§ i. The task before us in the present chapter is the re moval of certain mistaken ideas. And the first to go must be the major premise. We saw, at the end of the foregoing Book, that the necessary truth need be no more particular than the truth it depends on, and that logical necessity does not always come from the application of universals * to some thing less universal. But if so, there need not be always a major; and the examples we have given put this beyond doubt.
In (viii) our old friend is still to be found, but in (vi) and in (vii) you will hardly be able to distinguish him from the minor, and in all the rest he has totally vanished. You may say that in (iii) we really argue from " Things equal to the same are equal to each other," and I do not doubt you will find believers. But if such reasoning is reasoning from an axiom, how did people reason before axioms were invented? And if without axioms it is impossible to infer, I wonder where all the axioms can have come from (cf. Book II. Part II. Chap. I.). But if we take an example like number (i), will any one show me the major there? "A body is to the right of that which that, which it is to the right of, is to the right of." I know this major, because I have just manufactured it; but you who believe in major premises and who scores of times must have made the inference, confess that you never saw this premise before.
We must either admit that a major is not necessary, or else we must say that my examples are not inferences because they have no major. In either case an effete superstition will be doomed.
Begotten by an old metaphysical blunder, nourished by a senseless choice of examples, fostered by the stupid conserva tism of logicians, and protected by the impotence of younger 248 THE PRINCIPLES OF LOGIC BOOK II. PT. I rivals, this chimaera has had a good deal more than its day. Really dead long since I can hardly believe that it stands out for more than decent burial. And decent burial has not yet been offered it. Its ghost may lie quiet when it sees that the truth, which lent it life, can flourish alone (cf. Book III.). § 2. The major premise, we have seen, is a delusion, and this augurs ill we may think for the syllogism. Our suspicion is well founded, for the syllogism itself, like the major premise, is a mere superstition. It is possible, no doubt, as in our seventh example, to have a syllogism which has either no major premise, or at all events no minor. And it is unques tionably true that in many arguments a major premise is actually used. Nor will I deny that some three fourths of our valid arguments can be got within the forms of Barbara Celarent. But yet after all the syllogism is a chimsera, for it professes to be the model of reasoning, and there are reason ings which can not by any fair means be conformed to its pattern. In whatever sense you interpret it, it turns out insufficient; and in certain cases it will turn out worse. Let us examine the principles of reasoning it lays down.
§ 3. If we take first the axiom of inclusion in extension as it finds expression in the maxim De omni &c., we are forced to say that this principle is unsound. It sins against the third characteristic of inference (Chap. I. § 3), for it does not really give us any new information. And, as has been long ago remarked, it embodies a petitio; for if, asserting the premise " All men are mortal," I understand by the subject each single man, then I either am aware that John is mortal, or if not my major must be withdrawn. The major premise has asserted something of each member of a collection, and the minor and conclusion do but feebly re-echo one part of this statement. But that is no inference.
We might try to understand the assertion differently. We might say that what " All men " really means is the collection or class and not each one member. But, if so, we fall blindly into a second pitfall. John's personality perhaps has no unity, but he can hardly be called a collection of men, and our syllogism now fails through quaternio terminorum. It per haps fails too through falsity of the major.2 The dictum de omni thus turns out vicious. But if it were CHAP. II, SOME ERRONEOUS VIEWS 249 sound it would not be sufficient, for it does not cover all valid reasonings.
§ 4. There is another mode of interpreting the major. " All men are mortal " may be said to assert the identity of the subjects in " men " and " some mortals; " and " John is man and therefore mortal " assures us that the subject, which we distinguish as John, is identical with a member of the class of men and also of mortals. But we know already how this is to be read.3 The identity of the subject is another way of affirming the conjunction of diverse attributes. The fact we have got is either the co-existence in one single subject of the attribute mortal with the rest of John's attributes, or else the possession by a single thing of the several names " John," " man," and " mortal " (cf. Book I. Chaps. I. and VI.). And interpreted in this way, though the inference is valid, it will not fall under the dictum de omul.
