Elements of metaphysics

by A. E. Taylor

§ 8. The Problem of Relation.—More perplexing than the problem of Substance and its Qualities is the question to which the pre-scientific assumption that the world consists of a number of interrelated things gives rise. This problem of Relation becomes still more prominent when reflection upon the problem of Substance and Quality has made it manifest that what we call the qualities of things are one and all dependent upon their relations either to our perceptive organs or to other things. Put quite simply the problem is as follows: Things stand in a variety of relations to one another, and what we commonly call the qualities of each are dependent on (a) its modes of relation to other things, (b) its relation to our percipient organism. Again, the various qualities of one thing stand in relation among themselves. To begin with, they all exhibit the relations of identity and difference. They all so far possess a common nature as to be capable of being compared in respect of the special ways in which they manifest that nature, and are thus so far identical; again, they can be discriminated and distinguished, and are so far in the relation of difference. Further, the qualities of one thing are interconnected, as we have already seen, by various special laws or modes of relation, which exhibit the changes in the behaviour of the thing corresponding to changes in the surrounding circumstances.

Thus Phenomenalism, when it has banished the notion of a substantial unity in things, has to identify the world of things, as we have already seen, with qualities in relation to one another. But now the question arises, How are we to understand the conception of qualities in relation? Can we, on the one hand, reduce all qualities to relations or all relations to qualities, or, on the other, can we form an intelligible idea of the way in which a single whole or system can be formed by the union of the two? There are, of course, other questions of great though relatively secondary importance connected with the problem of relation, e.g., the question as to the number of ultimately irreducible kinds of relation, but the scope of the present work will permit of nothing beyond a brief discussion of the central difficulty. We will take the various alternatives in order.

(1) Philosophers have often been tempted to evade the difficulty of showing how qualities and relations together can make up a system by suppressing one member of the antithesis altogether. Thus it has been maintained, on the one hand, that the world of real things consists entirely of simple unrelated qualities, and that what we call relations between these qualities are merely our own subjective ways of apprehending them. On the other hand, it has been suggested that there may be nothing in the real world except relations, and that what we call qualities of various kinds are nothing but forms of relation. But neither of these views seems seriously tenable.

For (a) reality cannot consist of mere relations. Every relation implies two or more terms which are related. And these terms cannot be created by the relation itself. In every relation the terms have some character of their own over and beyond the mere property of being terms in that relation. Thus, to take a simple example, the successive terms of the series of ordinal numbers express in themselves nothing beyond determinate position in an ordered series, but when they are applied to the actual arrangement of any content in serial order, that content is (c) not created by the arrangement of it in an ordered series of terms, and (b) is dependent for the actual order of its terms upon some positive character of its own. In other words, whenever you actually count you count something other than the names of the numbers you employ, and you count it in an order which depends on the character of the particular things counted.[^[88]] And so generally of all relations. A question has been raised which presents considerable difficulty and cannot be discussed here, whether there are or are not merely external relations (i.e. relations which are independent of the special qualities of their terms). But even if we admit that there may be such merely external relations, which do not depend upon the nature of the terms between which they subsist, it is at least clear that there cannot be relations without any terms, and that the terms are not created out of nothing by the relation between them.[^[89]] Perhaps it might be rejoined that what I call the terms of a certain relation, though no doubt not created by that particular relation, may be themselves analysed into other relations, and those again into others ad indefinitum. Thus it might be said that the term A of the relation A-B may no doubt have a quality of its own which is not created by this relation. But this quality, call it A₁, is found on analysis to be resoluble into the relation C-D, and the quality C₁ of C again into the relation E-F, and so on without end. This would not, however, amount to a reduction of qualities to mere relations. For it would give us, as the unit of our scheme of things, a pair of terms or qualities in relation; and however often we repeated the process of analysis, we should still always be left with the same type of triad, two terms and a relation, as the result of analysis. Whatever its worth, this particular solution falls under our second alternative, and must be considered in connection with it.

(2) But again, it is even more manifest that we cannot reduce all reality to qualities, and dismiss the relations between them as simply our subjective mode of apprehension. This line of thought is capable of being worked out in two slightly different ways. We might hold that what really exists is disconnected simple qualities, each distinct from all others as red is from sweet, or loud from hot, and that the whole network of relations by which everyday and scientific thought bring these “reals” into connection is a mere intellectual scaffolding to which nothing in the real world corresponds. Something like this would be the logical outcome of the Humian doctrine that all relations are “the work of the mind,” and that reality is the residuum left after we have removed from our conception of the world everything which is of our own mental fabrication. The grounds upon which this doctrine was advanced by Hume and his followers have already been destroyed by the progress of Psychology and the consequent abandonment of the old hard-and-fast distinction between sensation and mental construction. It was the belief of Hume, and apparently of Kant, that what is given in “sensation” is single uncompounded qualities, and that all relations between these psychical atoms are produced by a subsequent process of subjective synthesis. But the advance of Psychology, by leading to the recognition that sensation itself is a continuous process containing a multiplicity of “marginal” elements which in all sorts of ways modify the character of its central or “focal” element, has made it impossible any longer to maintain an absolute distinction between the sensory and the intellectual factor in cognition.

