The Classical Theory of Relations: A Study on the Metaphysics of Plato, Aristotle and Thomism 0914744283

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THE CLASSICAL THEORY BY THE SAME AUTHOR

OF RELATIONS

A DIALOGUE BETWEEN BERGSON, ARISTOTLE, AND PHILOLOGOS

A STUDY IN THE METAPHYSICS OF PLATO, ARISTOTLE AND THOMISM

MAN AND THE UNIVERSE IN AMERICAN PHILOSOPHY

MODERN GREEK PHILOSOPHERS

BY

CONSTANTINE CAV ARNOS

ON THE HUMAN SOUL

BYZANTINE THOUGHT AND ART MODERN GREEK THOUGHT PLATO'S THEORY OF FINE ART INSTITUTE FOR BYZANTINE

PLATO'S VIEW OF MAN

AND MODERN GREEK STUDIES

115 Gilbert Road Belmont, Massachusetts 02178 U.S.A.

PREFACE This work began in 1947 as a paper written for Professor John D. Wild's seminar in metaphysics at Harvard University. In this paper I discussed the Thomist teaching on Relation as presented by Joseph Gredt in his Elementa Philoso phiae Aristotelico-T homisticae. He had chosen Gredt's book as the textbook for the seminar, and made all assignments from it. Wild liked my paper very much, and suggested that J take the problem of Relation as the topic for my doctoral dissertation. I was already acquainted with recent metaphysical discussions of the problem also, such as those of F. H. Bradley and William James, having written three papers on the subject for Prof. Donald C. Williams, then chairman of Harvard's Department of Philosophy. Two of these papers were in a research course and one in a course in metaphysics. As I had found the subject very interesting and worthwhile, I accepted Wild's suggestion without much hesitation. I decided to write my thesis on the views of Plato, Aristotle, and Thomism, presenting their teaching on Relations, pointing out that they have much in common, and refuting the charges made by certain prominent recent thinkers that Plato, Aristotle and Aristotelianism had neglected relations or had even denied their reality.

All rights reserved Copyright, 1975, by Constantine Cavarnos Published by THE INSTITUTE FOR BYZANTINE AND MODERN GREEK STUDIES, INC. 115 Gilbert Road, Belmont, Massachusetts 02178, U.S.A. Printed in the United States of America Library of Congress Catalog Card Number: 75-2659 ISBN 0-914744-28-3

The greater part of the thesis was written during my travels as a Sheldon Fellow in Philosophy, during the academic year 19471948, especially while I sojourned in Cambridge, England. In Cambridge I had free access to the library of the University, met and had private discussions with some of the philosophers I mention in this book, such as C. D. Broad, G. E. Moore and Bertrand Russell. The fact that most of the contemporary writers I refer to are English is due to my residence here, which was longer and more fruitful than that in other parts of Europe.

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My dissertation was completed in the spring of 1948, and was approved by Professors Wild and Demos, both of whom had provided considerable stimulus, and many helpful criticisms and suggestions, the first in connection with the chapters dealing with Plato, Aristotle and Thomism, and the second with the chapters dealing with Plato and Aristotle. CONTENTS

Since then, sufficient interest has been shown in this work to warrant publishing it, despite its specialized nature. Thus, Professors Demos (1892-1968) and Wild (1902-1972), and some former colleagues, including my friend Professor George Bosworth Burch (1902-1973) of Tufts University who read it in 1972, urged me to have it published. In preparing the text for publication, I have gone over the entire work and made many changes, rendering the thought clearer and more precise, and improving the language. Also, I have made corrections in the footnotes and added new references, an Index of Names, and an Index of Subjects.

Page

9

INTRODUCTION I.

PLATO .. . . 1. Realms of being. 2. The main kinds of en~1ty. 3. Analysis of the relational sit~ation. ~· Relations in the realm of Forms. 5. Psychical relations. 6. Relations between physical objects. 7. How we know relations. 8. Conclusion.

II.

ARISTOTLE .... 1. Realms of being. 2. The main kinds of enti~. 3. Analysis of the relational situation. 4. Properties of relation. 5. Classification of relations. 6. How we know relations. 7. Conclusion.

III.

THOMISM 1. Introductory 2. Analysis of the relational situation. 3, Classification of relations. 4. How we know relations. 8. Conclusion.

IV.

CONCLUSIONS

CONSTANTINE CAVARNOS February, 1975

v

PREFACE

39

67

103 107

BIBLIOGRAPHY

111

INDEX OF NAMES

113

INDEX OF SUBJECTS vi

11

vii

INTRODUCTION It has often been asserted recently that Plato, Aristotle, and Aristotelians neglected relations, did not understand them, or even did not believe in the reality of such entities. Thus, Bertrand Russell says that "Plato is perpetually getting into trouble through not understanding relative terms.'' 1 In fact, he asserts, Plato, Aristotle, and by implication the followers of Aristotle denied the reality of relations. 2 The same allegations are voiced by Alfred North Whitehead, a Francis MacDonald Cornford,4 and George Santayana. 5 In this work I undertake to show that Plato, Aristotle, and Thomism affirmed the reality of relations; that far from having neglected relations, they have explicitly discussed them and have said many interesting and important things concerning them; and that the theories they have developed have a great deal in common, so that they may be said to constitute one theory, which I have called "the classical theory of relations.''

I try to show this by bringing together and presenting systematically in separate chapters what Plato, Aristotle, and Aquinas and some of his followers, especially John of St. Thomas (Joannes a S. Thoma or Joao de Santo Thomaz, 1589-1644) and Joseph Gredt ( 1863-1940), have said about relations. As a discussion of their views on relations involves reference to reality in general, I discuss the realms of being recognized in each theory so far as is necessary. 1

A Histo1·y of Western Philosophy, p. 129; cf. p. 150. Cf. his book Our Knowledge of the External World, pp. 45-47, 50; A History of Western Philosophy, pp. 150, 164, 452, 461. 3 Cf. The Philosophy of Alfred North Whitehead, ed. by Paul Arthur Schilpp, p. 424. 4 See Plato's Theory of Knowledge, pp. 44-45, 282-284; Plato and Parmenides, p. 78; 'the Physics of Aristotle, Loeb Classical I:ibrary, Vol. 2, p. 20n. 5 Realms of Being, p. 30. 2

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THE CLASSICAL THEORY OF RELATIONS

My interest is not purely historical. While expounding the views of Plato, Aristotle and Thomism concerning relations, I at many points compare and criticize them, hoping by this to make clear the issues involved and to deepen my own insight into the subject of relation. I seek to clarify the general notion of relation, to discover the major classes of relations, their subdivisions, and the faculties by which we apprehend them, and further to envisage the various realms of being from the standpoint of relation. This study proceeds not only in the field of metaphysics, bu_i: also in those of epistemology and "material logic." Thus, many topics that are of broader interest than the bare notion of relation are discussed or touched upon.

Of all the ancient philosophers I find Plato the most satisfactory. Leibniz It is dangerous to neglect Plato's intuitions. A.N. Whitehead

ALPHABETICAL LIST OF ABBREVIATIONS OF PLATO'S WORKS REFERRED TO Charm.

Charmides

Crat.

Cratylus

Epist.

Epistle

Euthyph.

Euthyphro

Gorg.

Gorgias

Parm.

Parmenides

Phd.

Phaedo

Phdr.

Phaedrus

Phil.

Philebus

Pol.

Politicus

Prot.

Protagoras

Rep.

Republic

Soph.

Sophist

Symp.

Symposium

Theaet.

Theaetetus

Tim.

Timaeus

CHAPTER

PLATO 1.

Realms of Being

Philosophers have often spoken of 'realms,' 'orders,' or 'levels' of being. A 'realm of being' may be defined as an aggregate of entities which have a common differentiating attribute. 1 In Plato's universe we may distinguish three major realms of being: (a) the realm of forms, (b) the realm of psyches, and (c) the realm of physical objects. The realm of forms is the ultimate ground of determinateness; psyches assimilate this determinateness and introduce it into the physical world. 2 (a) The forms ( eide, ideai) s or universals ( koina) 4 are entities which, as they are neither in space nor in time, cannot be said to 'exist.' Hence they may be called 'non-existent' 5 or, better, to use a word which has been coined recently, 'subsistent.' They are eternal, unchanging, static. The totality of forms Plato calls the 'Limit' (Peras), because the forms are the source of limitation or determinateness. Viewed as a realm of eternal perfection, towards which all changing things aim, as to their final cause, the realm of forms may be identified with what Plato calls the Idea of Good. 6 (b) Within the realm of psyches are included the Supreme God, the subordinate gods, and the psyches of men, of infra-human animals, and of plants. These, being in time, may be said to 'exist,' or to 1 2 3 4 5 6

Cf. C. D. Broad, The Mind and its Place in Nature, p. 25. See esp. Phil., Tim., Laws X, passim. Phd. 102b, 103e, 104d. Theaet. 185e. Parm. 160b ff. Cf. H. W. B. Joseph, Knowledge and the Good in Plato's Republic,

pp. 21, 23-24, 68.

12

I

13

14

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THE CLASSICAL THEORY OF RELATIONS

Plato

be 'existents.' What is most peculiar about them, and distinguishes them from physical objects, is that they are not only themselves dynamic, but are also originative of dynamism or change in other things.7

sions.14 But in a number of other dialogues he speaks of loving as a relation. 1 5 In the Republic he says that thirst belongs either to the class of actions or to the class of passions, and then goes on to point out its relational nature. 16 Again, in the Sophist he speaks of 'knowing' as an action and of 'being known' as a passion. But in other works he emphasizes the fact that knowing is a relation.17 In the same dialogue he says that we may take 'power' (dynamis), whether active ability or passive capacity, as the 'mark' ( horos) or real things. 18 But it is nonsense to speak of the forms as having power, whether active or passive, in the ordinary sense of these words, which implies capacity for either physical or psychical action or passion. The only plausible interpretation of 'power' here is that suggested by Professor Demos. "Power,'' he suggests, means here the "capacity to sustain relationships.'' 19 It follows, on this interpretation, that, as power is either active or passive, some relations would come under the class of actions and others under the class of passions. Now I think it is plausible to regard the modes of being denoted by such words as carrying and being carried, striking and being struck, cutting and being cut, as actions and passions, respectively, as Plato does in the Euthyphro, Gorgias, 20 and elsewhere, and to hold also, as he seems to hold in the Sophist, that they are relations. We may say that these constitute a peculiar class of relations. What about loving, desiring, knowing, etc.? These, Plato emphasizes, are relations, or at least are experiences involving relations. But in what sense are we to say that where there is loving, knowing, etc. there is an 'action-passion' situation? We must distinguish, in the first place, between physical action and psychical action. Loving and knowing are psychical actions. Then, we may say, as Plato says, that the object loved or known is 'acted upon' or 'affected' in being

( c) Physical objects, too, are existents. Like psyches, they are dynamic; but unlike them, they are not originative of change. They can receive and communicate motion, but cannot originate it.s Both psyches and physical objects may be called 'particulars,' in contrast to the forms, which I have called universals. 2. The Main Kinds of Entity The word 'being' is used in many senses. Plato shows this admirably in the Parmenides. 9 I have distinguished three realms of being in the Platonic universe. When we say that an entity in one of these realms 'is,' we are using the word 'is' in a very different sense from the sense in which we use 'is' when we speak of an entity in one of the other two realms. Similarly, when we say that a certain kind of entity within one of these realms 'is,' the word 'is' denotes a very peculiar mode of being, distinct from that which another kind of entity has. In Plato we find the recognition of widely different modes of being, of supreme genera of being, in each of these realms. Plato distinguishes two major kinds of entities ( onta) : (a) 'absolute entities' (kath' hauta) and (b) 'relations' (pros alla).10 Within absolute entities he seems to recognize as peculiar, ultimate modes of being (i) 'substance' (pragma), 11 (ii) 'quantity' (poson),12 and (iii) 'quality' (poiotes). 13 He often speaks of 'action' (poiema) and 'passion' (pathema). But he seems to regard them as relations, and not as distinct modes of being. Thus, in the Euthyphro he places 'loving' in the class of actions, and 'being loved' in the class of pas7

Cf. Phdr. 245c; Laws X. 891e, 892a, 894b, 896a,e, 897a. Cf. Laws X. 897a; Tim. 46e. Cf. F. M. Cornford, Plato and Parmenides, pp. 110-111. lO Soph. 255c. Cf. Phil. 63b; Diog. Laertius Lives of Eminent Philosophers, Vol. 1, iii, 108-109. ' 11 Apo!. 27b; Phd. 103b; Crat. 413. Cf. F. M. Cornford op. cit., pp. 197-199, and W. D. Ross, Aristotle, p. 223. ' 12 Soph. 245d. Cf. Cornford, op. cit., and Ross, op, cit. 13 Theaet. 182a. Cf. Cornford, op. cit., and Ross, op. cit. 8 9

14

lOa-lla. Charm. 167e; Symp. 199c ff. 16 Rep. IV. 137b ff. 17 Charm. 168; Parm. 132b ff. 18 147e. 19 Raphael Demos, "Types of Unity According to Plato and Aristotle," Philosophy and Phenomenological Research, Vol. 6, No. 4, p. 538. 20 Euthyph. lOa; Gol'g. 476c ff. 15

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Plato

THE CLASSICAL THEORY OF RELATIONS

loved or known. In the Euthyphro Plato says that in being loved, holiness "is either becoming or undergoing something." 2 1 What happens to holiness? It acquires the 'affection' (pathos) of being loved.' 22 Something like this seems to be implied about 'being known' in the Sophist. 2 3 But holiness, which is an object of loving, and the forms in general, which are the objects of knowing in the strict sense, are not dynamic, but static, impassible. What justification, then, is there for calling their relations passions? Further, if the forms are immutable, how can they gain or lose relations? As regards the first question, Plato's reason for calling 'being loved' and 'being known' 'passions' seems to be the fact that their converses are immanent actions. As for the second question, his view is that the relations of 'being loved' or 'being known' are not constitutive of the essence ( ousia) of a form, and it is the essence which he believes to be immutable. 'Being loved' is only an accident of holiness. This is clear from the fact that we do not acquire knowledge of holiness when we are simply told that holiness "is loved by the gods." That the essence of the object known or loved is not changed follows from the fact that there is intelligence or understanding. If the essence, too, changed, intelligence would be impossible.2 4 But what about such relations as 'similar to' and 'greater than?' Here, both the relation and its converse seem to be static. How can we speak of action and passion here? So far as I can see, we can only speak of action and passion in a purely metaphorical sense. If A is greater than B, A may be said to act on B, and B to be acted upon by A, in the sense that by the very fact that A has the relation 'greater than' ('action') to B, B must have the converse relation 'less than' ('passion') to A. B has been 'affected' in the sense that it has gained a relation to A. But here the relation which is called an action will, if we reverse our point of view, be called a passion. What needs to be added here is that Plato is not a philosopher who adheres to a rigid terminology. 2 5 Hence, in seeking to find what

he says about relations, we should not be on the lookout merely for aes where he uses some technical term, such as. pros allo. pass at:> further, we should remember that Greek is an inflected language, d that in discussing relations a preposition like pros has to be an 'lb ·· dispensed with, the relation being expressed s1mp y yh t e ge111t1ve or dative cases of a word. 3. Analysis of tbe Relational Situation In the relational situation Plato distinguishes, though not always very clearly, the following: (a) the relation, (b) the converse of the relation, ( c) the terms of the relation, and ( d) the ground of the relation. (a) A relation for him is a characteristic which has the peculiarity that the thing which has it has it in some sense 'towards' (pros) some other distinct thing. 2 6 These two things I shall call, following current terminology, the referent and the relatum, respectively. Plato, however, has no special words ~or t~e11:1. Take the situation where Simmias is taller than Socrates. S1mmias 1s the referent and Socrates is the relatum of the relation 'taller than.' The rela. tion 'taller than' is a characteristic of Simmias. But it is not a characteristic which Simmias has in himself, apart from everything else, but a characteristic which he has in some sense 'towards' Socrates. 27 The statement that relation is a characteristic which a thing has 'towards' some other thing should not be taken as a definition of relation. Plato does not offer it as such. And it is doubtful that relation can be defined. It seems that any definition would either involve the reduction of relation to some other mode of being, and would therefore be false, or would be a mere tautology, since we would be 28 using words which are more or less synonymous with relation. But while relation may not be definable in the strict sense, some tau26

21 lOc. Cf. llb. 22 23 24 25

Op. cit. llb. 248d-e. Cf. Soph. 249b ff. Cf. Cornford, Plato's Theory of Knowledge, p. 256.

