the former : this we pro- ceed to do, and say, " No amiable men are unamiable " a judgment which supplies us with the desired premiss, and enables us to form a complete syllogism ; thus : * Here it will be seen that I allude to those writers who only admit A, E, I, and (). f Whately's " Elements," Book ii. chap. ii. 4. j Hamilton's " Logic," vol. ii. Appendix V. c. p. 267. Thomson's " Outlines," 86. ^f Supra, p. 20. SYLLOGISMS. 47 No amiable men are un amiable, All intellectual men are amiable ; .*. No intellectual men are unamiable. This conclusion is the converse required, and is seen to fulfil all the conditions of privative-conversion ; that is, its quality is changed, and its predicate is replaced by a cor- responding privative -conception. 5. Coincident Junction. When one class is said to be comprised in another we mean that all the members of the former are also members of the latter. Accordingly, these members may be considered as objects which (inter alia) are composed of two sets of ideas inseparably connected. We cannot, therefore, add anything to one idea and not at the same time add it to the other: nor for the same reason can we add one of the ideas to anything, with- out also adding the other. These considerations supply the general principles of what may be termed the doctrine of coin- cident-junction, and which is thus expressed : " From any judgment we may form another by adding some marks equally to the subject and to the predicate ; or we may add the sub- ject and predicate as marks to some fresh conception." Thus if " a metal is a solid " be true, we may also infer that " a red metal is a red solid ;" or if we admit that " Logic is the science of the laws of thought," we must equally admit that "the study of Logic is the study of the science of the laws of thought." The former of these inferences has been termed " immediate inference by added determinants ;" the latter, " immediate inference by complex conceptions." It will, however, be readily seen from the above investigation of the principles involved, that these reasonings may be exhibited in the syllogistic form, as easily as any of the others. This concludes the discussion of those arguments which are commonly styled immediate inferences ; and, accordingly, whenever we have occasion to employ them in any future portion of this work, they will be considered as falling under their own special rules, and not as regular syllogisms. Such a course will be the more convenient as it will be more familiar to the student ; for the general laws which constitute the third 18 OF REASONING OR ARGUMENT. propositions of such syllogisms as have been already con- sidered, are so firmly fixed in our minds, that we are scarcely conscious of their existence, until our attention is specially directed to them ; and, consequently, it may almost be said that they are never overtly employed in the eduction of so- called immediate inferences. It will of course be understood that these arguments are not limited to a single operation ; for it is possible to start with a judgment and successively employ the three processes of opposition, conversion, and coincident -junction, until we arrive at some other proposition which may satisfy our re- quirements. Such a proceeding is sometimes said to be merely a determination of a proposition's full signification ; but this may be said in effect of all reasoning whatever, for " an ex- tension of any science through Logic is absolutely impos- sible ; as by conforming to logical canons we acquire no knowledge, receive nothing new, but are only enabled to render what is already obtained, more intelligible by analysis and arrangement."* 6. Mediate Inference formally expressed as such. Its Divisions. When an act of reasoning is fully expressed in words, i.e., if the three judgments be articulately stated, we have what is termed a syllogism. But as we saw, when treating upon pro- positions, that these are of three kinds, categorical, condi- tional, and disjunctive ; so in like manner are syllogisms divided, according as they contain these respectively. Thus the syllogism, " All A is B ; C is A ; therefore is B," is cate- gorical ; " If A is B, C is D ; A is B ; therefore C is D," is conditional ; and, " Either A is B, or C is D ; A is not B ; therefore is D," is disjunctive. Now the two latter species of syllogisms may always be re- duced to the former when occasion requires, and therefore an examination of the necessary laws of reasoning, together with the systematic arrangement induced by these laws, will best find place under the head of categorical syllogisms. Accord- ingly, in the following analysis, I shall speak simply of the * Hamilton's " Logic," Lect. iii. p. 44. SYLLOGISMS. 4:9 arguments so denominated ; this plan being consonant with that pursued when judgments were discussed. 7. The Fundamental Law of Mediate Inference. " Thought," says Sir W. Hamilton, " is the cogniH'm of any mental object by another in which it is considered ao n- cluded ; in other words, thought is the knowledge of things under conceptions." This accords with what I have already stated concerning the grand principle of classification which underlies our faculties of acquiring knowledge ; and prepares us to appreciate the fundamental law of mediate inference, which is as follows : " Whatever belongs or does not belong to the containing whole, belongs or does not belong to each and all of the contained parts."* This law, commonly called the " dictum de omni et nullo" we owe to the commanding genius of Aristotle, who first placed Logic upon a sound and durable basis. It is not, however, to be understood that this dictum is directly applicable to every case of reasoning ; the assertion merely being that the validity of any argument is ultimately referable thereto.')' For practical purposes men seldom ascend to general and fundamental truths, but devise a system of rules which, being immediately applicable, may obviate much of the inconvenience and delay that would otherwise ensue. Hence it is that logi- cians have developed Aristotle's dictum into the following proximate canon. " If two notions agree either wholly or in part with one and the same third, they agree with each other ; but if one of them is agreed and the other disagreed with the same third, they disagree with each other." This canon is, however, differentiated still further, thus : 1. A syllogism must contain three, and only three, terms, con- stituting three, and only three, propositions. The force of this rule is at once evident when we consider that the object sought to be attained by syllogising, is to determine the agreement or disagreement of two notions by respectively comparing * Hamilton's " Logic," Lect. xvii. p. 321. f Some objections having been raised by Mr. Mill and others to this account of the fundamental law of mediate inference, I have discussed the question at greater length in article C of the Appendix. ^^^-^^ >> 0* THK 50 OF REASONING OR ARGUMENT. them with a third. This, of course, could not be done if we employed more or less than the three terms, or formed more or less than the three judgments. The names of these terms depend upon their position in the syllogism. The predicate of the conclusion is called the major term : the subject of the conclusion is called the minor term ; while the third notion with which the two former are each compared is styled the middle term. In like manner are the premises named, that in which the major term is com- pared with the middle being the major premiss ; the other, the minor premiss. Much objection has been taken to this employment of the words major and minor on account of their ordinary sig- nification being respectively " greater " and k< smaller,*' whereas it sometimes happens that the minor term is in reality greater than the major term, or that we are unable to compare them together as regards their extent. There is no doubt that these names were originally imposed from their representing the facts of the case in one particular form of syllogism which was considered the most perfect ; but as they have continued to be used by numerous logicians who were well aware of how the matter stood, it must be inferred that" major" and " minor," when used logically, have merely a technical meaning as dis- tinguishing the terms of the conclusion, and not as implying any relative degree of amplitude. A parallel case is to be found in the use of the word " opposition " (see p. 41). In consequence of such objections, the premises of a syllogism have been variously re-named, the appellations of proposition, lemma, and sumption, being bestowed upon the major premiss, while the minor is known as the assumption, subsumption, or hijpolemma. 