Chapter IV (2)

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 A_{1}, is found on analysis to be resoluble into the relation C-D, and the quality C_{1} 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. 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.

§ 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 (A_{1}) the quality as it was before the establishment of the relation, and A (A_{2}) 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 (A_{1}) and A (A_{2}) 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, 1^2, 2^2, 3^2 ... 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 (1^2)^2, (2^2)^2, (3^2)^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 1^2, 2^2, 3^2 ... we necessarily also construct the series (1^2)^2, (2^2)^2, (3^2)^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]

This reflection may serve to lead up to another which seems to take us into the heart of the matter. The researches upon which Prof. Royce’s defence of the relational scheme is based were in the first instance investigations into the significance of the number-series. As such they start with the conception of a system which is a whole of _parts_ external to one another[95] as the object of inquiry. Consequently, while such investigations are of the highest philosophical importance as bringing out the implications of this concept, they are only valid as an analysis of ultimate Reality, provided that the concept of whole and part is an adequate expression of the way in which the whole Reality is present in its constituents and they in it. But if, as we ourselves urged in a previous chapter, the conception of a whole of parts is entirely inadequate to express the intimate union between the absolute experience and finite experiences,[96] the proof that the indefinite process is logically implied in the relation of whole and part does not show it to belong to the structure of ultimate Reality. Rather, we should be inclined to urge, the fact that the relational scheme leads to the indefinite process proves that the conception of whole and part upon which it is based does not truly represent the mode of union between a completed experience and its components. And therefore the attempt to interpret this union in terms of the number-series cannot stand the test of criticism.

At the same time, Professor Royce’s argument in any case throws considerable light upon the problem of relation. For it shows _why_ the attempt to construct the world as a system of qualities in relation leads to the indefinite regress. For a complete experience embodying at one stroke the whole of existence, such a construction would, as we have seen, because essentially incomplete, be impossible. But when _we_ try to piece together the data of our fragmentary experience into a connected whole, we inevitably have to start with more or less isolated facts as fixed terms and weld them together by a relation. In doing so we unavoidably put ourselves at the point of view from which the numerical series arises; we unavoidably treat existence _as if_ it were a whole of mutually external parts. And so the indefinite regress involved in the nature of the number-system inevitably parades the whole of our discursive and relational thinking about existence. But its presence is due to the inadequacy of the conception of Reality with which discursive thought has to work.

On the whole, then, it seems that Prof. Royce’s investigations only make it more apparent than before that the relational scheme which discursive thought uses does not adequately express the true nature of the real, and that the mystics of all ages have been so far justified in their contention that the form of our experience which presents the truest analogy to the experience of the Absolute must be supra-relational, or, in other words, that the most real type of finite experience must be one which transcends the distinction of subject and predicate. To admit this is, however, not to admit that we are altogether ignorant how the one and the many are united in Reality. For there are many other types of human experience besides that which is dominated by the discursive and relational intellect.

In immediate simple feeling we have obviously a type of conscious experience in which distinction and relation have as yet not emerged. And I have tried in Bk. I. chap. 2 to show how in the direct intuition of an æsthetic whole by trained artistic perception we have at a higher level an experience which contains the results of an elaborate process of distinction and relation, but contains them in a way which transcends the relational form and reverts in its directness to the unity of immediate feeling. While again we have in the personal love which is one with mutual insight a form of experience that, if translated into the language of the intellect, would require for its description a whole world of relations and predicates, and is yet, as experienced, an intimate unity no relational scheme can more than faintly adumbrate. And it is worthy of consideration that religious emotion in all ages has borrowed from these forms of experience its favourite expressions for the highest modes of communion between the finite and the infinite, the “beatific vision,” the “love of God,” etc.

