THE REALITY OF RELATIONS

By: Paul Marhenke

This is the first part of an article taken from
Studies in the Problem of Relations,
Lectures delivered before the Philosophical Union,
University of California, 1930,
U of C Press, Berkeley, Calif., 1930.
University of California Publications in Philosophy, Vol. 13,
George P. Adams, J. Loewenberg, Stephen C. Pepper, editors
R 106 C153 v.13.

/p. 167/
Common-sense as exemplified in its linguistic usage presupposes the reality of relations. It is illegitimate, however, to turn to common-sense for a final answer to the question: Are relations real? Logicians have often condemned language as an unreliable guide in the analysis of logical questions. Nevertheless, if it were not for the fact that the propositions we think are crystallized in language, our logical analyses would have been abortive from the start. This is an obvious truism. We may have to refer to other considerations than those of languages in order to get a satisfactory answer to such questions. At any rate language gives us at least a provisional answer to the question: Are relations real? And that answer is in the affirmative. In order to show this we need to call attention merely to the fact that there are rather significant, even if only apparent, differences in the propositions we assert. The proposition "This table is brown" asserts a quality of a substantive. The proposition "This table is larger than that chair" asserts a quality neither of the table nor of the chair. This proposition asserts a relation between the table and the chair, or so it would seem, if we follow linguistic usage.

Even the current expositions of formal logic allow that there is a difference between these propositions. They indeed study systematically only those arguments which are syllogistic, i.e., whose component propositions are in the subject predicate form. Nevertheless these expositions devote at least a few pages to arguments relegated to a section captioned by the somewhat
/p. 168/
derogatory title of "irregular forms." These arguments are irregular for no other reason than that their component propositions cannot be stated in the subject-predicate form so as to form a syllogism. The logicians who thus grudgingly concede a place to extra-syllogistic arguments are laboring under the superstition that the vast majority of deductive arguments is of the syllogistic type. The reason why logician shave attributed this vast importance to the syllogism is not hard to find. Aristotelian logic was developed at a period which had made the discovery of forms. Forms are the characters or character-complexes which are repeated in different particular things. And the possession of a common form determines these particulars to constitute a class. Hence Aristotelian logic became a logic of classes. Accordingly we can express a proposition about a particular in two alternative ways. If "this" is characterized by the form "blue" we can either assert that "this is blue" or that "this is a blue thing." In the former case we are predicating a quality or form of a particular, in the latter we are asserting that the particular belongs to or is a member of a class characterized by the possession of a common property. These two propositions are equivalent. If the first one is true then the second one is true, and if the second one is true then the first one is true.

It has often been pointed out that many philosophical systems following Aristotle are vitiated by the fact that they assume that all propositions are reducible to this fundamental type. Yet it is not hard to see that not all particulars fall into classes as a consequence of the possession of a common form. Things that belong to me undoubtedly form a class yet this class is not determined by the fact that the particulars which belong to the class possess a common character that is intrinsic to them. For otherwise it would be a simple matter to distinguish between mine and thine when our possessions have been scrambled. The things in this case undoubtedly have a common character; but it is not a character intrinsic to them. The character they possess of belonging to me is determined by the primary fact of their relation to me and is hence extrinsic to them.

/p. 169/
In spite of the fact that the linguistic expression of propositions presupposes the reality of relations, their reality is denied by some philosophers. This denial implies that linguistic expression is an unsatisfactory region in which to seek answers to logical questions. And it makes the claim that propositions which in their linguistic expression apparently indicate relations besides substances and qualities may be so analyzed as to exhibit their subject-predicate form. These philosophers are therefore committed to two propositions: (1) that there are no exemplifications of relations in the actual world, and (2) that every proposition may be stated in the subject-predicate form. On the supposition that facts are relevant to the propositions we assert, i.e., render them either true or false, proposition (1) implies proposition (2). For if there are no relations, then any fact must be expressible in the subject-predicate form, provided of course that there are substantives and their properties, and any proposition not in that form must be reducible to that form, provided that its truth or falsity depends upon some fact. But proposition (2) does not imply (1). Proposition (2) merely asserts that for every proposition we can construct a logically equivalent proposition which is in the subject-predicate form. It does not assert that there are no entities corresponding to the words that indicate relations and which are neither substantives nor qualities. Mr. Johnson for example asserts proposition (1) and hence also proposition (2). Some idealistic writers assert proposition (2) without also asserting (1). They usually state their view in the form of the contention that all relations are internal. Philosophers who maintain that there are no exemplifications of relations have not meant to deny that there are entities which are properly to be called relations. They have merely meant to deny that they constitute a new kind of entity additional to substantives and qualities. According to Mr. Johnson, relations are qualities or a specific sort of qualities, and all propositions which employ terms that presuppose the reality of a third kind of entity may be reduced to propositions that assert qualities or a specific sort of qualities of a substantive.