2. The premises must not both be 'negative. This follows from the consideration that a term can only show the relation of agreement or disagreement subsisting between two others, in so far as it is applicable to one of them at least. If, for in- stance, we were first to say, "No mathematician is a good moral reasoner," and then that " Shakspeare was not a mathema- tician," these statements would give us no grounds of com- parison between the notions of " Shakspeare " and " good STLLOGISMS. 51 moral reasoner." We should still be uncertain as to whether the latter might or might not be predicated of the former. 3. If either of the premises be negative, the conclusion must also be negative; for this is precisely the case stated in the second portion of the proximate canon above laid down, viz., " If one notion is agreed and another disagreed with one and the same third, they disagree with each other." Thus, from the pre- mises, "no matter is imponderable," and " all gases are matter," we can only conclude that " no gases are imponderable ;" for the attribute of imponderability was totally denied of matter, which contains, inter alia, all gases. 4. When the 'premises are affirmative, if either of them be attributive, the conclusion must also be attributive. Since a substitutive premiss implies a total identicality in extent of the middle term with one of the terms of the conclusion, and an attributive premiss implies only a partial identicality of like nature, it follows that between the terms of the con- clusion a partial identicality of extent is all that can be in- ferred. An example of this will be found in the following syllogism : Compounds are all bodies which may be resolved into simpler forms (U), Sugar is a compound (A) ; /. Sugar is a body which may be resolved into a simpler form (A). 5. The middle term must be more than distributed in the premises, both taken together. For if this were not the case we should have no real inference whatever ; as witness this apparent syllogism Some beautiful objects are pictures, Some hideous objects are pictures ; /. Some hideous objects are beautiful. Here the two premises are in the form I, which we know does not distribute the predicate, this, in the present case, being the middle term " pictures." Accordingly, the major and minor terms may, for anything the form of expression can tell us, be compared with different portions of the same thing ; and this, being equivalent to employing two middle terms, would violate the first rule, which prohibits the appearance of D 2 52 OP REASONING OR ARGUMENT. more than three terms altogether. Of course it might so happen that when premises of the above nature were used, we arrived at a true conclusion, as in the following case : Some beautiful objects are pictures, Some valuable objects are pictures ; .*. Some valuable objects are beautiful. This conclusion would, however, still be considered as invalid, that is, as not following directly and inevitably from the pre- mises ; for Logic, it will be remembered, regards not the matter, but merely the form of reasoning. Usually the middle term is distributed in one of the pre- mises at least; we can then tell at a glance that the rule now under discussion is not violated. Take, for example, the syllogism All the metamorphic rocks have been subjected to the action of heat, Gneiss is a metamorphic rock ; .*. Gneiss has been subjected to the action of heat. The major premiss being A, distributes the middle term ; and as this must be again mentioned in the minor premiss, it will necessarily be more than distributed, and will not affect the validity of the conclusion. Sometimes, however, we meet with a syllogism whose pre- mises contain the middle term in such a manner as to show that the portions employed in each, if added together, would give more than the whole ; e.g. Twenty per cent, of these knives are bad, Ninety per cent, of them are apparently well-made ; /. Some of these apparently well-made knives are bad. In this case suppose that the notion " bad " coincides with the entire portion of " these knives," with which " apparently well-made " does not ; such portion being only ten per cent, would still leave a further extent of ten per cent, to be ac- counted for, and this it is evident must come out of the " ninety per cent. ;" so that we are sure that the notions " apparently well-made," and " bad," must correspond to the extent of ten per cent, at least : this is asserted in the conclusion. It will in this place be opportune to remark that much con- SYLLOGISMS. 53 fusion frequently results from the use of an ambiguous middle term, thus : Capes are articles of clothing, Some tracts of land are capes ; /. Some tracts of land are articles of clothing. This syllogism is logically correct, that is, in form ; but if we examine its matter, we shall see that it contains two middle terms, for in the major premiss one kind of "cape" is spoken of, while in the minor, another kind is alluded to. The discussion of such cases will be further conducted when we come to examine the subject of fallacies. 6. In the conclusion no term must be distributed, unless it has also been distributed in one of the premises. The terms of the conclusion only agreeing or disagreeing with each other in so far as they respectively agree or disagree with the middle term ; they can merely be compared with each other by means of those portions which were found to coincide in any way with the middle term. All trees are organised beings (A), Men are not trees (E) ; .*. Men are not organised beings (E) ; And again Diamonds are combustible (A), Some precious stones are diamonds (I) ; .*. All precious stones are combustible (A). In the former of these syllogisms we have an illicit process of the major ; that is, the major term is distributed in the con- clusion without being so in its premiss : in the latter there is, in like manner, an illicit process of the minor. The valid con- clusions which might be inferred would respectively be " men are not some organised beings " (*/), and " some precious stones are combustible " (I). By the six foregoing rules may all syllogisms be tested to ascertain whether they are real or only apparent, whether the reasoning is correct, or incorrect. They are of great practical importance, as they enable us to dispense with the reduction of many syllogisms into a form where the dictum of Aristotle might be directly applied ; but, as already stated, they must only be considered as proximate differentiations of one fun- damental truth. 54: OP REASONING OR ARGUMENT. 8. Of Figure. In order to facilitate a full examination of syllogistic argu- ments, that is, of arguments formally expressed, logicians have investigated the number of positions which the middle term may assume in the premises, and in accordance thereto, have formed four classes, under which all possible syllogisms may be ranged. These classes they call figures, the form of which may be represented as follows ; employing P to signify the major term (predicate of conclusion), S the minor (subject of conclusion), and M the middle. 