And apart from the illusory nature of the distinction on which the theory was based, it is sufficiently condemned for Metaphysics by its own inherent absurdity. For the fundamental presupposition of Metaphysics, as of all serious science, is that Reality is a coherent system. But, according to the view which regards relations as pure “fictions of the mind,” just that element in our thought which gives it its systematic character is an unwarranted addition of our own to the real. Order and system are in fact, on this view, mere illusion. And, as has often been pointed out by the critics of Hume, it is quite inconceivable how, in a world where nothing but disconnected simple qualities exist, the illusion should ever have arisen.[arisen.] If even our own inner life is simply incoherent, it is quite impossible to see how we can ever have come, even by a fiction, to read system into the world of fact.

A more plausible attempt to reduce all relations to qualities proceeds on the following lines. Relations, it is said, are of subjective manufacture, but they are, for all that, not mere fictions. For every relation between two terms, say A and B, is based upon the presence in A and B of certain qualities, which are called the fundamenta relationis or basis of the relation. These qualities may be the same in both the terms, in which case the relation is called symmetrical; such a case is that, e.g., of the equality of A and B, a relation having for its fundamentum the fact that A and B have both the same magnitude. Here the real fact is taken to be that A has this magnitude, and again that B has it. The subjective addition to the facts is thought to come in in the voluntary comparison of A and B in respect of this property and the consequent assertion of their equality. Or the qualities which are the foundation of the relation may be different in each of the terms, in which case the relation is technically called asymmetrical. Examples of such asymmetrical relations are, e.g., A greater than B, B less than A, or again, A father to B, B son to A. Here the actual facts would be taken to be A possessed of magnitude x, B of magnitude x-y, A qualified by the circumstance of begetting B, B by the circumstance of being begotten by A. The subjective addition would come in, as before, when we brought A and B under one joint of view by comparing them in respect of these properties.

The inherent difficulties of the reduction of relations to qualities are, however, only thinly disguised in this version of the doctrine. To argue that the establishment of judgments of relation presupposes subjective comparison of the related terms from a more or less arbitrarily chosen point of view, is metaphysically irrelevant. The whole question is as to whether the result of the process is to make things more intelligible as a systematic whole; if it is, the subjectivity of the process is no ground for discrediting the result as truth about the real. If it is not, the philosophers who insist on the subjectivity of relations should explain how we can coherently think of a systematic whole of reality in terms of quality apart from relation. This they have never been able to do, and that for obvious reasons. It is manifestly impossible to give any intelligible account of the qualities which we recognise as fundamenta of relations without introducing previous relations. Thus the possession of the common magnitude x may be assigned as the foundation of the relation of equality between A and B; but when we ask what is meant by predicating of A and B possession of the magnitude x, we find that we are thrown back upon a relation between A, B, and some third term S, which we take as our unit of measurement. A and B are both of magnitude x because each contains S, let us say, x times exactly. So again the fact “A begetter of B” was assigned as the fundamentum of the asymmetrical relation of paternity between A and B, and the same fact under another name as the fundamentum of the asymmetrical relation of filiation between B and A.

But now what is meant by saying that the same fact qualifies A and B in different ways? Any answer to this question plunges us back at once into a perfect network of relations. For first, that a fact x may be known to qualify A and B differently, A and B must themselves be discriminated, i.e. they must be compared and found different, and without relation difference is unmeaning. For ultimately two terms are different only when they also possess a common character which admits of their comparison with reference to a common standard. Thus only things which are like can be different, and the problem of the relation of their likeness to their difference is inevitably forced upon us by the very existence of the difference. And similarly, the common fact x qualifies either term in a definite way, which can be discriminated from the ways in which other facts qualify the same term, and this discrimination leads in precisely the same manner to the assertion of various relations among the different qualities of A and again of B.[^[90]]

It is not difficult to see the common source of the difficulties which beset both the attempt to reduce all reality to qualities, and the attempt to identify it with mere relations. In actual experience our world always comes to us as at once many and one, never as merely single nor as merely discrete. If you pay exclusive regard to the aspect of unity and interconnection, you will naturally be tempted to dwell on the relations between your elements to the exclusion of the various elements themselves; if you think solely of the aspect of variety, it is equally natural to treat the elements as real and their relations as fictions. But in either case you arbitrarily concentrate your attention on a single aspect of the experienced fact taken in isolation from the other, and are thus led to results which are bound to collide with the whole facts. A true view, if possible at all, can only be got by impartial adherence to the whole of the facts.