/p. 170/
It is time to inquire into the reasons why relations have been declared to be unreal.

"The chief reason (writes McTaggart) which has been given for the rejection of relations is that there is nowhere for them to be. They are not, it is clear, in either of the terms without being in the other. Nor are they in each of them, taken separately. They are, it is said, between the terms, and not in them. Then, it is asked, is there anything in which they can be? And, when this is answered in the negative, it is concluded that they are impossible." [1]

"assumes that a relation is impossible, unless some one thing can be found, in which it is or inhere like a quality. It takes, as the test of the possibility of relations, the question whether they can behave exactly as qualities behave, and when it is admitted that they cannot, it concludes that relations are impossible, and that, in a true view of reality, judgments of relation would be replaced by judgments of quality." [2]

"there is no justification for the assumption that a relation is impossible, if it cannot inhere in something as a quality does. To the question 'in what is a relation?' we may fairly answer that it is not in anything, but that it is between two or more terms, or between a term and itself, and that the conception of 'between' is as ultimate as the conception of 'in,' and has as much claim to be regarded as valid. Both are ultimate, neither contains any contradiction, and the justification of our use of both lies in the fact that it is impossible to state anything whatever without asserting or implying the reality both of qualities and relations." [3]

Relations, according to McTaggart, are indefinable. [4] If so, relations are not definable as qualities. One way, therefore, in which the reality of relations may be denied is to exhibit them as a kind of adjective. This is the procedure adopted by Mr. Johnson. If your can show that relations are a specific sort of qualities, you have by that very fact demonstrated that relations are definable, and do not constitute third kind of entity in addition to substantives and qualities. Another reason for denying the reality of relations is a consequence of the applications of Occam's razor. If you can develop a systematic logic or metaphysics with less, do not use more. But this reason is compatible with the reality of relations. To be sure, it does not affirm the reality of relations, but it does not deny it either. Even if there are relations, so this view would hold, we are not obliged to make any mention of them. For we can always express the fact such and such terms stand in such and such relations by means of propositions which assert only qualities of those terms. This doctrine therefore merely asserts that for every relational proposition we can find a predicative one that is equivalent to it. But Mr. Johnson asserts more than this. He asserts that every relational proposition is not merely equivalent to, but identical with, a predicative proposition. A so-called relational proposition is in reality, according to him, a predicative proposition in which a certain kind of adjective is predicated of a certain kind of
/p. 172/
substantive. And every relational proposition may be so transformed as to exhibit its predicative character.

Before examining this view in detail, let us examine the doctrine that every proposition may be stated in the subject-predicate form. This doctrine, as we have seen, does not deny the reality of relations, but it does maintain that we can dispense with them, even if there are such entities as relations. This doctrine is also false, according to McTaggart. He cites three facts which have led to the erroneous conclusion that every relational proposition may be stated as a predicative one.

(1) "A relation may no doubt be based on a quality in each of its terms. But this does not mean that it can be reduced to those qualities. If A is larger than B, this relation may depend on the fact that A cover a square mile, and B covers an acre.... But a statement of the size of A and a statement of the size of B are not equivalent to a statement that A is larger than B, though the latter may be a certain and immediate conclusion from them."

(2) "It is true that the existence of any relation between two substances involves the existence of a quality in each of those substances. 'A admires B' is a statement of a relation between A and B. But its truth implies the truth of the statement 'A is an admirer of B' and 'B is an object of admiration to A,' which states qualities of A and B. But we cannot state these qualities in term which omit the conception of relation, since the first is the quality of being a person who admires B, and the second is the quality of being a person who admired by A. And therefore neither of them can be stated without introducing the conception of admiration which is a relation."

(3) "A relation determines a quality of any whole which contains all the terms of the relation. We may say that it is a quality of this room, or of the universe to contain a chair A and a chair B, of which A is larger than B. But then this quality cannot be stated except by using the conception 'larger than' and therefore it cannot be stated without stating a relation." [5]

There is a doctrine in Philosophy which maintains that all relations are internal. It is commonly thought that the controversy concerning the externality or internality of relations is concerned with the relations in which terms stand. Mr. Moore I think has shown that controversy is not concerned with relations properly speaking at all, but with relational properties. "The doctrine [that all relations are internal] is that all relational properties modify their terms, in a sense which remains to be defined."[6] But since relational properties are derivative from the fact of relatedness of the terms, there is a sense in which relations are internal, a sense which corresponds to the sense in which the relational properties to which the relation gives rise are internal. Those relations will be termed internal which generate relational properties that are internal, and relations will be called external, if the relational properties they generate are external.[7] The question at issue then is whether the relational properties which are generated when terms stand in relation are all internal or all external, or some of them internal and some external. To say that they are internal is a capable of two different meanings. In Mr. Moore's formulation:

"If P be a relational property which belongs to A, then P is internal to A both in the sense
(1) that the absence of P entails qualitative difference from A; and
(2) that the absence of P entails numerical difference from A"[8]

/p. 174/
Whether such properties can be said to be internal in the first sense depends upon whether we can say that two colors differ in quality or qualitatively. The expression 'qualitatively different' may be legitimately used in the following two senses at least. Two sense-data, one of which is red while the other is blue, are said to be qualitatively different. The one sense-datum possesses a quality not possessed by the other. If the sense-data are characterized by more than one color, if, for example, we consider the difference between two sense-data one of which is a yellow circle with a red spot while the other is a yellow circle with a blue spot, the two sense-data may again be said to be qualitatively different. But in this second case we would perhaps speak with greater accuracy if we said that the one sense-datum contains a constituent, namely, a red spot, which is qualitatively different from any constituent of the other. Hence in the second case qualitative difference means having qualitatively different constituents and is therefore definable in terms of the qualitative difference that is exemplified in the first case. Thus simple sense-data may differ qualitatively, while only complex sense-data may differ in the fact that they have qualitatively different constituents.[9] The question remains whether the qualities characterizing two qualitatively different sense-data may themselves be said to differ qualitatively. If two colors, e.g. orange and green, where themselves qualitatively different, then the relational property of orange that it is intermediate between red and yellow would be internal since any quality which was not intermediate between red and yellow would necessarily be qualitatively different from orange.[10]

The assertion however that two colors can be qualitatively different seems to me to be highly dubious. It is the case that orange and green differ intrinsically, but unless all intrinsic difference is qualitatively, orange and green do not also differ qualitatively. If colors can be qualitatively different they are not qualitatively different is either one of the two senses mentioned. Orange does not possess a quality not possessed by green, and orange does not have a constituent which is qualitatively different from any constituent which green has. If the expression 'qualitatively difference' is employed in this fundamental sense, colors can be qualitatively different not more than they can be qualitatively similar. Colors do not constitute a class or account of the possession of a common qualities. If this is so colors cannot be said to be qualitatively different either. Only substantives can be either qualitatively similar or different.

But if we reject the view that the relations between universals are internal in the first sense, it is impossible to find any relational properties which are internal in that sense. We just argued that it was dubious whether the relational properties which are generated by the relations in which universals stand are internal in the first sense. The relational properties generated by the relations in which existents stand are certainly not internal in this sense. If A is taller than B it is simply false that anything which does not have the property of being taller than B must be qualitatively different from A. Some of the relations between existents, however, are internal in the second sense. The relation of the whole to the part generates a relational property which is internal in the second sense. If B contains A, then B has the relational property of containing A. And from the proposition to the effect that X does not have the relational property of containing A it follows that X is not identical with B. In other words, B could not have existed without containing A as a part. Consider now the relation which A has to B. We express this relation by saying that A is a part of B. In this case, then A has the property of being a part of B. But from the proposition to effect that X does not have the property of being a part of B, it does not follow that X is not identical with A. The whole B could not have existed with the part A, but the part A might perfectly well have existed without forming a part of B.

The doctrine that relational properties are internal in the first sense, in the sense, namely, that if P is a relational property of A then the absence of P entails qualitative difference from A, is, properly speaking, not a proposition about relational properties at all, but one about predicative properties. Relational properties are generated in a term when it stands in relation to other terms. The relation is hence fundamental and the relational properties presuppose the reality of the relation. But if we understand the doctrine that all relations are internal in the first sense, the reality of relations are impugned, for in that case any relational proposition can be reduced to a predicative one or to several of these. The relational proposition can be reduced is usually implied by what Moore calls the dogma that all relations are internal. This is certainly the proposition which Mr. Russell has taken to be logically involved in the doctrine. Mr. Russell states what he means by the externality of relations as follows: [12]

