An introduction to logic

Preface To The Second Edition

The present edition, the preparation of which has been somewhat delayed by reason of the war, has been carefully revised throughout, and is enlarged to the extent of some 40 pages. Though it does not differ in its main teaching from the first edition, there are very few pages without some slight alteration, if only for the sake of greater clearness, or of more consistency in phraseology. I hope the alterations are improvements ; I must confess to some dissatisfaction at finding how many I desired to make. The following list of some of the principal alterations and additions may be of use to any reader who is interested in a comparison.

c. i. On p. 5, n. 1 (upon the distinction between the form and matter of thought), I have endeavoured to show that the matter of thought, in this antithesis, is not the same as its ' subject-matter ' ; and I have altered the language of many passages accordingly. The latter part of p. 10, n. 1, and the last page and a half of the chapter, are new.

c. ii. Much of this chapter has been rewritten. In particular, the general discussion of the nature of a term on pp. 14-28, and that of the distinction between abstract and concrete terms, on pp. 32-35, are largely new. The former includes some discussion of concepts ; and both have involved small consequential alterations at many subsequent points.

c. iii. The note on p. 52, on the position of ' first substances ' in Aristotle's doctrine of categories, dissents from p. 39, n. 1, of the first edition.

c. V. In this chapter I have laid more stress on the makeshift character of most classification, and have done more justice to the use of negative differentiae.

c. vi. This chapter has been largely rearranged and rewritten. I now prefer, in order to express the truth in the contention

PREFACE TO THE SECOND EDITION

of those who have denied connotation to proper names, to distinguish between intension and connotation, allowing them the former, but not the latter.

c. viii. This chapter also has been largely rewritten, particularly in the discussion of the modality of judgements, and of the distinction between analytic and synthetic judgements. The close priat on pp. 192-195, 201-205, 214-215, is new matter. In this and subsequent chapters I think that much which in the first edition was said about judgements should properly have been said about propositions, and correction has been made accordingly. I have made use in certain places of expressions borrowed from Prof. Cook Wilson.

c. ix. On p. 228, and also on p. 120, n. 1, 1 have inserted a few remarks on Symbolic Logic, which wUl in some measure explain why the book does not deal more fully with that subject.

c. X. The discussion of the inferential character of so-called Immediate Inference (pp. 240-247) has been enlarged and recast ; pp. 241-242 are new matter.

c. xii. The discussion of the Fourth Figure of Syllogism, pp. 280-284, has been largely rewritten.

c. xiii. In the note beginning on p. 296, the discussion of the passage Cat. iii. 1* 10-15 (pp. 298-299) has been emended.

c. xiv. In pp. 310-311 I have emphasized the subsumptive and therefore inferior character of syllogistic thinking. The close-print discussion on pp. 331-334 is new.

c. xviii. The attempt in the last three pages, 897-399, to characterize the difference between inductive and deductive reasoning is new.

c. xix. The new matter in this chapter, which has also been considerably rewritten, is chiefly in pp. 403-404, 410-413, 418-419, 421, n.l.

c. XX. I have corrected language which spoke of an event causally connected with another as its cause, both here and subsequently ; the point is discussed on pp. 426-428.

PREFACE TO THE SECOND EDITION

c. xxi. In pp. 475-476 I have dwelt on one or two further matters belonging to the pursuit of the inductive sciences which are no part of their reasoning.

c. xxii. A rather obscure passage in the previous edition (pp. 459-460) is replaced by pp. 495-496.

c. xxiii. I have tried to improve the statement of what explanation is on pp. 502, 521-522 ; and p. 523, n. 1, is new. The close print on pp. 524r-527 is an answer to a criticism which Dr. Bosanquet has made upon the view of induction taken in this book.

c. XXV. I have on pp. 546-549 rewritten and to some extent altered the tenour of what was said before (on pp. 506-509 of the first edition) concerning the foundation of our power to generalize in mathematics.

c. xxvii. Some additional matter is contained in the first notes on pp. 572, 580, 582, 589, 595.

I have taken account of such criticisms as I have seen in print, though I have not thought all equally well founded ; for these, and also for various criticisms privately communicated, I desire to express my thanks. I should like here to name again Prof. J. A. Smith, Mr. H. H. Joachim, and Mr. H. A. Prichard, who were all good enough to send me comments on divers points. Besides these. Prof. W. 6. de Burgh, of University College, Beading, very kindly helped me with a list of criticisms and suggestions based on his use of the book with students ; and Miss Augusta Klein sent me a series of most careful notes upon the first eight chapters. These were particularly helpful upon points of science referred to by way of illustration, and upon the theory of classification, with the logical doctrines on which it rests; and the principal changes which I have introduced on those topics are due to her criticism, though not involving a full acceptance of it.