It seems indeed as if the function of the mere intellect were always that of a necessary and valuable intermediary between a lower and a higher level of immediate apprehension. It breaks up, by the relations and distinctions it introduces, the original union of the _what_ and the _that_ of simple feeling, and proceeds to make the _what_, which it deals with in its isolation, ever more and more complex. But the ultimate issue of the process is only reached and its ultimate aim only satisfied so far as it conducts us at a higher stage of mental development to the direct intuition of a richer and more comprehensive whole in the immediate unity of its _that_ and its _what_. The besetting philosophical sin of the mere mystic is not so much his refusal to accept the work of the mere intellect as the highest and truest type of human experience, as his tendency to satisfy his demand for the fuller union of the _what_ with the _that_ by reverting to the lower forms of immediacy upon which intellectual reflection has not done its work, instead of pressing on to the higher in which the effect of that work is preserved though its form is transcended.

These reflections may serve to obviate the objection that to reject the relational scheme when it is offered as the ultimate truth is to deny the value and significance of the scientific work we accomplish by means of it. Though the scheme of relations cannot adequately express the mode of union between the finite and the infinite, there is no fresh addition to the system of relations into which scientific analysis translates the real world of experience that does not increase our knowledge of what the real world must contain, though it may fail to explain how it contains it. And, in conclusion, let it be remembered that it is true not only of the religious mystic’s special experience of union with deity, but of all direct experience, that the relational scheme is quite inadequate to explain how it holds its double aspects, its unity and its multiplicity, its _that_ and its _what_, in complete interpenetration. For _no_ living experience is a mere whole of parts, and none, therefore, can be fully represented by a scheme based upon the concept of whole and part.[97]

_Consult further_:—F. H. Bradley, _Appearance and Reality_, chaps. 1-3, 15, 27; L. T. Hobhouse, _Theory of Knowledge_, pp. 172-181 (Qualities and Relations), 540-557 (Substance); H. Lotze, _Metaphysic_, bk. i. chap. 1 (The Being of Things), chap. 2 (The Quality of Things), chap. 3 (The Real and Reality); J. Royce, _The World and the Individual_, First Series, Supplementary Essay; B. Russell, “The Concept of Order” (_Mind_, January 1901), and article on “Position in Space and Time” (_Mind_, July 1901); G. F. Stout, “Alleged Self-contradictions in the Concept of Relation” (_Proceedings of the Aristotelian Society_, New Series, vol. ii. pp. 1-14, with the accompanying discussion, pp. 15-24).

-----------------------

SUPPLEMENTARY NOTE TO CHAPTER IV.

DR. STOUT’S REPLY TO MR. BRADLEY’S CRITICISM
OF THE CONCEPT OF RELATION.

Since the preceding chapter was written, I have had the opportunity of studying Dr. Stout’s paper in the current volume of _Proceedings of the Aristotelian Society_. I have not thought it necessary to make any alterations in the text of Chapter 4, in consequence of Dr. Stout’s criticism, but I may perhaps be permitted to add the following remarks, which must not be regarded as a systematic appreciation or examination of Dr. Stout’s views. The latter, as he himself pleads, cannot indeed be finally judged until he has worked out the theory of Predication for which his present paper merely prepares the way.

1. Dr. Stout begins by admitting what to my own mind is the essence of the anti-relational argument. “No relation or system of relations can ever constitute a self-subsistent and self-contained Reality. The all-inclusive universe cannot ultimately consist in (? of) a collection of interrelated terms” (_op. cit._, p. 2). This being once conceded, I should have thought it an inevitable consequence that a “collection of interrelated terms” cannot give us the final truth about the nature of anything. For the whole idealist contention, as I understand it and have tried to sustain it in the present work, is that the structure of the whole is so repeated in any and every one of its members that what is not the truth about the whole is never the _ultimate_ truth about anything. precisely because there is ultimately nothing apart from the whole, and the whole again is nothing apart from its members. So much, I had thought, we have all learned from Hegel, and therefore Dr. Stout’s dilemma that any proposition asserting relation (p. 5) must be false, unless the relational scheme, so long as it is not affirmed of the ultimate whole itself, gives us truth, does not seem to me to possess any real cogency. With Mr. Bradley himself, as quoted by Dr. Stout, I should urge that if the relational scheme is not itself internally discrepant, there remains no valid ground for disputing its applicability to the whole.

