B is the same amid difference, and though different is the same, for it is an ideal content, the product of abstraction, appearing in and differenced by two several contexts. So far as it is the one content B, so far it is absolutely and entirely the same; so far as it is a member of diverse connections, so far it carries with it a difference. And the process of inference depends entirely on this double aspect; for it is because B is different and yet the same, that its differences are able to be interrelated. If it were not different it would have nothing to connect, and if it were not the same there could be no connection. Inference rests upon the assumption that, if the ideal content is the same, then its differences will be the radii of one centre. In other words if B is the same, what is true of it in one context is true of it in another.
§ 5. We have returned to what we called the Principle of Identity (Book I. Chap. V.). We might call it again the Axiom of the Identity of Indiscernibles, and we can put the thing in more simple language if we say that inference rests on the principle that what seems the same is the same,2 and can not be made different by any diversity, and that so long as an ideal content is identical no change of context can destroy its unity. The assumption in this principle may be decried as monstrous, and I do not deny that perhaps it is false. In a CHAP. VI TWO CONDITIONS OF INFERENCE 2§Q metaphysical work this question would press on us, but in logic we are not obliged to discuss it (Book III. Part II. Chap. IV.). The axiom may be monstrous or again it may be true, but at least one thing is beyond all doubt, that it is the indispensable basis of reasoning. It may be false meta physically, but there is no single inference you possibly can make but assumes its validity at every step.
§ 6. It is easy to misunderstand it, and it is sure to be misunderstood. I shall be told that spaces and times are indiscernible and yet are not identical. But this objection rests on a complete mistake. As spaces or times of a certain character A and B surely are identical; as different elements within the same series A and B are surely not indiscernible. It is one superstition to think you have relations whose terminal points are nothing beyond the relation.* It is another superstition to fancy relations as an arbitrary network stuck on from the outside by destiny or chance, and making no reasonable difference to anything. And the root of both superstitions is the same. It is the refusal to recognize that * I am prepared to go a good deal beyond this.3 If occasion offered I should be ready to argue that you can not have a relation between points that are not different in quality. Not only, for instance, must spaces related be more than a mere relation in space, but they must also have a difference in quality. It is not possible to contemplate points in relation unless you distinguish them by a qualitative reference to the right or left or upper or lower sides of your body, and the different sensations which are at the root of these divisions, or again unless, by a qualitative mark such as A or B, you choose to make one different from the other. It may be objected that in certain cases the difference of quality is only one aspect of the whole relation. This view at least recognizes the existence of the difference, and I will not here discuss it. The ultimate connection of quality and relation is a most difficult problem. But it is clear that taken in their phenomenal appearance the one can not be reduced to the other. Is this double aspect true of the reality? Has that, as we are forced in the end to apprehend it, a single nature which combines two sides, and is so the root of the double appearance? Can we suppose that qualities are generated by the strife of some counterpart of what appears to us as relations? Or is it true that supersensible qualities are the reality which we perceive as phenomenal relations? Or is the question un answerable? If it is, we at least must not do violence to the given on the strength of a theory which we can not defend (cf. Book I. Chap.
2QO THE PRINCIPLES OF LOGIC BOOK II. PT. I the content of the given has always two sides,4 sensible quali ties and relations, and that one side can never, except by an artifice, be separate from or merged in the other. I do not say that these two elements are metaphysically irreducible; I do say that, taking them each as it stands, you must treat them each as a character of the given. It is a dire illusion to take the content of the given as either qualities without relation or relations without qualities, or to treat the one side as external to the other. Both are given together and given within the content. It was shown above (Bk. I. Chap. II. §21) that space and time-relations are no principium individuationis; for they fall within the what, and do not make the this.
