§ 9. We are thus brought to the second of our alternatives. Can we conceive of Reality as qualities in relation or qualities and their relations? This is really, in a somewhat more developed form, the same problem as that suggested by the definition of a thing as the “law of its states.” We are now to take the qualities as fixed terms with a character of their own which stand in or support further relations, and we have to ask if the view of the world thus formulated is entirely intelligible. And it speedily becomes clear that such a view is confronted by a formidable difficulty. For suppose that A and B are two qualities which stand in any relation C. (For simplicity’s sake we might suppose this relation C to be, e.g., that of being discriminated, and we might take as instances of A and B, say, two definitely discriminated shades of the same colour.) Then A and B, standing in the relation C, are not identical with A and B as they would be apart from this relation. (A, for instance, as qualified by contradistinction from B, is not the same thing as mere A not in any way affected by B, a fact which is frequently brought home to us with startling force by the effects of contrast.) At the same time the relation C cannot create its own terms; A, which is qualified in some special way by its standing to B in the relation C, may also exist out of this relation, and the mere fact of our recognising it as A shows that, both in the relation C and outside it, it has a recognisable identical character. (E.g., A as discriminated from B is not precisely the same thing as A before discrimination, but the difference of A from B has not been created by the act of discrimination; it must previously have been different in order to be discriminated.)
Thus we seem forced to split up the quality A, which we took as one of the terms of our relation, into two aspects, A (A1) the quality as it was before the establishment of the relation, and A (A2) the quality as it is after the establishment of the relation. And the two aspects thus discovered in what we took for the single quality A must again be somehow in relation to one another. Hence within A (A1) and A (A2) itself the same process will be repeated, and what we began by regarding as the fixed terms of the relation will turn out to be themselves systems of qualities in relation, and this process will have no limit. The classification of the contents of experience into fixed terms with relations between them, it is contended, is no solution of the problem how the experienced world can be both one and many but a mere restatement of it. “We have to take reality as many and to take it as one, and to avoid contradiction.... And we succeed, but succeed merely by shutting the eye which if left open would condemn us.” Hence the conclusion is drawn that “a relational way of thought ... must give appearance and not truth. It is a makeshift, a device, a mere practical compromise, most necessary but in the end most indefensible.”[[91]]
§ 10. The foregoing reasoning, which has been condensed from the fuller exposition in Mr. F. H. Bradley’s Appearance and Reality, demands most careful examination, as the consequence to which it leads is of supreme importance for our whole metaphysical view of the nature of ultimate Reality. If the conclusion of Mr. Bradley is sound, it is clear that our discursive thought with its scheme of predication, which is from first to last relational, can never give us adequate insight into the nature of the union of the one and the many. We shall then have to conclude that it is not in thought about Reality, but in some mode of experience, if such there is, which enables us to transcend the separation of subject from predicate, and is therefore suprarelational, that we come nearest to experiencing the real as it really is. We should thus be more or less in sympathy with the traditional Mysticism which has always made the transcending of the distinction of subject from predicate the keynote of its special way of experiencing the Divine. On the other hand, if the relational scheme of ordinary knowledge could be defended as a self-consistent way of regarding the facts, we should have the advantage of being able to construe the absolute Experience in terms of our own intellectual life much more completely than Mysticism allows.
How, then, might the interpretation of the world as a system of qualities in relation be defended against Mr. Bradley’s powerful formulation of the mystic’s objection, and what is the worth of the defence? Two possible lines of argument suggest themselves as sufficiently plausible to call for examination. (1) The edge of the objection would be turned, as far as it rests upon the unsatisfactoriness of the indefinite regress, if we could regard all relations as “external,” that is, as making no difference in the qualities they relate. Now, some relations, it has been asserted, are merely external, e.g., relations of position and again of sense in the geometrical meaning of the word (like the difference between a right-hand and a left-hand glove). Why, then, may this not ultimately be the case with all relations? But if all relations are external, we can no longer argue that the related terms must contain a further relation between themselves as the basis and themselves as the result of the first relation, and so the whole anti-relational case falls to the ground.
Such a view seems, however, to suffer from fatal deficiencies. For (a) it is at least hard to see how any relation can be ultimately external to its terms. For you cannot hold two terms in a relation of any sort without discriminating them; until they are at least discriminated as two they cannot be terms with a relation between them. Thus discrimination, and therefore the relation of distinction, is fundamental in all relation. But where we can distinguish there must already be in the discriminated terms some difference to afford a basis for discrimination. Only what is already different can be distinguished. And with this admission the door is once more opened for the indefinite regress.
(b) And even if this were not so, it seems unthinkable that all relations should be in the end external to their terms. If no relation in the end makes any difference to its terms, and thus has no foundation in their nature, it becomes a standing miracle how or why the terms should enter into relations to which they are all the time absolutely indifferent. The logical consequence of such a view would surely be the dismissal of all relations as pure illusion, and the reduction of real existence to a chaos of disconnected reals which we by some inexplicable intellectual perversity persist in taking for a system. The now universally recognised failure of Herbart’s attempt to work out a theory of Realism on these lines seems ominous for the success of any future doctrine of the same kind.