2. Dr. Stout’s introduction into a “relational unity” of the third term,—_relatedness_ does not seem to me to remove the difficulties inherent in our problem. And the illustration by which he supports it appears to be unsound. He argues that when my hat is on my head this state of things implies (1) the two related terms, the hat and the head,(2) a relation of _on_ and _under_. (3) the fact that the terms stand in this relation—their relatedness. For (1) and (2) by themselves would be compatible with my hat being on the peg and my head bare. But surely there is here a confusion between the relation of _above_ and _below_, and the very different relation of _on_ and _under_. The latter relation includes, as the former does not, immediate contact as part of its meaning. If there are (1) a hat and a head, and (2) the relation _on_ and _under_—in this sense—between the two, there is surely no need of a third factor to complete the concrete actuality of “hat on head.” If the hat is not actually on the head, then (2), the supposed relation, is not there at all. And if (2) is there the whole fact is already there. In a word, Dr. Stout seems to me to count in the concrete fact of “thing exhibiting related aspects” as a third constituent in itself, precisely as popular Logic sometimes counts in the actual judgment, under the name of _Copula_, as one factor of itself.[98]

Then to Dr. Stout’s use of his distinction between the relation and the fact of relatedness, I think it may be replied that it leaves us precisely where we were before. The hat is qualified by being _on_ the head, the head by being _in_ or _under_ the hat, and hat and head together by the relation of _on_ and _under_ between them. But how these various aspects of the fact are to be combined in a single consistent view we are no nearer knowing.

3. _The endless regress._ I think it will be seen from the preceding chapter that in my own view a genuine endless regress is evidence of the falsity of the conception which gives rise to it, and that I hold this on the ground that the endless regress always presupposes the self-contradictory purpose to sum an admittedly infinite series. Hence I could not concur, so far as I can see at present, in Dr. Stout’s distinction between the endless regress which does and that which does not involve self-contradiction. As to his illustration of endless regress of the second kind, the infinite divisibility of space (p. 11), I should have thought that there is no actual endless regress in question until you substitute for infinite divisibility infinite actual _subdivision_, and that when you make this substitution it commits you at once to the self-contradictory completion of an unending task. (Cf. what was said above, § 10, with reference to infinite numerical series.)

4. Dr. Stout goes on to deny that there is any endless regress, self-contradictory or not, involved in the relational scheme. According to him, what connects the relation with its terms is not another relation (which would of course give rise to an endless regress), but their relatedness, which is “a common adjective both of the relation and the terms” (p. 11). I have already explained why this solution appears to me merely to repeat the problem. The relatedness, so far as I can see, is a name for the concrete fact with its double aspect of quality and relation, and I cannot understand how mere insistence upon the concrete unity of the fact makes the conjunction of its aspects more intelligible.

5. Dr. Stout further supports his contention by a theory of the nature of continuous connection which I have perhaps failed to understand. Replying in anticipation to the possible objection of an opponent, that if the “relatedness” connects the terms with their relation there must be a second link to connect the term with its relatedness, he says “there is no intermediate link and there is need for none. For the connection is continuous, and has its ground in that ultimate continuity which is presupposed by all relational unity” (p. 12, cf. pp. 2-4). And, as he has previously told us, “so far as there is continuous connection there is nothing between [_i.e._ between the connected terms], and there is therefore no relation.”