And another result was brought out in that Chapter. Un less judgments of sense make a false assertion they affirm or deny connections of content, and they do not affirm any thing else whatever. It is absurd to object that if Caesar is the same, he is in Gaul and in Italy, two places at once, or that if he is thirty he is also twenty-nine. The " at once " and the "also " conceal the old error. Of course it is not true that the identical Caesar under the same conditions 5 can be differently related to Italy in space or to his own birth in time; but then surely the conditions vary indefinitely. The mere lumping together unspecified conditions under the head " is now " does not show that the conditions are indiscernible, and that striking the differences out of the account we are forced to predicate contradictions of Caesar. What is true of Caesar in a certain context is true of the same Caesar in any other context. But this does not mean that one context is the other or is to be confused with the other. It means that Caesar has two different contexts, and that the truth of one can be no reason whatever for the falsehood of the other. If we fancy this is so we have given to one or to both assertions a meaning which is false, and we must be sent back once more to study the discussions of Book I. Chapter II.
§ 7. And there is another misunderstanding against which we must guard. That what is true of B here is true of B everywhere, means that, wherever B happens to be, you can say of it always what you have said of it once. This B you assert of is the self-same B that appears in the differences, but CHAP. VI TWO CONDITIONS OF INFERENCE 2QI it is not the B just as it appears in those differences. In A — B, B — C, the B is identical, and A and C are connected by that identity. But A and C are not themselves identical, and you can not predicate B — C of A — B. The B, of which what has once been said holds good for ever, is not the B which is one thing with A or one thing with C. It is the ab straction,6 the idealized content B, which is different from its contexts and yet connected with them, and on the strength of its oneness connects them together. The identity is always a synthesis of differences which themselves are not identical the one with the other, and apart from these differences the identity disappears into blank indiscriminateness.
I will try to illustrate the whole question briefly. We have a shed in the corner of a field, and, that shed being burnt, another is set up not distinguishable in itself from the first. Let the first be B — A and the second B — C; in what sense is it true that what holds of B once will hold of it always? The objection is obvious, In the shed B — A an event D hap pened, but can we say that the event took place in B — C? And if we can not say that, and if B is not distinguishable, how are we going to defend our axiom?
We are in no kind of perplexity. The content B is ob viously not the individual shed. The two sheds are made individual by their places in the series, and those places fall outside the abstraction B. What is true of B is universal propositions and is nothing besides. The event D can not be asserted truly until it becomes a hypothetical statement (Book I. Chap. II.).
But the objection will be pressed, " The sheds and their environment are a certain content, and that content is the same. If, on the strength of this content, we said of the shed B — A ' D happened here yesterday/ why can we not also upon this ground now say of the shed B — C ' D happened here last year'? The content is what we go from, and we have that in both cases." I reply, By all means: the content is the same. Let us try to carry out the process you recom mend. We can not of course connect D with B — C unless we establish a chain of relations through the identity of their end-points (ibid.). You can not go direct from the content. to the temporal event D, for that, as we have seen, is not predicated categorically (ibid.).7 You must start from the content as given in one time. Well, starting from B — A you got a chain of events which took you back to D. But, if you start from B — C, you have a chain of events which takes you back first to the origin of B — C, when B did not exist, and then again through the destruction of B — A, to the time when B once more existed and was connected with D. Your process informs you that D the event will not fall within the identity of the ideal content B — C. That content has been qualified by a limitation in time, and qualified again by a definition of its component elements, which excludes their identity with the elements of B — A. If you deny that these qualifications are objects of knowledge, then I admit D is true of B — C, and why in the world should we not think it true? But if you admit that these qualifications are distinctions, then the content of the sheds is not indiscernible, and therefore by your admission is not identical.8 This, I think, is a sufficient answer to the objection, but it omits to take notice of several difficulties. There are ques tions which no doubt might occasion us trouble, but they do not seem to concern us here. We have been forced to notice a metaphysical problem which, at least in this work, we can not deal with, and hence objections which we can not here attempt to answer may be directed against us. But at least on one side I think we are safe; we need fear no col lision with the Philosophy of Experience, for that philosophy does not know the ground it stands on. Since Hume's bold speculations on the subject of identity were suppressed by himself, the English school has repeated a lesson by rote and flaunted a blind ancestral prejudice.