§ 5. We may illustrate the above from complete induction. I may show that all planets move in an ellipse by counting and observing each single planet. But in what sense am I then said to perform an inference? I say "therefore all planets move in an ellipse," but I know already that every single planet does so move. If there were any planet which I could not so qualify I could not go on to therefore all planets. Does the " therefore " simply reiterate the " because "? Then there is clearly no inference. Does the conclusion assert that the collection, or class, itself moves through space in an elliptical manner? If this were true the premises would not prove it. But perhaps it means that, if anything is a known planet, it must have a course which will be found elliptical. We are free to forget that the individuals we know do move in ellipses. We have firmly established a connection of at tributes, so that hereafter, given any single individual which we barely perceive to be a known planet, we can go at once from the base of that attribute to elliptical movement. But the conclusion here does not rest on enumeration complete or otherwise; it proceeds from and rests upon a distinguished connection of attributes (Book I. Chap. VI. and Bk. II. II.
We may sum up the matter thus. If you say Each individual has a certain attribute and therefore each has it, 250 THE PRINCIPLES OF LOGIC BOOK II. PT. I that is absurd. If you say " therefore the collection has it," that is invalid. If you say " Anything belonging to the col lection has it and therefore this has it," then that is valid, but the " anything belonging " stands for an attribute. Com plete induction shares the fortunes of the syllogism.
§ 6. The principle of inclusion within class extension is not merely insufficient, but unless we interpret it as a connection of attributes it is intrinsically vicious. Let us see if we can find any other view which will come to the rescue and will save the syllogism. " What stands," says Kant, " under the condi tion of a rule stands under the rule." It is thus he interprets " nota notes est nota rei ipsius" If you have an universal connection of two attributes, then, given one in a subject, you must also have the other.
It is evident that this principle of reasoning is valid, but it will not cover the whole of the ground; for, confined to the category of subject and attribute, it fails wherever you pass beyond. The subject no doubt is in some way qualified by whatever can be asserted about any of its attributes, but it is idle to expect a result from this where we are not concerned with subject and attributes. " A is prior to B and B to C, and therefore A is prior to C," but what here am I to call the "condition of the rule" or the "nota" or "attribute"? I can not take B as the attribute of A, and if I look for that attribute in " prior to B," I fall at once into quaternio termi- norum, since the second premise has got B simply.
And even when we keep to subjects and qualities, there are inferences which the principle will not justify. The syllo gistic third figure can hardly be supposed to exemplify the axiom which Kant has adopted. Not only is the category of subject and attribute (as commonly applied) unable to cover the whole field of reasoning, but within that category it is a further mistake to insist on the necessity of a major premise.
§ 7. It is evident that the syllogism can not be saved or can only be saved in such a way as to be syllogism no longer. The one chance there is of preserving the syllogism is for us to take our stand upon the third figure. c< The attributes of one subject are interrelated " will then become the axiom of inference. We have seen (§4) that all syllogisms in exten- CHAP. II SOME ERRONEOUS VIEWS 251 sion can be interpreted according to this axiom, since the identity of the subject was the other side of that relation of attributes which we wished to assert. And it is evident again that all relations of attributes can be regarded as based in a subject. We shall see hereafter (Part II. Chap. IV) that Sub stitution of Similars can be taken as syllogism within the third figure; and I will go yet further. There is and there can be no inference whatever which may not be reduced under the head of the axiom, since everything which in any way is con joined can be taken as related within some subject (Book III.
We may see hereafter how this reduction is effected. For our present purpose it is enough to remark that in many cases it can not be performed without processes which would hor rify the conservative logician, and which gain no end worth the violence they use. Unless " subject and attribute" are used in a way which is quite unknown to the traditional logic, the axiom fails of universal validity, for it does not apply to any of those relations which two or more subjects bear to each other. " Two pianos are in tune with one fork and therefore the one is in tune with the other." But in this instance, unless the terms are manipulated freely, you will not show one sub ject with its attributes.