1st Fig. MP SM .'. SP 2nd Fig. PM SM .'. SP 3rd Fig. MP MS /. SP 4th Fig. PM MS .-. SP Thus when the middle term is the subject of the major premiss, and the predicate of the minor, we have the first figure ; when it is the predicate of both, the second ; when it is the subject of both, the third ; and finally, when it is the predicate of the major, and subject of the minor, there results a syllogism of the fourth figure. 9. Remarks upon the four Figures. 1. The first figure is the most natural and obvious form into which an act of reasoning can fall ; the cause of this apparently being that it is the only one in which the Aristotelian dictum will at once and immediately apply. Thus, to give a concrete example The rushing of particles to a nucleus causes the body so formed to rotate, The earth was formed in this manner ; .-. The earth rotates. This argument, which is employed by the author of " Vestiges of Creation," I have expressed in popular language, but the student will find no difficulty in arranging it according to the model ; " All M is P ; S is M ; therefore S is P." 2. The second figure, though a somewhat distorted method of stating an argument, is yet very useful and ready in certain SYLLOGISMS. 55 cases, where we desire to prove that some distinction exists between two notions, so as to prevent one of them including the other. Suppose, for instance, we wished to prove that a certain substance did not contain the metal sodium ; we might employ such a syllogism as the following : Any substance containing sodium would give, when burnt, two yellow bands in its spectrum (U), This substance when burnt does not do so ; /. This substance does not contain sodium. Here the middle term forms the predicate of both premises ; consequently, the syllogism is of the second figure. If, how- ever, we wished to apply the Aristotelian dictum, it would be necessary to arrange this argument according to the first figure, such an operation being termed reduction. It consists in a skilful application of the doctrines of opposition, conver- sion, and coincident junction. In the present case all that we have to do is to substitute for the major premiss its simple converse, thus Any substance which when burnt gives two yellow bands in its spectrum, contains sodium, This substance when burnt does not do so ; .*. This substance does not contain sodium ; a syllogism most manifestly of the first figure. It has been held that in every case the rnind unconsciously performs the process of reduction, and that therefore the second, third, and fourth figures are merely elliptical expres- sions of trains of reasoning, the first figure alone being an adequate representation of a single mediate inference. This statement, as implying a more direct influence than is usually imagined of the dictum upon our minds, is not unworthy of attention ; but since a full examination of the question would occupy more space than could be conveniently devoted to the purpose, I shall remain satisfied with having shown that any argument may be overtly expressed in such a manner as to evince its dependence upon the great fundamental law of reasoning. 3. The third figure is of use when we wish to disprove a theory by instancing some example to the contrary. If we wished to combat the assertion that " no bodies except water 56 OF REASONING OR ARGUMENT. ever expand when cooling," we might do so in this manner : Bismuth sometimes expands when cooling,* Bismuth is a body other than water ; /. Some other body than water occasionally expands when cooling. The conclusion thus obtained is the contradictory (I) of the theory to be disproved (E), and accordingly our purpose is accomplished. In order to reduce this syllogism to the first figure, we must simply convert the minor premiss, when the whole will run thus Bismuth sometimes expands when cooling, Some other body than water is bismuth ; .*. Some other body than water occasionally expands when cooling. 4. The fourth figure is chiefly remarkable for the offence which it has given to many logicians, who accordingly have been neither sparing nor gentle in their attacks upon it : "tortuous," "unnatural," "perverse," "hybrid," "useless," " clumsy," " a monster," and " a caprice " may be taken as samples of the objections raised to its reception. It will, therefore, be advisable to examine the nature of some syllogism in this figure : take, for instance, De Quincey'sf explanation of the non-existence of duelling among the ancient Greeks and Romans, which is as follows : No duelling can exist wherever unlimited license of tongue is allowed to anger (E), Unlimited license of tongue was allowed to anger among the ancient Greeks and Romans (U) ; .'. Among the ancient Greeks and Romans duelling could not exist (E). Here it is objected that the mind naturally expects the converse of the conclusion, in accordance with the tendency of the argument this leading from " no duelling can exist where certain license is allowed," to " this license was allowed among the Greeks and Romans," and then in all symmetry to " no duelling could exist among the Greeks and Romans." Now the answer to this is, that the figure of a syllogism * It invariably expands at the point of solidification. f Works. Author's Edition. Vol. vii. p. 281. SYLLOGISMS 57 depending entirely upon the position of the middle term in the premises, it will not be affected by a change in the rela- tive positions of conclusion and premises. We have, therefore, only to state the conclusion first, and then give the premised as our reasons for forming it, when we shall at once obtain a smooth and naturally proceeding argument. Thus, we can say " Among the ancient Greeks and Romans duelling could not exist ; for this is impossible where unlimited license of tongue is allowed to anger, which was the case in Greece and Rome ;" than which a more harmonious expression could not easily be found. In like manner, if we take mere arbitrary symbols to repre- sent the three terms, we shall still have a perfectly clear syllogism, e.g. No S is P (conclusion) ; for No P is M (major premiss), and M is all S (minor premiss) ; the meaning of which is, that none of the objects comprised by S are included by P, since the latter is totally excluded from M, which contains the same objects as S. At the same time, however, that the fourth figure is thus shown to be perfectly legitimate and unforced, it may be readily conceded that it is but seldom used, as from the same premises and the converted conclusion we can form a syllo- gism of the first figure : thus, " M is all S ; no P is M ; therefore no P is S ;" which being, as it were, more familiar to the mind, is oftener suggested. The formal reduction of syllogisms like the above to the first figure, is effected by simply converting both premises ; e.g. No M is P, All S is M ; .-. No S is P 10. Of Mood or Mode. The arrangement of the propositions of a syllogism with reference to their quantity, quality, and relation, is termed the mood or mode of the syllogism ; and as we are in posses- sion of symbols which fully express the form of a proposition, we can at all times represent the mood by the arrangement i) 3 58 REASONING OR ARGUMENT. of these letters : the conclusion, it is well to remark, being always placed last. Now as there are eight kinds of propositions, viz. U, A, E, rj, Y, I, 0, and M, it follows that five hundred and twelve forms of syllogisms or moods may be made. Most of these, however, do not constitute valid arguments, and therefore we must reject them ; e.g. A A has an affirmative conclusion, though one of its premises is negative ; EGO has both pre- mises negative j III has either the middle undistributed or else an illicit process; and so on in numerous other cases. In like manner some moods are admissible in one figure, but not in another ; thus, A 1 1 is valid in each of the first and third figures, but in the second and fourth the middle term would be undistributed. 