§ 8. The importance of the subject may excuse a repe tition. That what is the same ideally is really the same is without any doubt an enormous assumption, and I do not say that this assumption is true. What I do say is (a) that all inference presupposes it, and (b) that the objection to it rests on nothing but metaphysics.
(a) If we only will look at the palpable facts, we must admit that logic stands or falls with this axiom. Wherever we join one premise with another we must do so by means of an identical point, which, given as it is in diverse presenta- CHAP. VI TWO CONDITIONS OF INFERENCE 2Q3 tions, is held to be the same because it has the same content, and which, so far as it is not ideally discernible, is taken as one. Failing this identity the construction falls apart. I confess I do not know how to make this any clearer. I can only say to any one who doubts it, Show me an inference where this does not hold good, and I will show you a vicious inference, and you yourself shall admit that it is vicious.
(b) It sounds terrible to say that Identity is an ideal syn thesis of differences, and that this identity is real fact. The words are strange to the common mind, but it has always tacitly accepted their meaning. We believe that a body has changed its place, but at the end of the movement the change that is past is no fact of sense. We abstract the body from its present position and, treating this abstraction as a con tinuous identity, we predicate of it the changing differences. But do we doubt that motion is a real fact? And if we are told, It is the material atoms which are the same throughout; then why I would ask do we take them for the same, despite their differences of time and space, except because their ideal content is the same? The identity of indiscernibles may be true or false, but not only is it impossible to reason without it, but it is the abstract formula for our common-sense belief.
The authority of common sense is no authority for me, but the result we have reached may bring out one fact.^ The objection, raised by the Philosophy of Experience against a real identity, does not rest on any difficulty felt by common sense, and it is not an objection it would ever think of raising. It is a metaphysical objection, and it rests entirely on a metaphysical doctrine. It is because the Philosophy of Ex perience is sure that there is no reality except exclusive par ticulars, that it is horror-struck at the thought of a real universal. And because its belief is not proved nor thought to need proof, nor in any way discussed, because it is a mere inherited preconception which has got to think itself a real fact, it is scarcely so much to be called a doctrine as an orthodox dogma and traditional superstition.
And, as it must happen with all orthodox dogmas, its votaries do not take their professions in earnest. If an uni versal content may ever be real, on what ground can they deny the identity of thoughts because one is yesterday and the other to-day? But if such ideal sameness is not real, then how can any process or change or continuity be any thing but illusion? If a thing is not now the same that it was, if it is only alike, then it can not have changed. And if it is the same, on what ground do we make that assertion except on the ground of identity of content? It is frivolous9 to say that identity may be real, where existence is continuous and is not broken in the series of time, but is not real any where else. For if you allow that any lapse or change is a fact, you have admitted the reality of an element not confined to this or that particular, and you have admitted it on the ground of the identity of indiscernibles. You have already thrown your principle overboard, and if it is false in one place it may be false in another. Or to put the same thing in another form, if you are afraid to break with common sense in one point, what makes you so very bold in another? If I am to answer the question for you, I am forced to say that you have partly no head and partly no heart. You do not see the consequences deducible from your doctrine, and when a consequence begins to look like a reductio ad absurdum, you refuse to follow it. And this is what we call or used to call " advanced thinking." 10 § 9. It is against such opponents that the syllogism is right. The doctrine of copula and terms which it cherishes is in defensible, but it is right in demanding an identity in reason ing. The middle is an identity which connects the differences, and, being such an identity, the middle is an universal. In this point again the syllogism is right. For though the major premise is a superstition, one premise at least must be uni versal or else there can be no inference at all. We have here again a condition necessary to reasoning.
