Logic; or, The analytic of explicit reasoning

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Form I

Introduction

OF THE FUNCTION OF LOGIC

§ i. THE THEORY OF KNOWLEDGE, A DE- PARTMENT OF THE THEORY OF OPINION. —The problem of the origin and nature of knowledge has occupied the attention of the philosophers for something over twenty-five centuries without much progress toward solution. This perhaps results from the fact that the problem itself is but part of a larger problem" that should be first considered; for knowledge is but a species of opinion, which may be either true or false. Hence the inquiry as to the origin and nature of opinion must be the first in order of investigation. Nor until this investigation has been made will we be prepared to determine the specific characteristics by which true knowledge is differentiated from opinion in general.

§ 2. KNOWLEDGE BUT VERIFIED OPINION. — Men generally confound this distinction, and regard all their settled opinions or beliefs as knowledge. This is not merely false, but absurd ; for not only do the opinions of men differ, but the opinions of the same man are often inconsistent and contradictory ; and some, it is clear, must be false. And this is apparent also from the nature and generation of our opinions. For, in general, these come to us not from any conscious process, but naturally and spontaneously and from many sources, as, e. g., from testimony, from authority, from inaccurate observation or careless reasoning, and even largely from mere prejudice or bias. Hence, familiar to us as our opinions are, their origin in general is as unknown to us as were anciently the sources of the Nile; nor have we any just notion of the grounds on which they rest, or of the nature and justice of their demands on our belief. Hence, until some means of verifying our opinions be found and applied, we can have no assurance of their rectitude. The first step in Science or Philosophy must, therefore, be to distinguish between verified and unverified opinions. The former constitutes true knowledge or science ; the latter — though it is in fact the stuff out of which most of the current philosophy is woven — has no just pretension to the name.

§ 3. THE SOURCES OF OPINION DISTIN- GUISHED.— With regard to the source of our opinions, we must distinguish between those derived from our own experience and those derived from the experience of others; of which those derived from the common experience of mankind are the most extensive and important. The last have come to us by means of language, which may therefore be said to be their source; nor could they otherwise have been transmitted to us. The former constitute — comparatively speaking — but a small and insignificant part of the sources of the mass of our opinions. For the greater part of what we know, or think we know, is not original with us, but has come to us from others by or from language. The distinction, therefore, is, not between opinions derived from experience and opinions not so derived, — for it may be said all opinions that are true, or rather that we know to be true, are derived ultimately from experience,1 — but in the manner of their derivation ; the one class being those opinions derived by us, each from his own experience, the other, those derived not directly from our own,

1 The distinction made in the text is of fundamental importance. The necessity of a constant resort to experience as the but from the experience of others from or through language.

§ 4, OF LANGUAGE AS A RECORD OF HUMAN THOUGHT. — Of the two classes of opinions, the latter is infinitely the more extensive in scope and important in character; for all that men have seen or thought or felt has been expressed, and is thus preserved to us in language; which thus constitutes, as it were, the record of the results of all human experience and reason. Here, therefore, is to be found the principal source of our opinions, verified and unverified — that is to say, not only of our opinions generally, but of our knowledge or science. But, regarding language as a record and source of opinion, we must distinguish between the forms in which opinion is embodied in it. These forms may be described, with sufficient accuracy for our purposes, as consisting in terms, propositions, and syllogisms. But of these the syllogism in its end and effect is but the reduction of two

ultimate source of our knowledge cannot be too strongly insisted upon. But to construe this proposition as referring to each man's individual experience is to fall into an error of the kind called by Bacon " Idols of the Den" ; and thus to fall under the reproach of Heraclitus " that men search for knowledge in lesser worlds, and not in the greater or common world," i. e., the great world of the common notions of mankind, derived from the universal experience and embodied in the common language. (Nov, Org., bk. i., aph. xliii.)