11. Table of Valid Syllogisms in each Figure. From the foregoing considerations it will be evident that a table may be constructed which will show all the valid syl- logisms falling under each figure ; and as such a table is of great practical use, I have drawn up the following : TABLE OF MODES. Fig. I. Fig. II. Fig. III. Fig. IV. Aff. Neg. Aff. Neg. Aff. Neg. Aff. Neg. A AA . E AE AU Y . AEE A A I . E A O A AI .AEE All . EIO AYY . AGO All .EIO AUA . E AO AUA . EUE . . . E AE AUA . E UE AUY .EIO A YI . EYO . . . EIO A YA . EYE . . .EUE EUE %. Tf V f~\ ...EYE "u 1 v r\ IUI . QUO ^ E Y XL IUI . . . I AI . O AO I AI I YI . OYO IYI . . . IUI . OUO IUI U A A . U E E UA A . UEE UAY .UEE UAY . UEE UII . UOO UII .UOO UII . . . UII .UOO U U U . . . UUU . . . UUU. . . UUU UY Y . . . UYY . . . UYA. . . UYA UYY YUY . YEE YAA . . . Y AY . YEE YII YY Y . YOO YII . . . YUY . . . YUA YUA Y YI Y YI SYLLOGISMS. 60 The above table is arranged alphabetically, so as to facili- tate reference, and enables us at once to determine the validity or invalidity of any syllogism whose figure is known ; for if legitimate, it will be found in its proper position, while if inadmissible, it will be absent. The propositions rj and w have been omitted from this table on account of their small importance (see p. 34). It may also be proper to remind the student that in most of the older treatises on Logic he will find tables of judgments which differ materially from the one above given, inasmuch as they only recognise the four propositions A, E, I, and 0. The usual form in which such a table is given consists of the following four mnemonic Latin verses : Fig. I. Barbara, Celarent, Darii, Ferioque, prioris Fig. II. Cesare, Camestres, Festino, Baroko, secundce ; Fig. III. Tertia, Darapti, Disarms, Datisi, Felapton, Bo kardo, Feriso habet : quarta insuper addit Fig. IV. Bramantip, Camenes, Dimaris, Fesapo, Fresison. These lines, or rather the first three, were the invention of Pope John XXII., whose work upon Logic, under his name of Petrus Hispanus, enjoyed great celebrity. To each of the four figures it will be observed that a verse is appropriated, consisting chiefly of a number of names distinguished by capital letters,* and containing three vowels ; the vowels thus employed serve to indicate the mood of the respective syllo- gisms. For instance, the syllogism " all M is P; all S is M ; therefore all S is P," is said to be in the mood barlara, which signifies A A A in Fig. I. The consonants of the various moods are intended to assist the process of reduction ; the initial letters show that each mood must be reduced to that mood in the first figure which is similarly characterised : s indicates that the proposition immediately preceding is to be simply converted (in its old acceptation ; see p. 46) ; p that it is to be converted per accidens, except in the mood bramantip, where it denotes that the conclusion (I) will, when the syllogism is reduced, become A ; m that the premises are to be transposed ; and k that the contradictory of the con- * Tertia, in the third verse, is merely employed for the sense of the expression, and is not a mood. 60 OF REASONING OR ARGUMENT. elusion is to be substituted for the immediately preceding proposition. The two moods, however, in which k occurs (baroko and bokarko) may be more simply reduced by em- ploying the process of privative conversion ; they will then become ferio and darii respectively. An example will perhaps assist in rendering the above description intelligible. Let us take a syllogism in disamis ; thus, Some rocks have been formed by the action of water (I), All rocks are solid (A) ; .-. Some solid things have been formed by the action of water (I). Here the ra indicates that the premises must be transposed, the major and conclusion being simply converted in accordance with the requirements of s and s. When this is done, we obtain the following : All rocks are solid (A), Some things which have been formed by the action of water are rocks (I) ; .'. Some things which have been formed by the action of water are solid (I) ; which is a syllogism in darii, that mood of the first figure which was indicated by D, the initial letter of disamis. I have thought it advisable to enter at some little length upon this subject, as these ancient names of moods are not confined to logical works, but are often to be met with in old authors ; in addition to which, it might be expected that in a work like the present, of professedly a practical character, some notice would be taken of a method so universally fol- lowed. In fact, the perfect adaptation of the above quoted lines to their purpose, would alone render them deserving of mention; for, as Sir William Hamilton observes, " it must be confessed that, taking these verses on their own ground, there are few human inventions which display a higher ingenuity." It must also be observed that so far from the method just described being out of date and obsolete, it may still be applied in many cases ; the only difference between it and the table of judgments given in the present volume, being SYLLOGISMS. 61 that the latter is much more complete, containing not only all that the A, E, I and system includes, but many other tjyllogisms in addition. 12. Induction and Deduction. We have now seen that all acts of mediate inference when formally expressed, i.e. all syllogisms, may be systematically arranged and discussed under the two heads of mood and figure. There are, however, some further divisions of syllo- gisms which require our attention ; the first of these being that into inductive and deductive. The distinction between these two methods of reasoning may be thus expressed : induction is the process of forming a general law ; deduction, that of applying a law so made to some particular case or cases. Or, in other words, induction consists in reasoning from the parts to the whole ; deduction, in reasoning from the whole to the parts. In formal Logic, however, this distinction is comparatively unimportant, as will be seen from the following considerations. Take some inductive syllogism, as follows : Oxygen, chlorine, and steam are elastic (A), Oxygen, chlorine, and steam are all gases (U) ; .*. All gases are elastic (A). Here we see that from predicating "elastic" of the various parts *'' oxygen, chlorine, and steam," we are enabled to pre- dicate it also of the whole thus constituted, viz., " gases." It is, therefore, evident that the general law or truth upon which the validity of such a syllogism depends, may be thus ex- pressed : " That which belongs, or does not belong, to each and every one of the parts, also belongs, or does not belong, to the whole." This law has been declared to differ from the dictum de omni et nullo, which, the student will remember, is to the following effect : " That which belongs, or does not be- long, to the whole, also belongs, or does not belong, to each and every one of the parts." Now if we admit the difference thus asserted that is to say, if we admit that these two laws are " equally necessary and independent " * then we must, in * Hamilton's " Logic," vol. i. p. 321. The italics are my own. 62 OF REASONING OR ARGUMENT. addition, admit that the division into inductive and deductive syllogisms is imperatively called for, since each species of reasoning will have been shown to rest upon separate funda- mental* laws. That this independence, however, does