But chiefly here I desire to put on record the debt which I owe, in common with so many other of his older or younger pupils to Prof. J. Cook Wilson, whose death occurred while these sheets were passing through the press. Various footnotes will show

PREFACE TO THE SECOND EDITION

the use that I have made of his unpubUshed teaching ; but his illness prevented me from submitting to him what I have written, and his authority must be made responsible for no errors that I may have made. His few and scattered publications can do little to convey to strangers the power and stimulus of his personal teaching. And there are subjects on which, by his combination of scholarly and mathematical with philosophic insight, he was qualified as few have been to produce new work of real value. The hope has vanished that he might put in permanent form the full results of his thinking. But those who knew him well will not misjudge this failvu'e. For they will remember him as not more patient and eager in philosophic reflection than in his devotion during many years to a suffering wife and in his endurance afterwards of his own wasting and fatal illness.

Advantage has been taken of reprinting to correct a number of small errors, mostly typographical, to which my attention has been called by the kindness of readers.

Janvary, 1925.

Preface To The First Edition

If an apology that precedes it could mitigate an offence, 1 should be inclined to convert my preface into an apology for publishing this book. Progress, and the hope of progress, in logical investigations, have lain perhaps during the last three generations chiefly in two directions, either of analysing more closely the processes of thought exhibited in the sciences, or of determining what knowledge is, and the relation of the knowing mind to what it knows. Though I have been compelled to deal in some degree with the first of these questions, I am well aware that it demands a scientific knowledge which I do not possess ; the second I have not attempted systematically to discuss. The aim of the following book is more modest. There is a body of what might be called traditional doctrine in Logic, which is not only in fact used by itself as an instrument of intellectual discipline, but ought also to be in some degree mastered by those who would proceed to the higher and abstruser problems. It is of this traditional doctrine that Benjamin Jowett is recorded to have said, that Logic is neither a science, nor an art, but a dodge. I could perhaps best describe the motive with which this work was begun, as the desire to expound the traditional Logic in a way that did not deserve this accusation. The accusation was doubtless provoked by the attempt to force into a limited number of forms processes of thought, many of which can only with pretence and violence be made to fit them : an attempt, it may be added, at least as characteristic of ' Inductive Logic ' as of any other.

In the course of centuries, the tradition has become divergent, and often corrupt. In this difficulty, I have ventured, like one or two other modern writers, to go back largely to its source in Aristotle. Problems of thought cannot in any case be studied without careful regard to their terminology, and their terminology

PREFACE TO THE FIRST EDITION

cannot be understood without reference to its history. The terminology of Logic owes more to Aristotle than to any one else ; but there is this further reason for attention to what he said, that much prevalent falsehood or confusion in the tradition is a corruption of truths expressed by him. At the same time, I have not pretended to believe in the verbal inspiration of his writings.

I have in particular been anxious to teach nothing to beginners which they should afterwards have merely to unlearn. They may of course come to dissent from the positions here taken up; but_ only, I hope, because they think I have the worst of the argument on a proper issue, and not because, as meat for babes, I have been dogmatically expounding acknowledged fictions.

While dealing largely with the more technical parts of logical tradition and terminology, I have done my best to avoid a superfluity of technical terms ; and the subjects discussed have been for the most part discussed in detail, and the principles involved in them debated. The dryness with which the more formal branches of Logic are often charged springs, I think, in part from their being presented in too cut-and-dried a manner ; those who go beyond the jejune outline, and get into an argument, often find the subject then first begin to grow interesting. At any rate I have tried to secure this result by greater fullness, and attention to controversial issues. In every study there must be something to learn by heart ; but Logic should appeal as far as possible to the reason, and not to the memory. Thus such a question as the * reduction ' of syllogisms has been dealt with at length, not from any wish to overrate the importance of syllogistic reasoning, or burden the student with needless antiquarianism, but because the only thing of any real value in the subject of reduction is just that investigation of the nature of our processes of thinking which is involved in asking whether there is any justification for reducing all syllogisms to the first figure.