17

Cf. Cornford, op. cit., pp. 282-283.

27 Phd.

102 ff.

Cf. S. Alexander, Space, Time, and Deity, p. 239, and "On Relation.s; and in particular the Cognitive Re'.ation," ~1ind, .1912-~,3, p. 306; E. B: McG1lvary, "Relation in General and Umversals in Particular, Journal of Ph1losophy, 36-1939, p. 5. 28

Plato

THE CLASSICAL THEORY OF RELATIONS

18

tologous or circular definition such as that of Plato is, I think, helpful. 29 • While the essence of relation is to hold from something to something else, with respect to its existence it inheres in the referent. In the relational situation "Simmias is taller than Socrates," the relation 'taller than' holds from Simmias to Socrates, but inheres ~nly in (en) Simmias. It is the first feature which distinguishes relations from intrinsic characteristics. An intrinsic characteristic, such as whiteness, also inheres in a thing, but the thing in which it inheres does not have it with reference to (pros) another. Cornford overlooks this point, when he says that in the Phaedo Plato thought of relations such as tallness and shortness as •·1~t ern.al properties' on the same footing as 'hot' or 'whi~e.' Pla~o's v1ew. m the Phaedo, Cornford believes, implies that a thm~ which ac~u1res or loses a relation suffers internal change. 30 He believes that m the Parnienides Plato rejected the view put forth in the Ph~edo abo~t relations as absurd.31 Further, in the Tbeaetetus, accordmg to :his interpreter, Plato seems to have ad~pted .the vie'; that rel~t10:s fall 'between' their terms. But even with this new view, he believe ' Plato still did not see any important distinction between such a characteristic as 'large,' on the one hand, and 'white,' on the other. For intrinsic characteristics, too, such as white and hot, now fall 'between' their terms (in the sense of emerge between the perceiver and the physical object). . As regards his interpretation of the Parmenules, that Plato rejected as absurd the views he ex~ounde~ ear~ier about relations such as greatness and smallness, I t~mk he. ts mist~ken. What Plato rejected as absurd here was the view which considers these as cha~ac­ ters which things have apart from anything else. But this conception of relation is not advanced in the Pbaedo. . . About Cornford's interpretation of Plato's view of relat10ns m the Parnienides I shall make the following obs.ervations. ~cc~rd~ng to Cornford, even here Plato does not see any important distmct10n Cf. J.B. Pratt, Personal Realism, p. 32. Plato's Theory of Knowledge, p. 44. 31 Plato and Parmenides, pp. 172-175. 32 Theaet. 155d.

29 30

19

between intrinsic characters and relations; If this is correct, I do not see how what Plato says about perception is this dialogue throws any light on the paradox of the dice, which Cornford thinks it does, and which Socrates says that it does.3 2 The puzzle about the dice, which is presented before the theory of perception is put forth, is how the very same set of dice can combine the contrary characters of 'more' and 'less;' how six dice can be 'more' than four and 'less' than twelve. 33 Cornford suggests that the light thrown on the puzzle is as follows. "The six dice will appear more to me when I compare them with four, and less when I compare them with twelve, but they have not become more or fewer in themselves." 34 Now there is no doubt that they will so appear. But this leaves unanswered the question of how the six dice can combine these two characteristics, apart from my comparing of them. Whether the dice are appearances or things behind appearances is here irrelevant. How can the apparent dice combine these relations? The problem of the characteristics 'more' and 'less' is not really solved by transferring the dice to the region of appearance; it arises there all over again. My view is that Plato's examination of perception throws light on the apparent paradox by bringing out not the distinction between 'being' and 'appearing to be,' but rather the distinction between 'being in itself' and 'being in relation to.' I submit, then, in the first place, that Plato does not place relations on the same footing as intrinsic characteristics, either in the Pbaedo or in the Tbeaetetus. In the second place, I submit that Plato does not advance in the Tbeaetetus and in the Parmenides views about relations which differ from these which he advances in the Phaedo. For Plato a relation is always a peculiar characteristic: one which a thing has 'towards' another. Cornford, it must be observed, recognizes this,3 5 Evidently this peculiarity does not strike him as important enough to distinguish relations from intrinsic characteristics, such as white, hot, etc. But what else can be the distinguishing feature of relation? He thinks that the formal nature of relation is that it is in some sense 'between' its terms. He does not define what 33 T heaet. 154c. 34 Plato's Theory of Knowledge, p. 45. 35

p. 78.

See Plato's Theory of Knowledge, p. 283, and Plato and Parmenides,

21

THE CLASSICAL THEORY OF RELATIONS

Plato

this sense of 'between' is. And it is doubtful that it can be defined, any more than Plato's word 'towards' can be defined. I suggest that Plato means by 'towards' what Cornford means by 'between.' I sug· gest further that Cornford believes that Plato does not see an im· portant difference between relations and intrinsic characters because Plato says that a relation inheres in the referent. But I have pointed out that we must distinguish between the being of a relation and its essence. With respect to its being, a relation inheres in the referent; with respect to its essence, however, it holds from the referent to the relatum. 36

refer at once to both the relation and its converse. Plato has no such term, however.44 ( c) That a relation must have terms is a fact that Plato recognizes. 45 A term which has a relation is called a 'relative term.' Plato denotes a relative term by the expression 'that which is of something' (to einai tou, to tinos). 4 6 In so far as such terms answer to each other, that is, stand in a certain relationship, he calls them 'correlative terms' (pros allela). 47 Thus, 'master' and 'slave' are correlative terms; they are terms standing in the relationship 'mastership-slavery.'48 Plato sometimes confuses the relatum with the converse of the relation. He speaks sometimes as if the relation related the referent not to the relatum but to the converse relation. Thus, he says that Socrates has shortness relatively to Simmias' tallness. 49 Now tallness is not the relatum of shortness but its converse. The relatum of shortness here is Simmias. Hence what Plato should have said here is that Socrates has shortness relatively to Simmias. This, in fact, he does say in the same passage. 50 He appears to see no difference between the two modes of expression. What things can serve as terms of relations? As there are relations within all three realms of being, entities in all of these realms are term:; of relations. In other words, the terms of relations may be universals, psyches, or physical objects. Let us turn now to the question of the number of terms a relation may have it. It is clear that Plato believes that a relation may have only one term, at least in certain senses. ( i) We may speak loosely of a relation having only one term in the sense that the relation holds between two parts of one and the same thing. Thus,

20

(b) Although Plato has no special term for what is currently called the converse of the relation, he nonetheless recognizes it as something distinct from the relation. His view is that relations occur in pairs; that, if x is related by r1 to y, then y is ahvays related by r2 to x. Examples are the following. If a thing is 'not equal to' other things, they must be 'not equal to' it. 37 If things are 'like' a thing, that thing must be 'like' them; 38 and if 'different from' it, it must be 'different from' them. 39 Again, 'above' is the converse of 'below;' 40 'soft,' of 'hard;' 41 'greater than' of 'less than;' 42 'loves,' of 'is loved.' 43 Since the word relation is sometimes used by modern writers to refer both to the relation and to the converse of the relation simultaneously; and since this either pre-supposses or suggests that the two are a single, indistinguishable entity; and since, further, Plato believes (and rightly) that they are distinct, I shall use the word relationship instead of relation on occasions where it is necessary to 36 For a similar conception of relation by a modern thinker cf. W. E. Johnson, Logic, Vol. 1, p. 203. He regards a relation as "a type of adjective whose meaning when analyzed exhibits a reference to some substantive other than that which it characterizes." 87 Parm. l6lc. 38 Ibid. 132d. 39 Ibid. 146d, 147c, 161b. 40 Tim. 62d-63e. 41 Rep. VII. 524a; Tim. 62b. 42 Parm. 149e; Pol. 283d-e. 43 Euthyph. lOc.

44 This use should not be confused with other uses of that word, such a5 that of McTaggart, by whom, too, the word 'relationship' is given a meaning different from that of relation. He thinks that it is convenient •to say that 'admiration' and 'equality' are relations, whereas '·the admiration of A for B,' and 'the equality of A to B' are 'relationships' (The Nat11re of Existence, Vol. 1, p. 96). 45 Cf. Parm. 163e-164b. 46 Rep. IV. 438b, 438d, 439a. 47 Charm. l66a;Prot. 331e; Theaet. 186a; Parm. 133; Tim. 62b, 63d-e; Epin. 979. 48 Parm. 133d ff. 49 Phd. l02b-c. Cf. Parm. 133e, 150c. 50 Phd. 102b.

22

THE CLASSICAL THEORY OF RELATIONS

though there must be two distinct terms if the relation 'master of' is to hold, we sometimes say, Plato observes, that a certain person is 'master of himself.' But he points out that the phrase 'master of himself,' taken literally, is an absurdity. For if 'himself' denotes a single and simple entity, then "he who is 'master of himself' would also be subject to himself, and he who is subject to himself would be master of himself.'' 51 What we really intend when we use the phrase 'master of himself,' says Plato, is that there are in the ~oul of the person who is said to be 'master of himself' two distinct parts, a better and a worse one, and that there holds the relation of mastery from the better to the worse part. Thus we do not have here a relation in which the referent and the relatum are strictly the same. We have a relation between one part of a thing and another part of it.

(ii) But Plato believes not only that one part of a thing may be related to another part of that thing, but also that a thing (or part of a thing) may be reflexively related to itself by certain relations, such as likeness,52 equality, 53 and sameness. 54 Sameness is a relation which a thing has to (pros) itself. Everything, Plato says, has this relation.55 The view that there are one-term relations in sense (ii) seems to be wrong. Relation, by its very nature, seems to demand terms which are distinct from one another. But may we not, asks DeWitt H. Parker, "take a term along with itself and thus get the couple that we need, without implying any diversity in the members of the couple?" No, he answers. For "to take a term along with itself is nonsense, ... " 56 But though there cannot be any relations which are reflexive, we must grant, he says, that the so-called notion of identity, as commonly used, is not meaningless. Parker thinks that what is generally referred to as the relation of identity is a one-many relation. We may say, for example, that 'dangerous' has the 'same' meaning as 'perilous.' Here there is a relation which holds between Rep. IV. 430e-43 la. Parm. 147c ff., 161b-c. Ibid. 149d ff., 151b ff. So/1h. 256b. Cf. F. M. Cornford, Plato's Theory of Knowledge, p. 285; Parm. 133c, 254d-255e. 55 Soph. 256a. 56 "Reflexive Relations," Philosophical Review, Vol. XLII, 1933, p. 304. 51 52 53 54

Plato

23

two expressions and a meaning, and is therefore triadic. A similar interpretation, he thinks, can be given to all cases of so-called reflexive relations.57 Does Plato believe in relations which logically require more than two terms, i.e., in 'multiple' relations? I do not find in his writings any suggestion that he has a clear conception of such relations. But there is nothing in his views that makes belief in such relations impossible.

( d) Plato believes that relations are grounded in the nature of their terms. He observes that ten is greater than eight and asks: By reason of what does ten have the relation 'greater than' to eight? He answers: By reason of number.58 Again, a two-cubit measure is greater than a one-cubit measure. By reason of what? By reason of magnitude. 59 How the intrinsic nature of the terms determines the nature of a relation holding from the one to the other can be seen by a consideration of thirst. Thirst is relational: it is the desire for something other than itself. Thirst qua thirst never wishes anything else, says Plato, than mere drink. But thirst becomes qualified according to the state of the person who is thirsty, or to the drink present before him or both. Thus, if you are feeling hot as well as thirsty, you will have a desire for cold drink. If, on the other hand, you are feeling cold and thirsty, you will have a desire for hot drink. If you are very depleted, you will desire much drink; while if you are slightly depleted, only little drink. Conversely, if that which is presented, either by sight, or by the imagination, etc. as an object of thirst is of such and such a particular kind, the thirst will become correspondingly qualified. So with other desires, which are relational. Each is qualified according as ( 1) the person having it is in such and such a state, or (2) the object of the desire is of such and such a particular kind. The nature of the state and of the object are the ground of the relation. 60 57 Op. cit., pp. 307-308. Cf. C. D. Broad, Examination of McTaggart's Philosophy, Vol. 1, pp. 91-92. 58 Phd. lOlb. 59 Ibid. 60 Rep. IV. 437b ff.

25

THE CLASSICAL THEORY OF RELATIONS

Plato

The same is true of such relations as 'greater than' and 'less than,' 'more than' and 'fewer than,' 'double of' and 'half of,' 'quicker than' and 'slower than,' 'knowledge of,' etc.61 A change of the ground in either of the terms results in a different relation. Thus the reason or ground of a relation is some characteristic (or characteristics) in both of the terms. Plato does not hold that every relation is grounded solely in the nature of the terms. He does not hold, in other words, that in the case of every relation the nature of the terms is the sufficient condition for its occurrence, though he seems to be aware that in the case of some relations, such as 'greater than' and 'less than,'6 2 'double of' and 'half of,' 'similar to' and 'different from,' the nature of the terms is the sufficient condition for the occurrence of the relation. And he is aware that it is this fact about such relations which enables us, from a knowledge solely of the intrinsic nature of their terms, to derive the knowledge that they have these relati.ons.6 3

their terms, in so far as they are not so grounded, are grounded in the law of sufficient reason or the principle of what is best.6 6 Other relations, those which are not grounded exclusively in the nature of their terms, and are not grounded in the law of sufficient reason, in so far as they are not so grounded, are grounded in the unintelligent, blind forces of nature. 67

24

But Plato holds that every relation presupposes sometbing in the nature of its terms as at least a necessary condition. Thus, in order to be able to have spatial relations, a thing must have extension. 64 But having extension, though a necessary condition for its having particular relations, is not the sufficient condition for its having them. Thus, though Socrates' being in a cell in Athens is determined by the fact that there is Athens, the cell, and the fleshand-bones Socrates, these facts are not sufficient to account for the fact that Socrates is in the cell in Athens. For the Athenian cell and Socrates could have existed and yet Socrates might have been in Megara or Boeotia, instead. The fact that Socrates is sitting in the Athenian cell cannot, therefore, be grounded merely in the Athenian cell and in the body of Socrates. The sufficient ground for his being there is these plus the more important fact of the decision of Socrates' rational self that it was best for him to stay there.6 5 Thus, some of the relations which are not grounded solely in the nature of 61 62 63

64 65

0 p. cit. 438b ff. Cf. above, p. 23. Phdr. 262a-b. Parm. 138a-b. Phd. 98b-99d.