(2) Much more subtle is the line of thought suggested by Professor Royce in the Supplementary Essay appended to his book, The World and the Individual, First Series. Professor Royce admits the indefinite regress as an inevitable consequence of the reduction of the world to terms in relation, but denies that it affects the soundness of the reduction. On the contrary, he regards it rather as a proof of the positive correctness of the interpretation of existence which gives rise to it. His argument, which is based upon the modern doctrine of infinite series, may be briefly summarised as follows:—It is a recognised characteristic of an infinite series (and of no others) that it can be adequately “represented” by a part of itself. That is to say, if you take any infinite series you please, you can always construct a second series such that it consists of a selection, and only of a selection, from the terms of the first series, and that every term is derived from and answers to the corresponding term of the first series according to a definite law. And this second series, as it is easy to prove, is itself infinite, and therefore capable of being itself represented adequately in a third series derived from it in the same manner as it was derived from the first, and so on indefinitely.
For instance, let the first series be the infinite series of the natural integers 1, 2, 3, 4, ... then if, e.g., we construct a second series, 12, 22, 32 ... of the second powers of these integers, the terms of this second series are derived by a definite law from those of the first to which they correspond, and again they constitute a selection out of the terms of the first series. Every one of them is a term of the first series, but there are also terms of the first series which are not repeated in the second. Again, if we make a third series from the second in the same way as the second was made from the first, by taking the terms (12)2, (22)2, (32)2, and so on, the terms of this third series fulfil the same conditions; they correspond according to a fixed law with the terms of the second, and are also themselves a selection from those terms. And thus we may go on without end to construct successive infinite series each of which “adequately represents” the preceding one. And we are led into this indefinite regress by the very attempt to carry out consistently a single definite principle of correspondence between our original infinite series and its first derivative. In constructing the first derived series in our illustration 12, 22[22], 32 ... we necessarily also construct the series (12)2, (22)2, (32)2, ... and the other successive derivatives. Therefore Prof. Royce claims that any consistent attempt to make an orderly arrangement of the terms of an infinite whole must lead to the indefinite repetition of itself. Hence that each term of every relation on analysis turns out itself to consist of terms in relation, is no valid objection to the soundness of our principle of interpretation, but a necessary consequence of the infinity of Reality.[[92]] Any consistent attempt to exhibit an infinite whole as an orderly system of terms must lead to the indefinite regress.
Now it strikes one at once that Professor Royce’s conclusion is in danger of proving too much. You certainly do not show a method of dealing with facts to be sound by showing that it leads to the indefinite regress. It is a common experience that the liar who tells his first lie must tell a second to back it, and a third to support the second, and so on indefinitely. And you cannot put a quart of liquor into a pint pot without first putting half the quart into half the space, and so forth ad indefinitum. Yet these considerations do not prove that lying or putting quarts of liquor into pint pots is a consistent way of dealing with reality. A purpose may lead in execution to the indefinite regress because it is self-contradictory and therefore self-defeating, as these familiar illustrations suggest. And this raises the question whether the purpose to arrange an infinite whole in an ordered system of terms may not lead to the indefinite regress for the same reason, namely, that the treatment of a true whole as a sequence of terms is incompatible with its real nature. It is at least worth while to ask whether Professor Royce’s own treatment of the subject does not contain indications that this is actually the case.[[93]]
To begin with, we may note one point of some importance in reference to which Prof. Royce’s language is at least ambiguous. He speaks of the indefinite succession of infinite series which arise from the single purpose of “representing” the series of natural integers adequately by a selection out of itself as if they could be actually constructed in pursuance of this purpose. But this is clearly not the case. All that you can actually do is to construct the various series implicitly by giving a rule for their formation. The actual construction of the series would be a typical instance of a self-defeating and therefore internally contradictory purpose, inasmuch as it would involve the actual completion of an unending process. Hence we seem forced to make a distinction which Prof. Royce has perhaps unduly neglected. If your purpose of ordering the number series on a definite plan means no more than the formulation of a rule for obtaining any required number of terms of the successive series, it can be executed, but does not involve the indefinite regress; if it means the actual completion of the process of formation of the series, it does involve the indefinite regress, but is therefore self-contradictory and cannot be realised in act. Similarly, we may say of the scheme of qualities in relation, that if it is taken for no more than a rule for the systematic arrangement and organisation of a finite material, it does not involve the completion of an infinite process, and is both workable and useful; but if presented as an account of the way in which a completed all-embracing and perfectly harmonious experience of the whole of Reality is internally organised, it involves the completion of the infinite process, and is therefore self-contradictory and finally inadequate.[[94]]