§ 10. (ii) We saw in the second chapter of Book I., and later on again in Chapter VI. § 39, that in the end no judg ment is really particular.11 They are all universal. And we might content ourselves here with recalling the result we there have reached, but, perhaps at the risk of superfluity, we may add some further remarks on the subject. If one of the premises were not universal, how could they both have a com mon identity? The term B must be shared by both the premises. It is a single content in two different contexts. But, CHAP. VI TWO CONDITIONS OF INFERENCE 295 since thus it is universal, at least one premise must have the same character.
This simple consideration is, I think, sufficient for any one who has put himself at the right point of view. But not withstanding all our previous discussions, there no doubt will be readers still unwilling or unable to follow us in this argu ment. " In ' A precedes B and B precedes C ' can B," we shall hear, "be really universal? Nay even in the syllogism, if we take the third figure, is the middle term really an universal? It is so technically because it is distributed, or understood in its full extension, but these technical distinctions have long ago been thrown overboard, and with them has gone the uni versality of singulars." I will briefly reply to the above objec tion.
§ II. An universal judgment is one that holds of any subject which is a synthesis of differences. It is a proposition the truth of which is not confined to any single this. The subject extends beyond the judgment, and, where the subject goes, the judgment is true. In this sense we have seen that all judgments are universal. But we are limited here to a simpler issue, for we have to show, given a valid inference, that at least one premise is universal. It is quite enough, as we have just remarked, to consider the identity of the middle term: but a more detailed exposition may perhaps be wel come.
There are certain cases which call for no discussion. Where the middle term is an abstract attribute, and this forms the subject of one of the premises, there one premise must be allowed to be universal.* The difficulty which is felt arises from those cases where the middle term is a singular, or where it is not the ostensible subject of either premise. Take for instance " A is to right of B, and B of C, and therefore A of C," or " A and C have the note B in common, and therefore C is in tune with A, and both related by the identity of B." How in such infer ences as these can we show that one premise must be universal?
* In order to bring arguments into this form we may freely convert any negative judgments. Thus in the second figure we may convert as required, negative premises or conclusions. The case presents no difficulty.12 § 12. Unless our previous discussions have led us quite wrong, such a question as this can be readily answered. " B is to right of C " is an universal judgment because B is an identity which has the differences of its spatial relations to A and C.ia It transcends the context B — C and is therefore universal. Or, from another point of view, the relation B — C is true of a subject which extends itself beyond those limits, and is the identical subject of which the relation A — B is also true. If you take the relations as qualifying B, then B is the universal which exhibits these differences. Or again if you go somewhat further back, then the unity of the common space is the genuine subject of which these relations are diverse attributes. We can always find an identical subject although that subject need not be apparent. In " Caesar is angry and Caesar is silent, and therefore silence may accom pany anger," it is the grammatical subject which supplies the universal within whose identity the synthesis holds good. But where from " A has a certain note B and C has also the self same note," we infer a relation between A and C, it is doubt ful where the actual subject lies. If we are willing to accept the grammatical subject, then in " C has the note B," C is our universal. For C is disturbed from its original context and expanded ideally so as to form a whole with A. And, if it were not universal, it could not be treated as a subject waiting to receive a predicate beyond its original given existence.* This would be the right interpretation if A and C are to be considered as subjects. But it is better here, I think, to take the middle as the actual subject of both the premises. B is the universal of which we predicate the difference B — A and the difference B — C, and it is the bond of identity which interrelates the whole.
§ 13. We shall see hereafter that every inference may be taken as holding within the identity of one subject (Book III. Part I. Chap. VI. § 34), and if we take this view it is obvious that the subject of both premises is universal. For the present it may prove sufficient to remember that, inference being an ideal construction and involving therefore an ideal centre, one premise must be taken as true beyond the limits of a par- * Of course if you suppose the relation A — C to be a perception got simply from the given, then there is no inference and cadit qu&stio.