4. Relations in the Realm of Forms Plato recognizes forms of relations, and relations between forms. 68 The latter are of three major kinds. There are relations (a) of blending, (b) of exclusion, and (c) of otherness. (a) A form blends or mixes (symmeignytai) 69 with certain other forms. Two forms are said to blend when they stand in such a relationship that their names can occur in a certain affirmative statement, such as "Motion exists." Plato holds that there are such relational forms as 'Equality,'70 'Greatness,' 'Smallness,' 71 and the like. On this view, the sides of the ideal Square would, I suppose, be said to 'blend' with the form of 'Equality' towards each other. Similarly, the ideal number Six would be said to blend with Greatness with reference to Four and with Smallness with reference to Twelve. (b) A form is said to exclude (anarmostein)72 another form when their names can occur in a certain type of true negative statement, such as "Motion does not rest," 73 or "Three is not even."74 Other examples of forms which exclude one another are Odd and Even,75 Three and Even, 76 Heat and Cold. 77 Such negative 66 Phil. 28d, 30c. 67 Tim. 48a et passim; Laws X. Cf. Aristotle, Metaphysics, I, ix. 990b16. Soph. 253c. Other metaphors used synonymously to denote this rela· tionship of blending are 'fit together' (synarmottein, 253a), to be 'consonant' (symphonein, 253b), to 'accept' (dechesthai, 253b), to 'combine' (koinonein 68 69

251d).

70 Phd. 74, 75; Parm. 131d. 71 Phd. lOla; Parm. 131d, 132b, 150.

72 Soph. 253a. Other metaphors used as synonyms of this are 'division' (diairesis, 253c) and 'disjunction' (diakrinesthai, Parm. 129e). 73 Cf. Cornford, Plato's Theory of Knowledge, p. 256. 74 Phd. 104c-e. 75 Phd. 102e ff. 76 Phd. 104c. 77 Phd. 103c-d.

26

THE CLASSICAL THEORY OF RELATIONS

statements express the fact that such forms are incompatible with one another. ( c) Statements of this type are to be distinguished from true negative statements such as "Motion is not Existence," which express the fact that the forms denoted by the words 'Motion' and 'Existence' are simply different from, or other than (thatera), 78 one another. Plato sometimes calls this the relation of not-being (me on). 79 'Motion,' for instance, has the relation of not-being to 'Existence' and 'Rest.' A form which has the relation of otherness or not-being (every form has it to every other form) to a certain other form may also have the relation of exclusion to that form. Motion has the relation of otherness to Rest, and also the relation of exclusion to Rest. Motion has the relation of otherness to Existence, but it does not have to Existence the relation of exclusion.so The number of relations of blending, exclusion, and otherness which a form has to other forms is vast, "In the case of every one of the forms,'' says Plato, "there is much that it is and an indefinite number of things it is not.'' 81 There is much that a form 'is' in the sense that it has a certain nature, distinct from all the relations it has, and also in the sense that it has relations of blending to a great number of forms. It 'is not' an indefinite number of things in the sense that it has relations of exclusion and otherness to an indefinite number of other forms. The relations between forms are eternal, as are their terms. Motion is eternally related, by the relations of blending and otherness, to Existence and, by the relation of exclusion, to Rest. The relations of a form to other forms are entailed by its own intrinsic nature and that of the forms to which it is related. Any form which does not have them must necessarily be other than that form. 82 Plato's view here seems to be the same as Whitehead's. Whitehead speaks of 'eternal objects' instead of 'forms.' Every 'eternal object' is 'determinately' related to all other 'eternal ob78 79 80 81 82

Soph. 254. Soph. 256. Cf. Cornford, op. cit., pp. 225-226. Soph. 256e. Cf. G. E. Moore, Philosophical Studies, p. 286.

Plato

27

jects.' 83 It is related to them "systematically and by the necessity of · its nature."8 4 The forms, being so related, constitute an eternal, static, perfect order of entities. Now the fact that each form has an infinite or indefinite number of relations, in which it stands determinately, makes it necessary, in order to know the full nature of a form, to know the whole realm of forms. Plato remarks that in order to learn "to the utmost possible extent" ( eis to dynaton) the truth of virtue and vice, "it is necessary to learn at the same time both what is false and what is true of the whole of being (tes holes ousias). 85 This view seems to imply the so-called 'coherence theory of truth.' In order to know one form or eternal object, it seems that we have to know the whole realm of forms. The coherence theory of truth thus means scepticism. But Plato is not a sceptic. He asserts that knowledge or intelligence is a fact. 86 Whitehead thinks we may escape from this difficulty by saying ( 1) that the relations of any form or universal 'A,' considered as constitutive of A, merely involve other universals as bare relata, without reference to their individual essences; and (2) that the divisibility of the general relation of A into a multiplicity of finite relations of A stands in the essence of that universal. 87 Plato's own answer seems to be that though a form has an infinite or indefinite number of relations to other forms, only a finite number of these relations are constitutive of its essence; the rest belong to it only as propria or necessary accidents. To 'know' a form, it suffices that one know its intrinsic essence and those of its relations which are constitutive of its relational essence. It is not necessary to know its other relations. 5. Psychical Relations Under this heading I do not propose to discuss so much relations between psyches, as relations of the human psyche or soul to what is not-psychical.

83 Science and the Modern World, p. 223. 84 85

86 87

Ibid., p. 224. Cf. G. Santayana, Realms of Being, p. 5. Epist. VII. 344b. Cf. Meno Slc-d. Cf. esp. Soph. 248e-249. Op. cit., pp. 230-231.

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THE CLASSICAL THEORY OF RELATIONS

Plato

On the question of the relations amongst psyches what I think is important to note is the following. There is, for Plato, a plurality of psyches, which plurality is ultimate and everlasting. 8 8 There are relations of dependence of the inferior to the superior psyches: of human and infra-human psyches to the Supreme God as well as to the subordinate gods, and of the subordinate gods to the Supreme God. 89 The Supreme God stands, either immediately or mediately, in the relation of 'generator of' ( demiourgos) to all other psyches; while they stand to Him in the relation of 'generated by' (gegonos).90 The Supreme God also stands, either immediately or mediately, in the relation of 'sovereign of' ( basileus) to all psyches, an is discussing relations, he is not, in general, discussing predij}ates. A predicate is a universal, such as a genus, species, etc. What he is generally discussing in such cases is particular relations, and these are not predicates. A particular characteristic, whether a quantity, quality, or relation, is never 109 "Types of Unity According to Plato and Aristotle," Philosophy and Phenomenological Research, Vol. VI, No. 4, p. 537. 110 Ibid.

Aristotle

65

predicated of a subject,111 These are, for him, attributes. (b) Now amop.gstattributes he distinguishes those which are intrinsic (siidi as quantity and quality) and relations. He points out, like Plato, that relation is a peeuliar kind of attribute, one which a thing has towards another. ( c) I do not see what, Aristotle can be speaking about, when he seems to be speaking about relations, except about relations. What are these strange entities, which seem to answer the description of relation, but allegedly do not? They are not substances, they are not qualities, they are not some other kind of intrinsic entity. What, then, are they?

111

Cf. Cal. II. la25·,0.

"We may say then, I believe, that if the Thomistic metaphysics may be called Aristotelian in the sense that it is to Aristotle they are directly indebted for their most fundamental formulae, it is a misapprehension to regard them as Aristotelian in the sense that they are in principle anti-Platonic." A. E. Taylor

LIST OF ABBREVIATIONS OF SOME OF THE WORKS REFERRED TO Ctmus Philos.

De Pot.

Cursus Philosophicm Thomisticus, Tomus Primus, Logica, by Joannes a S. Thoma. De Potentia, by St. Thomas Aquinas.

CHAPTER

III

THOMISM Elementa

Elementa Philosophiae AristotelicoT homisticae, V olumina I et II, by Iosephus Gredt.

In Ethica.

In X Libros Ethicorum Aristotelis Commentarium, by St. Thomas Aquinas.

In Met.

In XII Libros Metaphysicorum Aristotelis Commentarium, by St. Thomas Aquinas.

1.

Introductory Remarks

In the case of Plato and Aristotle I gave a sketchy account of their general conception of being. I do not think such an account is necessary in the case of Thomism. It is sufficient to remark that its general conception of reality is essentially that of Aristotle. Similarly, I do not think it is necessary to give an account of its view of the main types of entity, beyond the following. Thomism accepts Aristotle's list of categories as given in the latter's early works - the Categories and the Topics. That is, it regards the mllin types of entity, or the categories (praedicamenta) as ten: (a) 'substance' ( substantia), (b) 'quantity' (quantum), ( c) 'quality' ( quale), (d) 'relation' (ad aliquid, relatio), (e) 'where' (ubi), (f) 'when' (quando), (g) 'action' (agere), (h) 'passion' (pati), (i) 'position' (situs), and (j) 'possession' ( habere). It repeats Aristotle's phrase for relation, to pros ti, with the Latin equivalent ad aliquid, which it uses interchangeably with relatio. Its definition of relation follows closely that of the Greeks. A relation, in the broadest sense, is "the order of one thing to another." 1

Analysis of the Relational Situation The Thomistic analysis of the relational situation is very similar to that of the Greeks. Thomism distinguishes the same elements in the relational situation as they. Its distinctions are more clearly and explicitly made, and it has technical terms to refer to nearly all the elements it distinguishes. Thus it speaks of (a) the 'referent' as the subiectum, (b) the 'relatum' as the terminus, (c) the 'ground' 2.

1 "Relatio latissime sumpta est ordo unius ad aliud" (Elementa, Vol. I, sect. 190; Cf. Cursus Pbilos., Vol. 1, qu. XVII, art. I).

68

69

70

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THE CLASSICAL THEORY OF RELATIONS

as the fundamentum, ( d) the 'relation' itself as the ad aliquid or relatio. Further, it speaks of ( e) the 'converse' as the relation which 'answers back' (respondet). 2 It distinguishes these in the typical relational situation. In the case of certain relations, which it terms 'relations so-called' ( relationes secttndum dici seu transcendentales), i.e. entities which are not really relations but are called relations because they bear a certain analogy to relations in the strict sense (relationes secundum esse), it holds that a relation may sometimes exist even though it has no relatum. It holds also that a certain class of relations which it calls 'logical' ( rationis) do not have a ground. (a, b) Thomism holds that a relation must have terms. It does not believe in relations which exist apart from any terms. Even those which are 'relations so-called' must have at least one term, the referent. Other relations, i.e. relations in the proper sense, whether logical or extra-logical (or extra-mental), must have at least two terms. I shall not discuss here its view that in the case of relations which are so called only by analogy the relation may exist even if only the referent exists. I shall do this when I come to the systematic discussion of this class of relations. Its view about relations in the strict sense, that they must have at least two terms, raises at once the question about identity. Identity is commonly supposed to be a relation between a term and itself; in other words, it is supposed to involve only one term. The Thomistic conception of identity, which seems to be derived from one of the senses of identity which we found in Aristotle, is that identity is a 'logical' or 'mental' relation ( relatio rationis). The mind forms an image of a thing, and then causes this image to merge with the thing.a Does Thomism recognize the existence of relations that have more than two terms? It does not discuss relations which logically require more than two terms, but it does discuss relations, such as fatherhood, which do not logically require more than two terms, but which may in fact have more than two. It explicitly asserts that 2 8

Elementa, VoL I, sect. 190; Vol. II, sect. 741.1. Cf. H. Meyer, The Philosophy of St. Thomas Aquinas, p. 116.

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a relation may be terminatively multiplex, i.e. that a relation may have many relata. It believes, in current terminology, in 'one-many' relations. One cube, we are told, is related by one equality to all cubes equal to itself. Similarly, a father is by one paternity referred to all his sons.4 But it does not assert that a relation may be referentially multiplex or 'many-one,' i.e. that a relation may inhere in many referents. As regards the nature of the terms of a relation, Thomism asserts that in the case of 'logical' relations any kind of a logical entity may serve as a term. In the case of other relations, it holds that the terms have to be substances.5 By substances must be understood the 'things' of common sense, such as particular men, cats and tables, and also minds. Yet some of the examples of extra-mental relations given by 1'homists have as terms entities which they do not consider as substances. Thus one wall is said by Gredt to have the relation of similarity to another wall and of dissimilarity-to still another wall.6 Now apart from their own examples, the fat:t'cannot be denied that such things as walls, or the eyes of an individual, though not recognized by Thomists as substances but only as parts of substances, are nonetheless related by such relations as difference (numerical) and similarity. They would not disagree with Plato that there is such a thing as self-mastery, which is a relation holding between different parts or powers of the psyche. The Thomist here would, I suppose, say that we have in such instances relations between 'incomplete substances.' Accoi-dingly, I presume, the relations themselves must be called 'incomplete.' They are incomplete in a derivative sense, in so far as their terms are incomplete substances. Thomism speaks of terms having relations as relata or relativa, i.e. as relative terms. If the terms are mutually related, it calls them correlativa or correlatives.7 An example of correlative terms are 'father' and 'son.' As an Aristotelian, a Thomist may speak of the 'matter' and 4

Elementa, VoL II, sect. 744; Cursus Philos., VoL I, qu. XVII, art. I,

IV, VL 5 6 T

Cf. Elementa, VoL II, sect. 741. Ibid., Vol. I, sect. 192.L Ibid., Vol. I, sect. 190.

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'form' of a relative term. The 'matter' of a relative term is the relative term itself, in abstraction from the relation. The 'form' of the relative term is the relation. Thus father and son are concrete correlative terms. Father results from man as the matter and fatherhood as the form. Son results from man as the matter and sonship as the form. 8 The following are given as properties of relative terms: ( 1) A relative term enters into the explanation of the correlative. You cannot, for instance, explain what a father is, without mentioning the fact he is the father of a son (or daughter). And mutatis mutandis for son. o (2) Relative terms are at the same time by nature formally, though not necessarily materially. That is, they are at the same time by nature qua correlatives. Materially, one may be prior to the other, and one depend upon the other. Thus fatherhood and sonship commence entirely at the same time; nevertheless, the man who acquires the relation of fatherhood is prior, materially, to the son, and the son is dependent (causally) upon him. 10 Thomism here does not follow Aristotle, who believes that it is not true of all correlatives that they come into being and pass out of being at the same time. Aristotle's belief arose, as we saw, from his failure to make the distinction, which Thomism makes, between the being of correlatives qua correlatives, and their being simply. ( 3) Relative terms are at the same time cognition. 11 I do not think this is intended to be taken as meaning that we must directly apprehend both correlatives if we are to cognize one of them as relative. When I am told that someone is a father, it is not necessary for me to see his son ( s) or daughter( s). It is sufficient that they are represented by me as bare relata. ( c) Thomism has much to say about the ground of relations. As I have indicated, it holds that all relations, with the exception of 'logical' relations, are grounded in the nature of their terms. The 8 "Ex relatione tamquam forma et subiecto tamquam matevia coalescit concretum accidenta!e, ut pater ex homine et patemitate, filius ex homine et filiatione" (Elementa, Vol. I, sect. 190). D Ibid., sect. 192.3. 10 Ibid., sect. 192.4. 11 Ibid., sect. 192.5.

