Phenomenological Realism Versus Scientific Realism: Reinhardt Grossmann - David M. Armstrong Metaphysical Correspondence 9783110326062, 9783110325249

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Javier Cumpa & Erwin Tegtmeier (Eds.) Phenomenological Realism Versus Scientific Realism Reinhardt Grossmann – David M. Armstrong Metaphysical Correspondence

Philosophische Analyse Philosophical Analysis Herausgegeben von / Edited by Herbert Hochberg • Rafael Hüntelmann • Christian Kanzian Richard Schantz • Erwin Tegtmeier Band 32 / Volume 32

Javier Cumpa & Erwin Tegtmeier (Eds.)

Phenomenological Realism Versus Scientific Realism Reinhardt Grossmann – David M. Armstrong Metaphysical Correspondence

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.

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Table of Contents Acknowledgments

5

Preface by DAVID M. ARMSTRONG

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Introduction by JAVIER CUMPA & ERWIN TEGTMEIER

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Beginning: Universals 1

To Armstrong (18-VIII-76) The Start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2

To Armstrong (21-IX-76) On the Simplicity of Universals . . . . . . . . . . . . . . . . . . . . . . 21

3

To Grossmann (21-X-76) On the Complexity of Universals . . . . . . . . . . . . . . . . . . . . . 22

4

To Armstrong (30-XI-76) The Phenomenological Argument for the Simplicity of Universals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5

To Grossmann (4-I-77) The Scientific Argument for the Complexity of Universals . . . 24

6

To Armstrong (1-XI-77) Objections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

7

To Grossmann (14-XI-77) A Reply to Objections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

8

To Armstrong (29-XI-77) A Legacy: Gustav Bergmann . . . . . . . . . . . . . . . . . . . . . . . . 29

9

To Grossmann (8-XII-77) A Legacy: John Anderson . . . . . . . . . . . . . . . . . . . . . . . . . . 30

10

To Armstrong (7-VIII-78) The Nature of Universals . . . . . . . . . . . . . . . . . . . . . . . . . . .31

11

To Grossmann (14-IX-78) A Reply: 1. Grossmann on Exemplification . . . . . . . . . . . . 47 2. Are there Conjunctive Properties? 3. Structural Properties 4. Ontology and the Physical Universe

12

To Armstrong (25-IX-78) Objections: Exemplification, Complex Properties, the Universe and the World . . . . . . . . . . . . . . . . . .59

13

To Grossmann (16-X-78) Part I. A Reply to Objections: . . . . . . . . . . . . . . . . . . . . . . . .64 Part II. Universals and Classes: A Question . . . . . . . . . . . . .68

14

To Armstrong (12-I-79: Part I) Universals and Classes: An Answer . . . . . . . . . . . . . . .69

15

To Grossmann (30-I-79: Part I) Objections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

16

To Armstrong (6-II-79: Part I) A Reply to Objections . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Middle: Laws of Nature 17

To Armstrong (12-I-79: Part II) Laws of Nature as Quantified Facts . . . . . . . . . . . . . .76

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To Grossmann (30-I-79: Part II) Laws of Nature as Connections between Universals .77

19

To Armstrong (6-II-79: Part II) An Objection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78

20

To Grossmann (23-IV-79) A Reply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

21

To Armstrong (16-X-80) An Epistemological Problem: Synthetic A Priori Truths . . . 82

22

To Grossmann (4-XI-80) A Solution: Causation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84

23

To Armstrong (25-XI-80) An Objection: Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . .86

End: The Nature of Numbers 24

To Armstrong (29-IX-86) A Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

25

To Grossmann (4-XII-86) Numbers Tied to Aggregates . . . . . . . . . . . . . . . . . . . . . . . . 90

26

To Armstrong (21-I-87) An Objection: On Mereological Categories . . . . . . . . . . . . . .91

27

To Grossmann (1-III-87) A Reply: On Mereological Categories . . . . . . . . . . . . . . . . . 94

28

To Armstrong (16-III-87) Aggregates and Sets: A Question . . . . . . . . . . . . . . . . . . . . .95

29

To Grossmann (27-III-87) Aggregates and Sets: An Answer . . . . . . . . . . . . . . . . . . . . .97

30

To Armstrong (21-IV-87) A Problem: Wholes and Mereological Sums . . . . . . . . . . . . 99

31 101

To Grossmann (4-V-87) A Solution: The Identity Conditions for Mereological Sums .

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To Armstrong (23-V-87) Concluding Remarks on Numbers and Mereology . . . . . . . 103

Appendix I (1984): Reinhardt Grossmann’s Ontology by David M. Armstrong . . . . . . . . . . . 106 Appendix II (1987): Comments on Armstrong’s Universals: An Opinionated Introduction (Westview Press, 1989) by Reinhardt Grossmann. . . . . . . . . . . . . . . . . .122 Appendix III (1992): Comments on Grossmann’s The Existence of the World: An Introduction to Ontology (Routledge, 1992) by David M. Armstrong . . . . . . . . . . . .127

Bibliography

133

About Reinhardt Grossmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 About David M. Armstrong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135 About the Editors

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Author Index

137

Subject Index

138

Acknowledgements When I was reading “The Fourth Way: A Theory of Knowledge”’s page 63 (Indiana University Press, 1990) I suddenly realised that there was an extensive philosophical correspondence of Reinhardt Grossmann with David Armstrong. Immediately I told my friend Erwin Tegtmeier who is also a friend of Grossmann. We agreed that the letters would be important and revealing and deserved to be published. During that time I had tried in vain to locate an archive of Grossmann’s writings who had retired in 1994. Hence, I was aware that we could get hold of the letters only if they were with Armstrong. Tegtmeier who is acquainted with Armstrong contacted him and it turned out that they were in Armstrong’s archive. Armstrong very kindly sent to me copies of the correspondence in less than a month. I read all the letters in very few days and I was confirmed in my expectation that the letters were important and helpful for the interpretation of the philosophies of Armstrong and Grossmann. I proposed to Rafael Hüntelmann (the general publisher Ontos Verlag) a publication of the philosophical parts of the letters of Armstrong and Grossmann and he received the idea enthusiastically. I started to work unceasingly on the project, to which I had the fortune that Erwin Tegtmeier accepted to join me. This is my personal and philosophical debt with Erwin Tegtmeier, David Armstrong, and Rafael Hüntelmann. On one occasion, Peter Simons talked to me about his admiration for the metaphysical figures of Grossmann and Armstrong. My impression of his words was about two people who had made a great effort at what could be called: “A Revival of Metaphysics” in metaphysically inclement times. Madrid, Spain, April 2009 JAVIER CUMPA

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Preface Immediately after the Second World War the philosophy departments of the English-speaking universities gave little attention to metaphysics. It was a deeply unfashionable pursuit. In the period between the two world wars the logical positivists of Vienna used their Verification principle to outlaw metaphysical statements. In 1936 A. J. Ayer popularized their ideas in his book Language, Truth and Logic. In a revised edition in 1946 he said that he had come to think ‘the questions with which it deals are not in all respects so simple as it makes them appear’ but nevertheless said ‘I still believe that the point of view which it expresses is substantially correct’ (p. 5). A still more powerful influence was Wittgenstein, who claimed in his Tractatus (1922) to solve the problems of philosophy once and for all. But when he came back to philosophy in the 1930s he was claiming that he wished to show the fly the way out of the bottle, the bottle being philosophy. Gilbert Ryle held that there was still a role for philosophy, but it was a matter of ‘conceptual analysis’. These sorts of ideas ruled. There was no place for metaphysics. An unfortunate result, among many, was the divide that developed between the philosophers who espoused these new attitudes and Bertrand Russell, in my view the most important metaphysician of the 20th century. He cordially hated the new thinking, the philosophers of the new wave in turn ignored most of what he still had to say. For instance, in 1948 he published his important book Human Knowledge: its Scope and Limits. It was not just a work of epistemology, it put forward new metaphysical views, in particular his interesting idea that continuing things should be thought of as causal lines. But the book never received the attention it should have had. In at least two departments, however, the new ideas took no root. At the University of Iowa the presiding genius was Gustav Bergmann. He had begun as a member, one of the youngest members, of the Vienna Circle. Hitler drove him, as so many brilliant European intellectuals and scientists, were driven, to seek refuge in the U.S. Bergmann’s thinking eventually led him back to metaphysics, to ontology, to the attempt to delineate the general features of reality, the categories of being. As one might expect, there developed in his school an interest in going back to the classical figures of philosophy, and interrogating them in order to see what they had to offer, especially in metaphysics. Among a number of Bergmann’s students were included Reinhardt Grossmann and his friend Herbert Hochberg, though

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they were not contemporaries at Iowa. I thank Herb for information in this paragraph. Besides Bergmann’s teaching, he recalls Everett Hall giving a course on the great Idealist metaphysician F. H. Bradley, and Richard Popkin, a young professor just starting out as a historian of philosophy. Not quite your typical influences for a philosophy school in the early fifties. Grossmann was a young German who after the military collapse of Germany found himself in shattered Berlin with no high school education and no work. As he told the tale, he supported himself, and in great measure his parents, by successful operation on the black market. He and some of his like-minded friends were able to remedy the gap in their education. They got qualifications for high school by paying in black market kind for tutorials to suitable teachers. Eventually Grossmann got to the Free University of Berlin, and from there a scholarship took him to the University of Iowa. Another school where the flight from metaphysics did not occur was the University of Sydney. From 1927 the Challis Chair of Philosophy was held by a Glasgow educated Scotsman, John Anderson, who dominated the philosophical thinking at the university, indeed in all Sydney, for the next thirty years. Anderson had a systematic Realist view that extended to all the traditional spheres of philosophy, and included, centrally, a metaphysics. It took its inspiration from the metaphysical work of the English philosopher Samuel Alexander, but purported to be more rigorous and thoroughgoing than Alexander. Anderson, however, never published his full work in this area and it has to be gathered from his dictated lectures in 1949-1950, now published as Space, Time and the Categories by Sydney University Press, with an Introduction by myself. I attended these lectures, and they inspired in me a life-long devotion to the topic of metaphysics. Grossmann and I started by corresponding with each other, but met later, I think first at Austin in 1980 when I taught at the University of Texas for a semester. Later I saw him at the beautiful campus of the University of Indiana at Bloomington and he came to Sydney where he loved the sun and the surf of the beaches. We were both of the opinion that metaphysics should be central to a systematic philosophical position, though, like philosophers generally, were unable to agree on the details! We enjoyed our correspondence and our friendship, and I hope the correspondence may interest others. D. M. Armstrong

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Sydney, April 2009

Introduction We choose the title “Phenomenological Realism vs. Scientific Realism” because these two terms indicate what is common and what is different in their respective metaphysical positions. The realism common to them involves the ontological acknowledgement of concrete as well as of abstract entities such as universals and numbers which are taken as independent of mind. The attributes “phenomenological” and “scientific” which differentiate between Armstrong and Grossmann refer to the way they support their ontological realism. Armstrong uses evidences of the natural sciences, Grossmann evidences of perception and introspection. The epistemological differences explain part of the disputes between Armstrong and Grossmann, e.g., over the simplicity of universals. We have divided this work into four parts distributed in thirty two letters from 1976 until 1987, and three isolated commentaries on three works from 1984 until 1992. Thus, the structure of the book includes an important stretch of the intellectual development of both philosophers from the preparation of their cardinal works, Armstrong with “Universals and Scientific Realism” (Cambridge University Press, 1978) and Grossmann with “The Categorial Structure of the World” (Indiana University Press, 1983), until the publication of Grossmann’s “The Existence of the World: An Introduction to Ontology” (Routledge, 1992) and Armstrong’s “A Combinatorial Theory of Possibility” (Cambridge University Press, 1989). I The simplicity or complexity of universals is the main topic of the first section of the volume. Grossmann starts by referring to an ontological argument against complex universals contained in one of his papers and in a book which shows that complex universals cannot be further universals in addition to the universals they consist of. He agrees that science determines what properties there are but cannot see how scientific research would lead to the conclusion that perceptual properties such as a shade of colour or being square are complex. Grossmann insists that scientific analysis can conclude that those universals are connected with other properties but not that they consist of them. In his reply Armstrong describes phenomenologically simple universals as epistemologically simple and explains that this means only that they

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appear to be simple. He asserts that physical analysis give us good reasons to believe that the phenomenologically simple is really complex. He is astonished that Grossmann takes being square to be simple in spite of definitions of squareness by geometry. Since Armstrong advocates conjunctive universals he has to defend himself against Grossmann’s refutation of complex universals. Armstrong claims that his conjunctive universals are not entities in addition the conjunct universals. He argues that there is a partial identity between the conjunctive universals and their conjuncts and therefore no diversity. Grossmann argues that phenomenological simplicity is the only criterion of simplicity we have. And he claims that without it Armstrong cannot distinguish between properties of which a property consists and those which are merely connected with it. Armstrong, for his part, resorts in his answer to a phenomenological argument. He admits that redness appears simple but claims that squareness appears complex. He is convinced that he can distinguish between properties connected with squareness in a lawlike fashion and properties which are partly identical with squareness. Eventually, Armstrong offers tentatively a criterion of identity between properties according to which properties are identical only if they have the same causal powers. Grossmann doubts that Armstrong’s criterion works. He asks: “could not two properties, since they are lawfully connected, have the same causal powers”. Then he argues for the phenomenological simplicity of squareness. He points out that children recognize squareness though they cannot count the number of sides. That does not go together with Armstrong’s assumption that having four equal sides is constitutive of squareness. In his answer Armstrong admits that he has no clear-cut criterion to distinguish between constituents of a conjunctive property and properties lawfully connected with it but he thinks that there are reasons to decide on the alternative. Finally he offers an argument for the existence of conjunctive properties. It is that two particulars which have both the property P and the property Q resemble are equal not only with respect to P and Q but also with respect to being both P and Q. Grossmann tells Armstrong in the next email that they have not accomplished to make any progress concerning the issue of ontological reduction. Yet he also announces to him: “I shall try to write you a lengthy letter on this subject soon”. Then, he declares his universal realism as inherited from Gustav Bergmann. Similarly, Armstrong gives to Grossmann an account of the genesis of his advocacy of universals as derived from

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that of John Anderson. And concerning the question of the ontological reduction, Armstrong simply says that he has sympathy with the physicalist temperament and, therefore, with its usual reductions. The announced “lengthy letter” became Grossmann’s review of Armstrong’s “Universals and Scientific Realism” where Grossmann raised the issue of ontological reduction again. Mainly, Grossmann criticizes three points of Armstrong’s ontology. In the first place, Armstrong’s argues against an exemplification relation. For Grossmann, this argument shows rather that it is characteristic of relations that they need not be related to what they relate. In the second place, Grossmann deals with the argument against the existence of complex universals. Grossmann thinks that the argument for the existence of conjunctive universals precisely proves that not every well-formed propositional context represents a universal. In regard to the existence of structural universals, Grossmann suggests that Armstrong’s position is defective because an admission of wholes formed by universals seems to require, contrary to Armstrong, also an admission of the “ties” between such universals. Grossmann also appeals to the phenomenological experience as a proof that universals are simple rather than complex. Lastly, and in the third place, concerning Armstrong’s world-hypothesis, Grossmann objects that while it is true that particulars are spatio-temporal entities, it is not true that universals and states of affairs are. Almost two months later, Armstrong sent a reply to Grossmann’s three objections. This reply was intended as a paper, but finally it was not published by Armstrong. Fortunately, however, now we can read his reaction. As to Grossmann’s first objection, he thinks that to distinguish two non-relational elements of a state of affairs does not imply that they require be related by one additional relation; as to the second, Armstrong asserts that Grossmann’s hyper-atomism simply does not permit him to concede that complex universals are logically and epistemologically possible. Armstrong argues that Grossmann must offer a theory of possibility; thirdly, Armstrong does not see any reason to admit Grossmann’s two realms of the concrete universe and the abstract world. From his point of view, both he and Grossmann are talking about the very same realm. Grossmann sent to Armstrong a letter with some remarks on his own view on the debated issues. Concerning exemplification, Grossmann objects to Armstrong’s claim that it is possible to construe wholes without relations. Furthermore he maintains against Armstrong that these relations can be perceived. As to complex universals, Grossmann claims that what