Topics whose main interest is obviously historical pr antiquarian have been either relegated to footnotes or placed in closer type and between brackets ; and as I have followed the advice to translate what Greek I quote, I do not think that there is anything in these

PREFACE TO THE FIRST EDITION

discussions which a reader need be altogether precluded from following by ignorance of that language. I have also put between brackets in closer type other passages which, for one reason or another, might be omitted without spoiling the argument ; among the matters so treated is the fourth figure of syllogism ; for I have reverted to the Aristotelian doctrine of three figures, with the moods of the fourth as indirect moods of the first.

I hope that I have sufficiently acknowledged all detailed obligations to previous writers in the places where they occur. But I owe here a more comprehensive acknowledgement both to the published work of Sigwart, Lotze, Mr. F. H. Bradley, and Professor Bosanquet, and to the instruction received in private discussion with various friends. Among these I should like to mention in particular Mr. J. Cook Wilson, FeUow of New College, Wykeham Professor of Logic in the University of Oxford, whose reluctance to write is a source to many of serious disappointment and concern ; Mr. J. A. Smith, Fellow of Balliol College ; Mr. C. C. J. Webb, FeUow of Magdalen College; Mr. H. H. Joachim, FeUow of Merton College ; and Mr. H. A. Prichard, Fellow of Trinity College, Oxford. To the last three of these, and also to Mr. C. Carman, Secretary to the Delegates of the University Press, I am further indebted for the great kindness with which they read large portions of the work in MS. or in proof ; without their suggestions and corrections it would be even more imperfect than it is. Ld/Stly, I have to thank my sister, Miss J. M. Joseph, for the help she gave me in reading the whole of the proof-sheets and in undertaking the laborious and ungrateful task of checking the index.

Contents

CHAPTEE PAGE

I. Of the General Chabacteb of the Enquiet . 1

II. Of Terms, and their Principal Distinctions . 14

Chapter I Of The General Character Of The Enquiry

It is a common practice to begin a treatise on any science with a discussion of its definition. By this means the reader's attention is directed to the proper objects, and to those features of them, with which the science is concerned ; a real advantage, when, as with Logic, those objects are not apprehended through the senses, and for this reason ordinarily attract Kttle notice. But the same reason which makes a definition of Logic at the outset useful, makes controversy about its definition comparatively useless at such an early stage. The reader is too unfamiliar with the subject-matter of his science to be able to judge what definition best indicates its nature ; he cannot expect thoroughly to imderstand the definition that is given, until he has become familiar with that which is defined. The definition will at first guide more than enlighten him ; but if, as he proceeds, he finds that it helps to shew unity in the difierent enquiries upon which he successively enters, it will so far be justified.

Logic is a science, in the sense that it seeks to know the principles of some subject which it studies. The different sciences difier in the subjects which they so study ; astronomy studies the nature, movements, and history of the heavenly bodies, botany the structure, growth, history, and habits of plants, geometry the properties and relations of Unes, surfaces, and figures in space ; but each attempts to discover the principles underlying the subjects with which it has to deal, and to explain their great variety by the help of one set of principles. These principles are often spoken of as laws ; and in the physical sciences that deal with change, as ' laws of nature '. The phrase may suggest that ' nature ' is not the sum of things and of events in the physical universe, but a sort of power prescribing to these the rules which they are to follow in their behaviour ; as the King in Parliament prescribes rules of conduct to his people. That, however, is not what we have to understand in science by a ' law ' ; a law in science is not, like human laws, a rule enjoined but sometimes disregarded ; it is a principle illustrated — and existing only in the necessity of its being illustrated — ^in the department of fact to which it belongs. There are therefore no breaches of scientific law, or of a law of nature ^ ; if events are observed which do not conform to what we have hitherto called a law, we conclude not that the law is broken, but that we were ignorant of the true law ; if water, for example, were observed to boil on the top of Mont Blanc at a lower temperature than 212° Fahr., we should infer not that the law that water boils at 212° Fahr. was broken but that it is not a law of nature that water boils at 212° Fahr.,— that there are other conditions which have to be fulfilled, if water is to boil at that temperature ; and the ' law ' is that it should boil only when those conditions are fulfilled. Such laws, the general principles to which things in their properties and their behaviour do actually conform, are what the physical sciences seek to discover, each in its own department, and if Logic is a science, it must have a subject of its own, in which it seeks for principles and laws.