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existence and nature of non-logical relations is determined by their ground. "Ground" (fundamentum) has, for Thomism, two senses. There is the remote ground and the proximate ground of the relation.12 The terms are the remote ground of the relation, while the characteristic with respect to which things are said to be related is the proximate ground. The terms are called the remote grou.nd because the characteristic (or characteristics) with respect to which two things are said to be related, i.e. the proximate ground, is something which does not exist per se, but depends for its being upon inherence in a term. Henceforth, when I speak of the 'ground' of the relation, it is the proximate ground that I shall mean. Thomism sometimes speaks as if it considered the ground of the relation as something in the referent only; as if it regarded the relatum as a bare relatum.13 To think so is, I believe, an error. The ground of the relation consists of at least two characteristics ( i? the case of two-term relations) which may be either only numerically different, or different both numerically and conceptually; and these characteristics are present distributively in the referent and the relatum. In other words, the relatum also must have a certain characteristic in virtue of which the relation from the referent results. My point may be made clear by an example. Take the relation of similarity of two walls. Wall A is similar to wall B with respect to color. The ground of the relation of similarity which holds from A to B is, let us say, the color white. It is clear that the relation of similarity from A to B holds not simply because A is white, but also because B is white, or because B has a color similar to white. If B had been red, instead of white, the relation from A to B would not have been a relation of similarity but of dissimilarity. Thus it makes all the difference to the relation which holds from the referent to the relatum whether a certain characteristic is or is not present in the relatum. The same is true of the converse relation. Hence, the 12 Cursus Philos., Vol. I, qu. XVII, art. III. . 13 Elementa, Vol. I, sect. 191.2: "Ita fundamei;to reah, supe.r quod funda-

tur relatio causae ( creatae) ad effectum, quod est act~o, respondet in effectt~. fundamentum reale passionis, super quod fundatur relat10 effectus ad causam. Cf. Elementa, Vol. II, sect. 742, Prob. II p. and sect. 743.2.

74

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Thomism

ground of relation must be sought not only in the referent, but also in the. relatum. We may say that the characteristic in the referent is a necessary, but not the sufficient, ground of the relation; that the characteristic in the relatum is the other necessary ground; and that the two constitute the sufficient proximate ground of the relation. This seems to be in fact the Thomist position, though it is not always clearly stated. We are told that the relatum "specifies the relation through the mode of extrinsic formal causality or through the mode of object.... " 14 When the ground is spoken of as being something in the referent, as though this were the sufficient ground of the relation, by ground must be meant the ground which specifies the relation through the mode of intrinsic formal causality. This analysis is, I think, adequate so far as such relations as similarity and dissimilarity are concerned. But what about certain other kinds of relation, such as those of mastership and slavery? Can we say that the sufficient ground of these relations consists in certain characteristics intrinsic in the terms? But external conditions, such as wealth and poverty, or war, etc. are necessary conditions for one man becoming a master and another a slave. What about spatial relations? That an extended thing must have spatial relations to other extended things needs no argument. But that an extended thing has at a certain moment certain relations and not others is not determined solely by some intrinsic characteristic of the thing in question and of the things to which it is spatially related, as we noted in discussing Plato. The relation is said to be caused or determined by the ground formally, not efficiently. The relation can be said to be the effect of efficient causality only indirectly, insofar as the ground is the effect of efficient causal processes. 1 5 That is, given two objects, they will not be related in a certain respect, unless they have certain characteristics which can constitute the ground of the relation. Now these characteristics they may acquire as effects of efficient causality. But the relations themselves that result from the possession of these characteristics by the objects are not directly effects of efficient

causality, but entltles which result formally from characteristics which are direct effects of efficient causality.

''Terminus ... specificat relationem per modum causae formalis extrinsecae seu per modum obiecti ...." (Elementa, Vol. I, sect. 192.5). 15 Elementa, Vol. II, sect. 743.2. 14

Against those, like Duns Scoti:is, who reduce relation to what I have been calling the ground of the relation, Thomism argues, rightly, that relation is an entity distinct from the ground. It adduces as an argument against the reductivist view the fact that the ground may remain a reality even when the relation itself ceases. Take the relation of fatherhood. When the son dies, the relation of fathethood ceases. But the ground of the relation of fatherhood, i.e. the determination left in the father by the generntive act does not cease to exist. Thus the ground is separable from the relation; and if separable, the two ate surely distinct. 16 This argument is sound, except for one point. It ignores the fact that a certain determination in the son is part of the ground of the relation of fatherhood, and that this necessarily perishes when the son dies. According to Aquinas, a relation may be grounded in quantity, quality, action and passion, ot some other category, except relation. One relation, we are told, never founds another. 17 The reasons given fot asserting that a relation can never be grnunded in the category of relation may be summed up as follows.: (1) Relation is an entity so weak ( debilis) that it requires for its support an entity that is 'more perfect 'than itself. Just as a relation cannot spring and endure without an absolute ground, by which it is sustained in being, so, a fortiori, it itself cannot serve as a support ( sustentaculum) of another relation. ( 2) Thought judges contradictoty the process ad infinitum in relations. But if one relation could found another relation, this would follow. Thus, one fatherhood would found a relation of similitude to another fatherhood, and of dissimilitude to sonship, or to any othet relation whatsoever. On the other hand, this dissimilitude would found a telation of similitude with anothet dissimilitude, and the similitude again would found Elementa, Vol. II, sect. 742, Prob. II p. ,, "Unam vero relationem fundari in alia omnino negat D. Thomas .... (Cursus Philos., Vol. I, qu. XVII, art. I.; Cf. Elementa, Vol. II, sect. 744, Schol. b). 16 17

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THE CLASSICAL THEORY OF RELATIONS

Thomism

a relation of dissimilitude with another kind of relation; and so on.18 The statement that one relation never grounds another relation is meant to apply only to relations strictly so called, and of these only to those which are extra-mental. Such relations are called categorial (praedicamentalia). Thomism holds that relations which are called such only by analogy do found many relations.rn Thus, the generative potency (potentia generativa) is the ground of two relations from the parent to the offspring: the relations of measure and of causality. 20 "Ground," here, should be taken to mean the partial ground: the ground insofar as it is something in the referent. Thomism also holds that a logical relation may be grounded in another logical relation. According to Thomism, universals are logical relations; 21 and there are for it relations between universals. Let us consider the position of Thomism that in the case of categorial relations one relation never founds another. One of its reasons is, as we have seen, that a relation is an entity so weak that it requires for its support an entity that is more perfect than itself. Now it is not clear to me just what is meant by 'more perfect.' If it means, as I take it to mean, logically prior, then the following criticism may be advanced. Let us suppose that one relation may have as its ground (so far as the referent is concerned) another relation, and that this other relation founds another relation, and so on. Then, granted that a certain relation must have for its ground an entity that is more perfect than (i.e. logically prior to) itself, there is no reason to suppose that this condition is not fulfilled in this series. If the relations grow progressively 'weaker' in being (in the sense that the remoter conclusions of certain premises may be said to be weaker than the more proximate ones) as we get more and more remote from the terms which have intrinsic characteristics and ground the first relationship in the series, conversely, they grow progressively 'more perfect' or 'stronger' as we get nearer and

nearer the terms in question. Thus, even in an infinite series, there would be entities with sufficient perfection or strength to function as terms. It is important to note, however, that though relations are grounded in other relations in such a series, these presuppose ultimately terms having intrinsic characteristics, in which the first relationship of the series is grounded. 22 And this, I think, is an element of truth contained in the Thomistic contention. As to the process of ad infinitum in relations being selfcontradictory, I must say this is not obvious to me. There are other processes ad infinitum - in numbers, for instance-, but we do not judge these to be self-contradictory. Though this criticism is not anticipated in Thomistic literature, I suppose the answer would be that processes ad infinitum in numbers are mental, whereas the question is about extra-mental processes ad infinitum. Thomism may be right as regards this point; though I am not sure that it is right. But this still leaves unanswered the question whether the process ad infinitum in extra-mental relations is really self-contradictory. There are other objections that might be raised against the Thomistic thesis. One of them is anticipated by Thomism. It is pointed out that we do speak of, and consider, some relations as being similar to other relations and dissimilar to others; and that 'similar to' and 'dissimilar to' are relations. 2 3 This fact is prima facie incompatible with the Thomistic thesis that one extra-mental relation never founds another extra-mental relation. The answer given to this difficulty is that in such cases the relation which is said to be related to other relations is not related to other relations by means of mediating relations, but is related to them immediately, through itself. It is "referred ... quasi transcendentally to any other things whatsoever, to which it is naturally referable.'' 24 Thus, two fatherhoods, insofar as they are 'similar,' are mutually referred to each other quasi transcendentally, and not by a new relation which is superadded to their being (entitas). 2 5 Referred to here must be taken as synonymous with related.

18 Elementa, Vol. II, sect. 744, Schol. Cf. Cursus Philos., Vol. I, qu. XVII, art. III. 19 "Plerumque relationes praedicamentales fundantur in transcendentalibus" (Elementa, Vol. I, sect. 191.1). 20 Ibid. 2 1 Op. cit., sect. 117. 22 Fora similar view cf. J. N. Findlay, Meinong's Theory of Objects, p. 72.

23

Elementa, Vol. II, sect. 744Jb.

77

24 "... Refertur ... quas,i transcendentaliter ad quaecumque alia, ad quae naturaliter referibilis est" (Elementa, Vol. II, sect. 744.b). 25 Ibid.

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Hence "referred quasi transcendentally" must mean "related quasi transcendentally." The question now is what "quasi transcendentally" means. So far as I can see, it is a repetition of the phrase "refers (relates) itself immediately, through itself." One fatherhood relates not only its referent (father) to its rel atum (son), but also itself to other similar relations - to other fatherhoods - as relata. This sounds much more plausible than the other arguments advanced for the thesis in question. And if right, it does away with the great plethora of relations, which we should otherwise have to admit as existing, and which minds accustomed to common-sense ways of looking at things would find to so clutter the universe as to give them sensations of being choked.

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this mental or logical relation is, or why there must be such a relation in every case where there is a non-mutual relation. Does this relation consist in the fact that we think there is a relation holdin()' 0 from the thing to the mind? Supposing this is what is meant, is it true that we always do this extra thinking? I must confess that I am not conscious of doing this every time I cognize something. But I shall say more on this problem when I come to the systematic discussion of non-mutual relations.

But though this argument appears to be sound so far as certain situations are concerned, it does not appear to explain other cases where one relation seems to found another. Take the case where I cognize a certain relation. Now cognition is a relation, which has either the mind or sense as its referent and partial ground. This relation is extra-mental, in the sense that it does not depend for its existence upon being an object of the mind. The relatum of this relation is, as we said, a relation. Now if, as I have urged, and as Thomism itself seems to hold, the sufficient condition or ground of a relation is not only something in the referent but also something in the relatum; and since here the relatum is a relation, we have a case where a relation is grounded, though only partially, in a relation. ( e) Like the Greeks, though Thomism does not have a word for the converse of a relation, it does have the idea of the converse. It holds that every relation has a converse. This statement, however, needs qualification. Thomism accepts Aristotle's third genus of relations, which it terms 'non-mutual' ( non-mutua). It holds, like Aristotle, that there are certain relations, such as knowing, which do not have a converse that inheres in the thing known. But it holds - and in this it goes beyond what Aristotle explicitly says- that in such cases there is nevertheless a logical relation, or a relation of the mind, which functions as a converse. 26 It is not made clear what

Classification of Relations In classifying relations, Thomism proceeds along three modes of division: (a) 'analogous division' (divisio analoga), (b) 'accidental division' ( divisio accidentalis), and ( c) 'essential division' ( divisio essentialis). The analogous division of relations is the division of relations, taken in the broadest sense, into relations secundum esse, or relations which are truly relations, and relations secundum dici, or entities which are called relations only because they bear a certain analogy to the former, which are relations properly and strictly so called. The accidental division of relations is the division of extramental relations secundum esse from the point of view of certain conditions accidental to relations. It is the division of such relations into mutual and non-mutual, symmetrical and asymmetrical. The essential division of relations is the division of extra-mental relations secundum esse from the point of view of their ground. It is the division which we found sketched in Aristotle. I shall discuss each of these divisions in turn. (a) The analogous division of relations, as we said, consists in the division of relations into (i) relations secundum esse and (ii) relations secundum dici. (i) A relation secundum esse is defined as "an adventitious order, which consists in pure respect, or whose whole being is to hold itself towards another entity." 21 This is exactly Aristotle's definition of relation. An example of a relation secundum esse is fatherhood,

26 "Ex parte termini, si non respondet relatio realis, respondebit tameu rationis re!SJtio" (Elementa, Vol. I, 191.2).

2 7 "Ordo adventitius, qui in puro respectu consistit, seu cuius totum esse est ad aliud se habere, est relatio secundttm esse" (Elementa Vol. I, sect. 190).

3.

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which consists in pure respect, adventitious to a man. Relations secundum esse are divided, from the point of view of objectivity, into the 'real' (realia) or 'categorial' (praedicamentalia) and the 'logical' or 'mental' (logicae seu rationis). A real relation is one which has being in rerum natura, independently of the considerations of the mind. The relation of paternity is an example. A logical relation, on the other hand, is a relation which has being only as an object of the intellect.2 8 The relation of the predicate to the subject is an example.29 In the case of these relations, the name is used to denote the relation itself only, and not also the ground of the relation, as in the case of relations secundum dici. Although relations secundum dici are entities which have being in rerum natura, the term real is reserved by Aquinas for one of the two major classes of relations secundum esse. The reason for this is that relations secundum dici, as we have noted, are called relations only by analogy to relations secundum esse, and not because they are strictly relations. Thus a relation is called real for the twofold reason that it has being in rerum natura or extra-mentally, and that it is a relation in the strict sense. As regards real in the sense of extra-mentalness, it should be noted that Aquinas distinguishes sharply between 'real being' (ens reale) and 'logical being' (ens rationis). Logical being should not be taken to mean simply being characterized by mentalness. A thing, we are told, may be said to be mental or to 'to be in the intellect' in three different ways: subjectively, effectively, or objectively. An entity is said to be in the intellect 'subjectively' simply because it has being in a rational subject. In this sense, an act of cognition, or a desire, are just as mental as a logical relation. But cognitions and desires are not considered to be logical relations. An entity is said to be in the intellect 'effectively' in the sense that it is an effect of the intellect. Now intellection, which is relational, formal concepts, and logical relations are 'effectively' (as well as 'subjectively') in the intellect; but only the last are entia rationis. To be an ens rationis an entity has to

be mental in the third sense, namely, 'objectively.' An entity is in the intellect 'objectively' if its whole being consists in being apprehended, in being an object of the intellect. Entia rationis are divided into two classes: those which have their proximate ground in the abstract natures (or formal concepts) which are their terms, and their remote ground in the individual natures - and hence are not arbitrary; and those which are not grounded in the nature of the terms, but are formed arbitrarily, according to our desire.3° This means that "any two concepts may be thought together and thus be logically related, whether they are really related or not." 31

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28 "Relationes rationis non sunt nisi in intellectu apprehendente, a quo habent esse objectivum" ( Cursus Philos., qu. XVII, art. I). 29 Elemenla, Vol. I, sect. 190.