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matters is not whether universals can be logically complex, but rather whether they really are. For him, this possibility clashes with the phenomenological experience. Lastly, in regard to the dispute about Grossmann’s distinction between world and universe, Grossmann is prepared to admit that they both are talking about the very same thing. However, he insists that Armstrong is wrong because a particular is not the same as a state of affairs. Grossmann points out that while the former is spatio-temporal, the latter is not. A short time later Armstrong replied to Grossmann. Concerning exemplification Armstrong contends that a phenomenological ground is an illusory one for postulating relations in wholes. With regard to complex universals, Armstrong again insists on the importance of possibility —in particular on the possibility to divide universals in conjunctions of universals. Furthermore, in this letter, Armstrong raises another question to Grossmann. It concerns the relation between universals and sets. He asks Grossmann to give an example of a universal other than that of being a class which does not determine a set. Grossmann gives existence as an example of a universal which does not determine a set. Then Armstrong asks Grossmann whether is not preferable to drop the universal of being a class. Grossmann, however, replies that he has a direct awareness of that universal and also that without the universal of being a class set theory would be “a piece of fiction”. II A discussion of the semantics for the statements of laws of nature is the subject of the second section of this volume. Grossmann starts the debate. He takes the ontologically explicated Humean view that laws of nature are quantified conditional facts such as the fact that everything which is F is G. Armstrong, however, proposes in the idealist tradition that they are rather necessitation connections among universals F and G and thus facts of the form R(F,G). Grossmann then asserts that Armstrong’s understanding of laws is mistaken because such necessitation connections are not phenomenologically given to us. He points out that there is no other way to know the necessitation relation between F and G than through the things which are F and G. But Armstrong asserts that Grossmann’s viewpoint involves insuperable theoretical difficulties. Grossmann agrees with Armstrong that laws can be connections among universals. However, he raises an epistemological objection,

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namely, “If there were such a relation between universals as necessitation (or whatever else you may with to call it), then we should (in principle) never have to look at a second swan, a second electron, etc., in order to find out whether the relevant law holds. But we do have to conceive ourselves by induction, so to speak, that the law holds.” In other words, natural laws would be a priori truths. Armstrong’s reaction is saying that Grossmann is wrong because the form of the connections among universals is not that of relational facts, but rather that of the dyadic predicates to which no dyadic universals correspond. Furthermore, concerning Grossmann’s objection to the perception of the connections among universals, he holds that is possible to perceive them as causally related. In his reply, Grossmann summarizes his objection to Armstrong by claiming that if Armstrong’s analysis of the laws of nature were correct, then he should be able to establish a law of nature on the perception of a single instance of it. III The third section of this volume is about the correct categorization of numbers. Curiously, Grossmann and Armstrong were concerned during that time with this same subject. Armstrong together with Peter Forrest was working on “The Nature of Numbers” (published in 1987), and Grossmann on his “The Fourth Way”: A Theory of Knowledge” (published in 1990) which focuses on the ontology and epistemology of arithmetic. This circumstance is noted by Grossmann in the first letter of this section. Armstrong starts the discussion by making clear that according to his view numbers are tied to aggregates. Grossmann rejects Armstrong’s aggregates. For him, Armstrong is wrong because he confuses the arithmetic “+” with an aggregating of elements. Armstrong reacts claiming that he does not see any problem in considering the function values of “+” to be particulars exemplifying the complex universal of being an aggregate. Customarily, they are called mereological sums. For Grossmann, however, the identity conditions for such sums are not clear. It is not enough to be told that they differ from those of sets. Armstrong then gives a mereological account for the relation between aggregates, sets and sums. However, Grossmann holds that this particular sort of whole does not exist because “+” does not allow to define a whole-part relation. Armstrong, on the other hand, asserts that the main disagreement between them is about acceptable kinds of wholes. Accord-

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ing to him, mereological sums are not sets, but “wholes” in terms of Grossmann’s own terminology. Grossmann claims that Armstrong’s sums really are sets. And he rejects the sums unless they are taken to be sets. Grossmann raises an ultimate objection to Armstrong concerning the identity of the mereological sums. In his own words: “You must deny the law of the indiscernibility of identicals (at least, for relations) for sums. The first sum has a as a part, the second does not; yet they are identical (the same).” IV “Appendices” is the last section of the present volume. It consists of three commentaries of Grossmann and Armstrong on important books of the other. The first is a review made by Armstrong of Grossmann’s “The Categorial Structure of the World”; the second, a commentary by Grossmann on Armstrong’s “Universals: An Opinionated Introduction” (Westview, 1987); and the third, a commentary by Armstrong of Grossmann’s “The Existence of the World”. These commentaries, we think, will furnish to the readers of this volume overviews and comparisons of the ontologies of Grossmann and Armstrong. Finally, it should be noted that not all letters are printed entirely. In a few letters philosophically irrelevant passages have been left out. The omissions are indicated by points.

Madrid (Spain); Darmstadt (Germany) April 2009 JAVIER CUMPA & ERWIN TEGTMEIER

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Beginning: Universals

The Start

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On the Simplicity of Universals 21-IX-76 Dear Professor Armstrong: Thank you very much for your last letter. I must confess that I do not really have an argument against the existence of conjunctive properties other than the one mentioned in my Ontological Reduction and Russell’s Paradox and Complex Properties. However, even though I agree with you that science will in many cases determine what properties there are, I also think that color shades, for example, are simple properties (other examples: being square, pitches, etc.) I am convinced of this on phenomenological grounds, so to speak: What would I have to discover, for example, to find out that being square is not a simple property? The only thing I could discover, it seems to me, is that this property is connected with other properties (by “if and only if” or “if, then”), but not that it consists of them. Sincerely, Reinhardt Grossmann

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On the Complexity of Universals 21-X-76 Dear Professor Grossmann: Many thanks for your letter of September 21st. 1. I agree that there are qualities which are phenomenologically simple, epistemologically simple as I put it. But I think that this means is only that they appear simple. They may still be complex. And if we have other (e.g. theoretical scientific) reasons for thinking that they are in fact simple, then I think that scientific theory can outweigh phenomenology. (I agree with Russell who, in his last phase, said that we can know that many things are complex, but not that anything is simple.) I believe that physical theory gives us good reason for thinking that the phenomenologically simple qualities we perceive are in fact complex. Hence my Reductive Materialism. 2. I agree that we must distinguish between: (A) Property P is connected with Q, R, S … etc. (B) Property Q consists of Q, R, S … etc. It is the latter which I wish to maintain concerning the “simple” sensequalities. 3. I was fascinated to find that you think that being square is simple. I would say that it is obviously complex. The geometrical definition — four-sided, rectangular, plane figure— appears to mirror, more or less, the complexity of the property, although this is not always the case (e.g. with a definite description of a property it is not the case.1) Best Wishes, David Armstrong 1

Cf. your “Structures, Functions and Forms”, p. 25, second paragraph.

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The Phenomenological Argument for the Simplicity of Universals 30-XI-76 Dear Professor Armstrong: Thank you very much for your last letter. 1. In regard to simple properties, I suppose the best way to put my difference with you is to say, somewhat misleadingly, that phenomenal simplicity is for me the ultimate criterion for simplicity. I could perhaps even say: “That is what I mean by simple”. The reason for this is that in every case where P is phenomenally simple, but claimed by someone else like you, to be really (scientifically) complex, I think of the properties of which P supposedly consists as being merely connected with it. In effect, I am claiming that you cannot distinguish between the two: consists and connected with, or, if you prefer, I challenge you to do it. I surmise that you cannot find a stronger criterion than the one you will formulate for the latter relation (since you do not have the only one which in my opinion does the job, namely, phenomenal simplicity.) For example, why does the property of being square consist of the properties of being four- sided, rectangular, etc., but does not consist of the numerous other properties which squares, according to the laws of geometry, have (with which they are connected)? Naturally, if you give up the distinction between consists of and connected with, as I think you really do, even though you do not say so, then it is no wonder that you should also come to agree with Russell that many things are complex, as far as we know, but nothing may be simple. For to know that something is simple would amount to knowing that it is not connected with any other property in the relevant way, and one may well doubt that there is any such property. All the best, Reinhardt Grossmann

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The Scientific Argument for the Complexity of Universals 4-I-77 Dear Professor Grossmann: Thank you for your letter of November 30th. 1. I think that we are in a bit of an impasse about phenomenal simplicity. I agree that phenomenally simple P might really be simple (be as it appears) and merely be connected with a complex (scientifically established) property. What I do not see is that this has to be the case. In the case of the secondary qualities I suspect that it is not the case. Ad hominem. If you say that phenomenal simplicity is “what you mean by simple” are you not trying to secure your ontological point “by definition”? Ad hominem again. If squareness is not simple, it certainly appears not to be simple. The phenomenological difference between redness and squareness “strikes the eye”. Squareness appears to involve four-sidedness and rectangularity. I do not assert this dogmatically, but it looks quite a plausible assertion. (With my a posteriori Realism I am not even confident that squareness is a genuine universal, i.e. that all squares are identical in some respect.) You ask me about the other properties of squares with which they are connected according to the laws of geometry. Should I not include them also? I do not think so. It will depend what other properties of squares that you have in mind. Relational properties of (all) squares it seems that we can exclude, at any rate if we abstract from Relativistic considerations for simplicity’s sake. In a Newtonian universe squareness seems clearly not to be a relational property.

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Of non-relational properties the question will be whether the property in question is connected with squareness in a law-like fashion, or whether it is (perhaps only partially) constitutive of, i.e. identical with, squareness. You will naturally ask how the status of the property is to be determined in particular cases. That is a difficult question, and I do not have a clear answer off-hand. I think it can be linked with the causal powers bestowed by the properties. If squareness and X bestow the same causal powers, that seems a good (pragmatic) reason for thinking that they are the same property. If not, not. But perhaps counter cases will have to be dealt with individuality, in the light of total science. Yours, David Armstrong

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Objections 1-XI-77 Dear Professor Armstrong: Thank you very much for your letter. I shall comment on your letter of January 4th. 1. I fear you are correct: We have reached an impasse over the simplicity of properties. Let me make my point once more. When I said that phenomenal simplicity is what I mean by “simplicity”, I did not mean to secure an ontological point by definition. Rather, I think that unless one means this by “simple”, one cannot distinguish between mere lawful connection between properties, on the one hand, and complexity of properties, on the other. This is the only criterion I know of which allows one to make this distinction. You seem to propose a different criterion in terms of causal powers. But how can you apply this criterion, since it, as far as I can see, does not distinguish between complexity and lawful connection? Put differently, could not two properties, since they are lawfully connected, have the same causal powers? Squareness appears to me to be simple. Of course, we know that squares have four equal sides. But then we may also know other laws of geometry which link squareness to other properties in a lawlike fashion. Just because a law may be obvious to most people does not make it any less of a law. But could children, perhaps, sort squares by shape without being able to count to four? And how many adults know, without counting, how many edges a cube has, even though they can easily sort out cubes? Sincerely, Reinhardt Grossmann

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A Reply to Objections 14-XI-77 Dear Professor Grossmann: Many thanks for your letter of November 1st. I am glad that we are back in communication.

1. Phenomenal Simplicity and Ontological Simplicity: I am glad to be assured that you do not try to establish the ontological simplicity of the phenomenally simple by definition. Let me see whether I can reconstruct your argument. Suppose that there is a phenomenally simple property, P, and a complex structure of properties, Q, which qualify all and only the same particulars. Now consider the hypothesis that P = Q. It is clear, however, that there is alternative to this hypothesis viz. that (x) (Px ≡ Qx) is a law of nature, and where P is, as it appears to be, simple. What is worse, there seems to be no possible way of choosing between the two hypotheses. Ad hominem against Armstrong. He offers a criterion of identity for properties in terms of their causal powers. But it appears that P and Q will have the same causal powers. So Armstrong will be forced to conclude that P = Q and so reject the second hypothesis. But it is clear that the second hypothesis is always a real possibility. And since there is no way of showing that the first hypothesis is true, I, Grossmann, suggest that we should adopt the principle that the phenomenally simple is really simple.

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Against this, my own (Armstrong’s) view is that both P = Q and (x) (Px ≡ Qx) are genuine logical possibilities. I do agree that, in this situation, I would have to come down on the side of P = Q. But my causal criterion of identity for properties is pragmatic only, (x) (Px ≡ Qx) with P simple, remains a real possibility, even if a possibility that one has no reason to assume to be actual. There are, however, other scenarios where one might decide that P ≠ Q. Suppose that some Ps are associated with the complex structure Q but not with R, while the other Ps are associated with the complex structure R but not with Q. In such a case P cannot be identical with Q. As for squareness being simple, it may be simple, but I am amazed that you should say it appears simple. My phenomenological intuition is that redness is simple, but squareness is complex. You point to the possibility that children might sort squares without being able to count four. I accept this possibility. Indeed, I would say that there might be beings for whom square things had nothing more than an unanalysable, gestalt, quality. Amazingly enough, however, I have in the past used this case to argue that it is possible that a quality should appear simple (as the gestalt quality would appear) yet be complex, as (I think) squareness is! I suppose that it is logically possible that these beings are picking up a genuinely simple quality which is merely contingently connected with four sides, etc. But this quality would not be squareness because, I would contend, it is analytic in our language that squareness involves having four equal sides.

Sincerely, David Armstrong

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A Legacy: Gustav Bergman 29-XI-77 Dear Professor Armstrong: Thank you for your last letter. In regard to universals, you agree, as I see it, fully with my position; that is, the position which Bergmann and his students have held for many years now (and which was extremely unpopular twenty years ago!). I put it this way, because this is one view of Bergmann’s which in my estimate is correct and also much maligned. It is amazing indeed, and gratifying to me, that we should agree on so many rather unpopular issues; for example, I also agree that there are no unexemplified properties. However, there is one issue on which we have not made any progress: The issue of ontological reduction. It crops up in connection with several points you mention in your letter: simplicity, conjunctive properties, and complex entities. I shall try to write you a lengthy letter on this subject soon. Sincerely, Reinhardt Grossmann

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A Legacy: John Anderson 8-XII-77 Dear Professor Grossmann: Many thanks for your letter of November 29th. The position I take on universals was originally derived from John Anderson. However, I have differed from him in certain ways. He denied that anything was absolutely simple. I say only that I know of no reason to assert that anything (and, in particular, any universal) is simple. My sympathy with physicalist reductions —and perhaps, other reductions— derives partly from temperament and partly from the example of J. J. C. Smart. You appear to be both more sympathetic to simplicity and more hostile to reduction than I am! All the best. Yours, David Armstrong

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The Nature of Universals 7-VIII-78 Dear David: We have been back in Bloomington for about four weeks. I have not written sooner because I have been working hard on a review of your book! Well, it is finished. I just gave the manuscript to be typed to the secretary. As soon as I have clear copies, I shall send you one. Hector Castañeda is publishing it in Noûs. It is his practice to send a copy to the author of the reviewed book for comments before he publishes the reviews. So you will get another copy through him eventually. At any rate, it was a labor of love. As always, Reinhardt

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Armstrong’s Universals & Scientific Realism Armstrong’s latest book is excellent. (D. M. ARMSTRONG, Universals and Scientific Realism; vol. 1: Nominalism and Realism; vol. 2: A Theory of Universals, both vols. Cambridge, 1978). It compares favorably with most contemporary contributions to ontology. For one, Armstrong’s style is transparent and unaffected. More importantly, his positions are stated clearly. This quality cannot be praised enough. For being obscure seems to be a prerequisite for being in philosophical fashion. Just think of the ink that has been spilled on what indeterminacy of translation really means. Or try to puzzle out what the causal theory of names has to do with philosophy. Many a thesis, I fear, will receive more attention when formulated indistinctly than when espoused by Armstrong with his customary clearness. Furthermore, Armstrong’s book contains an abundance of arguments. And arguments, as most of us have realized, are hard to come by in ontology. Arguments are usually supplanted either by ringing profession or else by slander of the opposing view. Some philosophers, for example, rest content with announcing that they shall not countenance abstract entities, as if such entities could be blustered out of existence. Others make fun of other minds by calling them “ghosts in machines”, as if they could be shamed out of existence. Seldom do we find arguments, as I said, an even rarer is a book, like Armstrong’s, which tries to be fair to the opposition. Finally, this book is written from a point of view —“scientific realism”, as Armstrong calls it —and thus presents us with a metaphysical frame of reference. One can easily see how some of Armstrong’s fundamental assumptions originate in his empiricist Weltanschauung. In the first volume, Nominalism and Realism, Armstrong argues persuasively against three ontological positions. Firstly, he considers and rejects all forms of nominalism, that is, of the view that there are nothing but particulars. A property, he shows, is neither a predicate, nor a mental concept, nor a class, nor a concrete (spatio-temporal) whole. Nor can it be reduced to a resemblance relation between particulars. He thus joins that small group of contemporaries, consisting mainly of Bergmann and his students, who hold that properties form an irreducible category of the world. But even though Armstrong’s conclusions are not new, nowhere else has the case against nominalism been presented as clearly and cogently as in this