CHAP. VI TWO CONDITIONS OF INFERENCE ticular subject. If we keep hold of this reflection we shall not be shaken by any puzzles which are laid before us. In the previous Book I have endeavoured to anticipate and to cut the root of those difficulties which are the most likely to be raised, and it is to the discussion of that Book that I must refer back the reader who is still inclined to hesitate.
In the ensuing Part of the present Book we shall criticize some inadequate views of inference, and shall begin with that belief which is most opposed to the doctrines set forth in the present Chapter.
1 On Similarity, Likeness, and Identity, see the Indexes, to this volume and to Appearance and Essays.
2 " What seems the same is the same." It should be " is so far the same." Error as to the exact point of sameness remains possible. And after " diversity " should perhaps have come " further " or "added". What must be rejected everywhere is the idea of a simi larity which does not imply sameness. The " Axiom " — so far as it is an axiom — holds obviously also in Metaphysics. On the ultimate dif ficulty as to Identity, see Essays, Index.
3 These points have been taken up by me in later works. There is here a partial failure to realize the true conclusion that, just as terms and relations are neither present at the beginning of knowledge, so both alike are subordinated and transformed in the ultimate end. Terms and relations are (as is seen in this volume) alike abstractions, and (we must add) are, each alike, unreal as such.
* " The content of the given has always two sides." We must re member here that, if so, Immediate Experience or Feeling must not be called "given." See Bk. III. I. Chap. VII, and Appearance and Essays.
With regard (three lines below) to "metaphysically irreducible," we can not possibly (I should say) "reduce" these "elements." But we can know that in the ultimate whole they lose their characters, as such, and so far as irreducible.
5 "Under the same conditions." What is true of B once is true of B always under the same conditions. And, if you object that the different conditions must both be true of B, that must be admitted. It points to the conclusion that, while mere B — A and mere B — ( are in the end abstractions and neither in the end true, both are. still true relatively. We have to assume a concrete whole containing still further conditions such as to modify these terms and to unite them in something higher. But in this whole, we ^ must remember, con ditions and terms cease in the end, as such, to exist.
6 " It is the abstraction." It would be better to say " the universal," because the identity may perhaps be that of an organic individual whole, and, so far, not "abstract."
7 " Is not predicated categorically." " Unconditionally " would be better.
8 " Is not identical." And even in the case of a single shed, where it remains throughout one and the same, it still is qualified by its temporal diversity, so as to be also so far different, and, so far again, not indiscernible.
9 " It is frivolous to say, etc." " Frivolous " may perhaps in some cases go too far, but " irrational " would, I think, hold everywhere. If you keep to change as perceived, then within that perception you have identity in diversity, and you have ideality, though so far you do not abstract it. Either that, or your perception is not the percep tion of change.
On the relation of Continuity to Identity, see further Appearance, the Index and the Note on p. 616.
10 " Advanced thinking." The above tirade, if unnecessary, was in 1883, I still think, wholly justifiable.
11 " No judgment is really particular." We may put it thus, that all judgments are of content, and that no content sticks in the mere "this." See Appearance, Index. And further, on Designation, see Essays, Index. The lesser conclusion as to one premiss is, however, sufficient here. Cf. Bosanquet, Logic, II, pp. 203-4.
12 This footnote might without loss have been omitted.
13 " Because B is an identity, etc." " Because, in making the infer ence, B is used as an identity, etc.," would have been better. And so below, in " For C is disturbed, etc.," we should perhaps insert after C the words "in the inference."
BOOK II.— PART II THE THEORY OF ASSOCIATION OF IDEAS x § I. The end we had before us in the first part of this Book was to give a general account of inference. The account was m a certain sense provisional, since the examples it dealt with did not pretend to illustrate every kind of inference. But within those limits the result we arrived at seemed irref ragably The end we have before us in this Second Part, is the criticism and refutation of certain theories which are out of harmony with the conclusion we have reached.