The following relations are among those which are considered logical or mental: ( 1) The application of a predicable (which is a concept formed by our mind), i.e. of the genus, species, difference, proprium, or accident to a thing. Thus, every subject-predicate judgment is a relatio rationis. In such a relation we assert some particular kind of identity between the subject and the predicate. ( 2) The relations between two or more formal concepts (or abstract natures). For instance, the mind forms the concept of animal and the concept of man, and then it sees a certain relation between these two concepts. In this case the nature of animal is seen to be related to the nature of man as genus to species.3 2 ( 3) Self-identity. Self-identity is a relation which consists in the conception of one thfog by two concepts, and the merging of these into one. 33 ( 4) The comparison of being with non-being. In this comparison we employ two concepts, to one of which something real corresponds, whereas nothing corresponds to the other.3 4 ( 5) That relation in non-mutual relationships which has no Elementa, Vol. I, sect. 110. J. Wild, The Science of Philosophy, Part I, p. 41. 32 H. Renard, The Philosophy of Being, p. 114. Cf. Aquinas, In IV Met., lect. 574: "Ens autem rationis dicitur proprie de illis intentionibus, quas ratio adinvenit in rebus consideratis; sicut intentio generis, speciei et similium, quae quidem non inveniuntur fo rerum natura, sed considerationem rationis consequuntur. Et hujusmodi, scilicet ens rationis, est proprie subjectum logicae." 33 In V Met., 11.912. 34 H. Meyer, op. cit., p. 116. 30 31

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ground in the term to which it is applied by the mind. 35 ( 6) The relations between propositions, such as equivalence, opposition, etc., also are presumably logical relations. Here, as elsewhere, in its theory of relations Thomism has built on foundations laid by Plato and Aristotle. Plato, as we have seen, recognizes a realm of entities distinct from empirical things: the realm of forms. He also recognizes the existence of certain relations as holding between the forms, which are grounded in the nature of the forms. These relations have a mode of being different from that of empirical relations: they are themselves forms. The forms are neither mental nor physical. Aristotle accepts Plato's forms in a qualified way. He denies them an indepedendent status, placing them in the mind. The relations between them are regarded as operations of the mind. Aquinas adopts an intermediate position, holding that there are rtbsolute natures (or formal concepts) which are neither individual nor universal, but become universalized by the mind. That is, the mind takes some real aspect of a composite thing, distegards (but does not deny) its individual diffetences, and compates this abstraction with other individuals. The absolute nature, the absttaction, "becomes a univetsal simply in virtue of this relation which it is now seen to have to the whole class of similat individuals."3 6 Such a universal relation is held to exist only in the mind. Besides such relations, which ate to individual things, absolute natutes are also viewed as having cettain relations amongst themselves. The impottant difference here, between the Platonic position on the one hand, and the Atistotelian and Thomistic positions on the other, is that according to the fotmet univetsal telations or telations between forms ate not entities of the human mind - the mind simply discovers them, whereas accotding to the latter, the telations of the fotms or absolute natutes ate mental. Thomism asserts that such relations are not necessatily atbitrary. One class of such relations have a ground in the abstract natures. This position, nonetheless, is

clearly less 'realistic' than the Platonic. The important point of agteement is that in both positions thete is a place for arbitraty logical or mental telations, and that such relations ate sharply distinguished from telations which are not arbitraty. According to both positions, the mind may combine entities which do not belong togethet, and sepatate entities which do belong togethet. 37

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35 "Si . . . ex parte termini non habetur fundamentum reale respondens fundamento reali ex altera parte, terminus eo 'ipso, quod terminus est, fundamentum constituet relationis rationis" (Elementa, Vol. I, sect. 191.2). 36 ]. Wild, op. cit., pp. 136-137.

Let us now tum to categorial ot real telations. Thomism strongly opposes those who hold that all relations are logical. 38 There ate many relations, according to Thomism, which are extta-mental, real. A real relation is defined as "a real accident, whose whole being is to hold itself towards another."39 The definition asserts that this kind of telation is a 'real' entity, and thus distinguishes it from logical relations. It asserts also that this kind of relation is nothing but a relation, and thus distinguishes it from relation secundum dici, which is not merely a relation, but is an absolute entity in which a relation is included. It asserts, further, that this relation is an attribute (or 'accident'), which inheres 40 in the referent. Thomism advances here a conception of relation which we found in Plato and Aristotle. A categorial or real relation inheres in a subject (the referent) for its being, but its essence is to be towa~ds ( esse ad) something other than its subject, the relatum. Its being towards another is the essential peculiarity of this as of other relations, and is what distinguishes it from other categories. Agreeing with Aristotle, Thomism holds that the category of relation is the weakest or least real. 41 And it asserts that this is the · to be an ent1'ty of r easo n ·42 teason why many have th ought 1t Aristotle, it will be recalled, holds that some relations have contraries. Thomism holds that a relation never has a contrary. The 37 For Plato on this point, cf. especially what he says about judgment in the Theaetetus and in ·the Sophist. 38 Cursus Philos., qu. XVII, art. I. . 39 "Accidens reale, cuius totum esse est ad alrnd se hacbere" (Elementa, Vol. I, seot. 190; cf. Cursus Philos., qu. XVII, art. I, II). 40 Cursus Philos., qu. XVII, art. IV. . . . . ... 41 "Relatio praedicamentalis est acc1dens mm1mae entltatls (Elementa, Vol. I, sect. 190; cf. Cursus Philos., qu. XVII, art. II, IV). . 42 "Quia relatio est debilioris esse inter praed1camenta, ·1deo put~;erunt quidam earn esse ex secundis ·intellectibus ... Hoc autem esse non potest (De Pot., VII. 9).

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disagreement is partial. When Aristotle says that SQme relations have contraries, he means, as I have suggested, either that the ground of some relations has contrariety, or that two relations, such as equality and inequality, may be said, in a sense peculiar to relations, to be contraries. Thomism holds that per se a relation does not have a contrary, but may have one per accidens, by reason of its ground. Take the following example: A white wall has the relation of similarity to another white wall and at the same time of dissimilarity to a black wall. The relations of similarity and dissimilarity may be said to be contraries per accidens, because their grounds are contraries.43 I think it is all right to say this. But it seems to me that Thomism is not right in holding that this is the only valid sense in which we can say that two relations are contraries. I think that a certain relation may validly be said to be per se the contrary of another relation. Again, unlike Aristotle, Aquinas does not believe that a relation may admit of degrees. A relation, per se, he holds, does not admit of more or less, but only per accidens, by reason of the ground, which may admit of more or less. 44 It is interesting to compare St. Thomas with Bradley on this point. Bradley, though his general theory of relations is radically different from that of Aquinas, is in accord with him on this point. "Do relations differ in degree?" he asks. To this question, he says, we must answer "Yes" and "No." "If you mean the 'situation' - that is certainly capable of degree. If you mean the mere relation, abstracted from the situation, my answer is 'No.' " 4 5 He explains: whenever we speak of more or less, there is an underlying 'what,' of which we assert this more or less.... And ... if this 'what' is taken as the relation in the narrower sense (as abstracted from the situation), the answer is that it is everywhere incapable of degree. It is there, or not there - and not more or less of it there.... When I pass from one red to another, there may be no difference in respect of color. There are two cases and not two degrees of redness. When I pass from a pure to a dulled. or whitened red, I pass from more to less red; and the 'what' of which there are degrees, is the red which 43 Elementa, Vol. I, sect. 192.1. 44 45

Ibid., sect. 192.2. Collected Essays, pp. 674-675.

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underlies the process and the relation. 46 (ii) Let us now turn to relation secundum dici. The definition of relation secundum dici is "an order included in some absolute [or intrinsic] nature;"47 or, "A real intrinsic entity containing essentially an order to another." 48 In the case of such relations, the name is used to denote not only the relation itself, but also the quality, or whatever it is, in which the relation is grounded. A relation secundum dici is also called 'transcendental' ( transcedentalis), because it is a real entity (ens realis) which is not found only in one category, but pervades or transcends all the categories. Thus, in the category of 'substance,' matter and form are relations secundum dici; in the category of 'quality,' potency and act are relations secundum dici; and so on. Transcendental relations are distinguished sharply from relations secundmn esse, because while the latter are nothing but relations, the former have a dual aspect, being not only relations, but having also an intrinsic nature. 49 Let us consider some examples. Matter and immanent or material form are said to be transcendentally related to each other. The relation from the matter to the form is said not to be distinct from the matter. And the relation from the form to the matter is said not to be distinct from the form. The relation from the matter to the form is said to be the matter; and the relation from the form to the 51 matter is said to be the form. 5 0 Potency and are similarly related. Potency and act are said to be two principles which are mutually dependent, so related to .each oth~r that .there is a mutual exigency for each other; and this very ex1ge.ncy is the root and cause of all the activities of nature. We call this mutual need, 46

Ibid., pp. 675-676.

47 "Ordo inclusus in aliqua essentia absoluta" (Elementa, Vol. I., sect.

190; cf. Cursus Philos., qu. XVII, art: II). . . . . ,, 48 "Ens absolutum reale contmens essentiahter ordmem ad almd (Elementct, Vol. I, sect. 191.1 ) . 49 Cf. Cursus Philos., qu. XVII, art. I: "Relationes secundum did habent esse absolutum, et non totum sunt ad aliud." 50 Elementa, Vol. I, sect. 190. Cf. H. Renard, The Philosophy of Being, p. 251;]. Wild, The Science of Philosophy, Part I, p. 40. 51 Elementa, Vol. I, sect. 190.

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this relationship by which act and potency are referred to each other by their very entity, ~ transcendental relation.5 2 This relationship is distinct from neither act nor potency, but embraces both. The act and the potency are called the relata - that is, the related principles of being. The transcendental relation itself is the relata as ordered to each other. 53 Relations secundum dici, or transcendental relations, we are told, can exist even though there is no relatum. And this is another respect in which such relations differ from relations secundum esse. The latter can never exist without a relatum. An example of a transcendental relation which can exist even without a relatum is the human psyche. The human psyche, "even after the separation from the body in death, retains its exigency for, or its order ( habitudo) to, the body."54 Another example is matter, "which even when united with a substantial form still retains its desire, its hunger for all other possible material forms." 55 Still another example is potency. "Potency is transcendentally referred to its object, whether this exists or does not exist." 56 Thus, the generative potency is transcendentally related. to the offspring to be generated; and the transcendental rela· tion exists even when there is no offspring.57 Now it seems at first glance that the notion of a transcendental relation, as expounded by interpreters of Aquinas, is not self-consis· tent. We are told, on the one hand, that a transcendental relation is an entity which has two aspects: an intrinsic aspect and a relational aspect. It is said to be an 'order,' though not merely an order, i.e. a relation, but also an 'intrinsic entity,' which includes this order. On the other hand, we seem to be told that these two distinguish· able aspects are really indistinguishable, as when we are told that the relation from the matter to the form is the matter. But I think the contradiction between these two statements is only apparent. I submit that the statement: "The relation from the matter to the form 52 53 54

55 56 57

H. Renard, op. cit., p. 27. Ibid., p. 250. Ibid., p. 252. Ibid. Elementa, Vol. I, sect. 191.l. Ibid.

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is the matter" means simply that the relation in question is constitutive of the very essence of matter; that it is part of what is de 11oted by the word 'matter;' but not that it is constitutive of the whole essence of matter. But if there is such a duality of aspect, if the relational essence is distinguishable from the intrinsic essence of those entities which are called transcendental relations, why cannot we term the relational essence a relation? One reason is, I think, the purely linguistic one that we do not have a word for it. The word matter, for instance, denotes a whole which is constituted of an intrinsic essence and a relational essence. Another reason is that such relations can exist even when there is no relatum: something which is not true of what are ordinarily considered to be relations. Is the Thomistic view tenable, that such relations can exist even when they have no terms? It seems to me that it is, if we qualify the statement that such relations can exist without actual relata, though only because in such cases they are terminated by possible relata. The view, as thus qualified, has a parallel in Whitehead. An 'eternal object,' according to Whitehead, cannot be divorced from its reference to other eternal objects and from its reference to actuality generally. This principle, he says, is expressed by the statement that each eternal object has a 'relational essence.' Thus, in the essence of an eternal object, A, there stands a determinateness as to the relationships of A to other eternal objects, and an indeterminate· ness as to the relationships of A to actual occasions. Putting it differently, A stands in determinate relations to other eternal objects, while as regards actual occasions there stands in the essence of ~ a patience for relations to them.5 8 Now clearly, the absol~te entltl~s of Thomism (matter and form, potency and act, etc.) which are said to be transcendentally related cannot be identified with Whitehead's 'eternal objects.' The latter, for Thomism, are entities of reason, while transcendental relations are real entities: two radically different modes of being. But apart from this, there is great similarity. An eternal object, according to Whitehead, has determinate relations to other eternal objects; a transcendental relation, according to Thom58

Science and the Modern World, p. 223.

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ism, may found determinate, categorial relations to other actual entities. In the essence of an eternal object, according to Whitehead, there stands a patience for relations to actual occasions; while according to Thomism, the entity which is said to be a transcendental relation is transcendentally referred to either actual or possible things, or to both. Again, according to Whitehead, an eternal object has both an intrinsic and a relational essence; and the same is true of a transcendental relation. What Thomism says about transcendental relations is reminiscent also of some things Plato and Aristotle say about psychical events. Plato, as we have seen, holds that words such as 'thirst,' which are used to denote something psychical, do not denote something simple, but denote at once a certain quality in the psyche and a certain relation holding from this quality to something else. What is denoted by such a word cannot, however, be called a transcendental relation, because the relation in such cases always has an actual relatum, whereas this is not true of transcendental relations. But Plato considers certain other entities, namely active and passive potencies, as relations. These do satisfy the conditions of a .transcendental relation. And Thomism includes them amongst transcendental relations.

'mutual' ( mutua) and (ii) the 'non-mutual' ( non-mutua), and of mutual relations into (1) the 'symmetrical' (aequiparantiae) and (2) the 'asymmetrical' (disquiparantiae). 60 ( i) A mutual relation is defined as a relation "to which, from the part of the relatum, there answers back (respondet) another real relation."61 In other words, a mutual relation is one which has a real converse. An example of a mutual relation is that of fatherhood. To fatherhood, on the side of the referent, there 'answers back' sonship, on the side of the relatum. The qualification that the converse must be a 'real' relation is necessary to differentiate mutual from non-mutual relations. The converse of a non-mutual relation is not a 'real' but a 'logical' or mental relation. In a broader sense, every categorial relation is mutual; for, it is held, if there is not a real converse, there is a logical one, in the case of every categorial relation. 62 A mutual relation is said to be grounded in both the referent and the relatum. Thus, the relation of causality is grounded in action in the referent and passion in the relatum. 63 ( 1) Mutual relations are divided, as we have noted, into those which are symmetrical and those which are asymmetrical. A symmetrical relation is a relation such that, when it holds from the referent to the relatum, a relation of the same nature or denomination ( eiusdem rationis seu denominationis) holds from the relatum to the referent. 64 Similarity and equality are examples. If A is 'similar to' B, B is 'similar to' A; and if R is 'equal to' S, S is 'equal to' R.