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volume. And the same can be said about Armstrong’s treatment of the other two ontological positions. He argues, secondly, that “Particularism” is false. According to this view, held by such famous Brentano students as Husserl and Meinong, and most ably defended by Stout, the ordinary properties of things are particular. For example, the particular color shade of a billiard ball is said to be particular in that no other entity as a matter of ontological necessity can possess this identical color. Thirdly and finally, Armstrong argues convincingly that the bundle view of individuals is wrong: Individuals things are not bundles of properties. At the end of this series of arguments, Armstrong is left with two irreducible categories: Particularity and Universality. And the question naturally arises of how particulars are related to universals (properties and relations). It is at this point, I believe, that Armstrong goes wrong. He denies that there is any kind of relation between a particular A and the property P which it has. A is admittedly distinct from P. But their union is said to be closer than relation. (Vol. 2, p. 3). Armstrong refers to Scotus’ “formal distinction” as a possible explanation of how a particular can be united with a property without being related to it. He admits that they are somehow united. Such a unit is called a “state of affairs”. In general and in my own words, a combination of a particular with a property, or of several particulars with a relations, is a state of affairs. I fail to see how two nonrelational entities, a particular and a property, can form some kind of a whole (other than a class) without being related to each other in some way. Put differently, it seems to me to be one of the most fundamental laws of ontology that every complex entity (always: other than a class) involves at least one relation. In our case, the so-called nexus of exemplification holds between the particular A and the property P. Armstrong readily admits that there are relations. What is more, he thinks of many complex entities as involving relations. Why then should he also think that states of affairs form the exception to the ontological law just mentioned? Why should he deny the nexus of exemplification, even though he has no qualms about relations in general? 1. Armstrong’s Case against the Nexus of Exemplification There seems to be curious prejudice against exemplification. Philosophers who have nothing against relations in general will go to some length to discredit the view that individual things exemplify properties. Armstrong is

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a case in point. If we inquire into his reasons for rejecting exemplification, then we find just one argument, namely, a version of Bradley’s regress. All details aside, this fact alone is rather odd. For Bradley’s regress argument is supposed to show that there are no relations at all. How could it possibly be used, therefore, to excise the nexus while leaving all other relations safe and sound? According to the view I wish to defend, the nexus of exemplification holds between a particular A and a property P whenever A has that property. This relation is sui generis, irreducible to any other relation, and not to be confused with a spatial relation, a whole-part relation, or class-membership. Anyone who has ever perceived that some individual has some property is acquainted with this relation. Exemplification has certain obvious characteristics, for example, it is asymmetric. Now, how does Bradley’s regress argument affect this view? To see that it does not, we must sharply distinguish between two quite different arguments which may be attributed to Bradley. I shall call them “Bradley One” and “Bradley Two”. Bradley One is really not an argument against relations at all, but rather an argument against an argument for relations. Tailored to the case at hand, the argument for relations goes like this. (1) If the fact that A is P consisted only of A and of P, then it would have to exist if A exists and P exists. (2) But A may exist and P may exist without its being the case that A is P. (3) Hence this fact cannot just consist of A and of P. (4) Hence it must contain a relation which connects A with P. (5) Thus the nexus must exist. Bradley One points at one of the flaws in this argument. (1) Assume that the nexus R is a constituent of the fact that A is P. (2) Then A exists, and P exists, and R exists. (3) But from the fact that these three entities exist, it does not follow that the fact exists. (4) Hence, by the earlier reasoning, we would have to conclude that the fact cannot consist just of A, P and R. (5) But if we introduce a further relation, R´, the picture does not change: The existence of the class consisting of A, P, R, and R´ does not guarantee the existence of the fact that A is P. What Bradley One shows, in essence, is that premise (1) of the original argument is false. The fact that the fact under discussion consists of A, P, and R does not imply that, if the class of these constituents exists, then the fact must exist. In general, from the existence of any class of particulars, properties, and relations, nothing follows as to the existence of certain facts

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rather than others. But, of course, I do not claim that something does follow. Quite to the contrary, I insist that the existence of exemplification does not explain why some facts exist rather than others. Bradley Two runs as follows. (1) Assume that R holds between A and P, as I claim. (2) If A is related to something by R, then A is related to R. (3) If any two entities, E1 and E2, are related to each other, then there exists a third entity, a relation, which relates them. (4) Now, it follows from (1) and (2) that A is related to R. (5) But from (3) it follows then that there exists a relation, R´, which relates A and R. (6) Applying (2) again, it follows that A is related to R´. (7) It therefore follows by (3) that there is a relation R´´ which relates A and R´. And so on. Assumption (1) together with principles (2) and (3) thus leads to the conclusion that there exists an infinite series of further relations: R´, R´´, etc. Equivalently, it shows that the fact that A stands in R to P is infinitely complex. The first thing to notice about Bradley Two is that there is nothing vicious about it. If sound, it merely shows that an infinity of relations exists or, equivalently, that the fact is infinitely complex. Some philosophers, like Meinong, have simply accepted this consequence. Secondly, this conclusion can be avoided if we reject one or more of the assumptions which I conveniently numbered (1) to (3). I take it that Bradley accepts (2) and (3), but rejects (1). And this, obviously, must be Armstrong’s strategy. But I think that the proper response is to reject (3). From this point of view, what the argument shows is that not any two entities, in order to be related, require that a relation hold between them. (3) must be replaced by the weaker: (3´) If any two entities, E1 and E2, which are not relations, are related to each other, then there exists a third entity, a relation, which relates them. It is ironic that an argument considered to be the most powerful weapon against relations actually harbors one of the most important insights into the nature of relations. Relations differ from all other categories in that they and they alone need not be related to what they relate. Once realized, this insight is entirely obvious. Think of the nonrelational entities in the world as wooden boards, and of relations as the glue of the world. For two or more boards to stick to each other, to be connected with each other, some glue must hold them together. But this glue itself needs no “super glue” in order to stick to the boards. Thus to accept principle (3) is to over-

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look a fundamental categorial difference between relations, on the one hand, and nonrelational entities, on the other. It indicates a certain blindness to the peculiar nature of relations. Exemplification, being a relation, need not to be related to A and to P in order to connect A with P. Thus there is no infinite series of relations and, hence, no argument against exemplification. On the other hand, how fares the view, adopted by Armstrong, that A and P form a whole without being related? Obviously, no light is shed on this, to my mind, ontological impossibility by calling the property “unsaturated”. Those who appeal in this matter to Frege’s authority would do well to read his argument for the unsaturatedness of the falling-under relation at the end of his reply to Kerry. (On Concept and Object, in Translations from the Philosophical Writings of Gottlob Frege, ed. by Peter Geach and Max Black. Oxford, 1969, pp. 42-55). Nor will it do to fall back on Wittgenstein’s metaphor of the links in a chain. (Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F. McGuinness. London, 1961, 2. 03). If we take this illustration seriously, then it proves just the opposite from what our opponent intends. For two links must quite obviously stand in a certain spatial relation to each other in order to form the links of a chain rather than unconnected links. Nor, finally, does Armstrong’s own attempt at removing the mystery succeed. He compares the way in which A stands to P to the way in which size and shape are related to each other. But size and shape go together because whatever has the one has the other, and conversely. Their relationship is mediated by exemplification. Armstrong seems to realize that it is impossible to depict the fact that A is P without somehow representing the nexus of exemplification. And, surely, this is a most powerful argument for the existence of that nexus. Of course, instead of the copula “is” or some other word, we can use a different devise, like juxtaposition, to represent exemplification. But we cannot do without some means of representation or another. Armstrong suggests, in this context, that we may try to write A in green ink in order to state that A is green without hinting at a relation between A and the color. (Vol. 1, p. 111). Shades of Sellars’s attempt to bolster nominalism by getting rid of predicates! But just as little as this gimmick works in Sellars’s behalf, as little will it help Armstrong. Firstly, if it could succeed in the case of exemplification, it could also succeed in the case of the color. But Armstrong, the champion of realism, would hardly be impressed by Sellars’s

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move. Secondly and more importantly, it should be clear at any rate that, by writing A with green ink, one merely represents the nexus and the color by themselves. And that this way of representing them does not show that they do not exist follows from the fact that we can just as easily represent A by itself. After everything is said and done, Armstrong’s case against exemplification consists of one argument. And this argument shows, in my opinion, not that there is no nexus, but that exemplification differs importantly from non-relational entities. On the other side of the ledger is the fact that it is impossible to represent the fact that something has a property without representing the nexus of exemplification. 2. Armstrong’s Argument for the Existence of Conjunctive Properties In the second volume, called “A Theory of Universals”, Armstrong relies heavily on his contention that there are so-called conjunctive and structural properties. For example, he tries to elucidate the notion of number by invoking certain structural properties of wholes. Also, his account of similarities between properties in terms of partial identities depends on there being structural properties. I shall therefore concentrate on this basic contention and argue that it is false. But this second volume, just like the first, also contains many views with which I agree; and it, too, abounds with clever arguments. Armstrong argues that there are no disjunctive and negative properties. But he thinks that he cannot rule out conjunctive properties because his empiricism dictates that we leave open the possibility that there are properties which do not reduce to complexes of simple properties. In other words, his argument is that since it is logically and empirically possible for all properties to be conjunctive properties, we cannot deny the existence of conjunctive properties. (Vol. 2, p. 32). I have argued elsewhere that there are no complex properties, and I shall not repeat those arguments in detail. (Compare my Russell’s Paradox and Complex Properties, in Noûs, 6. 1972, pp. 153-164; and Ontological Reduction. Bloomington and London, 1973, pp. 116-122). But I shall discuss the significance of Armstrong’s argument for my position. If I am correct, then it is false, though not logically impossible, that there are conjunctive and structural properties.

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For the sake of illustration, let us assume that some individual thing A is both green and round, that is has these two properties. According to Armstrong, there exists then also a complex property, consisting of these two properties, which I shall call “ground”. According to my view, on the other hand, no such property exists. There exist these two properties, the color and the shape, and there also exists, most importantly, the fact represented by (1) “A is green and A is round”, but there exists no third entity of the category property. Furthermore, (1) can be abbreviated to (2) “A is green and round”, or, after coining the artificial “ground”, even to (3) “A is ground". But (2) and (3) are just convenient abbreviations of the longer (1) and represent, though less perspicuously, what (1) represents. Now for three comments. Firstly, I invented the artificial “ground” in order to leave open the question of how complex property is constituted. I take for granted, in this context, that conjunction between states of affairs (propositions, etc.) is noncontroversial. Now, the property ground consists presumably of the color and the shape, but what relation binds these two properties together so that they form a complex property? Armstrong, curiously enough, never raises the question. He simply seems to take for granted that this relation is ordinary conjunction and represents it by “&”. But, of course, it cannot be; for ordinary conjunction always holds between states of affairs; and its behavior is summarized by the familiar truth-tables. As far as I can see, only two possibilities are open to Armstrong. He could insist that the familiar relation of conjunction also holds as a matter of brute ontological fact, between properties. Or he may claim that a different, but “conjunction-like”, relation ties properties together into conjunctive properties. I cannot think of a plausible candidate for this latter role. As to the first alternative, is it not more plausible to hold, as I do, that “green and round”, as it occurs in (2),

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is, not the expression for a property, but merely a convenient contraction of a part of the longer (1)? I venture to claim that, if it were not for this kind of convenient abbreviation, the view that there are conjunctive properties would have little appeal. Secondly, to see this clearly, we must spell out Armstrong’s view implies. Either (2) and (3) are mere abbreviations of (1), or else they are not. If they are, then my case is closed: There are no conjunctive properties. Armstrong must therefore hold that they are not abbreviations of (1). Let us concentrate on (2). What (2) represents is, presumably, a fact which contains the complex property ground. But (1) does not represent such a fact. Hence the fact represented by (2) cannot be the same as that represented by (1). Thus the assumption that there are conjunctive properties leads to an unnecessary multiplication of facts. For every conjunctive fact of kind (1), there must then also exist a corresponding fact of kind (2) (or (3)) which contains a conjunctive property. And what could be the appeal of a view which has this implication? Armstrong, however, denies that his view has this unpalatable consequence. He says that we must not misunderstand the admission of conjunctive properties since there is “no reason to postulate conjunctive properties additional to the properties which go to make up the conjunctive property: the conjuncts”. (Vol. 2, p. 30). Presumably, there are no three “wholly distinct properties”, namely, green, round, and ground. “The blade of a knife”, Armstrong says by way of illustration, “is a thing, its handle is a thing and the whole knife is a thing. But this does not mean that there are three wholly distinct things: the blade, the handle, and the knife”. (Ibid.). It is clear from Armstrong’s subsequent exposition that by “wholly distinct” he means “not a part of” in a very wide sense of “part of”. The blade is not wholly distinct from the knife because it is a part of the knife. The color is not wholly distinct from the property ground because it is a part of it. I shall agree with Armstrong’s particular terminology. But this agreement does not affect the issue between us in the slightest. The blade is not identical with the knife, even though it is a part of it, and that is all that matters. For if the blade is not identical with the knife, and the handle is not identical with the knife, and the blade is not identical with the handle, then there are three things. Similarly, even though both green and round are part of ground, ground is not identical with either. A fact, therefore, which contains ground cannot be identical with a fact which, instead of ground, con-

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tains the two properties green and round. The view that there are conjunctive properties leads, as I shall say again, to an unnecessary multiplication of facts. Thirdly, we can now also appreciate why Armstrong’s argument from scientific progress is spurious. No conceivable discovery of science could possibly prove that there are conjunctive properties; for science cannot distinguish between facts of kind (1), on the one hand, and facts of kinds (2) and (3), on the other. Try to imagine that at some time everyone believes that certain things have the property of being ground. There is general agreement that this is a “simple” property of things. As it turns out, though, it is soon discovered that ground things are invariably green and round, and conversely. This, we shall assume, is a scientific discovery of great significance. Now, I shall concede, for the sake of making my point more forcefully, that in this case science discovered that a sentence like “A is ground” represents a conjunctive fact of the form A is green and A is round. But I deny that science proved ground to be a conjunctive property. In order to show the latter, science would have to be able to prove that there is, not only the conjunctive fact just mentioned, but also another, additional, fact of the form A is green-and-round. By the very nature of the question, science cannot decide whether we are dealing with a conjunctive fact or a fact containing a conjunctive property. Therefore, it cannot possibly discover that there are conjunctive properties. The existence of complex properties, contrary to Armstrong’s belief, is not a matter to be decided by science, but by ontology. 3. Armstrong’s Use of Structural Properties In addition to conjunctive properties, there are also, according to Armstrong, structural properties. Since structural properties, if there were such things, would be complex, I think that he is wrong again, and for the same reason. A structural property, roughly, is a property something has a matter of having certain parts, with certain properties, standing in certain relations. To have a simple example, assume that something is checkered just in case it consists of exactly two squares, one black, the other white, which stand in relation R to each other. Now, whether or not being checkered is a structural property depends on the precise meaning of the “just in case” in the last sentence, and “as a matter of” in the sentence before that. I shall

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again concede that the sentence “A is checkered” is a mere abbreviation for: (1) “A consist of a black square and a with square, which stand in R to each other”, which represents the fact under discussion more perspicuously. Thus I admit that this fact involves such properties as being a square, being black, and being white, and that it involves the relation R. But I deny, as before, that there is an additional fact which involves a complex property. Notice that the question of what ties properties together so as to form complex properties is especially acute for structural properties. In the case of conjunctive properties, there is at least the verbal bridge “A is green and round” which leads from “A is green and A is round” to “A is ground”. But no comparable intermediary exists between (1) and “A is checkered”. As a consequence, Armstrong cannot just go ahead and use signs ambiguously —as in the case of conjunctive properties— to stand both for (sentential) connectives and for relations between being square, being white, being black, R, and whatever else may be involved, so that a complex property of being checkered appears? Until Armstrong answer this question, his explication of what it means for properties to resemble each other in terms of partial identities between structural properties must remain obscure. Let me explain. Armstrong raises the question of what is common to all determinate shades of red, and he rejects the answer that the common feature is either a common property or a matter of a relation of similarity. He holds that what unifies, for example, the class of lengths is a partial identity that holds between any two lengths. In other words, any two lengths stand to each other as part to whole or whole to part. Assume that M and N are two length properties, and that M, as one ordinarily says, is a greater length than N. Now, in what sense can the property N be said to be a part of the property M? M cannot be a conjunctive property consisting in part of N; for then it would follow that anything which has the length M also has the different length N. M, according to Armstrong, is a structural property. I take this to mean that something has M as a matter of having parts A, B, C, etc., which have such lengths as N, O, P, etc. Now, I understand what it means to say that some individual has the spatial parts A, B, C, etc., because, if A and B

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are spatial parts of some individual, then they also stand in familiar spatial relations to each other, and conversely. But I do not know what to make of the fact that M consists of N, O, P, etc.; for I do not know how these lengths are related to each other so that they form the complex property M. The notion of a structural property is also important for Armstrong’s attempt to defend the view that numbers are properties of complex entities. Assume that there are three apples on a table before you. These three apples for, leaving time out, a spatial whole. This whole, call it “A”, has, according to Armstrong, the structural property of consisting of three apples. Something has this property as a matter of consisting of three different parts which are apples. But it is clear that the number three cannot be identical with this structural property; for otherwise A would also have to have the structural property of consisting of three oranges. This failure suggests that we turn to the more general property of consisting of three parts, of being three-parted, as Armstrong puts it. According to Armstrong, A has this structural property, but it also has the property of being four-parted, and the property of being ten-parted, etc. A complex entity has as many of these properties as it has parts. Frege’s famous deck of cards, conceived of as a spatial whole, is thus both thirty-two-parted (since it consists of thirty-two cards) as well as four-parted (since it consists of four groups of cards). Now, Armstrong suggests that, given certain reservations, these more general structural properties may be identified with numbers. But I do not think that they could, quite aside from the difficulties mentioned by Armstrong himself. For consider the alleged structural property of being three-parted. If there were such a property, then it would contain the relation of being three-parted. If there were such a property, then it would contain the relation of being a part of in addition to the number three —whatever that may turn out to be. Hence, it could not be identical with this number. But is numbers are neither specific nor general structural properties of this sort, what are they? Armstrong denies the existence of classes. Therefore, he cannot give one of the traditional answers that numbers are classes of properties (Frege), that they are classes of classes (Russell), or that they are properties of classes (Cantor). But until he shows that they can be taken account of by his ontology, his stand against entities other than particulars and universals appears arbitrary.