propositions to one, and, in this connection, is of interest to us merely as exhibiting one of the modes in which opinion is.formed. It will be sufficient, therefore, to distinguish the term and the proposition as the two forms in which opinions, or the elements of opinions, are embodied. But the proposition is itself of two kinds, differing essentially in nature. In the one — if not an inference — it is simply the statement of a relation intuitively perceived to exist between two terms or names, that is to say, between the notions or concepts denoted by them, — as, e. g., where we say, " Bodies are affected by gravity," or " Two islands cannot be contiguous," or " Fishes live in the sea," or " Man is rational"; in the other, it is a statement of a relation between terms, not intuitively perceived — or logically inferred — but assumed to be true from testimony or otherwise,— as, e. g., where we say, '' Brutus was one of the murderers of Caesar," or " Hannibal was conquered by the Romans." The former - in accordance with the definitions used throughout this work — will be called a judgment ; the latter, an assumption. In the former case the truth of the proposition is involved in the meanings of the terms, — i. e., in the nature of the concepts or notions denoted by them ; and this is true also of all inferences, or propositions inferred from judgments. So that with relation to all such propositions, whether intuitively perceived or inferred, the original sources of opinion are the notions or concepts in which they are involved. We may therefore distinguish, as the two sources of opinion afforded us by language, (i) the notions or concepts expressed in terms, and (2) assumptions, or assumed propositions.

With the truth of the latter, or the evidence on which they rest for credence, Logic is not concerned; nor is it concerned with them in any way, except as premises from which to argue ; or to reject them as such, if they can be shown by logical processes to be false. But where such propositions are justified by experience, and come thus to be generally received, the result universally, or almost universally, is the generation of a new notion, — i. e., the notion of the relation perceived between its terms; which is either expressed in a new term or added to the content or meaning of an existing term; and this, indeed, to the extent it is attainable, is the end of science, and, in a perfect language, — were such attainable, — would be the general result. Thus the general progress of human thought consists largely in the conversion of propositions into terms or names denoting the relations expressed in them ; and hence, generally, in terms are contained many propositions, as, e. g., in " gravity," ' justice,"

etc. — in the former of which is contained a large part of Physical Science, and in the latter nearly the whole theory of the State. In this way the stock of the common notions of mankind is continuously accumulated, until it may be said that the great part of all that has been achieved in thought by men is expressed or implied in terms or names. Here,' therefore, are to be found the principal sources of opinion ; and, compared with these, opinions embodied in propositions that cannot be, or have not been, reduced to single notions are limited in extent, and of secondary importance. And this is especially true with regard to the Moral Sciences; under which name I include all the various branches of the science of human nature; for in these sciences it is impossible to conceive of any rudimentary notion or thought that has not, in the long history of man, been conceived by the human mind and embodied in terms. With reference, therefore, to all that has been achieved in science or in popular thought, the sources of all our opinions, verified and unverified, — that is to say, of all our knowledge or supposed knowledge, — are to be sought in language, and, principally, in the notions expressed in terms or or names ' ; and consequently, with reference to

1 If the reader will thoroughly apprehend this proposition, he will find in it the key, not only to Logic, but to all Philknowledge or supposed knowledge of this kind, our method must consist in the study of language.

§ 5. RECEIVED OPINION DISTINGUISHED FROMTRUE KNOWLEDGE. — Our opinions, however, are derived from this source in two ways, which must be distinguished : namely, by tradition,— by which our opinions are delivered to us ready made in the form of propositions,— and by reasoning upon the notions embodied in terms. For the thought contained in language is embodied in two ways, namely, explicitly, in the form of propositions, and implicitly, in terms;, and of propositions, — as we have seen, — many are but explicit statements of what is implied in the notions

osophy. The elements of knowledge, so far as already achieved, we repeat, are the notions or concepts incarnate in terms ; and these must always constitute the principal source of our knowledge ; for, in comparison with the knowledge thus expressed or implied, the original contributions of the most gifted of men to the common stock must be inconsiderable. Nor can any such contribution to the knowledge of mankind be regarded as completely achieved until embodied in definite terms ; and hence the formation of such terms, or, what is the same, of the notions embodied in them, must be regarded as the end of scientific discovery. There is, therefore, nothing paradoxical in the assertion of Condillac that " Science is but language well made." Hence, to repeat what has been said, it is to the common stock of notions thus gradually accumulated by mankind and permanently secured by expression in terms, that we must resort as the principal source of all knowledge or science. See Appendix A.