not exist, may be shown by a few reflections based upon the nature of what we understand by the notion of a " whole." In the case under examination the " whole " of which we speak is the conception " gas." This, as the student will recollect from what was said in a previous chapter, is the result of our comparing various bodies together, and ascertaining those attributes in which they are all agreed ; the set of attributes so obtained being then abstracted to form the idea, and receive the name of " gas." Consequently, when we say " gases," we think of a class whose members are, not various individual objects, but various similar sets of attributes existing in separate bodies or objects, viz., "oxygen, chlorine, and steam;" and when we say that what may be predicated of the class " gases," may also be predicated of each of its members, w r e mean that the attri- bute " elasticity," for instance, may be predicated of oxygen, chlorine, and steam, not as individual objects, but as separate and similar sets of attributes ; or, in other words, we imply that each set of attributes must be capable of forming the idea "gas" in our minds, and must, consequently, be of similar constitution with the remainder. In like manner, when we say that whatever may be predicated of each member may be predicated of the class " gases," we mean that what- ever attribute is common to oxygen, chlorine, and steam must form part of that set of attributes which is called " gas ;'' that is, we imply that oxygen, chlorine, and steam, considered as definite sets of attributes, are of similar constitution, and must consequently each be capable of forming the same idea, " gas," in our minds. Now these two expressions, which are thus seen to have almost identical meanings, are the self-same laws which have been spoken of as independent of each other, this statement, therefore, is seen to be incorrect, and, accord- * As regards the use of the word fundamental in tins place, see Appendix C. SYLLOGISMS. 63 ingly, we need not consider the distinction between the pro- cesses of induction and deduction as more than a logical trifle. It must here be rigidly borne in mind, that the above remarks only apply to induction and deduction when con- sidered as divisions of pure Logic ; for when we come to treat upon applied Logic, it will be found that another kind of induction exists, which necessitates a particular mention, and which is of very great importance. The difference between these two kinds of induction is closely connected with a fact which the student has doubtless observed, viz., that the minor premiss of our inductive syllogism is obviously incorrect, for so far from oxygen, chlorine, and steam being all gases, they only constitute an exceedingly small portion of the class. This brings us to the consideration that in formal Logic we have nothing at all to do with truth or falsehood we can only ascertain whether a conclusion legitimately follows from pre- mises already granted. Accordingly, we merely look upon the minor premiss with reference to its form, i.e., its quantity, quality, and relation, and not as regarding its matter, viz., the reality and nature of the notions composing the subject and predicate : thus, for all purely logical purposes, the pro- position might be replaced by " X, Y, and Z, are all S " without in the least interfering with the reasoning process. Applied Logic, on the contrary, takes into account the relative natures of the objects furnishing notions, and would construct the syllogism in the following manner : Oxygen, chlorine, and steam are elastic (A), Oxygen, chlorine, and steam are gases (A) ; /. All gases are elastic (A). Here it will be seen that the minor premiss is indeed true, but then there is an illicit process of the minor term, so that the syllogism cannot be admitted as formally valid. The deductive syllogism corresponding to our inductivo example would be as follows : All gases are elastic, Oxygen is a gas ; .*. Oxygen is elastic where the general law is applied to a particular case. OF REASONING OR ARGUMENT. 13. Extension and Intension. In a former chapter it was explained that a proposition might have its meaning regarded from different points of view, according as the subject and predicate were regarded intensively or extensively. Thus, when we say, " All fluids are compressible," we mean not only that the attributes of " compressibility " are among the attributes of every " fluid " (intension), but, also, that the class of " compressible sub- stances " numbers in its ranks all " fluids " (extension). This differentiation of meaning, in like manner, finds place among arguments, and thence has arisen a distinction of syllogisms into extensive and comprehensive (intensive). An extensive syllogism is of this nature Motion is immaterial, Heat is motion ; /. Heat is immaterial, and would be thus interpreted : Motions are contained in the class of immaterial objects, Heat is contained in the class of motions ; /. Heat is contained in the class of immaterial objects. The same syllogism, if stated comprehensively, or inten- sively, would run as follows : Heat is motion, Motion is immaterial ; /. Heat is immaterial ; and its meaning, when broadly stated, would be this : Heat comprehends in it the attributes of motion, Motion comprehends among its attributes those of im- materiality ; /. Heat comprehends the attributes of immateriality. An examination of these four syllogisms will reveal their dependence upon each other ; all of them being evidently the same result of the same process of reasoning. This is rendered clear by a brief analysis of the import which attaches to pre- dication. We say, for instance, that " motion is immaterial," and in doing so we state that a certain relation of congruity exists between two compound ideas : " motion" which con- sists of two sets of attributes, viz., the generic feature " imma- teriality ' and certain specific differences ; and " immaterial SYLLOGISMS. 65 objects" which likewise is duplicate, containing the notion " immateriality " per se, and the notion of " immateriality " indefinitely repeated, as existing in combination with various sets of specific differences. It therefore results that the rela- tion implied by our predication is also compounded, its con- stituents being, that motion is an immateriality united with certain distinguishing marks ; and that motion is capable of producing on the mind, together with other impressions, the same idea that immateriality per se would do. These two relations it will easily be seen are those of extension and intension. But another fact remains to be noticed : that although the two ideas and relations are thus shown to be compound, yet the union of their respective parts is so inti- mate that they cannot be separated. We are unable to resolve the idea "motion" into its two sets of attributes, " immateriality " and " specific differences," so as to think of these separately, and at different times : we are also unable to divide the idea " immaterial objects " into " immateriality " per se, and " immaterialities " respectively combined with distinguishing attributes ; and, finally, we are unable to think of one of the relations above described without also thinking of the other. The utmost we can do is to bring one portion of the compound idea, or relation, into greater prominence than its fellow, by concentrating our attention as much as pos- sible upon the chosen part ; it being remembered that we can- not so concentrate the whole of our attention, and, therefore, we must always, in some measure, be impressed by the less important constituent. These observations, if taken in conjunction with those con- tained in the section upon induction and deduction, will, it is hoped, afford an intelligible and clear view of the manner in which the mind acts when comparing notions and judgments ; and as the operation is always identical, being, though com- plex, yet irresoluble, it follows that the only useful, or, strictly speaking, admissible division of judgments and reasonings, is that which merely refers to their form. Hence, in formal Logic the distinction between the processes of extension and comprehension must, like that between induction and deduc- tion, be considered as of trifling consequence. 