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4. Armstrong’s World-Hypothesis At the end of the first volume, Armstrong proposes the following “worldhypothesis”: (1) The world contains nothing but particulars having properties and related to each other. (Vol. 1, p. 126). But he also believes, as part of his Naturalism, that another very general thesis is true, namely, (2)

The world is nothing but a single spatio-temporal system. I would like to suggest that these are not so compatible with each other as Armstrong sees to believe. And I think that he does not recognize a clash because he does not appreciate the categorial uniqueness of state of affairs.

According to Armstrong, particulars and universals combine so as to form combinations of two sorts: (3) (4)

Particular A has property P: ‹A, P›, and Particulars A, B, … stand in relation R: ‹A, P …, R›.

These combinations, he says, may be called “states of affairs”. But, very surprisingly, he also holds that the recognition of such combinations does not imply that there is a third category of entity, namely, the category of state of affairs. (Vol. 1, p. 80). It is not evident, though, that a state of affairs is a unique combination of particulars and universals and, hence, categorially different both from particulars and universals? Here, too, Armstrong’s analogy to the case of a knife’s consisting of blade and handle is of no help. For it is not equally evident that knives constitute a third kind of thing in addition to blades and handles? Armstrong’s hesitancy to give full ontological status to states of affairs finds various terminological expressions. For example, he introduces a distinction between thin and thick particulars. A thin particular is a particular, but a thick particular is a certain kind of state of affairs, namely, a state of

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affairs of the form (3), which contains a conjunctive property consisting of all the properties of A. Let us depict this kind of state of affairs by (5) ‹A, N›; “N” for “nature”. Quite frequently, Armstrong speaks of “propertied particulars” when he means states of affairs of kind (5). And this creates the illusion that his ontological world can be identified with physical universe. Just look at his world-hypothesis (1) to the effect that the world contains nothing but particulars having properties and related to each other. The ambiguity is in the expression “particulars having properties and related to each other”. We may read it as something like: “particulars, which happen to have properties and which are related to each other”. And then it may be easy to imagine that such a network of particulars forms the spatiotemporal system of the physical universe. But this kind of reading is not faithful to Armstrong’s ontology. According to this ontology, the world contains nothing but particulars, universals, and certain combinations of these, that is, state of affairs. Or we may read the crucial phrase like this: “state of affairs of kind (3) and (4)”. This agrees, on the whole, with his ontology. But now there can be no illusion that this world, consisting of state of affairs, is the physical universe; for it is not state of affairs, I take it, which form a single spatio-temporal system. While Armstrong’s ontological world is a world of state of affairs, his naturalistic world is a world of spatio-temporal particulars, I believe that both worlds exist. But I object to Armstrong’s identifying them. I can put this objection differently. According to Armstrong, first order universals (properties and relations) can have second order universals. For example, nomic connections —the ontological ground of lawfulness— are conceived of as relations between first-order properties. When, then, does Armstrong not put forward the following hypothesis: (6)

The world contains nothing but universals, instantiated by particulars and universals and universals, and related to each other?

Of course, I think that (6) is just a misleading as (1), but this is not the point. Had Armstrong proposed (6), be it misleading or not, it would have

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been apparent that the world mentioned in (6) could not possibly be the world of his naturalistic bent. For the latter is not a complicated system of universals. This conflict between Armstrong’s realism and his naturalism comes to a head when he presents a general argument against the existence of all kinds of entity other than particulars and universals (Vol. 1, pp. 126-132). His argument rests on the naturalistic principle that, since such entities do not causally interact with particulars, they should be exorcised by Occam’s razor. But does this principle not equally apply to universals and states of affairs? Do not universals and states of affairs stand causally aloof from particulars? And if an exception to the principle must be made for universals and state of affairs, why not for classes and numbers? To escape from these questions, Armstrong, I believe, may have thought of the interacting particulars as thick particulars, that is, as states of affairs. At the end of his argument, he states that particulars act upon each other solely in virtue of their properties, that is to say, in Armstrong’s own words, “that it is states of affairs which are causes”. (Vol. 1, p. 132). But now he faces another set of questions. If only thick particulars interact with each other, should we not have to exorcise, not only universals, but also particulars? And does this mean that the only entities that can be said to exist by the naturalist’s light are states of affairs? Finally, there is a separate problem with Armstrong’s naturalistic criterion of existence. There are facts in his ontology which do not contain particulars at all, for example, relationships between properties. I take it that these entities cannot be causes at all, not even in the sense of involving propertied particulars. How, then, can we justify their existence in agreement with the naturalistic principle? The world of Armstrong’s ontology is not the same as the physical universe. But that should not disappoint someone like Armstrong who argues so brilliantly and pertinaciously for the existence of universals. Rather, it should be viewed as welcome confirmation of the truism that ontology is not physics. With Best Regards, Reinhardt

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A Reply 14-IX-78 Dear Reinhardt: Thank you for your last letter. I was only being jocular when I spoke about your preferring the critical to the constructive part of my book! It is the usual situation in philosophy and I never expected anything else. I quite agree with you also that the constructive part is by far the most exciting. I enclose four pieces which constitute a reply to the critical points that you raised in the review. In order to organize my thoughts I wrote them as I would for publication, rather than simply as a letter to you. Though I do not know at the moment what I want to do with them. Perhaps nothing. Anyway, I should be very grateful if you could tell me at least where I have misunderstood what you wanted to say.

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1. Grossmann on Exemplification In his recent review of Universals and Scientific Realism, Reinhardt Grossmann takes me to task for denying that, when a particular has a property, the particular stands in a relation of exemplification to the property. Following Bergmann, he calls this relation a nexus. He says: This relation is sui generis, irreducible to any other relation, and not to be confused with a spatial relation, a whole-part relation, or class-membership. Anyone who has ever perceived that some individual has some property is acquainted whit this relation. Exemplification has certain obvious characteristics, for example, it is asymmetric.2

In my argument against such exemplification in Chapter 10, Section III, I assume that one who introduced a nexus in the case where a particular has a property would feel equally constrained to introduce a nexus in the case where two or more properties are related. If Pa requires a nexus to relate P and a, then, I thought, Ra b requires a nexus to relate R, a and b. But since the nexus is itself a relation, the state of affairs N (P, a) has the form Ra and b. Hence a further nexus will be required to unite the element N, P and a. The resulting regress appeared to me to be vicious, or, at best, viciously uneconomical. Consider, for instance, the following argument, spelled out but rejected by Grossmann, purporting to prove that P and a are united by a nexus: (1) If the fact that a is P consisted only of a and P, then the fact would exist if a exists and P exists. (2) But a might exist and P might exist, But it be false that a is P (suppose a is not P, but b is P).

2

The last sentence quoted appears to commit Grossmann to denying that a property can ever have itself as a property. For F (F) is a symmetrical situation. But since I think that in fact no property can have itself as a property, I do not think that this is a difficulty for his position.

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(3) So a is P cannot just consist of a and P. (4) So, if a is P, then a is related to P. (5) This relation is the nexus. (N) Grossmann accepts the truth of all of (1) to (5), and would deny only the validity of the transition from (3) to (4) (and, perhaps, from (2) to (3)). This transition from (3) to (4) he rejects because, if he accepted it, he would similarly be forced to expand N (a, P), on the grounds that this state of affairs is something more than N, a and P. Furthermore, the same difficulty would arise where two ordinary particulars are related by a relation (Ra b). In fact, however, Grossmann holds that relations need not be related to what they relate to what they relate. Indeed, he says that it is “entirely obvious” that they need not. If a has R to b, there is no call for relations to attach a to R and b to R. Relations relate. Hence, if a is united to P by a nexus, which is a relation, there is no call for further relations, and so no infinite regress. But if Grossmann thinks that Ra b is “allright as it is” why does he not accept that Pa is “allright as it is”? Why expand the latter, but refuse to expand the former? Grossmann gives the following reason: I fail to see how two non-relational entities, a particular and a property, can form some kind of a whole (other than a class)3 without being related to each other in some way. Put fundamental laws of ontology that every complex entity (always: other than a class) involves at least one relation.

At this point, it seems to me that the position is a “stand-off”. I argue that, since the state of affairs Ra b can involve three distinguishable elements yet not require these three elements to be related, so the state of affairs Pa can involve two distinguishable elements yet not require these two elements to be related. Grossmann argues that, since Pa involves two distinguishable non-relational elements, yet is not a class, the elements 3

Many philosophers distinguish between classes and aggregates but hold that, for each class, there exists a corresponding aggregate. Would Grossmann accept this distinction? And if so, would he hold that aggregates involve relations?

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require to be related. How shall we decide between our competing principles? I do not know. My view seems to have two advantages, though I would not claim them to be decisive. First, it involves one less relation in the world. The epistemology of fundamental ontology, that is, the problem of how can know basic ontological truths, is notoriously difficult. In general, the fewer entities we postulate, the fewer problems we will have in explaining how it is that we know, or guess, that such entities exist. Second, it also seems to be a plausible principle, though I do not know how to prove it, that where a relation relates two or more terms, the terms are of the same ontological type. But the alleged nexus relates a particular to a universal. Grossmann, however, does exhibit a strong tendency to beg the question in his own favour. I suggested as a possible model for the way a particular stands to its property, the way that the size of a thing stands to its shape. Whatever the merits or demerits of this suggestion, Grossmann does not refute it by saying: But size and shape go together because whatever has the one has the other, and conversely. Their relationship is mediated by exemplification. This simply assumes that when a particular is of a certain size, and is of a certain shape, then in both cases the particular is related to a property. This is what I deny. Grossmann begs the question again in discussing my suggestion that, from the standpoint of metaphysics, the state of affairs where a is green might best be represented by a green “a”. The point I wished to make was very unambitious. Suppose I am correct in thinking that a’s having P is not a matter of a being related to P. Why nevertheless does it appear, as I agree that it does appear, that a relation is involved? (Though equally, I should have added, when a has R to b further relations appear to be involved.) I suggested that this might be explained by the fact that even the symbolism “Pa”, much less “a is P”, uses relations to symbolise what is, in my view, a state of affairs which does not involve

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a relation. I then pointed out that if a’s being green was symbolised by a green “a”, a non-relational state of affairs would be symbolised by a nonrelational state of affairs (again, in my view), and, it might be, the illusion of a relation would not arise. This was not meant as an argument against the nexus, and, of course, if Grossmann’s view is correct, I would be using the nexus to symbolise the nexus. But Grossmann is not entitled to assume his view and then argue that, with my green “a”, I have covertly assumed the existence of the nexus. 2. Are there Conjunctive Properties? Suppose that a particular, a, has the property P and the wholly distinct property, Q. Then, I maintain, a has the conjunctive property P & Q. Grossmann denies that there are any conjunctive properties. Indeed, he holds the very radical view that every property is simple. We might call this a hyper-atomism concerning properties. It might be useful to begin by mentioning points of agreement between my position and Grossmann’s. They are reasonably extensive. First, Grossmann and I agree that the fact that it is possible to introduce a predicate which applies to an object if and only if it is both P and is Q, is no reason for thinking that there is such a property. There is no valid argument from predicates to properties. (I am, however, somewhat more radical than Grossmann in my application of this point. He assumes that there are such properties as greenness and roundness—apparently simply because the corresponding predicates exist and are applied. I have no such confidence. I should look to the hypotheses of total science to give suggestions for “property-predicates”—predicates which apply in virtue of identical properties in all cases where they do apply.) Second, we agree that the fact that there is a non-null class of particulars which are both P and are Q, is no reason for thinking that there is such a property. There is not valid argument from classes to properties. Third, we agree that, given that a is P, and also that a is Q, there is no additional fact of the matter that a is (P & Q). Following F. P. Ramsey, Grossmann thinks that to postulate this additional fact is unnecessary ontological reduplication. Indeed, this is his positive argument for rejecting

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conjunctive properties. Although I heartily accept his Occamist case here, I do not think that it should lead us to deny conjunctive properties. Grossmann complains that I am at fault because I give no account of the conjunction relation between properties. I agree that I failed to give any explicit account, and that this was an omission. But I think that my view is clear enough. I hold that it is a logically necessary truth that P & Q is a conjunctive property if and only if there exists a particular, x, such that x is P and x is Q. Conjunctive properties are co-instantiations of two or more properties. A co-instantiation of properties is a property. What reason is there to accept conjunctive properties? Since both Grossmann and I hold that properties are universals, we agree that if a has property P, and b also has P, then a and b are identical in that respect. Now it seems very natural to convert that principle, and hold that if distinct particulars, a and b, are identical in that respect, then that respect is a property. But suppose that a has P and has Q, while b also has P and has Q. Is there not a respect in which a and b are identical, viz. having P & Q? So, do not conjunctive properties exist? Grossmann, however, rejects this reasoning. Discussing the case of two things which are both green and round is his paper “Russell’s Paradox and Complex Properties” (Noûs, 6, 1972) he says: It is true that in a manner of speaking there is something common to both A and B in this example, but what is common is not a shared property. Rather, A and B are constituents of similar facts. …Both facts contain the further constituents: exemplification (twice) green, round, and and. We may say that the structure of (the rest of) the two facts is exactly the same.