Now there seems to me to be a contradiction latent here. Continuous connection, of course, implies distinct but connected terms which form a series. Where there are no such distinct terms there is nothing to connect. Now it is, as I understand it, part of the very nature of a continuous series that any two terms of the series have always a number of possible intermediate terms between them. And therefore, in a continuous series, there are _no_ immediately adjacent terms. Dr. Stout’s own illustration brings this out—

│ │ │
──────┼──────┼──────┼──────
β │ α │ _a_ │ _b_
M

In a diagram like the accompanying _b_ and β are, he argues, “mediately conjoined,” but _a_ and α are “immediately co-adjacent.” Surely Dr. Stout forgets here that what can be intelligibly called “co-adjacent” are not lines but points or positions on the lines. And between any point in α and any point in _a_ there are a plurality of intermediate positions, except for the special case of the extreme left point of _a_ and the extreme right point of α. These, of course, coalesce in the single point M, and there is therefore no connection, mediate or immediate, left in this case.[99] The illustration, I think, may serve to reveal a serious discrepancy in Dr. Stout’s theory. He sees that relations presuppose a unity which is supra-relational, and which he calls “continuous,” on the ground of its supra-relational character. At the same time, to save the relational scheme from condemnation as leading to the endless regress, he has to turn this supra-relational unity itself into a sort of relation by calling it an immediate connection between _adjacent_ terms, and thus ascribing to it the fundamental character of a _discontinuous_ series. And I cannot help regarding this procedure as unconscious evidence to the truth of the principle, that what is not the truth about the whole of Reality is not ultimately the truth about any reality.

-----

Footnote 73:

See the admirable account of the “natural conception” of the world in
the final chapter of Avenarius, _Der Menschliche Weltbegriff_.

Footnote 74:

May I say here once for all, that when I oppose _practice_ to
intellectual speculation, I must be understood to mean by practice the
alteration by myself of some datum of given existence. The activity of
thought is thus for me not practical, precisely because the “truths”
which I know or contemplate are not _quà_ truths given existences
operated upon and altered by the act of thinking.

Footnote 75:

Such a view of the mental life of the animal seems to have been
actually held, for instance, by the late Professor T. H. Green. Yet
see Green, Works, ii. 217.

Footnote 76:

Strictly speaking, the “solidity” or “impenetrability” of the ultimate
particles of matter, which is with Locke and Newton one of the most
prominent “primary” qualities, is not a “mathematical” property, but
it still owes its inclusion in the list to the conviction of these
philosophers that it is, like extension and form, fundamentally
important for mathematical Physics. The explanation of the “secondary”
qualities as _subjective_ appears to go back to Democritus.

Footnote 77:

See the further elaboration of this analogy in Bk. III. chap. 3, § 2
ff.

Footnote 78:

Professor Sidgwick’s defence of the Lockian view (_Philosophy: its
Scope and Relations_, p. 63 ff.) seems to me to ignore the point at
issue. namely, that in any sense in which “secondary” qualities get
their meaning from the content of sensation, primary qualities do the
same. The whole point is that the sensation is not merely (as process)
the _occasion_ of our cognition of, _e.g._, hardness or softness, but
also (as content) furnishes the very meaning of “hard” or “soft.” Cf.
with what follows, _Appearance and Reality_, chap. 1.

Footnote 79:

The former alternative is that of scholasticism; in modern science the
latter has been more or less consciously adopted by those thinkers who
retain the notion of substances. The various qualities are on this
view consequences of the relations in which each substance stands
(_a_) to other interacting substances, and (_b_) in particular to the
unknown substratum of our “consciousness.”

Footnote 80:

See chaps. 1 and 2 of bk. i. of his _Metaphysic_.

Footnote 81:

The reader who desires to study Kant’s doctrine in detail may begin by
taking up Kant’s own _Prolegomena to the Study of any future
Metaphysic_, which may be profitably consulted even by those who find
the _Critique of Pure Reason_ too diffuse and technical. The latest
and cheapest translation is that included in the Open Court Publishing
Co.’s series of Philosophical Classics.

Footnote 82:

“Arbitrarily” because it is, as all recent psychology insists, the
direction of our attention which determines _what_ qualities shall be
presented together, and thus become “associated.”