66 OF REASONING OR ARGUMENT. 14. Denomination. When speaking of the interpretation of the copula, I men- tioned that another mode of doing so had been suggested, in addition to those connected with the doctrines of extension and intension. This was the interpretation of denomination, and is as applicable to arguments as to propositions : for ex- ample, the syllogism All planets are stars, Mercury is a planet ; /. Mercury is a star, may be thus translated : Planets may be called stars, Mercury is a planet ; .*. Mercury may be called a star. This interpretation is, of course, merely verbally significant, and is not intended to imply any approach to a radical, or even formal difference between the syllogisms. The doctrine, if doctrine it may be called, must, therefore, be received as nothing more than a practical hint for turning a syllogism to some special account, and as such belongs properly to applied Logic. Former usage, however, is my excuse for placing it here. 15. Syllogistic Arrangement of Propositions. Before concluding the subject of pure-categorical syllo- gisms, it will be advisable to mention a matter about which the student might otherwise entertain an erroneous opinion. I allude to the order of the three propositions constituting a syllogism. It will have been observed that the usual course pursued is to place the major premiss first, the minor next, and the conclusion last ; and it may consequently be thought that this order is the one most in accordance with natural laws. Such, however, is not the case ; the arrangement in question being merely an arbitrary practice adopted by logicians in order to facilitate their expositions of the science. In fact, it frequently happens that the conclusion occurs to the mind as a problem or thesis, which requires certain judgments (premises) to be formed, in order that its validity SYLLOGISMS. 67 may be apparent. Thus, I might suspect a certain gas to be hydrochloric acid, but in order to be sure it would be necessary for me to find some proof of this. Accordingly, knowing the general law that ammonia produces white fumes only when brought into contact with hydrochloric acid, I should proceed to test the suspected gas in this manner ; and, the anticipated result following, I should be enabled to con- struct the syllogism : This gas is hydrochloric acid ; Because, It produces white fumes with ammonia, And, Everything which does that must be hydro- chloric acid. Hero the premises and conclusion are reversed. Again, some fact comes under our notice, such as, " This metal takes fire upon touching water ;" we make inquiries, and find that " The only metal behaving in such a manner is potassium ;" hence we draw the conclusion that " This metal is potassium." An argument so expressed is a syllogism of the first figure, but with the premises reversed. Accordingly, it thus appears that there is no natural and definite order of judgments; it cannot, therefore, be said that any arrangement is incorrect, or alone correct, the disputes between logicians upholding different models being so many lost words, we can scarcely say arguments. 16. Conditional Syllogisms. We have now to consider the case of syllogisms whcse con- stituent propositions are not all pure-categoricals ; and first we will examine those in which one or more conditional* judgments appear, the argument being then termed a con- ditional syllogism. Now these reasonings may be treated in two ways prac- tically, and theoretically ; that is to say, their own special canons or proximate rules may be applied to them as they stand ; or they may be reduced to categorical syllogisms, when, of course, they immediately fall under the law r s which * I omit modal propositions, as these cannot be treated otherwise than as pure-categoricals. See p. 28. 68 OF REASONING OR ARGUMENT. have been analysed in the foregoing pages. And, first, as they stand. Every conditional proposition consists of two parts the antecedent and the consequent between which a certain rela- tion is asserted to exist. These parts are both distinct judg- ments, the relation being that the consequent depejids upon the antecedent in such a manner as to necessitate the inference of the former if the latter be granted ; e.g., " If the anchor holds out, the ship will be saved," where " If the anchor holds out " . is the antecedent, " the ship will be saved" is the consequent, and the relation asserted is, that if we admit that the anchor will hold out, then we must also admit that the ship will be saved. A complete syllogism having such a proposition for a premiss, would be of the following form : If the anchor will hold out, the ship will be saved, The anchor will hold out ; .*. The ship will be saved. In cases where both the premises are conditional, then the conclusion must be conditional also, e.g. If the anchor will hold out, the ship will be saved, If the storm does not increase, the anchor will hold out ; .*. If the storm does not increase, the ship will be saved. Now, from a consideration of the relation subsisting between the antecedent and consequent of a conditional proposition, logicians have devised two practical rules, which suffice to determine the validity of any conditional syllogism without reducing it to a categorical form. These are : 1. If the antecedent be granted, the consequent may be in- ferred; for this is merely to state the nature of the assertion made by the form of the proposition. Nothing, however, follows from granting the consequent : thus, in the proposi- tion " If he is truly wise, he will be happy," we must infer that he will be happy, if we admit that he is truly wise ; but admitting him to be happy will not prove him to be wise, as it is possible for an ignorant person to enjoy himself. 2. If the consequent be denied, the antecedent may also be denied. This follows from the consideration that the truth of the consequent is necessitated by that of the antecedent, o that if the latter were true, the former would be so too. SYLLOGISMS. 69 If, for example, we deny the consequent of this proposition, " If he be shot through the heart, he is dead," and say that he is not dead, we may evidently infer that he is not shot through the heart; but to deny the antecedent would not enable us to say that he is not dead, because he may have been killed by many other causes. These two laws have given occasion to a division of con- ditional syllogisms into two moods, viz., the ponent, wherein the antecedent is granted, and the tollent, where the conse- quent is denied. These moods are reciprocally convertible, as may be seen from the following example : If the moon is not shining, the night is dark, The moon is not shining ; .