I agree that if one was determined to deny the existence of complex properties, then this is the best one can do by way of explaining away their apparent existence. But I see no need for such an elaborate epicycle. One important reason for allowing complex properties is that it seems logically and epistemically possible that every property is complex. (Grossmann incorrectly represents me as saying that it is empirically possible.) Nor do I think it merely barely epistemically possible, i.e. barely logically compatible with all that we know or rationally believe. Given what we know and rationally believe, I think it is an open question whether

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or not some are any simple properties. The apparent simplicity of some properties is no guide. To believe in simple properties on this basis would be like believing in particulars without parts because there are minima visibilia. Middle-size particulars like ourselves do not know whether any genuinely atomic particulars exist. Equally, I think, we do not know whether there are any genuinely atomic properties (or relations)? One way properties can be complex is by being conjunctive. Now it seems possible that for every property, P, there exists a conjunction of properties, Q and R, such that P = Q & R. If this situation obtained, then there would be no simple properties. Given that this is an epistemically real possibility, it seems wrong to insist that all properties are simple. Grossmann alludes to this argument of mine, but I cannot see that he does anything to meet it. Would he admit as an epistemically real possibility that all properties are complex (perhaps because they are all conjunctive)? Or would he still try to analyze such “properties” into facts? And what would be the nature of these facts? He agrees that it is not logically impossible that there should be conjunctive properties. Does he agree that it is not logically impossible that every property should be conjunctive? And, if he does, has he any reason for not taking the logical possibility with epistemic seriousness, and accommodating the theory of properties to the possibility? I think that one source of stumbling for Grossmann is his failure to appreciate the importance of the notion of partial identity. Suppose a has property P and property Q. I allege that we can then speak of (1) the property P; (2) the property Q; (3) the property P & Q. At the same time, I deny that P & Q is wholly distinct from P and from Q. P, and Q, are parts of P & Q, parts which, taken together in the relation of co-instantiation, make up the whole. Since they are parts of P & Q, they are each partially identical with P & Q. I offer as an analogy (1) the blade (of a knife); (2) the handle (of the knife); (3) the knife. The knife is not something over and above the blade and the handle. Blade and handle are parts of the knife, parts which, taken together and related in a certain way, make up the whole knife. Since they are parts of the knife, they are each partially identical with the knife.

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Grossmann complains that blade, handle and knife are still three things. Similarly, he wants to say, if he admitted conjunctive properties, then P, Q and P & Q would be three properties. And that, he thinks, leads to unnecessary multiplication of facts. But are blade, handle and knife really three things? It is surely obvious that the answer is “Yes and No”. We are easily seduced by the following dialectic. Either a and b are identical, or they are not. If they are, there is one thing; if not, there is two. To reason in this way is to try to press all cases into one of two moulds: The Morning Star/ Evening Star mould, and the Morning Star /Red Planet mould. But it should surely be obvious that there are intermediate cases. Only consider the relation of a terrace house to its neighbour (sharing, as they do, a party wall), or the relation of New South Wales to Australia. Overlap and part/whole are, fairly obviously, cases of partial identity. Once we see this point we shall agree that, although blade ≠ handle ≠ knife, blade and handle, though completely distinct from each other, are, taken individually, partially identical with the knife, and, taken together, are identical with the knife. The same reasoning can be applied to P, Q and P & Q, and then the spectre of unnecessary multiplication of facts, which I abhor at least as much as Grossmann, is removed. 3. Structural Properties If conjunctive properties can be admitted, then there should be no difficulty about structural properties, which Grossmann explains as “a property which something has as a matter of having certain parts, with certain properties, standing in certain relations”. Suppose we have an F standing in the relation R to a G, where F & G and R are universals. I maintain that we then automatically have a particular (the mereological sum of the two particulars), having the structural property being and F standing in R to a G. Grossmann, of course, considers that all we have here is a certain complex fact involving the two particulars. I acknowledge that there is such a fact (state of affairs, in my terminology), but I say that the situation may also be correctly described as one where the particular which is the sum of the two related particulars has a certain structural property. Yet, in agreement with Grossmann, I do not want to say that there are two facts here.

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My reasons for admitting structural properties are exactly the same as those I advance for admitting conjunctive properties, and the two sets of reasons seem to stand or fall together. First, two different mereological wholes might be an F standing in R to a G and this is most naturally taken (pace Grossmann) as a respect in which the two are identical, and so as a property. Second, and more importantly, it may be that being an F and being a G are themselves structural properties and so ad infinitum (“structures all the way down”). The same may hold for every other property. This is no mere logical possibility, but a live intellectual option. In view of the way that physics has shown that successive candidates for genuine atoms are really structures of more fundamental entities, we must take the hypothesis of “structures all the way down” even more seriously than the parallel hypothesis that all properties are conjunctive. Our theory of properties should therefore be accommodated to this possibility, and so structural properties should be admitted. If we do admit structural properties, then it is clear that we must admit that they can have common parts. The conjunctive properties P & Q and Q & R have the common part Q. Similarly, being an F having R to a G and being a G having Q to an H have a common part being a G. It seems irrelevant that the particulars which have the latter property are, at best, mere parts of the particulars which have the two structural properties. I will say nothing about Grossmann’s criticism of my view that numbers, or their ontological foundation, are properties of particulars, except that, while granting that my analysis is not in a well worked-out state, I do not see Grossmann’s criticism does it any serious damage. 4. Ontology and the Physical Universe Grossmann believes that two theses which I propose (Vol. I, p. 126): (1) The world contains nothing but particulars having properties and related to each other. (2) The world is nothing but a single spatio-temporal system. are not really compatible.

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The view I put forward is that particulars, properties and relations are found only in what I call states of affairs (Grossmann: facts) having the form Fa, Ra b, Ra b c, … . In a passage in Vol. I, p. 80, I say: I do not think that the recognition of states of affairs involves introducing a new entity. At any rate, it seems misleading to say that there are particulars, universals and states of affairs.

The first of these sentences was perhaps misleading. It leads Grossmann to say, incorrectly I think, that I hesitate to give full ontological status to states of affairs. If anything, it is particulars divorced from their properties and relations, and properties and relations divorced from their particulars, that “I hesitate to give full ontological status to”. For it is only states of affairs which are logically capable of independent existence. Grossmann would insist that particulars, universals and states of affairs form three distinct categories. But, as in the case of the blade, the handle and the knife, I find this insistence profoundly misleading. There is a sense, however, in which particulars may be said to be logically capable of independent existence. The particular in its bare particularity, its thisness to use the Scotist phrase, in abstraction from its properties and relations, is not so capable. But the particular along with its properties and relations is capable of independent existence. For a particular in this sense is already a state of affairs. Grossmann goes on to say: It is not states of affairs, I take, it, which form a single spatio-temporal system,

and on this basis he distinguishes my “ontological world” of states of affairs from my “naturalistic world” which is a world of spatio-temporal particulars. He says that he believes both worlds exist, but objects to my identifying them. I think that Grossmann will find insoluble problems when he comes to give an account of the way his “two worlds” stand to each other. I hold that there is but one world. Unlike Grossmann, I see no objection to saying that it is states of affairs which form a single spatio-temporal system. What we have, I believe, is simply different ways of talking about the same thing, different ways which bring out different aspects of the nature of this thing.

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Indeed, why should we not conceive of the spatio-temporal system as a single state of affairs? If we are prepared to countenance conjunctive and structural properties, we can think of the spatio-temporal system as a single particular having a single vastly, perhaps infinitely, complex structural/conjunctive property: a state of affairs of the form a is N. Just as we think of the spatio-temporal system as made up of particulars, so we can think of this state of affairs as made up of states of affairs. Grossmann tries to restate his objection. After mentioning my view that first-order universals (properties and relations) can themselves fall under universals he asks why I do not render (1) as: (1´) The world contains nothing but universals, instantiated by particulars and universals, and related to each other. The answer, I think, is that (1´) would be a possible, if eccentric, way of rendering my view, though it might be best to leave out the comma after the first occurrence of the word “universals”. I can see no reductio here. Finally, Grossmann argues that the clash between my Realism (Principle 1) and Naturalism (Principle 2) comes to a head when I argue, in the spirit of Naturalism, that whatever entities do not causally interact with particulars should be exorcise by Occam’s Razor. He suggests that this will require me to exorcise, along with classes and numbers, universals, states of affairs, and relations between universals. I agree that there are some problems here, to which I have not given careful enough attention. Grossmann points out that I conceive of causally interacting particulars as particulars with their properties and relations, that is, as states of affairs. The justification for this is that, although we think of particulars as acting causally, we also think of them as acting in the way that they do in virtue of their properties (and their relations to other particulars). But then, Grossmann asks, what of particulars in abstraction from their properties and relations, properties and relations themselves, and relations between first-order properties and relations? Does not my causal principle rule out positing them?

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The question is a fair one. But may I not reply that my causal principle interdicts entities which fail to act upon particulars, except those entities which are themselves included in the analysis of causal interaction? This will automatically exempt from interdiction the “constituents” of states of affairs: particulars in the “thin” sense, and first-order universals. It will not exempt classes. I think it will also exempt relations between first-order universals. For causation, I maintain, is nothing but a nomic connection. And relations between first-order universals, I further maintain, are all and only the nomic connections. If this is correct, we can actually use causation as a partial clue, al least, to ontology. Postulate no entity in your ontology which is not required in your account of causation. (I say “partial” because the maxim by itself gives us no assistance in giving an analysis of causation.) We might call this the Eleatic Principle in ontology, after Plato’s Eleatic Stranger (Sophist, 257-e). I agree with Grossmann that ontology is not physics. But I do not agree with him that they study different realms. Yours, David Armstrong

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Objections 25-IX-78 Dear David: Thank you very much for your letter and the thoughtful discussion of my review. I have now the impression that I know you well enough to discuss philosophical problems with you in perfect candor. You react to critical remarks with arguments and questions, and I shall try to emulate you in this respect. Above all, let me assure you once more, if that be necessary, that I care nothing for “winning” arguments or debates. (There are stories about Strawson vs. Austin, etc. which make one wonder whether these are really grown men). I have tried to comment on what I consider to be the outstanding disagreements between us. Some things are now clearer. Others, have come in sharper focus. I think that, on the whole, we understand each other’s positions fairly well. (I am sorry for the misinterpretations which you point out to me.) It is likely that disagreements will remain, no matter how long we debate the issues. But that is alright, too. So, I do not necessarily expect new comments from you soon. On the other hand, if you have the time and inclination, I would be happy to hear what you have to say about my remarks. Of course, it would save time if we could discuss some of these matters in person!

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1. Exemplification 1. My strategy was two-pronged. Firstly, I wished to expose what I consider to be a curious British prejudice against exemplification cloaked in the claim that a version of Bradley’s argument — usually, in the form of Ryle’s argument— shows that there is no such nexus. Second, to hint at the possibility that the denial of exemplification is no more plausible than the denial of any other relation and, hence, of all relations. 2. I goofed: Exemplification is nonsymmetric. (Not: asymmetric). The property of being a property is a property. 3. I do not know how to answer the questions of note 3 because I am not sure that I understand what an aggregate is. I distinguish between classes and structures. For every structure there exists the class of its parts (relational and nonrelational). I am no sure, though, that there is a structure for every class. What is the structure corresponding to the class consisting of the color olive green, the number three, and the last medicine taken by Louis XIV? Structures contain relations (and so do facts): no structure without a relation, and whenever there is a relation, the there exists a structure. 4. I was not trying to beg the question in my favour in my answer to the size-shape analogy. My point was simply to claim that the analogy does not help anyone like me who cannot see how two entities can form a whole without being related to each other. In the case of size and shape, too, insofar as they “stand to each other” at all, there obtains a relation. 5. Nor was I trying to beg the question in my response to your suggestion to write “a” with green ink. But this leads us to the start of our disagreement. It seems to me that you are now (after abandoning Ryle’s and Bradley’s argument) in precisely the same position as someone who denies the existence of, say, the relation of earlier than, or of any other particular relation. He, too, could claim that this view has the two advantages which you mention. And his view would be just as vulnerable as yours.

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Furthermore, if this is correct, then you are in the same boat as someone who denies the existence of all relations; for if any one relation can be denied with impunity, so can they all. And finally, if this can be carried through for relations, then it can be done for properties as well. There, then, goes your case against nominalism. Now for a few details. What would you say to someone who denies the existence of the earlier-than relation? (Take any relation, as an example, that us dear to your heart.) That you can perceive this relation when you perceive that something happens earlier than something else? Well, I claim that I can perceive that something has the color olive green. But, perhaps, such appeal to perception cuts no ice with you. What else could we bring up? That the class of ordered couples of things which stand in that relation must “get its unity” from somewhere? Well, the same holds for the ordered couples of particulars and properties which stand in the nexus. That the relation term “earlier than” must apply to certain couples in virtue of something? Well, the same holds for the relation term “is” (“has”). I cannot think of a single argument which you can bring up against this fellow which would not equally apply to your denial of the nexus. Shall we then call it a “stand-off”? But if we do, then our chap will go on to claim that just as the fact that a is earlier than b contains only a and b, so does every other relational fact contain only the terms (of the relation). And, finally, I do not see how we can stop him from holding —and calling it a “standoff”— with us that the fact that a is white only contain a, but does not contain white. To bring this out, he may even add —adding cheek to stubbornness— that we could write “a” with red ink! In brief, it seems to me that your case for realism and your acceptance of the nexus stand or fall together. (unless, of course, you have a special argument against the nexus!) 2. Complex Properties As I see it, our disagreement centers around two questions. Firstly, does your argument from the possibility of complex properties go through? Secondly, does your view imply a multiplication of states of affairs?

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1. I admit, as I have said before, that it is logically possible that

there are complex properties; only the contradictory is logically impossible. But I do not admit, if I understand your notion of epistemically possible correctly, that it is epistemically possible that there is even a single complex property. The assumption that all properties are conjunctive, for example, it is not compatible, in my view, with what we know. Firstly, it is not compatible, always in my opinion, with the fact that midnight blue, square, etc. are simple properties. Secondly, it is not compatible with the fact that there is only one fact —A is Q and A is R— rather than two facts —the one just mentioned plus A is Q & R. Thus my arguments against complex properties are to be construed as arguments against the epistemic possibility of there being complex properties. Assume that we would have reason to believe, on the basis of some instances, that whenever we believe x to have the property P, it really has the two properties Q and R. In this unlike case, we would have reason to believe that any fact that seems to be of the form A is P is really an infinite conjunction of the form A is L and A is M and A is N and… . In my view, we would still have no reason to believe in complex properties. 2. I disagree with the paragraph “the knife is not…”.

It seems to me possible that there is a fatal ambiguity in the word “and” as it occurs in this sentence of yours. I have read this sentence like this: “The knife is not something over and above the blade and it is not something over and above the handle”. And I have taken “over and above” to mean: “not identical with”. But one can mean something else; and it seems that you do. One may read the sentence like this: “The knife is not something over and above the blade and the handle together, related to each other in a certain fashion”. Or, better: “The knife is not something over and above that thing which consists in part of the blade, in part of the handle, as they are arranged in a certain way”. So interpreted, the sentence is of course true, with the same reading of “over and above” as before. (The same ambiguity resides in your phrase “taken together”. Let us look at your sentence starting with

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“Once we see this point”. I still do not see how blade, handle, and knife, since they are not identical (different from) with each other could fail to be three things (entities, individuals, etc.). The fact that the blade is partially identical with the knife and that the handle is partially identical with the knife does not touch upon this fundamental fact that we have three different (non-identical) things. Nor does the fact that the knife is identical with that thing which consists of the blade and the handle in a certain arrangement. I grant both of these facts, but I cannot see how they bear on the issue of whether or not there are in this case three different things. And as long as this is true, namely, that there are three different things, we get for every conjunctive fact another, superfluous, fact. A is P and A is Q, I take it, is a conjunction of the two facts A is P and A is Q. If P & Q is not identical, as we have just seen, with either P or with Q, then it cannot a part of either of these two facts, Hence, it is not a part of the conjunction. But it is presumable a part of the fact that A is P & Q. If two facts differ in part, they cannot de identical. It follows that the conjunctive fact cannot be identical with the fact A is P & Q. But I suppose that I am repeating myself. Where do I wrong here? I take it the following is true: For all properties f: there are 3 things which are f if and only if there is an x which is f, there is an y which is f, and there is a z which is f, and x is not identical with y, and x is not identical with z, and y, and y is not identical with z. It seems to me that you want to deny the truth of this principle or law. But on what basis? I do not see how the fact about partial identity and the fact about the knife being identical with that thing, etc., bear on the falsity of this law. 3. The Universe and the World Let me call “single spatio-temporal system” the “physical universe” or, for short, the “universe”. I maintain that the world is not identical with the universe. And, contrary to what you say about what you say, you seem to agree with me! Look at sentence starting with “If we are prepared…”. You say:

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… we can think of the spatio-temporal system as a single particular”. (my italics) Now this seems to mean that we can think of it as a particular. I take it that to think of it as a particular is to think of it not as a state of affairs. But then you cannot continue, later in the same sentence, to identify this particular with the state of affairs A is N. Either you think of it as a particular (which may be complex, of course) or you do not. If you do, then you cannot also think of it as a state of affairs. On the other hand, if you really meant “state of affairs” when you said “particular”, then you get: … we can think of the spatio-temporal system as a single state of affairs… (namely, a is N.) But what is now the a in a is N? I thought this was the (complex) spatiotemporal system? I do not think that I have any difficulty, as you suggest, when it comes to giving an account of the way the world stands to the universe. As a matter of fact, their relationship is perfectly clear from your own account! Assume you are right about complex properties, etc., then the world is a state of affairs (fact) which involves (contains) a “single, vastly, perhaps infinitely, complex structural/conjunctive property”. The universe, on the other hand, is that single, vastly, perhaps infinitely, spatio-temporally, complex individual a which is also contained in the fact a is N. Thus the world contains the universe in the sense in which a fact contains the individual of which it attributes a property. This is the relationship between them. No mystery! But, I emphasize, the world is not identical with the universe. (That was my point). The former is a state of affairs; the latter is an individual. The latter is spatio-temporal, the former is not. Etc. I see no reason why you could not make this distinction within the framework of your basic convictions. As always, Reinhardt

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A Reply to Objections 16-X-78 (Part I) Dear Reinhardt: This is the philosophical reply to your letter of September 25th.