expressed in terms, as, e. g., in the proposition, " All bodies are affected by gravity," etc. With reference to these, though they may be true, their mere reception cannot be said to constitute knowledge; but — in the proper sense of the terms — we can know them only when we have reasoned them out for ourselves from the primary notions in which they are involved; as, e. g., in the Mathematics, where we cannot be said to have mastered a theorem until we are able to work it out from the premises by the exertion of our own powers unassisted by memory. With reference to all that has been achieved in thought, therefore, our method in the pursuit of knowledge must begin with the apprehension of the notions already formed by men and embodied in terms; and this involves the testing of those notions for ourselves by comparing them with the realities to which they are supposed to correspond.

$ 6. THE PHYSICAL AND MATHEMATICAL, DISTINGUISHED FROM THE MORAL SCIENCES. -These observations apply equally to the Physical and Mathematical as to the Moral Sciences ; but there are differences, partly essential and partly accidental, between the two classes of sciences, which must be adverted to ' :

(i) In the Physical Sciences and in the

1 See Appendix B.

IO LOGIC

Mathematics, technical terms expressing accurately the concepts or notions involved are exclusively used, but in the Moral Sciences it is otherwise; for there the notions developed by the experience and reasoning of mankind— which must always constitute the principal source of our knowledge — are in general loosely and inaccurately expressed, and the same vocal sign, or vocable, is commonly used to denote many different notions more or less nearly related ; nor, with reference to these, does the term in general express the notion accurately. Hence the necessity of definition, which is at once the fundamental and the most difficult of the logical processes. But in the Physical Sciences the notion is always accurately defined by the thing itself; and so in the Mathematics, though highly abstract, our notions are always clearly defined. Thus in these sciences the logical processes are so simple that it is impossible to err, unless by inadvertence, and all errors are quickly corrected ; and hence a technical knowledge of Logic is but little needed.' But in the Moral Sciences it is different, for here the difficulty of defining our terms is

1 Hence, from disuse of the more difficult of the logical processes, a man in the former case, may be a competent naturalist without being much of a reasoning creature ; and in the latter, a great mathematician and yet a child in the practical affairs of life, individual and social.

great, and often insuperable, and hence, in the prosecution of these sciences, Logic must always be an indispensable instrument.

(2) To a certain extent this difference between the two classes of sciences is an essential one, and cannot be altogether removed. But to a large degree the Moral Sciences are susceptible of apodictic treatment, and by such treatment may be indefinitely assimilated in nature to what are commonly called — though not exclusively entitled to the name — the Exact Sciences; for a large part of the Moral Sciences, including nearly all the fundamental principles upon which they rest, are purely apodictic. For, though it is commonly supposed there is an essential difference between Mathematical and what is called Moral Reasoning, this is not true; all ratiocination (not fallacious) is essentially of the same character and equally conclusive.1

(3) Hence it may be observed as a corollary,

1 This is much insisted upon by Locke : " Confident I am," he says, "that if men would, in the same method, and with the same indifferency, search after moral, as they do after mathematical truths, they would find them to have a stronger connection, one with another, and a more necessary consequence from our clear and distinct ideas, and to come nearer a perfect demonstration than is commonly supposed " (Essay, bk. iv., chap, iii., 20). "By what steps we are to proceed . . . is to be learned in the school of the mathematicians, who, from very plain and easy beginnings, by gentle degrees, the principal task before us, with reference to the Moral Sciences, is to reduce them as far as possible to apodictic or scientific form. This, under present conditions, will still leave an immense field of investigation in which we must resort directly to experience, and especially to experience as embodied in history and statistics; but until all that is susceptible of being so reduced is reduced to scientific form, no progress can be made in dealing with matters depending upon experience.