§ 8. It is obvious, if we fairly consider the examples which have been adduced at the end of Chapter I., that the syllogism, if it keep its traditional form, is in great part impotent. And I confess I do not know what policy will seem good to the friends of the syllogism. They may boldly accept the violent alternative of excluding all examples which they can not deal with. But I think we may say that such a course as this would be nothing short of a confession of bankruptcy. If a savage may know the road that will take him from A to B, and the road that will take him from B to C, and yet may not know, and may be unable to find out, the way he should go from A to C (cf. Spencer, Sociology, I. 91), I do not see bow it can be denied that he is ignorant because he is incapable of an operation.5 And if that operation is not an inference, I can not see why anything else should be inference. The plain and palpable facts of the case will, I think, be too hard for the friends of the syllogism. And if they embrace another alterna- 252 THE PRINCIPLES OF LOGIC BOOK II. PT. I tive, and find their amusement in the manufacture of majors, which would never have been seen if the arguments had not come first, then I think once more that the end must be near. So barren a shift will be the dying effort of a hard-run and well-nigh spent chimsera.
But there is, as we saw, another alternative; it may per haps be thought possible to save the syllogism by first reform ing it. Throw the major premise overboard, and call anything a syllogism which can be brought into the form of elements related within one whole. But if the friends of the syllogism resolve on this policy, I think they are friends it might pray to be saved from. It is better to bury a delusion and forget it than to insult its memory by retaining the name when the thing has perished. And it is better to profess that delusion openly than ostensibly to abandon all but the name, and then covertly to re-instate the errors it once stood for. When a mistake has lasted some two thousand years I am ready to believe that it must contain truth, but I must believe too that the time is come when that truth should be able to stand by itself. We can not for ever with eyes fast closed swallow down the mass of orthodox rubbish in which that truth has wrapped itself up. And if the time has not come for extracting the kernel, the time has come for rejecting the shell.
§ 9. But if the principle of the syllogism is not the axiom of reasoning, can we find any other which will stand the test? We shall see hereafter that the logic of " Induction " is no more satisfactory. We shall allude to the doctrine of Mr. Spencer, and review the theory of Substitution which has found an advocate in Professor Jevons. For the present it will suffice to mention a principle adduced by Mr. Spencer, and which has succeeded in gaining the authority of Wundt. " Things related to the same are related to each other " is the axiom, we are told, of all valid reasoning. " Where judg ments are placed in relation to one another by means of con ceptions they possess in common, the other conceptions, which the judgments possess but do not possess in common, must stand themselves too in relation to one another, and that rela tion is expressed in a new judgment." — (Wundt, Logik, I.
We may confine ourselves to the simpler formula.
CHAP. II SOME ERRONEOUS VIEWS 253 " Related to the same are related to each other " is wide enough to cover the examples we have given. We shall cer tainly hereafter have occasion to question if it is wide enough to cover all possible examples (Book III. Part I. Chap. I.). But though I may object to it hereafter as being too narrow, I must object to it here because it is too wide. It is a principle of falsehood as well as of truth; " A runs faster than B and B keeps a dog (C)," "A is heavier than B and B precedes C," " A is worth more than B and B is on the table (C)," or " A is like B and B is like C." You may doubtless extract some kind of inference out of these premises, but you can hardly go from them to any definite and immediate relation between A and C.6 § 10. It is true no doubt that, if A and C are both related to a common term B, we know that some relation must exist between them, since both must be elements in one world of knowledge. But unfortunately we knew thus much before, and independent of the relation of both in particular to B.7 And again in defence of the axiom it may be said, In " A is like B and B is like C " the terms are not related to a common third term. B resembles A perhaps in one point and resembles C in another different one, and so it is with the other examples. It is not in so far as B keeps a dog that A outstrips him, it is not the B which has a place in time which is heavier than A, B is on the table in one capacity and is worth more than A in an other and different one. Thus the terms related are not related to the same, and, if they were, they would be related to each other.
The defence I have invented points towards the truth, and yet it is vitiated by a fatal mistake. It is true to say that in every relation there must always be an underlying identity; that relations, such as those of space and time, presuppose a common character in the things they conjoin. And it is there fore true that, if a third term C stands first in spatial relation with A and again in temporal relation with B, its character in those two relations is different. Hence, if two relations are of different classes, the term common to each will so far not be the same.