1. Exemplification: You are agree that I, who deny the relation of exemplification, am in the same position as those who denies the relation of, say, earlier than. I do not accept this parallel. I give two arguments. First, the existence of such relations as earlier than is uncontroversial, at least among those who believe that these are such things as relations. But philosophers dispute about the existence of exemplification. Second, Consider the two states of affairs: a’s having the relation, R, to b, and a’s having the property F. You wish to construe the having in the second state of affairs as a relation: for you, it has the form E (a, F). But you wish to deny that the having in the first state of affairs is a relation: for you, it has the form R (a, b). Now I assert, against you, that we have no more reason (phenomenological or otherwise) to think that the having in the second state of affairs is a relation than we have to think that the having in the first state of affairs is a relation. Since I also assert, with you, that the having in the first state of affairs is not a relation, I draw the conclusion that it is not a relation in the second state of affairs. I conclude that that is an ontological illusion in both cases, and that the form of the second state of affairs is Fa. The element of “stand-off” is this. I cannot see any way to prove that my symmetrical analysis of the two states of affairs is correct (though its symmetry made it seem natural.) But I cannot see that you have advanced

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any argument for your asymmetrical analysis. (In USR I failed to notice that somebody might take the asymmetrical position.) 2. Complex Properties: You assert that “it is logically possible that these are complex properties; only the contradicting is logically impossible”. I take this to be a conjunction of two assertions: 1. It is logically possible that these are complex properties. 2. It is not logically possible that every property is complex. If you have (2), what are your grounds for it? Is it a Leibnizian or Wittgenstenian (Tractatus) principle that the complex must be composed of the simple? As you …, (2) seem to me to be logically possible. 3. Epistemic Possibility: I take it that p is logically possible iff p is logically compatible with everything we … . Thus, that the earth is flat is logically possible, but not epistemologically possible. Now, do we … that midnight blue, square, etc., are simple properties? Philosophers disagree about these matters. Most of those who accept properties allow that properties can be complex. (Indeed, you are the first explicit hyper-atomist about properties whom I have been encountered) So, while I … concede that I do not … (but simply believe) that those are complex properties, I do not … that you … that all properties are simple. Similar remarks apply to your principle (which, as you …, I accept) that A is Q and A is R is the state of affairs as A is Q & R. You allow as a possible (but …) case that whenever we believe x to have the property P, it really has the two properties Q and R. You say that we … … have a case where a fact that seems to be of the form A is P where really be an infinite conjunction of the form A is L and A is M and A is N

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and … . We … …, you think, have no reason to believe in complex properties. L, M, and N … presumably be simple properties in your view (and so, … … this hypothesis, unbearable to us). This appears to me to be similar to Tractatus 4.2211—simples search “at infinity”. It seems to me that it is a logical possibility. But it seems to me also that these might not be any simple L, M, etc., because all properties, without exception, may dissolve into conjunctions of properties. As ever, David Armstrong

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Universals and Classes: A Question 16-X-78 (Part II) Dear Reinhardt: You and I agree that there can be, and are, classes whose members lack a common property, much less a property peculiar to that class. You, however, also think that that there are properties which are instantiated (we agree that all properties are instantiated), but to which, nevertheless, no determinate class corresponds. The example you always give is that of being a class. This enables you to escape Russell’s class paradox. Since I am inclinated to deny that there are such things as classes (though there is true class-talk), I wish to deny that being a class is really a property. (This denial will presumably enable me also to escape the classparadox.) My question to you is this. Have you any other example of a property which does not determine a class? As ever, David Armstrong

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Universals and Classes: An Answer 12-I-79 (Part I) Dear David: Thank you for your last letter. In answer to your query, the only properties which do not determine classes I can think of are the usual ones picked out by the appearance of paradox (contradiction). I also think that the property of all properties, namely, the property of being an entity (a being, something that has being) is of this sort since it is even wider than the property of being a class. I admit that this looks ad hoc, but then so does every other solution to the paradox short of denying the existence of classes altogether. The latter move can be justified on ontological grounds, hence, is not ad hoc as far as the paradoxes are concerned. But then you have, of course, the task of making sense of set theory even though there are, presumably no sets. I do not think that this can be done. (I shall have to look at your attempt carefully). As always, Reinhardt

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Objections 30-I-79 (Part I) Dear Reinhardt: Many thanks for your letter of January 12th, which I received the other day. 1. Properties which do not determine classes: I am a bit disturbed by the fact that the only properties which do not determine classes are those which involve paradox in the form of contradictions. It is, after all, rather a natural notion that to every property a perfectly determinate extension corresponds, far more natural than the idea, which we both reject, that to every class there corresponds a unique property (still less, that to every class there corresponds a unique property). So, if these are the only cases to which you can point, why not draw the moral that there are no such properties? You and I, at least, could put this in the form, e. g. to the predicate “class” no property corresponds. You could still argue, e.g. that to the predicate “first-order class” a property, being a first order class, does correspond, but that in the case of “class” the predicate does not apply in virtue of a single property. (“Class” would be a bit like “game”, supposing Wittgenstein to be right about “game”.) By the way, I do not really think that what I have said about sets constitutes any serious contribution to the attempt to do without them. I merely gestured towards the Black-Stenius attempt. Michael Tooley, who also wants to get rid of sets, thinks that there is promise in the Russell “no class” theory (but reworked to take account of the distinction between predicates and properties). Yours, David Armstrong

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A Reply to Objections 6-II-79 (Part I) Dear David: Thank you very much for your letter. About classes, your suggestion deserves further thought. Up to now, I have taken for granted (1) that I am acquainted with certain classes and, hence, with the property of being a class, and (2) that the property is univocal, so that I cannot split it up into first-order, etc. I do not think that I would ever want to give up the view that there is the property of being a class; otherwise, set theory would be either a piece of fiction or a silly way of saying something else. And I do not see how I can get around (2). I do not see any merit in Russell’s “no-class” theory. We have here one more example of the insidious practice of doing ontology “by definition”. H s definition can be taken in one of two ways. Firstly, in order to have ontological bite, Russell must maintain that (1) The class determined by the property F has the property G is merely a version of the more perspicuous (2) There exists a property H which is equivalent to F, and which is G. But this claim is highly implausible. When we are talking about classes, we are not talking about properties; just as when we are talking about mermaids, we are not talking about dolphins. I make this comparison deliberately with mermaids; for even if we grant that there are no classes, it seems to be evident that when we are talking about them, we are not talking about properties!

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Or else secondly Russell’s definition may be taken to be the following equivalence: (3) All properties f and g are such that: the class determined by f has the property g if and only if there is a property h which is equivalent to f, and which is g. But this equivalence does not show that there are no classes. Quite to the contrary, it presupposes that there are classes. As always, Reinhardt

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Middle: Laws of Nature

Laws of Nature as Quantified Facts 12-I-79 (Part II) Dear David: Thank you very much for your letter. I have not had time to study your Laws of Nature. I have always been inclined to hold the traditional view: The perspicuous representation of a law is of the general form Everything which is F, is G. The connective may not be the horseshoe. (I think this is really a minor point, as far as ontology goes.) May main objection against a view like yours has always been that I cannot make sense of the relation between F and G other than by telling myself that it is presumed to be that relation which holds between F and G just in case everything which is F, is also G (or some such phrase with some kind of necessity added: just in case everything which is F is necessarily (not logical necessity) G. (I do not think that there is this special necessity, but this is not important for my point, as long as the law is a quantified fact rather than of the form: R (F, G), as you propose.) But it is obvious to me that I shall have to think about this whole topic more thoroughly. I shall let you know what I come up with. As always, Reinhardt Grossmann

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Laws of Nature as Connections between Universals 30-I-79 (Part II) Dear Reinhardt: Many thanks for your letter of January 12th, which I received the other day. 1. Laws of Nature: Since sending you Laws of Nature I have read it at Canberra and at London School of Economics. A good discussion each time (Jonathan Bennett was at the latter), and as a result I am rethinking the paper. Perhaps you should wait for the next draft before studying it! If laws have general form, for all x, if Fx, then Gx, and the connection is the horseshoe, then you are faced with the problem, emphasized by Popper, that it is possible to have states of affairs of this sort (“All moas died before the age of 50”) which are definitely not laws of nature. I am not at all impressed by various attempts to fix up the difficulty within the Humean framework. (See Dretske’s paper mentioned at the beginning of my paper for a good discussion of these attempts.) Suppose that the connective is stronger than the horseshoe, then an answer is automatically provided for Popper’s difficulty. But the problem now is to give a semantic for the new connective. It seems to me that the connective can only hold in virtue of (i) whatever it is about x which makes “F” applicable; together with (ii) whatever it is about x which makes “G” applicable. At this point we seem to be coming very close to a connection between properties. But I, too, feel the force of your objection that it seems impossible to give an account of the relation between F and G except by saying that it is the relation which holds between them when whatever is F is G. However, here are two points which I hope may blunt the force of the objection.

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2. Michael Tooley (in “The Nature of Laws”) suggests that we think of the relation as a theoretical entity; we postulate it as “that relation between Fness and G-ness, whatever it is, which accounts for the fact that whatever is F is G”, much as we might postulate a dormitive virtue in opium, to account for the latter’s power to make us sleep. 3. Consider any fact of the form R (F, G). (Since you accept universals, presumable you have no objection to there being fact of this form.) Can one ever explain such a relation, except by pointing to the consequences involved for particulars? Suppose, for instance, that one believes that the fact that red resembles orange than it resembles yellow has the form Res (R, O, Y). How could one explain this relation which has the result that each read thing resembles in colour an orange thing more than it resembles in colour a yellow thing? And so, I would claim, for all facts of the form R (F, G …). This is connected with what I call in Universals and Scientific Realism “the descent to first-order particulars” which I think is involved in all higher-order universals. I am pretty well determined, now, to write a book on the topic “What is a Law of Nature?”, so I should value any thoughts which you may have. I am still thinking about Bradley’s regress, and other matters in dispute between us, and may write to you about the latter. It appears to be relevant to the issue about laws of nature, via the question about unistantiated universals, besides being central to the general theory of universals. Yours, David Armstrong

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An Objection 6-II-79 (Part II) Dear David: Thank you very much for your letter. I have to think more about the nature of laws. So far, I have always opted for the Humean (horse-shoe) position. I thought that the usual objections could be overcome. However, I was always willing to accept something stronger than the horse-shoe, if —a big “if”— this relation could be made clear (“a semantics could be given”). You see, it does not matter all that much for my ontology what relation is involved, since I accept relations in general and all kinds of relations in particular. I was willing to let other philosophers fight it out, confident that I could live with whatever they would come up with. However, I felt a little more certain about your proposal, namely, that it could not be true; and this for the reason I mentionated in my last letter. I am afraid that Tooley’s suggestion rubs me the wrong way (I hope you will forgive me!): It is so unphilosophical! To postulate “a dormitive virtue” in opium, if it is to make sense at all, is to postulate a certain chemical compound which one may hope to isolate later (just as the active ingredient in marijuana was isolated). Nothing like that us possible for our ontological case: Presumably, we admit at the very outset that there simply is no other known way of getting at that relation except through the things which are F and G. As I see it, to adopt Tooley’s suggestion is to admit the full force of my objection, except that we substitute “to postulate” for “to conceive of”, and that we draw a misleading analogy to future scientific discoveries. Your own suggestion seems to speak for my point rather than against it. It is precisely by comparison with such relations as, say, being darker than among colors that I find the causal relation between properties wanting. Midnight blue is darker than canary yellow: Here we have truly a relation between properties. I can see this relation, I understand it, I do not describe it in a round-about way. Moreover, when I say that some individual thing is darker than another, I mean that it is has a color which is darker than the color which the other thing has. Here, there is no relation among the individuals. With the causal relation, I have the feeling, it is just the opposite.

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As I said, the only sense I can make of the relation between F and G is that it is that relation which holds when every F is a G, where we still must decide on how to analyze (ontologically) the latter fact. I shall look forward to your new book on laws of nature. If I can think of anything profound about the topic, I shall let you know. Let me tell you how much I enjoy our correspondence. As always, Reinhardt

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A Reply 23-IV-79 Dear Reinhardt: Just a note to assure you of my continued existence. I have thought about various things in your letter of February 6th —in particular, the objections you raise against my attempts to make plausible that laws of nature have the form R (F, G). But I have nothing very constructive to add so far. However, the Humean (horse-shoe) position seems to me to be riddle with insuperable difficulties, and the only alternative which I can see is that of a relation between universals. Yours, David Armstrong

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An Epistemological Problem: The Synthetic A Priori Truths 16-X-80 Dear David: It seems to me that there are no ontological objections to your conception of laws of nature as relations among universals. But I see a very weighty epistemological problem. Upon your view, it seems to me, the traditional distinction between laws of nature, on the one hand, and so-called synthetic a priori truths, on the other, disappears. But never mind the tricky Kantian terminology, the distinction seems to me quite obvious. I know that every midnight blue object is darker in color than every canary yellow object because I see that the property (color) midnight blue is darker than the color canary yellow. I see a relation between these two colors. The fact I perceive is of the form R (F, G). This is why I do not have to verify my observation by looking at further midnight blue and canary yellow objects. There is no induction. Similarly, but much more controversial, I also think that one can see that two plus two is four by observing two peas and tow peas. Here too, one can grasp a fact which consists of a relation holding between three abstract entities + (2, 2, 4). But when it comes to so-called laws of nature, the situation is quite different. If I ask myself whether or not it is a law that all swans are white, I cannot decide this question by grasping a relation between swanhood and whiteness. If I could, then I would not need induction. One instance of this swan here and his white color would be enough in principle. To put in a nutshell: If there were such a relation between universals as necessitation (or whatever else you may wish to call it), then we should (in principle) never have to look at a second swan, a second electron, etc., in order to find out whether the relevant law holds. But we do have to convince ourselves by induction, so to speak, that the law holds. By the way, this is precisely the problem which I see in Husserl’s phenomenology: In eidetic intuition, we allegedly see connections among pure essences. This is how we find out, for example, what judgments are, that is, what laws hold for them. But this makes phenomenology a purely a priori

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enterprise and, more importantly, leaves no room for laws of nature. (You may want to have a look at Husserl). Now, I understand that you are trying to explain in terms of your intermediate fact (between R (F, G) and (x) (If Fx, then Gx) why laws of nature are not known in the a priori fashion. But it is simply not clear to me how this is supposed to work at this point. I do not know what, precisely, this fact is; and I do not see how it would distinguish between lawful and accidental generalities, unless it is, after all, of the form R (F, G). As always, Reinhardt

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A Solution: Causation 4-XI-80 Dear Reinhardt: Many thanks for your letter of October the 16th. I wish to question whether the fact that midnight blue is darker than canary yellow is really a relational fact. It would be generally agreed, if a relation is involved, it is an “internal” relation, logical supervenient upon the relative terms. This makes me think that it is not a relation at all, but that what we have is a dyadic predicate “is darker than” to which no dyadic universal corresponds. Compare “is similar in a certain respect”. In the latter case, I take it, we Realists ought to say that there are the similar things, each with their properties, but not, over and above this, a relation of similarity. But in the case of the relations which constitute laws of nature we have external, that is, real relations. It might be enough if we simply postulated such relations without ever observing them (I know that you think this is unphilosophical!). However, I think that there are cases where we do have some (vague and indeterminate) awareness of nomic relations. We do seem to perceive causal sequences (perceiving them as causal). The best cases are perception of pressure. We perceive that something is pressing upon us (acting causally upon us). This seems to me to me very likely a non-inferential of causes. Certainly, it is hard to shown how it is inferred from simpler data. (What would this data be?) Now, not only are we aware (at a sub-verbal level) of the laws of action of solid bodies on earth. The biological good sense of all this is evident. So: we perceive causation and, at the same time, are dimly aware of the nature of some of the laws governing the perceived causal sequence, Here, I suggest, is our experience of the necessitation relation between universals. We can then hypothesize than it is present in cases where we do not