(4) With regard to the Physical Sciences another difference is to be noted, namely, between what has been achieved and the discovery of new facts; with reference to which the instrument of discovery is mainly experiment and observation, or, as it is commonly called, the Inductive Method. In this respect these differ from the Moral Sciences, where, though the same method must always be used, its function is confined chiefly to the process of definition.1

and a continued chain of reasonings, proceed to the discovery and demonstration of truths that appear at first sight beyond human capacity " {Id., bk. iv., chap, xii., 7, 8). " This gave me confidence to advance the conjecture which I suggest, Chap, iii., viz., that Morality is capable of demonstration as well as Mathematics."

1 The nature of Logic, and of the relation of the Inductive Method to Logic, is thus precisely expressed by Bacon :

" The syllogism consists of propositions, propositions of

§ 7. OF THE MODES IN WHICH OPINION is GENERATED. — With reference to results achieved and embodied in language, and to our opinions generally, the process by which our notions or concepts are derived is the reverse of what is commonly supposed. In the discovery of new facts, or the formation of new concepts, we commence with the conception of the concrete, and, the concept being formed, we find the name. But this, in the development of thought at which we have arrived, can occur only in the Physical Sciences. For, as we have observed, it is hardly probable that in the Moral Sciences any rudimentary thought can ever occur that has not already occurred to some one and been expressed in language. Hence, with regard to all matters dealt with in the Moral Sciences (as also in the Physical Sciences with regard to results already achieved), the order of our cognitions is, first, to learn the words, — /. e., the word-signs or

words, words are the signs of notions. If, therefore, the notions (which form the basis of the whole) be confused and carelessly abstracted from things, there is no solidity in the superstructure. Our only hope then is in genuine induction " (Nov. Org., bk. i., aph. xiv).

The subject is more fully developed in aph. lix., and beautifully illustrated in aph. xcv. See also his doctrine of Idols, aph. xxxviii. et seq. It may be observed here, in passing, that no student of Philosophy, and still less of Logic, can afford to neglect the first book of the Novum Organum or the De A ugmentis.

vocables, — and afterwards, the concepts or notions expressed in them.'

§ 8. OUR SUPPOSED KNOWLEDGE OFTEN NONSENSE. — And as the latter function — outside the Exact Sciences — is in general very lamely performed, the result is that the greater portion of our supposed knowledge in abstract matters consists of words without definite notions attached to them, and is therefore merely nonsense. For when we reason with undefined or ill-defined terms we are dealing with mere delusions or dreams — like Ixion embracing clouds and begetting monsters. Thus, e. g. , when we assert, with Bentham and Austin, that General Utility is the ultimate test or principle by which the just and the unjust and right and wrong generally are to be determined, we are in fact talking nonsense; for it cannot be determined from this expression whether we have in view the welfare of a mere majority, or two thirds, or three fourths, or other proportion of mankind, and hence from this premise all sorts of extravagant opinions are deduced. Hence the mass of us

1 The logicians, from and including Hamilton, have entirely overlooked this distinction, and have thus substituted for the old logical doctrine of Simple Apprehension, the psychological doctrine of Conception, — a doctrine necessary to be understood, but which is concerned rather with the original formation of language than with its use as an instrument of reasoning.

generally, and all of us in many matters, — like Moliere's hero, who was surprised to find that he had been talking prose all his life, — have all our lives been talking nonsense.1 And this is true not only of opinions commonly regarded as nonsensical, but of all opinions involving either undefined notions or notions to which there are no corresponding realities.