*. The night is dark. This is in the ponent mood ; but if we wish to make it tollent, we may do so by reversing the hypothetical, and duly negating, thus : If the night is not dark, the moon is shining, The moon is not shining ; /. The night is dark. These moods are also termed constructive and destructive, answering respectively to ponent and tollent. The second method of treating conditional -syllogisms is, by reducing them to categoricals. Such a proceeding has, indeed, been condemned by high authority* on the ground of its being unnecessary and not always possible. I venture, however, in common with many logicians,")* to think that this condemnation is erroneous, as both of the objections urged may be thus disposed of. The reduction is necessary, as, by this means, conditional-reasoning being brought under the same proximate la\vs with categorical arguments, is shown to be of exactly the same nature, and so the unity of the reasoning process is maintained ; at the same time, however, I do not contend that it is necessary for practical purposes, as then the rules above explained would become inept. Again, that the * Krug's " Logik," p. 258. Bachmann's " Logik," 89, Anm. 2. Sir W. Hamilton's " Logic," vol. i. p. 342. f Esser's "Logik," 99; Wolfs " Philos. Rat.." 412; Whately'a " Elements," book ii. chap, iv., 6; Thomson's <% Outlines/' 73. 70 OF REASONING OR ARGUMENT. reduction is never impossible, may be seen from the very case adduced as presenting insuperable difficulties, viz., " If A is C, B is D ; but A is ; therefore, B is D ;" where we have only to say, "The case of A being C is a case of B being D ; the present case is a case of A being C ; therefore, the present case is a case of B being D" and ihe obstacle is surmounted, the resulting syllogism being a categorical in A A A, Fig. I., or, as the old logicians would say, in Barbara. The re- spective terms are here distinguished by being printed in italics. That these objections should have been brought against the reducing process as applied to conditional syllogisms, is apparently owing, first, to the acceptance of the principle, " Infer nothing without a ground or reason " as a necessary and primary law of thought ; and, secondly, to its being lost sight of that a term may be composed of more than one conception. With regard to the first of these causes, it may be observed, that the law there mentioned, called the law of reason and consequent, has been a subject of much discussion among metaphysicians and logicians, but should properly be referred to the former alone. By it the antecedent is ex- plained as being " the complement of all, without which something else would not be," and the consequent as being " the complement of all that is determined to be by the existence of something else." This, which is Sir William Hamilton's explication, given with especial reference to con- ditional propositions, is, however, too wide and general for application in such cases ; since, were we to admit that the consequent " could not be " without the antecedent, we must also admit, that by denying the antecedent we may deny the consequent, which is contrary to the second rule above given. It is likewise too wide and general to be considered as a separate law, for if the antecedent be the " complement of all, without which something else would not be," it must necessarily be that " something else " itself. Now, a thing cannot be something else ; and, therefore, in order to attach any admissible meaning to the definition under question, we must interpret it thus : " The antecedent is the same thing as the consequent, but from a different point of view," a state- SYLLOGISMS. ment much the same as " a thing is itself," and answering to another primary law, viz., " whatever is, is." * Indeed, Sir William Hamilton's latest views would appear to have been in accordance with those advocated here, as we find him saying, that the law of reason and consequent " should be excluded from logic." ( The second source of objection which led to the statement that some conditionals could not be reduced, probably arose, as stated above, from an incomplete view of the structure of terms. Thus, in the syllogism, " If A is B, is D ; but A is B ; therefore, C is D ;" it was hastily concluded that there are four terms, A, B, 0, and D ; but, in so doing, it is as- sumed that the reasoning process concerns these simple notions ; whereas, in fact, it is occupied with the more com- plex ideas, " A is B " and " C is D." Accordingly, instead of four terms, which of course would be incompatible with a categorical syllogism, we have only two, and require a third, viz., " the present case," before we can draw a conclusion. This third term is implied in the second premiss, when we say "A is B." During the course of the preceding remarks, the student will doubtless have observed the technical method of reduc- tion employed in these cases. It may be articulately enounced as follows : " Each conditional proposition is to be considered as a universal-affirmative-attributive categorical, with the antecedent for a subject, and the consequent for a predicate." Thus, the syllogism here stated, If a body is struck, heat is generated, But if a meteorite falls into the sun. a body is struck ; .-. If a meteorite falls into the sun, heat is generated, may be reduced in the following manner : All cases of " a body is struck," are cases of " heat is generated" (A), All cases of " a meteorite falls into the nun," are cases of " a body is struck " (A) ; . . All cases of " a meteorite falls into the sun," are cases of " heat is generated." * As regards the primary laws of thought, see Appendix C. f " Discussions," p. 603. 72 OF REASONING OR ARGUMENT. In this way, or by using equivalent expressions, any condi- tional syllogism may be thrown into the form best adapted for displaying its real import aa an act of reasoning. 17. Disjunctive Syllogisms. A disjunctive syllogism is an argument in which there is one, or more than one, disjunctive proposition, and may be represented by these formulae : 1. " A is either C or D ; B is neither nor D ; therefore, B is not A." 2. "A must be either or D ; but it is not C ; therefore, it is D." 3. "A is either C, D, or E ; but it is not C ; therefore, A is either D or E." 4. " Either A is B, or C is D ; but A is not B ; therefore, C is D," &c. &c. The import of the disjunctive propositions in all these syl- logisms is, that the cases enumerated are the only possible ones, and that they are mutually exclusive ; a perfect logical division has in fact been performed. Accordingly, the prac- tical rules which result are 1. Prom the assertion of one alternative, we may deny all the others ; e.g., if in the proposition, " All men must be either white, black, red, or yellow," we were to affirm, " These men are red," we might infer that " they are neither white, black, nor yellow." 2. From the disjunctive assertion of more alternatives than one, we may deny the rest. Thus, in the above example, if we were to say, for our second premiss, that " these men are either white or black," we should then conclude that " they are neither red nor yellow." 3. From the denial of one, or more than one alternative, we may assert such as remain ; directly, if one, disjunctively, if more. Accordingly, the following syllogism would be valid : All poems are either epic, lyrical, or didactic, The poem of Paradise Lost is neither lyrical nor dadactic ; /. Paradise Lost is an epic. The reduction of disjunctive syllogisms to categoricals is similar to that of conditionals. Take, for instance, the syllogism just quoted it will become : SYLLOGISMS. 73 Poems which are neither lyrical nor didactic, are epics, Paradise Lost is a poem which is neither lyrical nor didactic ; .'. Paradise Lost is an epic. And here it must be stated, that in order to have a true conditional or disjunctive syllogism, it is necessary that the reasoning should hinge upon the consequence in the one case, and on the alternative in the other ; for it is possible for a conditional or disjunctive proposition to exist in a categorical syllogism; thus, All simple forms of matter are indestructible as such, If the caloric theory be correct, heat is a simple form of matter ; .