That subject is thought, but thought is always thought about something ; and thinktag cannot be studied in abstraction from anything thought about. But yet in the same way that we may study the laws of motion, as they are exemplified ia the movement of all bodies, without studying all the bodies that ever move, so we may study the laws of thought, as they are exemplified in thinking about all subjects, without studying all the subjects that are ever thought of. This comparison may be pushed further. Just as we must have experience of moving bodies, before we can investigate the laws of their motion, so we must have experience of thinking about things, before we can investigate the principles of thinking ; only this means, in the case of thinking, that we must oiirselves think about things first, for no one can have experience of thinkiag except in his own mind. Again, although, in studying the laws of motion, we do not study every body that moves, yet we must always have before our minds some body, which we take as representing all possible bodies like it ; and in the same way, when we investigate the principles that regulate our thinking, though we do not need to study all things ever thought of, we must have before our minds something thought of, in order to realize in it how we think about it and all possible things like it. For example, it is a general principle of our thought, that we do not conceive of qualities

^ The question of the possibility of a ' miraculous ' breach of natural law need not be considered here; something is said of it in o. xix, infra, }-p. 417-421,

I] GENERAL CHARACTER OF THE ENQUIRY 3

except as existing in some substance ; and that nevertheless the same quality is thought to exist in many substances ; green is a quality, which exists not by itself, but in grass and leaves of trees and so forth ; at the same time, green may exist in many different leaves or blades of grass. The general principle which is thus illustrated in the quality green is readily understood to be true of all possible qualities ; but unless we were able to think of some particular quaUty to illustrate it, we could not understand the general principle at all.

What has been now said will serve to remove an objection which Locke brought against the study of Logic. ' God ', says Locke ^, ' has not been so sparing to men, to make them barely two-legged creatures, and left it to Aristotle to make them rational.' He is urging that men thought rationally, or logically, i. e. in accordance with the principles that Logic discovers to regulate all sound thought, long before those principles were recognized ; and that this is still so with each of us ; we do not therefore need Logic to teach us how to think. That is quite true, and would be a pertinent criticism against any one who pretended that no one could think rationally without studying Logic ; but it isjtio]bJhebuswegS of Lg^c to make men rational, but rather to teach them ia. what their being rational consists. And this they could never learn, if they were not rational first ; just as a man could never study (say) the principles of voluntary motion, ii he was not first accustomed to move his limbs as he willed. Had God made men barely two-legged creatures, Aristotle would in vain have taught them to be rational, for they would not have understood his teaching.

Logic^^en, js the science which studies the general principles in accordance jwith which we think about things, whatever things they may be ; and so it presupposes that we have thought about things. Now our thought about them is expressed partly in the daily conversation of life or musings of our minds ; partly and most systematically in the various sciences. Those sciences are the best examples of human thinking about things, the most careful, clear, and coherent, that exist. In them, therefore, the logician can best study the laws of men's thinking ; and it is in this sense that we may accept the old definition of Logic, scientia scientiarum? What ' the courses of the stars ' are to astronomy, what figures, Unes, and

' Essay, Bk. IV. c. xvii. § 4.

^ Joannes Philoponus cites it ad Ar. AtmI. Post. a. ix, 76* 15.

B2 surfaces are to geometry, what plants are to botany, or the calendar of Newgate to the criminologist, that the other sciences are to the logician : they are the material which he has to investigate, the particular facts which are given him, in order that he may discover the principles displayed in them. He has to ask what knowledge is as knowledge, apart — so far as possible — from the question, what it is about ; and he must therefore examine divers ' knowledges ', and see in what they are alike ; and among the best pieces of knowledge that exist, the best ' knowledges ', are the various sciences. But he is not concerned with the detail of any particular science ; only with those hinds (or forms) of thinking which are exemplified in all our thinkings — ^though not necessarily the same in all — but best exemplified in the sciences.

It is important to understand what is meant by saying that Logic is concerned with forms of thinking ; for many logicians who have laid stress on this, and pointed out that Logic is a formal science, have understood by that expression more than seems to be true. There is a sense in which Logic is undoubtedly formal. By form we mean what is the same in many individuals called materially different — the device, for example, on different coins struck from the same die, or the anatomical structure of different mammalian vertebrates, or the identical mode in which the law requires the different Colleges of the University of Oxford to publish their accounts. And all science is formal, in the sense that it deals with what is common to different instances. A scientific man has no interest in a specimen exactly similar to one which he has already examined ; he wants new types, or fresh details, but the mere multiplication of specimens all alike does not afiect him.'^ So the logician studies the forms of thinking, such as that involved in referring a quality to a substance possessing it ; but when he has once grasped the nature of this act of thought, he is quite uninterested in the thousand difierent such acts which he performs during the day ; they differ only materially, as to what quality is referred to what substance ; formally, so far as the notion of a quality as existing in a substance is concerned, they are the same ; and the forms that run through all our thinking about different matters are what he studies.