§ 9. THE CRITICAL SPIRIT ESSENTIAL TO WISDOM. — Our wisdom is therefore to be measured, not by the extent of our learning, or by knowledge of detached facts, or by vivacity of thought or expression, or by the confidence of our belief, but chiefly by the capacity to judge our supposed knowledge, and to detect its falsity or non-significance. In this way Socrates modestly explained the oracle of the Delphic god, that he was " the wisest of mankind." For, he said, he alone had discovered that all men were ignorant, including himself; but others mistook their ignorance for knowledge.2 We conclude, therefore, as we began, that what we regard as our knowledge consists mainly of unverified opinions or beliefs, and that however firmly these may be established,

1 See Appendix C.

2 As explained by Grote (cited infra, § 16, App. H), the thesis of Socrates was that " the natural state of the human mind " is "not simply ignorance, but ignorance mistaking itself for knowledge."

l6 LOGIC

or however passionately they may be asserted and believed, they do not necessarily, or even generally, constitute true knowledge. Hence, until we are enabled to distinguish the true from the false, we can have no assurance of their rectitude or truth.

§ 10. LOGIC THE ULTIMATE TEST OR CRI- TERION OF TRUTH. — We must, therefore, seek some tests or criterions — if any there be — by which the truth or falsity of our beliefs may be determined ; and of such two only can be conceived ; namely, Experience and Reasoning, or Logic. Of these the former is more or less efficiently used by men in general ; and in concrete matters and in the ordinary familiar affairs of life, its operation is moderately satisfactory. For thus, by actual contact with the hard facts of our experience, our opinions or beliefs are, to a large extent effectually, and often painfully, modified and corrected. But the function of experience is simply to furnish Reason with materials on which to work; and of Reasoning, or Logic, as Hobbes says: " So far are the mass of men from using it, that they do not even know what it is."

1 " The most part of men, though they have the use of reasoning a little way, as in numbering to some degree, yet it serves them to little use in common life ; in which they govern themselves, some better, some worse, according to their differences of experience, quickness of memory, and inclination to several ends ; but especially according to good or evil

§ ii. THE DECADENCE OF THE AGE IN

LOGIC AND THE MORAL SCIENCES. — And this is true not only of the common people, but of the educated, and even of the philosophers and the professors; who in the last century, owing to the disuse of Logic, have in fact lost the very idea of it; so that in our schools and universities, under the name of Logic, anything but Logic itself is taught, and it has thus become a lost art.1 Yet, obviously, in all abstract matters, and especially in Morality, Politics, and all the different branches of the Science of Human Nature, experience, while useful to us, can go but a little way, and therefore Logic must be an indispensable instrument. Hence it is to the disuse of Logic that the existing incoherent and chaotic state of the Moral Sciences is to be attributed." It may therefore be confidently hoped that by the renewed use of Logic a revival of these sciences is to be anticipated, vying in extent with that of the concrete sciences in modern times, and

fortune, and the errors of one another. For as for 'science,' or certain rules of their actions, they are so far from it that they know not what it is" (Lev., chap. v.).

1 " We live in an age," says De Morgan, " in which formal logic has long been banished from education ; entirely we may say from the education of the habits." The proposition is even truer of the present day ; for in De Morgan's time there still survived some of the old style of logicians.

* See Appendix D.

far surpassing them in practical utility to the human race.1

§ 12. OF AUTHORITY AND PREJUDICE. — I would not, however, in thus explaining and commenting upon the general dominance of authority and prejudice over men, be understood as altogether condemning it. Under existing conditions, and perhaps under all conditions, the opinions of the masses of mankind, in Politics and other matters of common concern, must be determined mainly by custom and authority. Hence the distinction made by the old philosophers between their esoteric and exoteric doctrines; the latter consisting of those that could be taught to the masses, the former, of those that required the peculiar training of the philosopher to comprehend — a profound distinction that has been lost in modern times. But though it may not be possible, or perhaps even desirable, to make all men philosophers, yet it is possible to make the masses of them logical in the matters with which they are con-