Russell seems to imply that there are some cases in which a relational proposition can be reduced to a predicative one. It is not clear why this should be possible. It seems that xRy in no case can be reduced to a xα, yβ, (x,y)γ or to any one or two of these, if relations are not qualities. Russell is obviously thinking of symmetrical relations in the case of which "some kind of plausibility can be given to the doctrine. A symmetrical relation which is transitive, such as equality, can be regarded as expressing possession of some common property, while one which is not transitive, such as inequality, can be regarded as expressing possession of different properties." [13] It is undoubtedly true that in the case of any relation the terms would not have have the required relation unless they had had certain properties. When the relation is symmetrical as in the case of the proposition A is different from B, it is therefore plausible to argue that what we are here asserting is that A has the property α and B the property β. The proposition, A is different from B, is have equivalent to the joint assertion of the two propositions 'A is α' and 'B is β'. But although the relational proposition and the predicative propositions are equivalent, their meanings is not the same. As a matter of fact it is not even always possible to find predicative propositions which are equivalent to a relational one. If A and B are colors, it is not the case that we can find qualities α and β such that, 'A differs from B', is logically equivalent to 'A is α' and 'B is β.' For qualities, as we argued before, differ intrinsically and not qualitatively. In the case of asymmetrical relations it is not even possible to give this specious plausibility to the doctrine as Russell goes on to show. The proposition 'A is greater than B' is not equivalent tot he joint assertion of the two propositions 'A is α' and 'B is β' where α and β are different magnitudes. For if this were the proposition we are asserting, we would be unable to distinguish between the proposition 'A is greater than B' and 'B is greater than A'. If B is greater than A their magnitudes are also different. the propositions 'A is α' and 'B is β' are therefore not equivalent to the proposition 'A is greater than B.' We should have to add to them the proposition α is greater than β in order to get a proposition which is equivalent to last. But if so we have failed to eliminate the relation 'grater than'. [14]

Let us recapitulate the salient points of our analysis. We have examined the contention that relations are unreal and that every proposition is therefore expressible in the subject-predicate form, and also the contention that we may dispense with them if they are real, and that therefore similarly every proposition is expressible in the subject-predicate form. The doctrine that all relations are internal makes this claim on the supposition that relations are real. If all relations are internal in the first of Mr. Moore's senses, then every relation determines a quality in the related terms, and conversely the qualities of the related terms determine the relations in which the terms stand. When A has the relation R to B, neither A nor B would have been the terms they are unless they had stood in that relation, and they would not have had that relation unless they had been the terms they are...

The contention that relations are unreal is of course not committed to the doctrine that all relations are internal in either one of Mr. Moore's senses for these two senses presuppose that relations are real. It would be committed to an analogous doctrine, if it were maintained that every predicative proposition is analytical. If the proposition 'aRb' is identical with the proposition 'aα, bβ', '(a,b)γ' or to any one or two of these, and if these propositions are all analytical, then substantives are internally related to the qualities that characterize them. But the view which denies the reality of relations is committed to the doctrine that all relations are internal in the sense in which Russell defines what is to be meant by the internality of relations.

That a relational proposition can always be reduced to a proposition predicating a quality of a substantive is the view of Mr. Johnson. ...
/p. 180/
But if so, we are curious to know why the characterizing this the former case is expressed by 'is-as' instead of more simply by 'is' as it is expressed in the latter case... (analogy - p. 207)
/p. 181/
And this is nonsense because the relation of A to B is of a different logical type than the relation of 'greater than' to 'less than'. ... For example, the relations 'greater than' and 'equal' are of the same logical type, because '17 greater than 9' and '17 is not equal to 9' are both facts. Now the relation of A to B in our proposition is 'greater than', and the relation of 'greater than' to 'less than' is 'converse of'. If they are of the same type, it should be a fact, either that A is the converse of B or that A is not the converse of B and it should be a fact, either that 'greater than' is grater than 'less than' or that 'greater than' is not greater than 'less than,' and this is not the case. Mr. Johnson's formulation must therefore be rejected because it involves a confusion of types...

/p. 186/
The futility of Mr. Johnson's attempt to reduce the relational proposition to the predicative form must now be apparent. Any attempt to do this must result in the same failures for the reason that a relation is an entity of a type that is different from either a substantive or a quality. This fact comes to the surface even in Mr. Johnson's formulation. Relations, he maintains, contain a qualitative element, namely the adjective-couple. But in addition they contain another element, the relational determinable, denominated either as the coupling tie, or as otherness, which is non-qualitative. I have tried to show that this doctrine is inconsistent with Mr. Johnson's own view of the nature of the determinable. If therefore we accept this view as correct, it constitute a further reason for the rejection of Mr. Johnson's formulation of the relational propositions.

Finally, there is no reason why we should not accept relations into our Logic or Metaphysics. Relations may be dispensed with in logic, on the assumption that they are metaphysically real, if all relations are internal in the first of Mr. Moore's senses. But if all relations are internal in the first sense, they must also be internal in the second sense. Mr. Moore I think has shown that there is no reason to believe that all relations are internal in the second sense. But if some are not internal in the second sense, these relations are likewise not internal in the first sense. If relations are unreal, logic again needs to consider only predicative propositions. But if relations are unreal there is only one substantive, the absolute, which is the subject of every proposition. In so far as these doctrines give reasons for denying the reality of relations, I consider these reasons to be false. In so far as they do not give such reasons, I consider them to be flatly contradictory of my common-sense experience, which includes the experience of relations. And for that reason again, I consider them to be false.

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[1] J.M.E. McTaggart, The Nature of Existence, I:81.

[2] Ibid., I:81.

[3] Ibid., I:82.

[4] Ibid., I:79.

[5] Ibid., I:83.