The title of this chapter calls for explanation. "The Association of Ideas," it may be objected, "is not so much a theory as a fact; a fact which on the one hand is quite indisputable, and which on the other hand can be discrepant with no theory except a theory which runs counter to fact." But the objection would rest on an entire misunderstanding. The psychological fact of "Association" is of course un questionable. The account of that fact which is given by the orthodox English philosophy, is in my judgment not only questionable but false. And, beside being false, it is incom patible with any tolerably accurate theory of reasoning. For the universality and identity, which we saw were necessary for every inference, do not exist in the theory of " Experience." We are offered in their stead a fictitious substitute, which does not exist and therefore can not work, and which would not work even if it existed.
§2. "Inseparable Association," and the "Chemistry of Ideas," are phrases which are only too familiar to most of us. They recall a controversy which has served in some measure to obscure the questions it professed to elucidate. But the more refined developements of the Association doctrine do 3OO THE PRINCIPLES OF LOGIC BOOK II. PT. II not immediately concern us here.* For they have no direct bearing on the theory of inference; and it is solely as it touches the subject of reasoning that we have here to do with Association. We may confine our attention to the common doctrine, as exemplified in the ordinary working of the Laws of Resemblance and Contiguity.
§ 3. The " association of ideas " is a phrase which may be taken to express a well-known psychological fact. And if taken so, it is nothing but a title. The fact, which it stands for, is a familiar experience, and the meaning of the title is not proposed as an accurate theory of that fact. It is a name which must not be pressed into a doctrine.
But, as understood by the Philosophy of Experience, the " association of ideas " has long ceased to be a way of marking a thing which we all admit has real existence. It has become the battle-cry of a school, and a metaphysical doctrine and theory of things. It contains a belief as to the nature of the mind, or at least as to the mode in which the mind works, which is irreconcileable with the views we have already adopted. Hence if " association " is to stand for a mere psychological fact, then of course, like every one else, I believe in it; and I propose to give here the explanation of that fact. But, if " association " means that view of the fact which has been embraced by a certain school, then I do not believe in it; and I propose to show that in this latter sense " association " has no real existence. It has not only been extended to take in phenomena which can not properly come within its limits, but within any limits, however narrow, it is a false view of things.
§ 4. The word Association, I suppose, implies properly some kind of voluntary union. That signification of course disappears, but it leaves a shade of meaning behind. For things are not associated by their own necessity, and by virtue of some internal connection. Such a group as the family, and even the state, can hardly be called associations in any strict sense. Association implies chance, that is, it depends on circumstances external to that which is conjoined. And so, when we use the term, we must be taken to suggest that, if A and B had not been associated, they would nevertheless * We shall append some remarks at the end of this chapter, CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 30!
have been A and B. For the conditions, which happened to bring them together, do not follow in fact, nor are deducible in idea, from the existence or character of mere A and B. We may perhaps explain by a reference to the hypothetical judgment. In such a judgment, if the condition is known,2 you assert not a conjunction but always a connection. But in a categorical judgment of perception, and that means in a hypothetical judgment where the condition is unknown, you assert a conjunction and not a connection. The former word corresponds to Association. The conjunction with B is pre dicated of A on the strength of a condition, that does not come into the subject, but is imported by the force of such circumstances as, in their relation to A, are chance.
Association thus comes to mean chance-conjunction, and in our mental history we find of course very often that ideas are conjoined by the merest accident. If you take these ideas and consider them by themselves, you can find no con nection and no reason for their union. Mere circumstances, which, so far as the ideas are concerned, might never have existed, did bring them together. And a union caused by such chance-conjunction is the common meaning of Mental Association. In this sense of the term it answers to that which, I suppose, we all admit to be fact; but it conveys no theory of any kind whatever. It makes no assertion as to the nature of ideas, and it makes no assertion as to the laws of their reproduction. It calls attention to one fact among others. It does not profess to reduce well-nigh everything in the mind but sensations, impressions, or feelings, to this single fact.