*. If the caloric theory be correct, heat is indestructible as such. In this case, " If the caloric theory be correct, heat " must be considered as the minor term, for it is evident that the reasoning is merely a comparison of this, and the major term " indestructible as such," with the middle " simple forms of matter ;" leaving the consequence of the conditional proposi- tion altogether untouched. 18. The Dilemma. If in a syllogism there be a conditional premiss, whose ante- cedent or consequent is composed of a disjunctive proposi- tion, such an argument is termed a dilemirtaTorhypothetico- disjunctive syllogism. Take, for example, the following : If the army were defeated, it must either have sur- rendered or retreated, But it did neither of these ; /. It was not defeated^ The rules upon which the validity of such syllogisms depend, are compounded of those referring to both condi- tionals and disjunctives ; thus, 1. The antecedent being affirmed, either disjunctively or not, as the case may be, the con- sequent is also admitted ; and 2. The consequent being denied, either disjunctively or not, as the case may be, the antecedent is also denied. An argument of the above description is termed a dilemma 74: OF REASONING OR ARGUMENT. in consequence of its having two disjunctive members in the consequent of the major premiss: that is to say, it contains a double lemma, or double supposition. If there are three such members, it is a trilemma ; if four, a tetrakmma, and so on ; but the name polylemma is usually applied to those containing more than four. Any one of these would, how- ever, be loosely called a dilemma. Such is the account commonly given of those arguments to which the name of dilemma is applied ; but it is incom- plete, as it does not refer to a class of syllogisms which, if anything, would fall more properly under that denomination. I allude to those in which several antecedents and consequents are disjunctively affirmed or denied ; e.g. If he leaps out of the window, he will severely injure himself; if he does not do so, he will be burned, But he must do either the one or the other ; /. He must either severely injure himself, or be burned. Or again If this man were happy, he would not be angry ; and if he retained his self-command, he would not be excited, But he is either angry or excited ; /. He is either unhappy, or has lost his self-command. In these syllogisms, we see that the major premiss (so to speak) is composed of two distinct conditional propositions, thus being a truer di-lemma than the cases previously con- sidered. All hypothetico-disjunctive arguments may be reduced, either to conditionals or categoricals at pleasure. There is no difficulty in the process, it being merely a judicious com- bination of the methods already studied, and as a general model, the following formula will be all that is needed. It- shows the categorical reduction of a complex-dilemma, that is, where the major premiss is composed of two distinct conditionals. Syllogism : If A is, B is ; and if C is, D is, But either A is, or C is ; /. Either B is, or D is. SYLLOGISMS. 75 Reduction : 1. Take for a major premiss the categorical equivalent of the given minor ; and for a minor term, the denial of the consequent in the first conditional of the given major premiss : complete the syllogism, thus All non-A's are C's, All non-B's are non-A's ; .*. All non-B's are C's. 2. Take for a major premiss, the categorical equivalent of the second conditional in the given major ; and for a minor premiss, the conclusion of the syllogism last formed : the conclusion resulting from these premises, will be the cate- gorical equivalent of the disjunctive conclusion in the syl- logism given for conversion : e.g All C's are D's, All non-B's are C's ; .*. All non-B's are D's ; or Either B is, or D is. 19. Incomplete Syllogisms. When any one of the propositions forming a syllogism is not overtly enounced, such an argument is termed an Enihy- meme. It will be evident that there is no difference in the reasoning process between enthymemes and formal syllogisms, as the premises and conclusion are in both cases the same : the distinction merely consists in the number of judgments that may be actually expressed in words. Accordingly, since there are three propositions in every syllogism, enthy- memes are divided into three orders, w 7 hich respectively suppress the major premiss, the minor premiss, and the con- clusion. Examples of them may be thus given : The formal syllogism : All women are inquisitive, Julia is a woman ; .'. Julia is inqusitive. Enthymeme of the first order (the major suppressed) : Julia is a woman ; .*. Julia is inquisitive. 76 OF REASONING OR ARGUMENT. Enthymeme of the second order (the minor suppressed) : All women are inquisitive ; .*. Julia is inquisitive. Enthymemeof the third order (the conclusion suppressed): All women are inquisitive, And Julia is a woman. Into one or other of these three forms, nearly all argu- ments, as popularly expressed, fall ; for it is seldom that a person takes the trouble to state a syllogism in full. This elliptical method of overt inference, is most strikingly de- veloped in those arguments which were discussed under the heads of Opposition, Conversion , and Coincident- Junction . where not only is a premiss not expressed, but it is almost unconsciously thought ; so much so. indeed, that it requires a searching investigation to become convinced of its exis- tence. We need not wonder, therefore, at their being often termed immediate inferences. Conditional judgments too, are frequently of an enthymematic nature, such as, for in- stance, " If Pegasus be a horse, it must be a quadruped," which manifestly proceeds upon the assumption that " all horses are quadrupeds." 20. Complex Arguments, or Chains of Reasoning. It often happens that we arrive at a conclusion through a string of correlative syllogisms, and when this is the case we have what is termed a chain of reasoning. These arguments are, however, generally of an enthymematic form, and are divided according as they suppress the conclusion, .or one of the premises, in each syllogism. Those chains of reasoning, where all conclusions but the one desired are suppressed, must necessarily consist of pre- mises, and this form is known as a sorites. It may be of two kinds first, where the predicate of each premiss is the sub- ject of the next succeeding one, and where the conclusion is the last predicate affirmed of the first subject ; this is termed the ascending, regressive, or Aristotelian sorites: and secondly, where the subject of each premiss is the predicate of the next, and where the conclusion is the first predicate affirmed of SYLLOGISMS. 77 the last subject ; this is styled the descending, progressive, or Goclenian sorites. The formulae of these are : Aristotelian. Goclenian. A is B, D is E, BisC, CisD, C is D, B is C, D is E ; A is B ; .'. AisE. /. AisE. Or, concrete examples may be given, as follows : Aristotelian : Red is a colour, A colour is a kind of light, All light is a kind of motion ; .*. Red is a kind of motion. Goclenian : All light is a kind of motion, A colour is a kind of light, Red is a colour ; .*. Red is a kind of motion. It will have been observed, that the formulae are entirely affirmative ; this arises from the rule that we can draw no con- clusion from negative premises. We may, however, have the last premiss of the series negative, but then the conclusion must be negative also, thus : Red is a colour, A colour is a kind of light, All light is a kind of motion, No motion is material ; .'. Red is not material. A sorites containing premises of the above description, may have its validity directly tested by this modification of the dictum : " Whatever belongs, or does not belong, to a given whole, belongs, or does not belong, to each and every one of the parts constituting any whole contained in the given whole." 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