But this line of argument, if we follow it out, will make an end of all kinds of relation (cf. Chap. VI. §6). To say that, 254 THE PRINCIPLES OF LOGIC BOOK II. PT. I when A is related to B, it is related so far as B is nought else but its relation to A, is quite suicidal. And, if we will not say that, and if already B is something different from its relation to A, on what ground can we refuse it a right to another relation with C, when at all events it has one point in which it differs from A? Let us try to see clearly; the terms of a relation must always be more than the relation between them, and, if it were not so, the relation would vanish. "A is equal to B," but if B were mere quantitative identity with A, we should have no equality; there would be nothing but A. " A is the same as B or different in quality," but if A and B were not both different and the same, then the terms and the relation would all disappear together. " A is north of B or prior to C; " but if A, B, and C were no more than mere naked positions in space or time, they would not be even that, and their relations would sink to utter nothingness. There always must enter into the relation something more than the actual relation itself. And this being admitted, if you deny that the B, which for instance is spatially related to C, is the same as the B which has a relation in time with A, you must be taken to assert that in the relation A — B the character of B is perfectly simple, and that B is nothing but that which constitutes its relation in time. But, if so, it is nothing which can be related, and the axiom can find no possible application. The mistakes, which arise from a too wide axiom, may indicate the truth that related to the same are not related to each other unless they are related under certain conditions. We shall return to this point in Chapter IV., and the following Chapter will endeavour to convey some general idea of the nature of inference.
ADDITIONAL NOTES 1 " Given universals " would be better here than " universals."
2 On the "Collective Judgment" and on "Class" see the Index. The "falsity of the major" refers to the ambiguity involved in the above ideas. On Complete Induction and Counting see Bk. II. II.
3 " But we know...read." It would be better to say " But we CHAP. II SOME ERRONEOUS VIEWS 255 know already how this identity of diverse subjects is here to be read."
4 See § i of the next Chapter.
5 " If a savage &c." The case, as stated, is so extreme as to be perhaps abnormal, but as an illustration it may stand.
6 " Definite and immediate " should be " fresh and special." See again as in Note 4.
7 After " in particular to B " add as follows. " Further, when we have got to know that A and B, B and C, are related in a par ticular whole which is before us — this mere knowledge, that A and C are both together as members of that whole, will not be the con clusion that we seek' We presumably are looking for some further and special relation between A and C, other than their mere co-pres- ence within one subject."
CHAPTER III A GENERAL IDEA OF INFERENCE L § I. Every inference combines two elements; it is in the first place a process, and in the second place a result. The process is an operation of synthesis; it takes its data and by ideal construction combines them into a whole.* The result is the perception of a new relation within that unity. We start with certain relations of elements; by virtue of the sameness of two or more of these elements we unite their relations in one single construction, and in that we perceive a fresh rela tion of these elements. What is given to us is terms conjoined; we operate on these conjunctions and put them together into a whole; 2 and the conclusion is the perception of two terms in relation, which were not related before the operation. Thus the process is a construction and the result an intuition, while the union of both is logical demonstration.
§ 2. Demonstration in logic is not totally different from demonstration elsewhere; proof is only one kind of demon stration. Logicians however seem generally not to be aware of this fact. When the mathematician " demonstrates " a conclusion the logician feels uneasy, though he can not deny that the conclusion is proved. But uneasiness becomes protest and open renunciation when he attends at the " demonstra tions " of the anatomist. He shudders internally at the blas phemous assertion that " this which I hold in my hand " is " demonstrated." But his trials are not over; the illiterate lecturer on cookery overwhelms him by publicly announcing the " demonstration " of an omelette to the eyes of females.
But I think the logician has no real cause of quarrel even with the cook. For demonstration is merely pointing out or showing; 3 and if the conclusion of an inference is seen and thus may be shown, so also may a nerve or again an omelette.
*As we remarked before, the statements in this Book are subject to correction by the Book that follows.
CHAP. Ill A GENERAL IDEA OF INFERENCE 257 It is useless to deny this, and the task of the logician is to distinguish inference from other kinds of demonstration.
§ 3. When in ordinary fact some result can be seen and is pointed out, perhaps no one would wish to call this " demon stration." It is mere perceiving or observation. It is called demonstration when, to see the result, it is necessary for us first to manipulate the facts; when you show within and by virtue of a preparation you are said to demonstrate. But if the preparation experiments outwardly, if it alters and ar ranges the external facts, then the demonstration is not an inference. It is inference where the preparation is ideal, where the rearrangement which displays the unknown fact is an operation in our heads. To see and, if it pleases us, also to show a new relation of elements in a logical construction,4 is demonstration in the sense of reasoning.