Footnote 83:

In Psychology this comes out in the rejection by the best recent
writers of the whole associationist account of the process of
perception, according to which the perception of a thing as a whole
was taken to mean the actual presence in sensation of one of its
qualities _plus_ the reinstatement by association of the “ideas” of
the others. For the modern doctrine of the perception of a whole, as
distinct from the mere perception of its constituent parts, consult
Stout, _Analytic Psychology_, bk. i. chap. 3, or _Manual of
Psychology_,^3 bk. i. chap. 3.

Footnote 84:

This is just as true of the so-called primary qualities of things as
of any others. Thus the mass and again the kinetic energy of a
conservative material system are properly names for the way in which
the system will behave under determinate conditions, not of modes of
behaviour which are necessarily actually exhibited throughout its
existence. The laws of motion, again, are statements of the same
hypothetical kind about the way in which, as we believe, particles
move if certain conditions are fulfilled. The doctrine according to
which all events in the physical world are actual motions, rests on no
more than a metaphysical blunder of a peculiarly barbarous kind. Cf.
Stallo, _Concepts and Theories of Modern Physics_, chaps. 10-12.

Footnote 85:

Thus, _e.g._, so fundamental a proposition in our current mechanical
science as the “first law of motion” is avowedly a statement as to
what _would_ be the behaviour of things under a condition which, so
far as we know, is never actually realised. On the thing as the “law
of its states,” see Lotze, _Metaphysic_, I. 3. 32 ff. (Eng. trans.,
vol. i. p. 88 ff.), and L. T. Hobhouse, _The Theory of Knowledge_, pp.
545-557.

Footnote 86:

Mr. Hobhouse (_op. cit._, p. 541 ff.) thinks that the solution is
simply that those qualities belong to one “substance,” which are
apprehended together as occupying one space. As a working criterion of
what we mean by one bodily thing, this account seems satisfactory, and
has probably suggested itself spontaneously to most of us. But it
leaves untouched the more fundamental question how the identification
of a certain sight-space with a certain touch-space is effected, and
what are the motives which lead to it. Mr. Hobhouse is content to take
the identification as “given in adult perception,” but it seems to me
to emerge from his own good account of the matter that it is the still
more primitive apprehension of my own body as a felt unity upon which
the synthesis between sight and touch spaces is based. If so, the
ultimate source of the “unity of substance” must be sought deeper than
Mr. Hobhouse is willing to go for it. And _quaere_, whether his
account, if accepted as ultimate, would not lead to the identification
of substance with space? For the difficulties which arise when you say
the substance is the space and its filling of qualities, see
_Appearance and Reality_, chap. 2, pp. 19, 20 (1st ed.).

Footnote 87:

_Monadology_, §§ 8-16, 57-62.

Footnote 88:

This is true even where we merely count a number of qualitatively
equivalent units in order to ascertain their sum. It is their positive
character of being qualitatively equivalent which makes it permissible
in this case to take any one of them indifferently as first, any other
as second, etc. Whenever you apply the numerical series to the
arrangement in order of the qualitatively dissimilar, the nature of
your material as related to the character of your special interest in
it decides for you what you shall call first, second, third, etc.

Footnote 89:

As to the possibility of relations which are in this sense external to
their terms, see B. Russell, _The Philosophy of Leibniz_, p. 130, and
the articles by the same writer in _Mind_ for January and July 1901.

Footnote 90:

See the elaborate discussion of the relational scheme implied in any
assertion of difference in Royce, _The World and the Individual_,
Second Series, lect 2.

Footnote 91:

Bradley, _Appearance and Reality_, chap. 3. Compare also chap. 15,
“Thought and Reality.”

Footnote 92:

The reader who desires further knowledge of the researches in the
theory of Numbers upon which Prof. Royce’s doctrine is based, may
profitably consult Dedekind, _Was sind und was sollen die Zahlen_, and
Couturat, _L’Infini Mathématique_.