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observe it. If our hypothesis yields fruitful predictions, then we have some reason for thinking the hypothesis true. I myself am much more worried about the ontology of my proposals. If my only worries were epistemological, then I should be a happy man indeed! Yours, David

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An Objection: Induction 25-XI-80 Dear David: Thank you very much for your last letter. I think that I can sum up my misgivings about your analysis of laws of nature in this fashion: If your analysis were correct, then one should be able to establish a law on the basis of the observation of one instance, just as one is able to establish in such a manner that all midnight blue things are darker than all canary yellow things. Put differently: all laws of nature would be synthetic a priori. As always, Reinhardt

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End: The Nature of Numbers

A Coincidence 29-IX-86 Dear David: Thank you very much for your interesting piece on the nature of numbers. As always when I get the piece of work from you, I immediately read it. But I also realized that I shall have to study it very carefully in the future. So, I shall let you know what I think of it in detail at some later time. As I said, on first reading, it is very interesting! By some sort of coincidence, I have been working at the present time on related topics: the nature of number and how we know them. As always, Reinhardt

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Numbers Tied to Aggregates 4-XII-86 Dear Reinhardt: A reply to your letter of September 25th. I have a new idea about number (approved of by Forrest). In effect, we identified the numbers —naturals, rationals and reals— with ratios or proportions, holding between unit properties and aggregating properties. But this does not do full justice to the naturals. The relation between being a 19-electron aggregate and being an electron is a ratio, but that is not all it is. The unit-property also operates upon the aggregating property to yield a class. This feature is not present in the rationals and the reals. So the naturals are richer. There ought to be some special link between the naturals and classes after all. Yours, David

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An Objection: On Mereological Categories 21-I-87 Dear David: Thank you for your last letter. We are back from our vacation and, as I promised, I studied your paper on numbers. In your paper (I shall simple ignore Forrest in order to make things simpler), you speak of “electron-aggregates”. Then you go on to categorize numbers as properties which belong to the properties (I shall not distinguish between universals and properties) one-P aggregate, two-P aggregate, etc. At this very point I was baffled: I did not know what to make of your aggregates at this early point. Knowing your general inclination to locate everything (even universals!) in space (and time), I naturally thought of your aggregates as spatio-temporal structures (for example, of electrons). But if this is what you mean by an aggregate, then you cannot speak of a two-electron aggregate; for there are many such aggregates. Let me from now use as my example a four-square aggregate. If an aggregate is a spatial (I shall leave out time) structure, then there is a difference between the aggregate of Figure 1 and the aggregate of Figure 2: a

b

c

d

Figure 1

a

b

c

d

Figure 2

On the other hand, if an aggregate is something akin to a class (set), then the difference between Figure 1 an Figure 2 disappears. In this case, there is the aggregate consisting of a, b, c, and d; and this may be said to be a four-square aggregate. So, I could not make up my mind, at this point, about whether you mean a structure (in my sense of the term) or something like a class by “aggregate”.

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When I got to objection 5, I thought that the die was cast: an aggregate is something like a class! You say “We should be inclined to say that wherever a class can be formed… there an aggregate of these things also exists.” So, take the color olive green, the French Revolution, the number seven, and Cambridge University: they constitute and aggregate, even though they do not form a spatio-temporal whole. Or do they? But hardly had I satisfied myself that by aggregate you must mean something like a class when I came to objections 6 and 7! In both of these objections, you obviously think of aggregates as spatio-temporal structures. The figure of the two overlapping squares is obviously a spatial structure; and so is your figure for objection 7. If they are conceived of as something similar to a class, then the objections do not get off the ground. To repeat, objections 6 and 7 only apply if aggregates are conceived of as spatial (temporal) structures. But this conclusion of mine about your meaning of “aggregate” was once more shattered later. There you describe an aggregate as the mereological sum of its (a class’s) members. And you symbolize it as: [a + b + c, …]. I take it that an aggregate, so conceived, consists of the parts a, b, c, etc., and a certain relation, +, which you call the mereological sum, and of nothing else. But if this is what an aggregate is, then your figure of the overlapping squares is not an aggregate, and neither are my figures 1 and 2! If this is what an aggregate is, most importantly, then an aggregate could not possibly be both a one-square and also a two-square aggregate! This follows, it seems to me, from the very notion of an aggregate; from its identity condition, if your prefer. Take any one-part aggregate, it will be symbolized as [a]; and any two-part aggregate will be symbolized as [a + b]; and obviously these cannot be the same aggregate; aggregates, as characterized in the fashion mentioned above, are completely determined by their parts, and just like a class cannot have one member and also two members, so an aggregate cannot have one part and also two parts. Of course, a spatio-temporal structure can! Your figure of the overlapping squares is a structure, not an aggregate in the above sense. And it can be said to consist of only one, not overlapping square, or of the two overlapping squares, etc. If I am correct, then it is false to say, as you do, that “the diagram taken as a universal, is a one-square, two-square, and three-square aggregate”. The diagram is not an aggregate at all, but is a spatio-temporal

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structure, involving, not only the mereological sum relation, but certain spatial relations among lines, squares, etc. And the same considerations apply to your discussion of objection 7. Your figure e, my Figure 2, consists of four squares or of two oblongs, if we mean by “figures”, not an aggregate, but a spatial structure. To sum up. I do not know whether numbers “belong” to structures (in my sense) or to aggregates, whether they belong to spatio-temporal figures or to mereological sums. I take for granted that these are obviously not the same; for the latter only involve the sum relation. Put differently, I think that you confuse spatio-temporal structures with mereological sums by sometimes thinking of the former as “aggregates”. From my point of view, there are no mereological sums: There are all of those spatio-temporal structures (as well as other structures) and there are also classes, but there are no mereological sums and, hence, no aggregates (in this meaning of the term). My difficulty with aggregates revolves around the notion of a mereological sum: I can make no sense of this relation. From my point of view, and dogmatically asserted without argument, the “+” is either the “and” of conjunction (and then holds between states of affairs), or else it is the “plus” of addition (and then holds between numbers). In the first case, we get a conjunction of states of affairs; in the second, a sum. From this point of view, your analysis of number would have to result in either the view that numbers “belong” to structures or in the view that they belong to classes; for example, that they are properties of classes. What I say about the confusion of structures with mereological sums applies automatically to your discussion, for example, when you say: “The aggregate is related by K19 to the property of being an electron because of its structure”. But this cannot be correct if by “aggregate” you mean a mereological sum; for such sum has no structure other than the one it gets from the +-relation. And of course, all such sums have the same structure: they can only differ in the parts which are connected by +. As always, Reinhardt

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A Reply: On Mereological Categories 1-III-87 Dear Reinhardt: Many thanks for your letter of January 21st. I was naturally disappointed by your failure to understand what Peter and I meant by “Aggregate”. But light dawned a bit when I discovered that it is a philosopher’s “I don‘t understand”. You hold that there are no mereological sums. Naturally, you cannot “understand” what our aggregates are, since they are mereological sums. How should the argument proceed? You do not tell me why you do not believe in such sums. Consider the class of cells in my body now. Do not these cells form an aggregate? As a matter of fact, that particular aggregate is just my body now. It weighs so many pounds, but the class of cells in my body now does not weigh that number of pounds, or so I would take it. Consider also the class of molecules in my body now. A different class, I take it, from the class of cells in my body now, but the aggregate of the two different classes happens to be the very same thing viz. my body now. All this is very standard stuff. (See, for instance, my Universals and Scientific Realism, Ch. 4, pp. 29-30) Now, lots of standard stuff is false. But I need to know why you think it is false before I can defend myself. If aggregates exist, and are different from classes, then, since they are particulars, they can instantiate universals, such as being a two-electron aggregate (in your terms, perhaps, being a two-electron structure. The structure is a very elementary one, failing to involve relations.) And the way is open for our hypothesis that for each class, their members form (just one) aggregate. After that, we start thinking about numbers! Yours, David

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Aggregates and Sets: A Question 16-III-87 Dear David: Thank you very much for your letter. It is always good to hear from you. I realize that you are somewhat impatient with me and my confession that I am puzzled about your category of aggregate, but I assure you that this is not a “philosopher’s I don’t understand” (as you say), if this means that I am playing some kind of Oxford-type game”. You say: “All this is very standard stuff” and refer to your Universals book. Naturally, I went back to pp. 29-30 where you explain the difference between aggregates and classes, but this passage did not enlighten me. Let me explain again, at the risk of appearing dumb and/or obstinate to you, what I find puzzling about the notion of aggregate. In your letter, you state: 1. That the class of cells in your body and the class of molecules in your body is not the same (identical). 2. That the cells in your body and the molecules in your body form aggregates. 3. That the two classes and the respective aggregates are not the same (identical), since the aggregate, for example, has a certain weight, but the class does not. 4. “But the aggregate if the two different classes happen to be the very same thing, viz. my (your) body”. I take it that this means that the aggregates are the same (are identical). (See your book, p. 30: “The aggregate of all armies is identical with the aggregate of all soldiers”.) I take it, therefore, that while the two classes are not the same, the “two” aggregates are.

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I can now express my puzzlement concisely: I do not see how your aggregates could possibly differ from the classes and, hence, how they could be the same, while the classes are no! The first class is a class of cells: {C1, C2,… Cn}; the second, a class of molecules: {M1, M2,… Mn}. I understand that these classes are not the same because their members are not the same. This is the identity criterion for classes. Now, the first aggregate in an aggregate of cells: [C1+C2,… +Cn]; the second, an aggregate of molecules [M1+M2,… +Mn]. Are not these aggregates just as different from each other (non-identical) as the corresponding classes? Let me use, arbitrarily, the term “ingredient” for the C s and M s in the aggregates. Do not these two aggregates have different members? (The “+” cannot play a role for the identity or non-identity of aggregates since it is common to all aggregates.) I take it that you will be angry with me at this point and reply that is obvious that aggregates with different ingredients can be identical; see your body for example. But this is not obvious to me (on your notion of aggregate). If non-identity if ingredients is not the criterion of non-identity of aggregates, what then is? Why then is not the aggregate of molecules in my cat’s body the same as the aggregate of molecules in your body? In short, my question is: What is there in or about and aggregate, as you conceive of it, other than its ingredients, that could determine whether “two” aggregates are identical or not? Put differently, what is the identity condition for aggregates according to which the two aggregates mentioned above are identical? I do not know whether or not I have succeeded in explaining my reluctance to acknowledge the category of aggregates, but I hope to have convinced you that this reluctance is not frivolous. I am sure that you have a plausible answer to my questions, but I have not found in your book, your article on numbers, or in your last letter. As always, Reinhardt

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Aggregates and Sets: An Answer 27-III-87 Dear Reinhardt: Thanks for your letter of March 16th. It is sad that we are hung of on this preliminary point, and so cannot even reach the Forrest/Armstrong theory of number. One last attempt. Is the word “aggregate” causing the trouble? For it, substitute the word “whole”. Checking in your book, I find that you accept the categories (?), anyway the notions, of whole and part. Let a, b, c, … be the cells in my body. Let d, e, f … be the molecules in my body. We could think of “{}” as an operator. It takes a, b, c, … to the class {a, b, c, …} a, b, c, … are then members of the class of cells in my body. Similarly, d, e, f, … are members of the class of molecules in my body. Think of my “[… + … + …]” as the part-whole relation operator. It takes a, b, c, … to a certain whole —as it happens, my body. a, b, c, … are parts of this whole it also takes d, e, f, to a certain whole —as it happens, the very same object, my body. d, e, f …, are parts of this whole. I hope this is not controversial. (But fear it may be —though, I cannot see why.) Now for something that is controversial, which I could well understand you contesting. We think that for each class {a, b, …} there exists just one whole, such as a, b …, are different parts of that whole, and together add up to that whole. These are the “mereological sums”. It is these wholes which instantiate the structural universals which we need for our theory of number. For instance, my body may instantiate the universal made up of just N-cells. The internal relation this universal has to the universal being a cell we identify with the number N. Yours, David

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A Problem: Wholes and Mereological Sums 21-IV-87 Dear David: Thank you very much for your last letter. It is really remarkable that two such brilliant philosophers should not be able to see each other objections! I do not have the faintest notion why don’t seem to be able even to understand each other on this issue. Like you, I shall try one more time. (I promise that unless you answer, I shall not bring it up again.) 1. The problem lies not with the category of whole (structure), but

with those particular wholes which you introduce (mereological sums). I believe that there are wholes, but not these wholes; just as I believe that there are human beings, but no Hamlet. 2. The reason for my doubts about the existence of this particular

kind of whole is that I do not believe that there is this particular relation +. Of course, there are relations, and there is also the genus partwhole relation, but there is no specific relation (+) that holds both between the cells of my body and my body and also between the natural numbers and the series of natural numbers. 3. But let me try to put things as sharply as possible: Please, tell me

what is the identity conditions for mereological sums. Is a, b, c, … identical with A, B, C, …, given that a is not identical with A, etc.? It all comes down to this: It seems to me that you must say that these two sums can be identical —as in the case of cells and molecules— but need not be identical as in the case of your cells and the series of natural numbers. When then are they identical? To say again: When are mereological sums identical? 4. An anticlimactic remark: I do not understand why you need the

mereological sums. Would not the classes do just as well? Does not a class instantiates the universal made up of just N cells? Better: consisting of just N cells? Having just N cells as members? If so, then

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the internal relation between this universal and the universal being a cell could be the number N. As always, Reinhardt

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A Solution: The Identity Conditions for Mereological Sums 4-V-87 Dear Reinhardt: Thanks for your letter of April 21st. I will go on a little longer. 1. The identity conditions for mereological sums: When, for instance, is [a + b + c] identical with [A + B + C], given that none of the six things are identical with each other? I suppose the answer is that they are identical if and only if there is (just one) x such that [a + b + c] = x and [A + B + C] = X. If I asked you for identity conditions for your wholes and parts —when, among the wholes you recognize, different parts sum to the same whole —I imagine you would give the same answer. Surely, the dispute between us is not about identity conditions, but about how promiscuous the whole/part category is. I think that any collection of entities at all have a sum, e.g. the natural numbers form a whole as well as a class. You deny this. I do not know how we settle this. Perhaps you have a principle which tells you when the members of a class have a sum and when they do not? You seem to need one, anyway. 2. It is an interesting suggestion to use the internal relation between the class having just N-cells as members and being a cell to give an account of the number N. One disadvantage I see is that it will not generalize to the rationals and the reals, as our account in terms of wholes (aggregates) does. I think it is an attractive idea that the natural, the rational and the real 19 are all the same thing. (This was the old view, e.g. the Newton’s view.) Another thing I do not like is this. Suppose you have being a class of just 38 cells, and the unit universal is being an aggregate of just two cells (you won’t like that one much, perhaps, the relation seems straightforward, as it

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is if the 38 are taken as an aggregate. But if the 38 are taken as a class, you will need to take members pair-wise, and so that the pairs have no common member, Even then, there will not be one class, but very many classes. The central idea is that numbers —natural, rational, real, perhaps others— are ratios or proportions between universals. Surely, no need to answer, unless you feel moved. Yours, David

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Concluding Remarks on Numbers and Mereology 23-VI-87 Dear David: Thank you for your last letter. You say in your letter: “Surely, the dispute between us is not about identity conditions, but about how promiscuous the whole/part relation is”. Quite so. But here is how my reasoning went. Your sums are really nothing else but sets; the relation “+” does not really make any difference. It is only there to give the appearance of a “whole”. And your analysis of number could therefore proceed just as well in terms of sets as in terms of sums. (More about this latter). But this must be false: David’s sums are completely different from his sets, for sets with different members are different, while sums with different parts can be the same! This is where the identity conditions come in. Now, in my way of thinking, since your sums are really sets —whether you know it or not!— something must have gone wrong with the sums. In short, I do not think that there are any sums, if these sums are not sets. Let me start again: Now, if you hold that [a + b + c] and [A + B + C] can both be identical with the same X, then there seem to exist only two horns: (1) (2)

Either you deny the transitivity of identity or (2) you hold on to it.