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Aristotle, too, it will be recalled, believes that words used to denote habits and dispositions denote both a quality and a relation. Such entities seem to have also the second characteristic of a transcendental relation, that of being capable of existing without an actual relatum. Further, Thomism takes from Aristotle his view of the relationship between matter and form in general, and between the psyche and the body in particular. (b) The remaining two divisions of relation, the accidental and the essential, pertain exclusively to categorial or real relations. I shall discuss them in turn. The accidental division of relation is the classification of real relations" from the point of vfew of certain conditions accidental to them." 5 9 It consists of the division of real relations into (i) the 59

" ...

XVII, art. III) .

Penes conditiones accidentales relationes" ( Cursus Philos., qu.

The relation and its converse are denoted, in the case of such relations, by the same word, as can be seen in the examples just given. Symmetrical relations are grounded in quantity, quality, or substantial form. 60

Ibid. and Elementa, Vol. I, sect. 191.2. Cursus Ph!los., qu. ~V~I, art. II~: mutua est, qttando ex parte utriusque extremt datur ad mvtcem relatto ordinis, seu entitatis ." Cf. Elementa, Vol. I, sect. 191.2. I bid., sect. 191.2. Cttrsus Philos. 1 qu. XVII, art. III. ,

61 Elen:enta, Vol. I, sect. 191.2. "Relatio ej11sdem

62 63 64

q.

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(2) A relation is asymmetrical if it is such that, when it holds from the referent to the relatum, a relation of a different nature or denomination holds from the relatum to the referent.65 The relations of father to son and of master to slave are examples.66 If A is the 'father of' B, B is the 'son of' A; and if R is the 'master of' S, S is the 'slave of' R. In the case of such relations, just as the nature of the relation and its converse is different, so are their names, as is evident in the examples that have been cited. Asymmetrical relations are founded on action and passion, and on quantity. (ii) A non-mutual relation is defined as a relation to which, from the side of the relatum, there does not answer back another real relation, but only a relation of reason. 67 Thomism's non-mutual relations correspond to Aristotle's third genus of relations, whereas its mutual relations correspond to his first two genera. Non-mutual relations are relations of measure and measurable. An example of a non-mutual relation is that of the creature to God. Another example is the relation of knowledge to its object.Gs The creature is related to God by a real relation, whereas God is related to the creature only by a logical relation. Similarly, the intellect is related to the object it knows by a real relation; but the object known is related to the intellect only by a mental relation. Why Thomism asserts the existence of such relations, apart from the fact that it finds them in the Stagirite, is not, at first glance clear. We are told that the relation from the object known to the intellect is only an ens rationis. The reason given for the view that this relation is only logical, not real, is that the relation "posits something in the intellect but nothing truly in the object."69 But this does not seem right. It is plain that the object must have some kind of 65

Ibid.

66 Ibid. 67 "Relatio non mutua est quando tantum in uno extrema est 1·elatio vera et proprid' ( Cursus Philos., qu. XVII, art. III). 68 Ibid. 69 "Ponit aliquid ·in intellectu, nihil vero in obiecto" (Elementa, Vol. I, sect. 191.2).

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reality and character, since knowledge is always of something. This, of course, Thomism does not deny. But then why does it say that the cognitive relation posits nothing in the object known? Since both the intellect and the object arc admittedly real, in what other sense can it be maintained that 'something' is posited in the intellect but not in the object? What is this 'something?' Perhaps it is some change, for we are told that "the object known is not changed."70 The question now arises, what kind of change is involved in the intellect, which is not involved in the object known? We are not told. But it seems that the only change posited in the intellect which is not posited in the object is an intrinsic change in the intellect, that is, a qualitative change which is the intrinsic formal cause or ground of the relation from the intellect to the object known; while there is no intrinsic change involved in the object qua known. But this change in the intellect, though a necessary condition for the occurrence of the relation of knowledge from the intellect to the object known, is not the sufficient condition for its occurrence. Besides this change in the intellect, there must be something extrinsic, the relatum, through which the cognitive relation becomes measured in its truth. The nature of the relatum, of the object known, is here the extrinsic formal cause or ground of the cognitive relation. Thus, though it is true that the cognitive relation does not posit any intrinsic change in the object, it posits the nature of the object. So far, I see nothing to set the cognitive relation apart from other categorial relations, specifically from those called mutual, insofar as its ground is concerned. It is grounded, like a mutual relation, both in the referent and in the relatum. But then why is it held that the converse of the cognitive relation is not a real relation, but only a logical one? Perhaps it is assumed that the converse, to be real, presupposes some intrinsic change in the relatum as its ground. But since knowing as such produces no intrinsic change in the object, in the relatum, there cannot be a real relation from the object to the intellect. But granting that there is no change in the object, I do not see that it necessarily follows that the object cannot therefore be really related to the intellect. If a new house, B, is built, an old house, A, acquires the relation of similarity (or dissimilarity) to B; but A does not 70 "Eo quod scitur, non mutatur" (Elementa, Vol. I, sect. 191.2).

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have to suffer any intdnsic change before it can enter into this relation to B. Hence, if the relation from the object known to the intellect that knows it is to be regarded as not real but only logical, there must be some other reason than that the knower undergoes some intdnsic change while the object known undergoes none. What is this reason? It is not given. And if we can find none, we may assume, until a good reason is found for believing otherwise, that the cognitive relation is mutual. It seems to me that one strnng reason behind the Thomistic insistence that the relation from the object known to the intellect is not real, but only an ens rationis, is the desfre to avoid subjectivism in epistemology. The assumption appears to be that unless we take this stand, we are committed to subjectivism or 'idealism.' For if the relation from the object to the knower is real, then we do not grnsp the object as it is in itself, but as it is for us: we grnsp it as altered by being known. Though the object known, it may be said, by vfrtue of the fact that it is being known, is not altered at all intdnsically, it is altered relationally, by having acqufred the relation of being known. This relation, although it may be held to be accidental, is nevertheless a real, extm-mental charnctedstic. Now the 'idealist' holds that an object, in being known, is changed by our cognition of it. But he does not hold that the relation is accidental: for him all relations are essential to their terms, or 'internal.' When a philosopher asserts that the object known is related to the knower by a real relation, he is not necessarily taking the standpoint of idealism. In opposition to the idealist, he may hold that this relation is not essential to the thing known, is not constitutive of its essence, but is accidental. He may say that when we know a thing, we know its essence, not its accidents; that in knowledge we abstract the essence from its accidents. This, I have suggested, is the position of Plato. Thus, so far as realistic epistemology is concerned, the admission of a real relation as holding from the object known to the knower does not necessarily imply an acceptance of subjectivism. Another example of a non-mutual relation is perceiving.n The 71

Cursus Philos., qu. XVII, art. VII.

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reasons advanced here for regarding the relation of 'being perceived' as an ens rationis are the same as those advanced for regarding the converse of the relation of rational cognition as a logical relation. Hence, similar criticisms could be offered. An additional criticism that might be advanced here, but which I would not advance, is the following. Since the referent of perceiving is psychophysical in nature, one may argue that according to physics and psychology we do affect, however slightly, the objects which we perceive. My reply to this is that the question is not about such action on the part of the perceiver, but whether the sheer awareness of the object by the perceiver affects the object perceived. Thus, the criticism that really applies here is the criticism that I have advanced in connection with rational cognition. The relation of desire to the object desired is given as another example of a non-mutual relation. 72 Thomism is here following Aristotle, when the latter says that God is an Immovable Mover, who is the ultimate end of all aspiration, but is not altered either essentially or accidentally by this fact. Desire is really relative to the good, but the good is not really relative to desire. Now all that 'desire is really relative to the good' can mean is that there cannot be a desire of the good without there being some kind of an object (the good) which is the object of desire; in other words, that the relation cannot exist without a relatum. And the assertion that the good is not really relative to desire can mean no more than that the goodness of the good is not constituted by the fact that it is really desired; that the relation of 'being desired' is not constitutive of the essence of the good. But I do not see how from this we can pass to the conclusion that the latter relation is not real but mental. The relationship of cause and effect, where the cause is uncreated, i.e. where God is the cause, is another example of a non-mutual relation. 73 According to Thomism, the relation both from the side of the referent and from the side of the relatum is real when the cause and the effect are unl,vocal, that is, when the cause brings into being effects like itself, as in the case of the father and the son; but not otherwise. Hence, while the effect is always really related to the 72 73

Ibid.; cf. Elemnta, Vol. I, sect. 191.3. Elementa, Vol. i, sect. 191.2.

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cause, the cause is not always really related to the effect. In cases where the cause and the effect are univocal, there is a real ground both in the referent and in the relatum; but in cases where they are equivocal, where the cause is uncreated and the effect is a creature, there is no real ground in the cause for a relation to the effect. The reason given for this is that God is an immovable mover, whose action does not superadd anything to his substance. 74 This relationship is even more dubious than the preceding three. In knowing, as we have seen, the thing known was said not to be really related to the knower, because knowing posits something in the intellect but nothing in the object known. But here God is said not to be really related to his creatures, even though he acts. The relation of being an effect, a creature, posits an action in God, but this action does not superadd a relation to him. The implication in the case of knowing was that if knowing did posit change in its relatum, the converse relation would be a real relation. The Thomistic view is evidently inconsistent here. It seems to me that the stand is taken that God is not really related to his creatures simply because it is thought to be required by the doctrine that God is immutable. Aquinas found a precedent for such a relationship in Aristotle. But the relation of Aristotle's God to the things of Nature could with greater plausibility be regarded as a logical relation, because his God is not a Creator, does not act, and moves only in the sense that things move 'towards' him as the object of their aspiration. Aquinas' God, however, is a Creator; and to say that he creates his creatures, but is not really related to them, seems to be the same as saying that he creates creatures but does not really create them; which is absurd. But the case is not so simple. St. Thomas does not deny that God acts, and in this sense is their Creator. What he denies is that God's actions produce relations in God. But while this view saves the immutability of God so far as such relations are concerned, it does not save it so far as actions are concerned; for how can God act, without in wme way changing? Now if the view that God is immutable has to be abandoned so far as actions are concerned, I cannot see any good reason why the view that God is immutable so far as relations are concerned should be 74 Ibid.

95

insisted upon. It must be added that the admission of such changes in God is not tantamount to a negation of the doctrine of his immutability, since these do not affect the essence of God, to which, I submit, the doctrine strictly pertains. The relation of a copy to its archetype is given as another example of a non-mutual relation. An artifact is said to be really related to its model, but the model itself is said to be only logically related to the artifact.7 5 It is not clear why the second relation is said to be only logical. When one thing is a copy of another, it is trne both that the copy is similar to the archetype, and that the archetype is similar to the copy. I think that the Thomist would grant that both the relation of similarity of the copy to the original and its converse are, in his sense, real. But, as Proclus pointed out, the relationship between copy and archetype is not merely a relationship of similarity: the copy is not only similar to its archetype, but is derived from it,7 6 whereas the archetype is not derived from the copy. This means that in addition to the symmetrical relationship of similarity, there must be an asymmetrical relationship between the two. But what reason is there for supposing that in this relationship the relation from the copy to the archetype is real, while the relation from the archetype to the copy is an ens rationis? It seems to me that a fallacy similar to those underlying the previous examples of non-mutual relations underlies this one. ( c) Let us turn now to the essential division of categorial relations. We have seen that a relation is specified by its ground in the referent and the relatum. Now the essential division of relations is the classification of them by reference to their ground. It is the division which we found in Aristotle. Thomism takes Aristotle's division of relations into three genera and completes and refines it. It divides the supreme genus categorial relation into three genera, on the basis of the distinction of three major kinds of ground. These kinds of ground are: (i) transcendental quantity, (ii) action and passion, and (iii) measure and measured. 77 Elementa, Vol. I, sect. 191.3. F. M. Cornford, Plato and ParmenideJ, pp. 93-94. 77 Aquinas, In Met. V, lect. 17, no. 1004; Cursus Philos., qu. XVH, art. III, VII; Elementa, Vol. I. sect. 191.3. 75 76

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(i) Relations which are grounded in transcendental quantity are divided into relations of ( 1) 'equality' and 'inequality' ( aequaJ,.. itas et inaequalitas), (2) 'proportion' (proportio), (3) 'similarity' and 'dissimilarity' ( similitudo et dissimilitudo), and ( 4) 'sameness' and 'diversity' (identitas et diversitas). 7 8 All these are said to be relations grounded in quantity, because 'quantity' here is taken in the sense in which Aristotle takes it when he speaks of the different kinds of relations which belong to the first genus and which he terms 'numerical.' All of these relations involve unity or number, and hence quantity. That which all of these senses of unity or number have in common is called 'transcendental quantity.' The latter is not this kind of quantity or that kind of quantity, but is something that pervades all kinds of quantity and is not identifiable with any one kind. ( 1, 2) Relations which are founded on categorial quantity, as distinct from transcendental quantity, are either relations of equality and inequality, or relations of proportion, such as 'double of' and 'half of.' ( 3) Relations which are based on the category of quality are relations of either similarity or dissimilarity. In order to be the ground of such relations, however, quality must possess the attribute of transcendental quantity. Thus, similarity rests upon the unity, and dissimilarity upon the plurality, of qualities. ( 4) Sameness and diversity or otherness are relations of things with respect to their essence. To be the ground of such relations, essence, like quality, must possess the attribute of transcendental quantity. Sameness is founded on oneness of essence; otherness, on a plurality of essences. Sameness may be either generic or specific. Numerical sameness is not a categorial relation, and hence does not belong to this classification. It is a logical relation, as we saw earlier. Diversity is either generic, or specific, or numerical. Relations of 'position' (positio), 'distance' ( distantia), and of 'priority' and 'posterity' ( ordo secundum prius et posterius) are instances of numerical otherness. These, we are told, are relations of numerical otherness because they involve different parts of categorial

quantity, and each part of a quantity has its own essence. The ground of relations of distance, and of priority and posteriority, is assumed to be the plurality of the essences of the quantities of things. The foundation of the relation of position is assumed to be the plurality of the essences of the parts of the quantity of a thing. This view of the relations of position, distance, etc. does not appear to be satisfactory. It does not seem to me correct to say that one quantity, or part of a quantity, is essentially different from another quantity or part of a quantity, in the sense that red, let us say, is essentially different from blue. Further, the fact that one quantity is distinct from another quantity, though a necessary condition for a thing's having relations of distance and other spatial relations, is not a sufficient condition (as I indicated earlier) for the thing's having the particular spatial relations it in fact has. For two things may, over a period of time, suffer no change so far as their quantity is concerned, but may enter into different spatial relations during this time. This shows that something besides their quantity is involved as the ground of their spatial relations: some kind of active agency. It should be noted, incidentally, that position, although elsewhere listed as a different category (situs), is here regarded as a relation. This ambiguous stand with respect to position we also found in Aristotle, from whom Thomism evidently inherited it. (ii) The second and third genera of relation are referred to by the common term 'relations of causality' ( relationes causalitatis). In order to distinguish them from one another, the former are called 'relations of causality which is not measured' (relation es causalitatis quae non est mensura) and 'relations of causality which is measured' (relationes causalitatis quae est mensura). Relations of causality which is not measured are relations of action and passion. These are divided into relations of ( 1) 'efficient causality' ( causalitas efficiens), ( 2) 'material causality' ( causalitas materialis), ( 3) 'intrinsic formal causality' ( causalitas f ormalis intrinsica), and ( 4) 'final causality' ( causalitas finalis). 79

96

78

Cursus Philos., qu. XVII, art. VII; Elementa, Vol. I, sect. 191.3.