Footnote 93:

Professor Royce’s own illustration of the map of England executed upon
a portion of the surface of the country is really a typical instance
of a self-contradictory purpose. He argues that such a map, to be
theoretically perfect, must contain a reduced facsimile of itself as
part of the country mapped, and this again another, and so on
indefinitely. But the whole force of the reasoning depends on
overlooking the distinction between the surface of England as it is
before the map is made, and the surface of England as altered by the
presence of the map. Prof. Royce assumes that you set out to represent
in the map a state of things which can in fact have no existence until
after the map is made. The previous existence of the map at a certain
spot is falsely taken to be one of the conditions to which the
map-maker is to conform in executing it. Every one of the supposed
“maps within the map” will thus involve distortion and
misrepresentation of the district it proposes to map. It is as if
Hamlet had chosen “Hamlet” as the subject of the “play within the
play.” The professor’s illustration thus does less than justice to his
theory.

Footnote 94:

The fundamental defect in Professor Royce’s reasoning seems to me to
lie in the tacit transition from the notion of an infinite _series_ to
that of an infinite completed _sum_. Thus he speaks of the series of
prime numbers as a “whole” being present at once to the mind of God.
But are the prime numbers, or any other infinite series, an actual sum
at all? They are surely not proved to be so by the existence of
general truths about any prime number.

Footnote 95:

See, _e.g._, Dedekind, _op. cit._, § 2: “It frequently happens that
different things _a_, _b_, _c_ ... are apprehended upon whatsoever
occasion under a common point of view, mentally put together, and it
is then said that they form a _system_; the things _a_, _b_, _c_ ...
are named the _elements_ of the system”; and § 3 (definitions of
_whole_ and _part_).

Footnote 96:

_Ante_, Bk. II. chap. 2, § 5.

Footnote 97:

It is no answer to this view to urge that as soon as the intellect
undertakes to reflect upon and describe Reality it unavoidably does so
in relational terms. For it is our contention that the same intellect
which uses these relational methods sees _why_ they are inadequate,
and to some extent at least how they are ultimately merged in a higher
type of experience. Thus the systematic use of the intellect in
Metaphysics itself leads to the conviction that the mere intellect is
not the whole of Reality. Or, in still more paradoxical language, the
highest truth for the mere intellect is the thought of Reality as an
ordered system. But all such order is based in the end on the
number-series with its category of whole and part, and cannot,
therefore, be a perfectly adequate representation of a
supra-relational Reality. Hence Truth, from its own nature, can never
be quite the same thing as Reality.

Footnote 98:

Or does Dr. Stout merely mean that there may be a hat and a head, and
also a relation of on and under (_e.g._, between the _hat_ and the
_peg_), and yet my hat not be on my head? If this is his meaning, I
reply we have not really got the _relation_ and its _terms_; if the
hat is not on the head, hat and head are not terms in the relation at
all. I do not see why, on his own principles, Dr. Stout should not add
a fourth factor to his analysis, namely, qualified_ness_, or the fact
that the qualities are there, and so on indefinitely.

Footnote 99:

If you consider the _lines_ _a_ and α, as Dr. Stout prefers to do, I
should have thought two views possible. (_a_) There are not two lines
at all, but one, the “junction” at M being merely ideal. Then there
remains nothing to connect and there is no relation of “immediate
connection.” Or (_b_), the junction may be taken as real, and then you
have a perfectly ordinary case of relation, the terms being the
terminated lines _a_ and α, and the relation being one of contact at
M. On every ground (_a_) seems to me the right view, but it is
incompatible with the reduction of continuity to “immediate
connection.” Thus the source of the difficulty is that (1) immediate
connection can only hold between the immediately successive terms of a
discontinuous series, and yet (2) _cannot_ hold between them precisely
_because_ they are discontinuous.

-----