But those who have insisted most that Logic is a formal science, or the science of the formal laws of thought, have not merely

^ Unless indeed he is collecting statistics as to the comparative frequency of difierent types.

I] GENERAL CHARACTER OF THE ENQUIRY 5

meant that Logic is in this like other sciences, which all deal with what is formal or universal in their subject-matter.''' They have meant to exclude from Logic any consideration of forms or modes of thinking which are not aUke exemplified in thinking about absolutely every subject. It is as if the botanist were to regard only those laws which are exemplified in every plant, or the geometer were to consider no properties of figures, except what are common to all figures. They have thought that one might abstract entirely from and disregard all question as to what he thinks about, and BtUl find that there are certain principles in accordance 'with which, if he is to think about anything, he will think. But the truth is, that we think in different ways about subjects of different kinds, and therefore we must, if we wish to study the principles that pervade our thinking, consider to some extent the differences in our thought arising from differences in that about which we think. The distinction between form and matter may as it were be taken at different levels. This is plain in a science that deals with some order of sensible things, like zoology. We may say of all men and all horses that they have severally a common form, that as compared to a man a horse is formally different, but as compared to one another all horses are formally the same, though each horse in his body is materially different from every other. Or we may consider not the form of horse common to Black Bess

^ It is important to realize that the subject-matter of Logic is our thinking about divers things, not the things 'vrhich that thinking is about ; they are the subject-matter of that thinking. Just as the form and matter of a coin are both in the coin, so the form and matter of thought (if we are to keep the meaning of the antithesis) must be both in the thought ; 'we must not suppose that the formal identity is in the thought, the material differences in the things thought about. An analogy may help to make this point clearer, on which I confess that there was some confusion in the first edition of this book. Hunger and thirst are formally the same as being both appetites, materially different as being the one for food, the other for drink ; but the material difference is not the difference between food and drink, nor the matter of the appetites food and drink respectively ; the matter is rather the special character which the appetites have through being/or these objects. So the matter of a thought is the special character which it has through being about a certain subject, not the subject which it is about. It may be added, as a caution to the unwary, that the antithesis of form and matter is used in various ways by no means all of them analogous ; and its application to thought is not really the same as its application to coins or animals. What is different in particular thoughts is not related to their Common form as the gold or silver of two coins to their common device, or the flesh and bones of two animals to their common structure, but rather as the specialty of their structures to the generic identity, or as particular instances to the common nature of which they are instances. Cf . infra, pp. 76-77.

and Bucephalus and Rosinante, but the form of vertebrate common to man, horse, eagle, crocodile, &c. ; and now man and horse (as compared with oysters for example) are formally alike. Or we may take the four orders in Cuvier's now obsolete division of the animal kingdom, vertebrata, coelenterata, radiata, and annulosa, and regard them as only different examples of the common form of animal ; and from this point of view a horse and an oyster differ materially, but not formally. When however we have reached this stage, and achieved the conception of animal, as something ex;emplified equally in kinds of animal so different, it is clear that we can only understand what animal structure is by seeing it as it exists in all the different orders of animals ; whereas we can understand fairly the structure of a mammalian vertebrate without seeing it as it exists in every genus of mammals ; still more can we understand the structure of a horse without familiarity with all horses. The higher the level therefore at which in Zoology the distinction between form and matter is taken, the less can we study the form in isolation from variety of matter ; no example taken from one order of animals, say the starfish, will enable us to realize what animality is. It is the same in studying the forms of thought. The most general forms of thought exist diversely modified in thinking about different subjects ; and they can no more be fully known without attending to the different matters in which they appear differently, than animal nature can be fully known without attending to the different orders of animal in which it appears differently. Thus we may take the Proposition, and point out that in every affirmative categorical proposition there is a subject about which something is said, and a predicate, or something which is said about it. This is true equally of the propositions, ' A horse is an animal,' ' First-class railway tickets are white,' and ' Londres is London ' . We may it we like, because in all propositions there is formally the same distinction of subject and predicate, take symbols which shall stand for subject and predicate, whatever they are, and say that all affirmative categorical propositions are of the form 'SisP' . But when we ask for the meaning of this form, and in what sense S is P, it is clear that the meaning varies in different propositions.^ Londrea is just the same as London ; but a horse is not just the same as an animal ; it may be said that ' animal ' is an attribute of horse, and