97

( 1 ) By the relation of efficient causality Thomism means the 79

Elementa, Vol. I, sect. 191.3.

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relation which is grounded in action and passion, not insofar as these are potential, nor insofar as they are being actualized, but insofar as they have been actualized. (2, 3) By relations of material and intrinsic formal causality are meant relations based on action and passion which have not been actualized and are not being actualized. In placing these relations, like the preceding, in the second genus, Thomism is following Aristotle. But inasmuch as Thomism is concerned in this classification with categorial relations, and relations of material and formal causality are transcendental, it errs in placing them in this genus. ( 4) In dealing with Aristotle's classification, we noted that he did not discuss the teleological relation. Thomism places this, the 'relation of final causality,' in the second genus and also in the third. It belongs to the second genus insofar as the being which desires the end is passive with respect to the end, which in a sense acts on the being, and is thus based on action and passion. But the relation also belongs to the third genus, insofar as the end moves - in an improper sense (improprie) of this term, i.e. as an unmoved mover the being which desires it.so (iii) Let us turn now to relations of the third genus. These, as we have seen, are called relations of causality which is measured. They are relations of 'measure,' not with respect to quantity, but with respect to being ( esse) and truth. They are also called relations of extrinsic formal causality, because the measures of these relations, being and truth, are extrinsic formal causes. Again, they are called non-mutual relations, because the relation from the extrinsic formal cause - or the thing measuring - to the thing measured is not real but logical. Such relations have already been discussed in the section on non-mutual relations. Relations of the third genus are divided into two sub-genera: (1) those of which the measure is an 'object' (obiectum), and (2) those of which the measure is a 'prototype' (exemplar).B 1 ( 1) Under the first sub-genus fall relations of (a) 'potency' (potentia), (b) 'habit' (habitus), and (c) 'act' (actus). Each of

these is in turn divisible into different sub-species. Thus, the first species is divided into sub-species according as the potency is active or passive, cognoscitive or appetitive, etc. (2) Under the second sub-genus fall relations of the artifact to the artificer's idea of the exemplar. These are measured by the idea of the prototype in the mind ,of the artificer. I shall not discuss these relations any further, since I have already dealt with them in another context. This brings us to the end of the Thomistic classification of relations. As we have seen, Thomism classifies relations according to three modes of division. Each of these is, in its way, thorough, though not always satisfactory. In all of them, except the third, Thomism goes beyond not only Plato, but also Aristotle. The third division, though already developed in outline by Aristotle, is taken over and further elucidated and refined. But even in the first two modes of division Thomism goes beyond the Greeks more in the form of the divisions than in their matter. That is, we find in the Greeks nearly all the kinds of relation which it discusses in these divisions. We find its 'transcendental relations' in both Plato and Aristotle. We find its 'arbitrary logical relations' in both Greek philosophers. We find its 'non-arbitrary logical relations' in Aristotle, and their analogue in Plato's universal relations. Although the universal relations of Plato have a very different ontological status from Thomism's non-arbitrary logical relations, being subsistent entities and not entities of reason, as those of Thomism are, they may nonetheless be said to correspond to the non-arbitrary logical relations of Thomism. Plato, for instance, distinguishes his transcendent relations as sharply from relations between particulars, as Thomism distinguishes logical relations from categorial relations. We find in Aristotle the distinction between 'mutual relations' and 'non-mutual relations.' One important division which we find in Thomism but not in the Greeks is the division of relations into 'symmetrical' and 'asymmetrical.' The major contribution of Thomism, however, as regards the classification of relations lies, to my mind, in the dear distinction of, and the development of a terminology for, these different kinds of relations, and the systematic ordering of them.

98

so Elementa, Vol. I, sect. 191.3. Cursus Philos., qu. XVII, art. VII; Elementa, Vol. I, sect. 191.3.

81

99

100

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Thomism

101

The classification of relations by Thomism shows that it believes in a world which is ordered by a great variety of relations, such as quantitative relations 82 in the corporeal realm, qualitative relations in every part of the world, and causal relations in every part of the universe except God, and so on. 83

5. Conclusion Thomism built its theory of relations upon the foundations laid by Plato and Aristotle. Just as Aristotle refined Plato's theory of relations at certain points, so Thomism developed the theory which it inherited from Aristotle.

4. How We Know Relations To the question of how we know relations, the answer of Thomism is that we know them by reason. It says that "though the sensible faculties know things absolutely, to know the order of one thing to another pertains only to the intellect."8 4 This, I believe, should not be taken to mean that our senses are not involved in our cognition of relations. Thomism is empiricistic, and as such it could not hold that in the cognition of extra-mental relations our senses are not involved. So it seems to me that when it says that it pertains only to the intellect to know relations, its meaning must be, as regards such relations, that the intellect is required to grasp them as distinct entities. The senses, as Aristotle says, present us with "confused masses" (ta synkechymena). 85 They do not give us relations as distinct entities, but as present in certain relational situations. Thus, though our senses in a way do apprehend a relation, they do not, as Plato points out, apprehend it "adequately." T bought is required if we are to apprehend it adequately. Thomism explicitly makes the important distinction between our apprehension of a relation and the relation itself, so far as extra-mental relations are concerned. It charges the nominalists with confusing these two: the apprehension of a relation with the relation itself. Our apprehension of a relation by the intellect, it states, is itself a relation; but this relation has as its object a relation which exists in rerum natura. The nominalists, asserts Thomism, confound these two relations. 86

The contribution which Thomism made to the classical theory of relations consists mainly in the following: (a) The development of a more complete terminology. It coined, for instance, terms for the referent ( subiectum), the relatum (terminus), the ground (fundamentum) of the relation, and for many kinds of relation.

82 Quantitative in the sense of being grounded in the category (praedicamentum) of quantity. 83 Cf. H. Meyer, The Philosophy of St. Thomas Aquinas, p. 118. 84 "Etsi vires sensitivae cognoscant res aliquas absolute, ordinem itamen unius rei ad aliam cognoscare est solius aut rationis" (In I Ethic., I; cf. Elementa, Vol. II, sect. 644) . 85 Phys., I. 184a22-27. 86 Elementa, Vol. II, sect. 743.1.

(b) A sharper distinction of the elements of the relational situation. Thomism distinguishes the same elements in the relational situation as Plato and Aristotle, but distinguishes them more sharply, and shows more clearly how each of them is involved in the relational situation. ( c) A thoroughly worked out classification of relations. Plato, as we have seen, did not undertake to classify relations, though he distinguished two classes of relations very sharply from one another: universal from particular relations. Aristotle put forth an outline of one way of classifying relations, from the point of view of their ground. Thomism followed up Aristotle's classification, refined it, and classified relations in two additional ways, which it called the 'analogous division' and the 'accidental division.' The Thomistic classification of relation, though, to my mind, not always satisfactory, is as thorough, carefully worked out and suggestive as any metaphysical classification of relations that has been developed. I said that Thomism built on the foundations laid by Plato and Aristotle. This statement may be questioned as regards Plato. The Athenian philosopher, if my interpretation is right, did not believe in non-mutual relations. Further, his universal relations cannot be identified with Aquinas' logical relations. But the first difference does not seem to be an important one. For both the Platonic view that one of the relations in a so-called non-mutual relationship is

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extra-mental but accidental, and the Thomistic view that it is mental, are compatible with realism in epistemology and in metaphysics. The same, I believe, is true as regards the second difference. Both the Platonic view that universals are extra-mental, and the Thomistic view that they depend (in some way) on the mind, are compatible with a realistic epistemology and a realistic metaphysics. Apart from these two differences, there is much that the Platonic and the Aristotelian-Thomistic theories of relations have in common, and this important. For instance, the general conception of relation and the analysis of the relational situation of both is the same. They are in accord on the question whether all relations are universals or all are particulars (leaving aside the question of the ontological status of universals), and on the question of whether all relations are accidental or all are essential, holding that some are universals and some are particulars, some accidental and others are essential. There are other points of agreement. In light of the fact that Aquinas and his followers have developed the theory of relations which I have set forth in this chapter, the view that they did not believe in relations, or had no theory of relations, is ill founded. One source of this view is the neglect of the works of Aquinas and· of his commentators. It is generally assumed that they merely repeated what Aristotle had said, and that since Aristotle supposedly did not believe in relations, neither could they have believed in them and offered a theory of them. Another source of this erroneous view is probably the opinion that Thomism could not have accommodated relations in its doctrine of substance. As I have already dealt with this point in connection with Aristotle, I shall not say anything further about it here.

CHAPTER

IV

CONCLUSIONS The expos1t10n and discussion in the preceding chapters has made it manifest that Plato, Aristotle, and Thomism affirmed the existence of relations and have said a great deal about them, having dealt with at least the following points concerning relations: ( 1) the general notion of relation, ( 2) the analysis of the relational situation, ( 3) the classification of relations, ( 4) the ontological status of relations, ( 5) the cognition of relations. It has shown, too, I believe, that Plato, Aristotle, and Thomism are in accord on most basic points regarding relations; and that there is fundamentally a continuity of doctrine and a development in relational theory. Though their views, which together we may call 'the classical theory of relations,' are here and there open to certain objections, which I have pointed out, I think that they are on the whole sound, interesting and important. A rapid survey of the classical position on the five points just listed will, I believe, make more evident the justice of the preceding conclusions. ( 1) As regards the notion of relation, the classical philosophers had a word and a suggestive definition for it. They singled out relation as an entity to be contrasted with absolute or intrinsic entities, such as substance, quality, etc. For them relation is an entity which holds from one thing to another. The fact that they have considered extra-mental relation as an attribute of the referent, 'inhering' in it, has given rise to the belief that these philosophers made no distinction between relations and intrinsic characteristics. I have tried to show that this interpretation, which we find for instance in Cornford, is a result of noting certain statements made by these thinkers, such as that a relation 'inheres' in the referent, and ignoring their statements which call attention to 103

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what is distinctive about relation. I may add here, to what I said earlier on this point, the following. The fact that a relation is said to 'inhere' in the referent should not lead us to think of it, or to imagine it, as a quality or quantity of a thing. The relation inheres in the referent in an unique and indefinable way - a way very different from that in which qualitative or quantitative characteristics inhere in things. It may be questioned that we have to hold that a telation inheres in the referent and not hold, as is sometimes done today, that the relation does not really belong to either term. 1 With regard to this view, I shall say the following. We speak of a thing as having a certain relation. Consider the following case. Peter is the father of John. Now here the relation of 'father of,' which holds from Peter to John, seems really to belong to Peter. Being the 'father of' John is something to Peter. What the classical theory of relations emphasizes about relation, as distinguishing it from other characteristics or entities, is not inherence, but its being in some sense towards an entity other than that of which it is an attribute. A relation, it asserts, requires a relatum, towards which to hold. This it emphasizes strongly. But it notes that a relation requires a relatum in a different way from that in which it requires a referent. ( 2) The classical theory of relations distinguishes in the relational situation the referent, the relatum, the ground, and the converse of the relation. A relation is said to hold from the referent to a relatum. It is viewed as involving both, but differently. Relation requires both the referent and the relatum for its being and nature, but is an attribute of the former. According to the classical theory of relations, a relation requires a referent and a relatum not as bare terms, but as terms with a certain character, by reason of which they can give rise to relations, The 'ground' of the relation, which is generally a very neglected part of current theories of relation, is certainly not ignored by this theory. What it says about the ground of relations is very interesting and 1 Cf. J. E. McTaggart: "To the question,. 'ii;i what is a relation?' we may fairly answer that it ,js not in anything, but that 1t 1s between two or more terms, or between a term and itself" (The Nature of Existence, Vol. I, p. 82).

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105

valuable for us, as the question of the ground is connected with the dispute of whether relations are external or internal. It is clear that, according to this theory, some relations are grounded entirely in the nature of their terms, and others only partly. Therefore, if an 'internal' refation is defined as one which is grounded solely in the nature of its terms, to the question whether all relations are 'external' or all are 'internal,' the answer, in accordance with the classical theory, should be that some relations are 'external' and others ar~ 'internal.'

In connection with the recent dispute of whether relations are 'internal' or 'external,' it should be added that if the former is taken to mean essential and the latter accidental, the answer of the classical theory is that some relations are 'internal,' i.e. essential to their terms, while others are 'external,' i.e. non-essential or accidental. The converse of a relation is not ignored in the classical theory of relations, but is duly recognized and discussed. (3) Although Plato did not attempt a classification of relations, his great disciple made a substantial contribution here. He outlined the 'essential division' of categorial relations, as Aquinas calls it. The latter supplemented this with two additional modes of classification. Plato, Aristotle, and Aquinas recognized clearly the existence of many important kinds of relation. They saw relations between physical things, such as quantitative relations, qualitative relations, causal relations. They saw relations between psychical beings, minds, and other kinds of entities. Finally, they saw relations between certain very peculiar objects: Plato, between 'forms;' Aristotle, between 'concepts;' Aquinas, between 'absolute natures.' ( 4, 5) It has often been asked in our time whether relations are real? The answer given by these philosophers is, "Yes, in several senses." Firstly, relation is not self-contradictory. Bradley asserts that it is self-contradictory "in the end.'' 2 Plato's view is that relation seems to be self-contradictory "in the beginning," but is self-consistent "in the end.''3 It is facts about relations which appear to be contradictory that lead us to 1·eflect. According to Bradley, thought 2 3

F. H. Bradley, Appearance and Reality, Ch. III. Rep. VII. 523b ff.

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makes relations, and leads to contradictions. But according to Plato, thought discovers relations and removes contradictions. The relation is distinct from the apprehension of it. The Platonic view reappears, so far as relations in the external world are concerned, in Aristotle and Thomism. Secondly, relations are real, according to the classical theory, in the sense that they are not reducible to intrinsic characteristics. Thomism, as we have seen, explicitly opposes the reductionism of Scotus. Finally, relations are real, according to the classical theory, in the sense that not all of them are entia rationis, entities having being only as objects of the mind. There are many kinds of relations which are extra-mental. Plato goes farther in this direction than either Aristotle or Aquinas, regarding as extra-mental or as subsistent entities relations which for them are entities of reason. The view that there are real, extra-mental relations implies a qualified pluralism. The universe is a plurality, but it is ~ot a plurality of closed, solitary monads. The members of the universe are ordered together by real, extra-mental relations, and constitute a hierarchical and in general orderly totality.