§ 4. In what does this mental preparation consist? We have seen in our account of the synthetic judgment its general character. It demands in the first place certain data;5 it must have two or more connections of elements, as A — B B — C C — D; and these are the premises. It is necessary again that these premises should be judgments actual or sug gested,6 and what they assert or suppose must consist in logical connections of content. For if the data consisted of unrefined sensuous material, or were mere imaginations, the result would be sensuous or merely imaginary; it would be a psychological effect and not a logical consequence. The premises are thus so far two or more judgments, and the operation on these data will consist in joining them into a whole. We must fasten them together, so that they cease to be several and are one construction, one individual whole. Thus instead of A — B B — C we must have A — B — C.
Now if this were done arbitrarily it would not be done logically, and we should have no reason to think the result true. If we took A — B and C — D and joined them together as A — B — C — D, our procedure would be as futile as if in anatomy we showed connections by manufacturing them, or as if in order to clear a preparation, we employed some agent which radically changed it. In relation to fact our results in this case would be invalid.* *A11 this is subject to correction by Book III.7 258 THE PRINCIPLES OF LOGIC BOOK II. Pi. I We can not logically join our premises into a whole unless they offer us points of connection. But if the terms between which the relations subsist are all of them different,8 we are perfectly helpless, for we can not make an arch without a key-stone. Hence, if we are to construct, we must have an identity of the terminal points. Thus, in A — B B — C, B is the same and we connect A — B — C; in A — B — C and C — D, C is the same and we connect A — B — C — D. The operation consists in the extension and enlargement of one datum by others, by means of the identity of common links. And because these links of union were given us, therefore we assume that our construction is true; although we have made it, yet it answers to facts.
Having thus turned our premises into one whole, we pro ceed to our conclusion by mere inspection.* If A — B — C — D is true of reality, then in that we can see A — C or A — D, or again B — D, relations which previously we did not know. Then, leaving out of view those parts of our construction in which we are not interested, we extract the conclusion we desire to assert. We first do a certain work on our data; and this work is the construction. We then by inspection discover and select a new relation, and this intuition is the conclusion.10 § 5. I will illustrate the above by several examples. Take three pictures on a wall A, B, and C; if I see them all at once as A — B — C there seems so far no inference,11 for my mere analytic judgment will give me A — C (Book I. Chap. II.). But suppose I see first A — B, and then afterwards B — C, no mere analysis will give me A — C. I must first put them together as A — B — C, and this is the construction of a synthetic judgment. I then perceive A — C, and this is the conclusion, which is inferred not because it is seen in fact, but seen in my head.
Let us take an instance from geographical position. A is ten miles north of B, B is ten miles east of C, D is ten miles north of C; what is the relation of A to D? If I draw the figure on a piece of paper that relation is not inferred; 12 but if I draw the lines in my head, in that case I reason. In * I omit to consider here the selective action. That is not of the essence of all inference.9 Vid. Book III. Part I. Chap. I.
CHAP. Ill A GENERAL IDEA OF INFERENCE 259 either case we employ " demonstration," but only in the latter do we demonstrate logically.
" A = B and B — C therefore A = C." In this argument there is no demonstration to sense, for the showing is ideal. The terms are put together through the sameness of B, and are combined into a whole united by the relation of quan titative identity. The whole is a series united by that charac ter, and here is the construction. We then inspecting the series find a new relation A — C, and here is the conclusion.
Take an example we have given in Chapter I.; if three strings A, B, and C are struck together and we hear that they all produce the same note, we hardly infer13' that they are in tune with one another. But first strike A and B, and then strike B and C; on this, if A and B have no difference in note, and B and C have no difference in note, I proceed to construct the ideal group of ABC united throughout by sameness of note. This is a mental synthesis; and a mere analytical percep tion then adds that A and C are in tune with one another.
We may see this again in an ordinary syllogism. We must not state it so as to beg the question, or to have no com mon term, but may state it thus, " Man is mortal and Caesar is man and therefore Caesar is mortal." There is first a construction as Csesar-man-mortal, and then by inspection we get Caesar-mortal.