1 The argument of Demosthenes in the first Philippic may be readily applied to the proposition asserted in the text : " First I say, you must not despond, Athenians, under your present circumstances, wretched as they are ; for that which is worst in them as regards the past is best for the future. What do I mean? That your affairs are amiss, men of Athens, because you do nothing that is needful ; if, notwithstanding you performed your duties, it were the same, there would be no hope of amendment."

versant ' ; and for those who aspire to be leaders of opinion, Logic is essential. For these, if worthy of the function to which they aspire, cannot afford to be deficient in this respect; they must either be logicians, or false prophets, or blind leaders of the blind.

§ 13. PLAN OF THE WORK.— Though I regard the study of Logic as essential to the cultivation and the use of the reasoning powers, — and hence as indispensable to the Moral Sciences,— yet it is chiefly as a test or criterion of fallacy that I propose to treat it. This use of it will, of course, necessitate some consideration of the elementary principles and rules of Logic as necessary to the understanding of the Doctrine of the Fallacies. But this part of my essay will be abbreviated to the utmost extent consistent with this object ; that is to say, I will try to include everything essential to the understanding of the rudiments of Logic, but nothing more. If I should fail in this, and anything necessary should be omitted, the defect may be readily obviated by reference to the work of Whately, who, among elementary writers, may be regarded (in any true sense of the word) as the last of the logicians.

The subject will be treated in two books, the first entitled " The Analytic of Right Reasoning," the second, " Applied Logic " ; the latter

1 See Appendix E.

of which will include two subjects, namely: ' The Method of Logic " and " The Doctrine of the Fallacies," or " The Analytic of Wrong Reasoning." In treating of the last, the examples of the several fallacies will be taken almost exclusively from current theories of Politics and Morality. Our examples will therefore consist, not of mere trivialities, such as are so common in books on Logic, but of fallacies that, in perverting moral and political theory and in corrupting practice, have dominated, and still continue to dominate, the fortunes of mankind. They come to us, therefore, as veterans of what Hobbes calls the " Kingdom of Darkness," crowned with the laurels of victory.1

1 Lev., chap. xliv. : see Appendix F.

BOOK I

THE ANALYTIC OF RIGHT REASONING

BOOK I

THE ANALYTIC OF RIGHT REASONING

Chapter I Rudimentary Notions

§ 14. DEFINITION OF LOGIC AND OF IN- VOLVED TERMS.— Logic is defined by Whately as the science and also the art of reasoning. Reasoning may be defined as consisting in the exercise of the comparative or discursive faculty of the mind — that is to say, the faculty by which our notions or concepts are compared with each other, and with the realities to which they are supposed to correspond, and their relations with each other, and with such realities are perceived. Or we may define reason as the faculty, and reasoning as consisting in its exercise.1 But Logic — by which I mean the

1 The terms reason and reasoning, though conjugate, have unfortunately been divorced by logicians, and, following traditional Logic — is not to be regarded as having to deal with reasoning in general, but with explicit reasoning only, or ratiocination ; which may be defined as reasoning expressed in language, or, so far expressed that the missing parts are understood. Hence it is rightly said by Whately that Logic is exclusively conversant with language; by which is meant, not merely the signs of thought, but also the thought signified.1 This follows from the definition, and also from considering the several subjects of which it treats, which, by the universal consensus of logicians, consist of the Doctrines of the Term, of the Proposition, and of the Syllogism. But all these are simply parts or kinds of language.

§ 15. RATIOCINATION DEFINED. — But Ratiocination, being a species of reasoning, must consist in the comparison of concepts or notions, and these, in order to fall within the province of Logic, must, ex vi termini, be expressed in terms. Hence, Ratiocination must be defined as consisting in the process of com-