BIBLIOGRAPHY 1.

Books

Alexander, S., Space, Time, and Deity, Vol. I. London: Macmillan and Co., Ltd., 1920. Aquinas, St. Thomas, In X Libras Ethicorum Aristotelis Commentarium. Quebec, Universitas Lavallensis, 1943.

- - In XII Libros Metaphysicorum Aristotelis Commentariutn. Quebec: Universitas Lavallensis, 1943.

- - De Potentia, in Opera Omnia, Vol. VIII. Parma: Typis Petri Fiaccadori, 1856. Aristotle, Works, Loeb Classical Library. Cambridge, Massachusetts: Harvard University Press; London: William Heinemann Ltd. Bradley, F. H., Appearance and Reality. Oxford: Clarendon Press, 1930. - - Collected Essays, Vol. II. Oxford: Clarendon Press, 1935. Broad, C. D., Examination of McTaggart's Philosophy, Vol. I. Cambridge: Cambridge University Press, 1933. - - The Mind and its Place in Nature. London: Kegan Paul, Trench, Trubner & Co., Ltd., 1923. Cornford, Francis Macdonald, Plato and Parmenides. New York: Harcourt, Brace and Co., 1939. - - Plato's Theory of Knowledge. London: Kegan Paul, Trench, Trubner & Co., Ltd., 1935. Demos, Raphael, The Philosophy of Plato. New York: Charles Scribner's Sons, 1939. Findlay, J. N., Meinong's Theory of Objects. London: Oxford University Press, 1933. Gredt, Iosephus, Elementa Philosophiae Aristotelico-Thomisticae, Vols. I and II. Friburgi Brisgoviae: Herder & Co., 1937. 107

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Bibliography

Hobhouse, L. T., The Theory of Knowledge. London: Methuen & Co., 1905. James, William, A Pluralistic Universe. New York: Longmans, Green and Co., 1909. - - Collected Essays and Reviews. London: Longmans, Green and Co., 1920. Joannes a S. Thoma, Cursus Philosophicus Thomisticus, Vol. I, Logica. Paris: Ludovicus Vives, 1883. Johnson, W. E., Logic, Vol. I. Cambridge: Cambridge University Press, 1921. Joseph, H. W. B., Knowledge and the Good in Plato's Republic. Oxford: Oxford University Press, 1948. Laertius, Diogenes, Lives of Eminent Philosophers, Vol. I, Loeb Classical Library. Cambridge, Massachusetts: Harvard University Press; London: William Heinemann Ltd., 1942. McTaggart, J.E., The Nature of Existence, Vol. I. Cambridge: Cambridge University Press, 1921. Meyer, Hans, The Philosophy of St. Thomas Aquinas. St. Louis and London: B. ·Herder Book Co., 1944. Moore, G. E., Philosophical Studies. London: Kegan Paul, Trench, Trubner & Co., Ltd., 1922. Plato, Dialogues, Loeb Classical Library. Cambridge, Massachusetts: Harvard University Press; London: William Heinemann Ltd. Pratt, James Bissett, Personal Realism. New York: The Macmillan Co., 1937. Renard, Henri. The Philosophy of Being, 2nd ed. Milwaukee: The Bruce Publishing Co., 1947. Rey, Abel, L' Apo gee de la science technique grecque. Paris: Editions Albin Michel, 1946. Ross, W. D., Aristotle. London: Methuen & Co., Ltd., 1945. Russell, Bertrand, A History of Western Philosophy. New York: Simon and Schuster, 1945. - - Our Knowledge of the External World. Chicago and London: The Open Court Publishing Co., 1914. Santayana, George, Realms of Being. New York: Charles Scribner's Sons, 1942.

Schilpp, Paul A., editor, The Philosophy of Alfred North Whitehead. Menasha, Wisconsin: George Banta Publishing Co., 1941. Whitehead, Alfred North, Science and the Modern World. New York: The Macmillan Co., 1925. Wild, John D., Plato's Theory of Man. Cambridge: Harvard University Press, 1946. - - The Science of Philosophy, Parts I and II. Cambridge, Massachusetts: John D. Wild, 1946.

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2.

109

Articles

Alexander, S., "On Relations; and in Particular on the Cognitive Relation," Mind, New Series, 1912, No. 83. Bode, B. H., "'Pure Experience' and the External World," Journal of Philosophy, Vol. II (1905), No. 5. Demos, Raphael, "Types of Unity According to Plato and Aristotle," Philosophy and Phenomenological Research, Vol. VI (1946), No. 4. McGilvary, E. B., "Relations in General and Universals in Particular," Journal of Philosophy, Vol. XXXVI (1939), No. 2. Parker, DeWitt H., "Reflexive Relations," Philosophical Review, Vol. XLII (1933), No. 3. Ryle, Gilbert, "Plato's 'Parmenides,'" Mind, Vol. XLVIII (1939), N.S., No. 190.

INDEX

OF NAMES

Alexander, S., 17, 107, 109 Aquinas, 9, 67-102, 103, 105, 106, 107 Aristotle, v, vi, 9, 10, 25, 37, 39-65, 67, 69, 78, 79, 82, 83-84, 88, 90, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107 Bergson, 37 Bode, B.H., 30, 109 Bradley, F.H., v, 84-85, 105106, 107 Broad, C.D., v, 13, 23, 107 Burch, George Bosworth, vi Cavarnos, C., 37 Cornford, Francis MacDonald, 9, 14, 16, 17, 18-20, 22, 25, 26, 38, 44-45, 64, 95, 103, 107 Demos, Raphael, vi, 15, 64, 107, 109 Findlay, J.W., 76, 107 Gredt, Josephus, v, 9, 68, 6986, 89-98, 100, 107 Hobhouse, L.T., 108 James, William, v, 108 Joannes a S. Thoma, 9, 68, 69, 71, 73, 75, 76, 80, 83, 85, 88, 89, 90, 92, 95, 96, 98, 108

John of St. Thomas, see Joannes aS. Thoma Johnson, W. E., 20, 108 Joseph, H. W. B., 13, 33, 108 Kant, 43, 57 Laertius, Diogenes, 14, 108 Leibniz, 11 McGilvary, E. B., 17, 109 McTaggart, J. E., 21, 23, 104, 108 Meinong, 76 Meyer, Hans, 70, 81, 100, 108 Moore, G. E., v, 26, 108 Parker, DeWitt, H., 22, 109 Plato, v, vi, 9, 10, 11-38, 41, 42, 43, 44, 46, 48, 49-50, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63-64, 65, 69, 71, 74, 82, 83, 88, 92, 99, 100, 101, 102, 103, 105, 106, 108 Pratt, James B., 18, 108 Proclus, 95 Renard, H., 81, 85-86, 108 Rey, Abel, 32, 108 Ross, W. D., 14, 108 Russell, Bertrand, v, 9, 37-38, 64, 108 Ryle, Gilbert, 34, 109 Santayana, George, 9, 27, 38, 108

111

112

THE CLASSICAL THEORY OF RELATIONS

Schelling, 39 Schilpp, Paul Arthur, 9, 108 Scotus, Duns, 75, 106 Taylor, A. E., 67 Thomaz, Joao de Santo, see Joannes a S. Thoma

Whitehead, Alfred North, 9, 11, 26-27, 64, 87-88, 109 \Vild, John Daniel, v, vi, 29, 81, 82,85, 109 Williams, Donald C., v Zeno,32

INDEX

OF

accidental relations, 16, 27, 30, 33, 92, 101-102, 105 action-passion, category of, 42, 54-56, 58, 63, 69, 75, 89, 90, 95, 98 action-passion relations, 14-16, 52, 54-56, 63, 75, 89, 90, 97-98 Aristotelianism, v, 9, 67 asymmetrical relations, 79, 8990, 95, 99 being, 14, 19,42,69,81,98 'blending,' relation of, 25, 26, 54 categorial relations, 76, 80, 83, 88-100 categories, 14-17, 42-43, 49, 63, 69, 83 causal relations, see causality, and relations of causality causality: efficient, 74-75, 89, 93-94, 9798 final, 13,93,94,97,98 formal, 74-75, 91, 97-98 material, 97-98 classification of relations, 10, 48, 52-62, 64, 79-100, 101, 103, 105

SUBJECTS cognition of relations, 10, 35· 37,62-63, 100, 103 cognitive relations, 29, 30, 36, 46, 56-57, 58, 60, 78, 80, 90-93 conative relations, 23, 29, 30, 36, 57 concepts, 41, 43, 61, 80, 82, 105 contact, 32, 61-62 contrary relations, 31-32, 46-47, 50-51, 83-84 converse, 16, 17, 20, 33, 43, 4647, 50, 57, 58, 69-70, 73, 78-79, 89-95, 104, 105 copy-archetype relationship, 95 correlatives, 21, 46-48, 62, 71-72 definition of relation, 17-78, 20, 43-44, 46, 69, 79, 85, 103 diversity, see otherness empirical relations, 31-37, 83; see also particulars epistemology, 10, 92, 101-102 equality and inequality, 20, 25, 49, 50, 51, 52, 84, 89, 96 essence: intrinsic, 27, 87, 88 relational, 27, 87, 88 essential relations, 27, 30, 33, 62, 92, 102, 105

113

114

Index of Subjects

THE CLASSICAL THEORY OF RELATIONS

'exclusion,' relation of, 25-26, 54 'external' relations, 104-105 extra-mental relations, 70, 71, 76, 78, 79, 83, 106

forms, Aristotelian, 41-42, 45, 62, 85, 86-87 forms, Platonic, immanent, 31-35, 42, 54 transcendent 13-14, 15, 16, 25-27, 30, 31, 33-35, 36-37, 41, 42, 53, 54, 58, 60, 82, 105 foundation of relation, see ground of relation

God, 13-14, 28-29, 32, 41, 58, 90, 93-95, 100 ground of relation, 17, 23-25, 32, 34, 35, 36, 43, 49, 50, 51, 55-57, 60, 69-70, 72-78, 82, 84, 89, 91, 94, 95, 96, 97, 98, 101, 104-105 proximate, 73, 81 remote, 73, 81

'idealism,' 92 identity, 22-23, 33, 48, 49, 5354, 70, 81, 96; see also sameness 'internal' relations, 92, 104-105 intrinsic characteristics, 14, 1820, 31, 38, 43, 65, 77, 103, 106

judgment, 37, 82-83

knowledge, 16, 27, 37, 43, 4648, 50, 56-57, 59-60, 62-63, 78, 90-91, 94, 100

logic, 10, 61, 64, 68 logical being, 80-81 logical relations, 70, 71, 72, 76, 78-79, 80, 81-83, 89-95, 96, 98, 99, 101, 106

material logic, 10 matter, 42, 45, 62, 71-72, 85, 86-87, 88 mental relations, 79, 88-90, 99; see also logical relations metaphysics, iii, v, 10, 64, 67, 101-102 mind, 32, 43, 56-57, 71, 78, 82 minds, 41, 47, 58, 71, 105 multiple relations, 23, 49, 70-71 mutual relations, 79, 88-90, 99

not-being, relation of, 26 non-mutual relations, 78-79, 8182, 88-95, 98, 99, 101-102 'numerical' relations, 52, 54, 63, 96

one-many relations, 22-23, 70-71 ontology, 64 otherness, 25, 26-27, 52, 54, 63, 96

'par~icipation,' 14, 30, 33, 42 particulars, 31-35, 42, 59, 61, 6263, 64, 71, 99, 101, 102 perception, 19, 46-48, 56, 57, 92-93 physical objects, 13, 14, 21, 3135, 41-42, 47, 58, 71, 105 pluralism, 28, 32, 96-97, 106 position, 42, 61, 62, 69, 96 potency and act, 85-86, 98-99 properties of relation, 49-52, 6364, 83-84 proportion, relations of, 32, 50, 52, 96 propositions, 25-26, 64, 82 psyche, 13-14, 21, 27-31, 41, 42, 48,62, 71,86,88, 105 psyche-body relationship, 30-31, 62, 88 psychical relations, 27-31, 88

qualitative relations, 100 105 ' qualtty, category of, 14, 29, 38, 42, 46, 49, 50, 51, 52, 53, 59, 63, 65, 69, 75, 85, 88, 89, 96, 103, 104 quantitative relations 20 24 25 ' 105 ' ' ' 52, 61-62, 63, 100, quantity, category of, 14, 42, 46, 49, 50, 51, 52, 61, 62, 63, 69, 75,89,90,96, 104 transcendental, 95-96

.

realism, 36-37, 43, 56-57, 60, 82-83, 92, 101-102 reality of relations, 9, 105-106 'real' relations, 36-38, 80, 83, 88100, 106

115

realms of being, 10, 13-14, 4142, 69 reason, 35-37, 41, 42, 62, 100 reductionism, 75, 106 referent, 17, 20, 22, 30, 31, 34, 38, 44, 51-52, 57, 69, 70, 73-74, 76, 77, 78, 83, 89, 90, 91, 93, 95, 101, 103, 104 reflexive relations, 22-23, 48-49 relational situation, analysis of, 17-25, 43-49, 69,79, 84, 102, 103, 104-105 relations of causality, 97-100, 105; see also causality relations of measure and measurable, 52, 56-62, 76, 9095, 97, 98 relations of reason, see logical relations relations secundum dici 70 76 ' ' 79-80, 83, 85-88, 99' relations secundum esse, 70, 7980, 85, 86 'relationship,' 20-21 relative terms, 21, 44-46, 54, 7172 relatum, 17, 20, 21, 22, 30, 31, 38, 44, 51-52, 57-58, 69, 70-71, 72, 73-74, 78, 83, 86, 87, 88, 89, 90, 91, 93, 95, 101, 104 sameness, 22, 26-27, 52-54, 96-97 senses, 35-37, 42, 43, 56-57, 63, 100 similarity and dissimilarity, 32, 49, 51, 52, 53, 54, 73-74, 84, 89, 95, 96

63, 6220, 63,

116

THE CLASSICAL THEORY OF RELATIONS

soul - body relationship, see psyche-body relationship space, 13, 61-62, 63 space relations, 24-25, 32, 61, 74, 96-97 subject-predicate relationship, 59, 64, 80, 81 subjectivism, 92 substance, 14, 31, 42, 45, 46, 51, 53, 64, 65, 69, 71, 85, 102, 103 symmetrical relations, 79, 89, 95, 99 teleological relation, 13, 57-58, 93, 94, 98 terms of relation, 17, 21-23, 36, 43, 47, 48, 49, 51, 70, 73, 81, 104

number of, 21-23, 48, 49, 70 Thomism, v, vi, 9, 10, 57, 67102, 103 time, 13, 42, 61, 62, 63 time relations, 61 transcendent relations, 36-37, 82, 99, 101 transcendental relations, see relations secttndum dici universal relations, 25-27, 41-42, 62-63, 82-83, 101, 102; see also transcendent relations universals, 13, 14, 21, 27, 29, 31, 33-34, 35, 37, 41-42, 61, 6263, 64, 76, 82, 99, 101, 102 world-order, 32, 58, 100