The first course would be a rather severe step to save the existence of sums. It would indicate, to my mind, that there really are not such things. So you take the second horn. As a consequence, you now have sums which, though they differ in their parts, are yet identical. (This is the surprising difference from sets and, may I add, from all my wholes!) But now I see another difficulty, and this is why I spoke of a horn a moment ago: You must deny the law of the indiscernibility of identicals (at least, for relations) for sums. The first sum has a as a part, the second does not; yet

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they are identical (the same). Your sums are different from all other entities, then, in this respect. And this, to my mind, also throws some doubt on whether there really are such things. It is at this point that the identity condition directly bears on the question of whether or not your notion of a whole (sum) is too “promiscuous”. It is very interesting that you think that I would give the same answer as you do to the question about identity conditions for wholes (structures). It is interesting, because I have always insisted that structures are the same if and only if (a) their non-relational parts are the same (!), (b) their relations are the same, and (c) the parts appear in the same order. Thus I have always held (emphatically) the opposite from what you hold. [a + b + c] and [A + B + C] are thus not the same in my ontology. But how can one and the same have two different structures? At this point, a subtle but allimportant distinction must be made: X cannot be both of these structures, that is, cannot be identical with both of them, but it can have both of them. The latter means: X has a, b, and c, as parts (which stand in certain relations to each other), and it also has A, B, and C as parts (but in other relations to each other). Ultimately, what this comes down to is that X can be described in two different ways: as having this and that structure. Well, this is all for today. I almost forgot, I do not quite understand your objections to my proposal to use sets should instead of sums for your analysis of the concept of number. I see no reason why sets should not work just as well; this, of course, shows my conviction that sums are really sets. At any rate, let me thank you for your patience and for the opportunity you provide for me to think about these matters more thoroughly than I have before. As always, Reinhardt

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Appendices

1. Reinhardt Grossmann’s Ontology I. Introductory This book is a major contribution to metaphysics. It is a systematic ontology, bias empiricist, which attempts to give a general theory of categories of being. Grossmann is a member of the school which Gustav Bergmann established many years ago at the University of Iowa. Its members have always been distinguished by their persistent and unembarrassed concern with fundamental ontological questions, even during decades when such inquiries were at best unfashionable, and at worst condemned, by the so-called analytic tradition. One mark of this school of philosophers has been their deep interest in the study of the great dead philosophers. This interest, however, has never been primarily historical or cultural. The Iowan philosophers wanted to know what their predecessors thought about the great questions of ontology. What were their arguments for thinking as they did, and how good are these arguments? In this way, the past was fruitfully brought in to assist with present problems, and that temptation of contemporary philosophy, provincialism of the present, was in a degree overcome. The school has not been without quirkiness, and has its own, sometimes trying, tricks of expression. It stands a little aloof from the main stream. But, to repeat, it must be honoured for the steady way in which it has kept in view, and worked away at, fundamental ontological problems. The founder of the school, and some of its epigoni, have not always written with great clarity. This has contributed to their relative lack of influence. Grossmann, however, writes with admirable clearness, and his material is extremely well organized. He shares in full the Iowan interest in ransacking the work of previous philosophers, and arguing with them, in order to lay them under contribution to the present. Past philosophers whose reasonings figure prominently in the present work are Aristotle, Scotus, Leibniz, Berkeley, Bolzano, Brentano, Frege, Husserl, Meinong, McTaggart and Russell.

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The attempt is to bring Aristotle’s Categories up to date by giving a list of, and stating the laws which govern, the fundamental categories of the world. These categories, Grossmann holds, are individuals, properties, relations, classes, structures, quantifiers and facts. Facts are the allembracing category, everything else that exists being a constituent of a fact. The world as a whole is one gigantically complex fact. Negation and existence are thought of as so fundamental that they lie below even the categories. Grossmann confesses to not having worked out the topic of negation sufficiently for the purposes of this volume. He does devote a final, relatively brief, part to existence. But since he threatens us with a further work on Negation and Existence, I propose to confine myself to his categorical theory in this notice. That theory, or set of theories, constitutes the second, middle, and major, part of the book. The first part contains an articulation of fundamental epistemological attitudes, in particular a defence of Realism about the external world and a defence of Empiricism, together with a familiar Grossmannian theme, a polemic on, one could say; against definition. II. Equivalence or Identity? Grossmann’s empiricism is inherited from the Iowan tradition. It is a phenomenological, rather old-fashioned empiricism (not necessarily the worse for being old-fashioned, of course!). You look very closely at the ontological scene, and then declare what you seem to yourself to see there. That is a good guide to what is there, or as good a guide as one is likely to get. It is thus opposed to another empiricist tradition, one which I confess to belonging to, which in its metaphysical theorizing pays a great deal of attention to scientific results and plausibilities. This latter tradition is currently much more popular than the tradition of phenomenological empiricism. It, the scientific empiricist tradition, takes a more sceptical view of the finer details supposedly revealed to an ontological gazer. It, the scientific tradition, maintains that, however theory-laden observation may or may not be in the realm of the natural sciences, it is certainly theory-laden, and therefore to be treated with great caution, in the realm of metaphysics. As a result, the scientific empiricist tradition is much less hostile to the postulation of entities on purely theoretical grounds, and less hostile to theoretically motivated identifications. The phenomenological tradition is more positivist in spirit, seeking always to save the appearances. (Acquaintance has always been a key notion in Bergmann’s philosophy.)

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In Section 4 of his book Grossmann remarks very wisely that it is not the task of ontology to decide whether there are such things as numbers. It is sufficiently obvious that they exist. The task is rather to decide what category numbers fall under, to declare their nature as one might put it. Concerning that nature, I think the matter is more theoretical than Grossmann is prepared to admit. As Grossmann himself maintains, the only test which we have for factuality is coherence (Sec. 155). Now in the circle of our beliefs, the ones which we ought to cling to above all are the absolutely basic deliverances of commonsense, together with the securer results of the sciences. It is about them that intersubjetive can be obtained, while no such agreement can be obtained about the intuitions of philosophers. Grossmann himself very sensibly says “today’s self-evident proposition is tomorrow’s falsehood” (Sec. 58). Yet he seems to assume, or to proceed as if, philosophy has an observational fund of its own which can be called upon to give a decision about the nature of the categories. Grossmann’s trust in his phenomenological method leaves him to take up a certain attitude to almost all equivalences. Suppose that P if and only if Q. Prima facie, this could be a case of identity (P = Q), or it could be a mere equivalence, the co-obtaining of P and Q without identity (P ≡ Q & P ≠ Q). Now suppose that it is not obvious that P = Q, suppose, that is, that P and Q present themselves to our minds as different things. If one trusts in phenomenology, then one is likely to decide that it is false that = Q, that what we have here is mere equivalence. In almost every case, this is what Grossmann decides. (I note, for the interest of old Sydney hands, that John Anderson was wont to argue in the same way. Empiricism, plus a certain coolness towards science, produces the same result in Grossmann and Anderson.) This theme of equivalence rather than identity is raised early, and often, in Grossmann’s book. In Section 8, in the preliminary Part of epistemology, Grossmann considers a now traditional dilemma for scientific realism. In barest outline, (1) the particles of which ordinary physical objects are made up are colourless. But (2), it is physical objects which we perceive, and (3) they are, and are seen to be, coloured, where the colour is an intrinsic property of the object. Yet how is (3) possible, given (1)? Grossmann is prepared to concede (1), but he also wants to uphold (2) and (3). (The present reviewer would agree with him up to this point.)

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Grossmann’s solution is to say that there are laws pertaining to macroscopic objects such that (roughly) “a perceptual object has a certain colour if and only if its atomic structure is in a certain state”. (I would call such laws “emergent” laws because they could not be deduced from the rest of the structure of the laws of physics. But not so Grossmann.) To this solution, of course, thinkers like J. J. C. Smart have raised theoretical-scientific objections, objections which Grossmann passes over without mention. Smart has pointed out how badly such laws sit with the fundamental laws of physics, which seem likely to be the laws of natural science. The laws Grossmann wants to postulate would be a sore thumb on the corpus of science, nomological danglers as Herbert Feigl put it. The natural solution for the scientifically-minded (scientistically-minded, Grossmann would say!) is that the equivalence marks not a law, but an identity. The perceived colour is the atomic structure. But I think it is obvious why Grossmann ignores this solution. For him, phenomenology rules. Can we not “see the difference” between a colour and an atomic structure? So the hypothesis that what we have here is an identity, despite the scientific simplification it brings, must be set aside. It is the same line of thought, no doubt, that leads him to turn his back so briskly upon the Materialist identification of mental states with states of the brain. In the cases of colour, and the mental, the putative identity is usually claimed to be either contingent or at least one established a posteriori. When the equivalence from which the argument starts is a logical one, the case for identity would seem to be stronger. Does not “P ∨ Q” say the very same thing as “~(~P & ~ Q)? But even for this equivalence Grossmann wants to deny identity. (So did Anderson.) The De Morgan equivalence simply tells us that a state of affairs of a certain sort obtains if and only if a state of affairs of another sort obtains. After all, we can grasp one of the propositions without grasping the other. So why treat them as asserting the very same thing? Grossmann is unquestionably right that innumerable philosophers have simply assumed that what is involved in such a logical equivalence is an

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identity. In questioning the assumption he usefully awakes us from dogmatic slumbers. (He is utterly right to reject the absurd Quinean idea that mere isomorphism between structures entitles us to treat them as identical. Take Harvard Yard, or the null class. Form unit-classes with these as sole member. Form unit-classes with these classes as members, and so on. The resulting progressions are isomorphic with the natural number series, but to say that they can be taken to be the number series is the sort of absurdity it takes a pragmatist philosopher to be guilty of.) Nevertheless, to assume that logical equivalences are identities leads to a great simplification of our world-picture. It also goes a good way to explaining why theses equivalences, though not discoverable without labour, are discoverable a priori. This last has always been a problem for empiricism. So, even more strongly than in the case of colour and the mental, there is a plausible inference to the best explanation from the fact of equivalence to the hypothesis of identity. But for Grossmann an equivalence is almost always mere equivalence. For me, an unbelievable climax is reached in Section 67, where he argues that all relations, even symmetrical ones, have directions, and so that A is identical with B is not the same fact as B is identical with A since two different, if co-existent, directions are involved. I should have thought it obvious that, even granting that identity is a relation, there is here in the world only a single fundamentum relationis, as the Scholastics say, picked out by two different, but semantically equivalent, sentences. Grossmann has what might be called a rather reductive definition of analysis (Sec. 2). For him an entity is analyzed when a class is specified containing the elements, non-relational and relational, which go to make up that entity. Since the elements can often be “put together” in more than one way, different entities can have exactly the same analysis. But in truth this nominal definition of analysis reflects Grossmann’s stand on equivalences. For suppose that he adopted a stronger version of analysis, so that analysis not only provided a list of the elements of an entity, but also indicated just what structure the elements formed. It is certain that Grossmann would think that, for almost all cases, what had been given was a mere equivalence. The entity exists if and only if a certain structure of elements exists. But this is not to be taken as an identity.

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Grossmann’s devotion to the methodological principle of “equivalences not identities” carries him at times beyond his phenomenological starting point which, I have suggested, provides the original inspiration for the principle. The non-identity of A is identical with B and B is identical with A is a case in point. It seems very implausible phenomenologically, and Grossmann has to appeal instead to his doctrine that all relations have a sense. Another case in provided by Grossmann’s theory of properties. He holds that every property is simple. The chief motivation for this claim seems to be that where some property is associated with a structure of elements in relation, this will, as usual, be mere equivalence, not identity. But Grossmann then faces problems with a property such as squareness. He cannot bring himself to deny that it is a property. Yet, at the same time, it seems obviously to be a structure of elements: a square is a plane rectangular figure having four equal sides. But despite this appearance Grossmann clings to the idea that squareness is really simple, and merely associated with that structure of elements. So, it seems, phenomenology leads him to a principle which in turn he defends even where it seems to be false to the phenomena. III. Laws One result of Grossmann’s stand on equivalence is a great multiplication of the laws that he must recognize. He is committed not simply to laws of nature, including equivalence laws, but also to laws governing all logical equivalences. In fact, however, he recognizes not only laws of logic and laws of nature but many different sorts: ontological laws, logical laws, mathematical laws, physical laws, biological laws and so on. Different sorts of law govern spheres of different size, each type of law yielding its own notion of necessity and possibility. Ontological laws govern the widest sphere of all, wider even than the laws of logic. For instance, according to Grossmann it is ontologically possible that there be facts of the form p and not-p. The latter is merely logically impossible. This particular view of Grossmann’s seem to me to be very implausible. It is an ontological law, according to him, that no property exist unistantiated. But while I myself accept this view about properties, I would hesitate to think that it was a law whose scope was wider and more fundamental than

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the law of non-contradiction. Other philosophers have held views like Grossmann’s. Descartes, for instance, held that the laws of logic were established by God, thus at least implying the existence of a set of principles wider and more basic than logic. But without laws of logic, at any rate without the law of non-contradiction, it seems that anything would go. As a result, I do not think that there can be any more basic necessity than logical necessity. This, however, is perhaps a point of relative detail in Grossmann’s system. What seems more important is that the notion of law is one on which Grossmann must inevitably put great weight, but to which in fact he does not give much explicit attention. One is left with the impression that he thinks that laws are no more than purely general universally quantified facts, or some sub-species thereof. This is a thoroughly reductive position, and so appears to be opposed to at least the spirit of Grossmann’s position on equivalences. Here, however, he seems to yield to the Iowan tradition which, in its thinking about laws, seems not to have gone much beyond Hume. I think that a Humean or quasi-Humean position on laws is thoroughly unsatisfactory for many reasons, but centrally for epistemological reasons. It leaves unsolved, and I think makes insoluble, the question of how we can have any rational confidence that a law will continue to hold for instances of which we have no experience. That is to say, it makes the Problem of Induction insoluble. Grossmann, I believe, requires a “strong” conception of laws to provide a sufficient cement for his universe. (Perhaps laws should be recognized as an additional category, or at least an important subcategory.) One stumbling-block here for Grossmann may itself be epistemological in nature. In the case of “strong” laws of nature, it is natural to take them to be theoretical postulates, whose existence we believe in because of their explanatory value. But such postulation runs against the spirit of Grossmann’s “observational” empiricism. In the case of logical and mathematical laws, an opposite problem looms. We seem to be able to conduct such enquiries, and eventually arrive at such laws, a priori or relatively a priori. What does that tell us about the

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nature of these laws? (It must be admitted, however, that that is a problem for all empiricist, not simply for Grossmann.) Before leaving the logic of laws, I will note one extraordinary omission in Grossmann’s discussions. Nothing is said about causality, In Grossmann’s world, it almost seems, nothing makes anything happen. This is, if not Hamlet without the Prince, at least Hamlet without, say, the new King of Denmark. I suspect again the fatal influence of Hume on the Iowan tradition. Causes are thought of, like laws, as mere regularities. But it goes without saying that such a reductive doctrine of causality is utterly at odds with a phenomenological empiricism. IV. Properties and Relations Much of the interest of this book lies in its detailed discussion of the individual categories. I shall discuss, in particular, Grossmann’s view on properties and relations. Grossmann admits individuals, properties and relations into his ontology. Things really do have properties and are related to each other. To admit properties and relations is not, ipso facto, to admit universals, because one can take the view that properties and relations are as particular as the things which have them, a view which Grossmann documents in a number of philosophers. But Grossmann holds that properties and relations are in fact universals; holding, for example, that two different particulars can have exactly the same property. At the same time, things (that is, individuals, particulars) are not to be reduced to structures of universals, a doctrine associated with Russell. Grossmann, following in the Iowa tradition, devotes a lot of attention to this view, offering a number of forceful arguments against it. But things do instantiate universals: they have properties and stand in relations. Universals in their turn do not exist unistantiated. Grossmann thus accepts what I call the Principle of Instantiation. According to Grossmann every entity, including properties, itself has at least one property (Sec. 16). This will lead to an infinity of higher-order properties, unless at some point the very same property recurs in the regress.

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Given that Grossmann upholds the Principle of Instantiation, one might think that he was upholding an “Aristotelian”, in rebus, position about universals. In fact, however, his assent to such a view must be carefully qualified. According to Grossmann, all properties are exemplified by, and all relations, relate individuals. The individuals are in space and time or, in the case of mental entities, time. Nevertheless, he holds that the properties and relations themselves are “abstract”, by which he means that they are not spatio-temporal. Individuals and universals are constituents of facts, but facts have an abstract as well as a concrete component. There is a gigantic, complex, all-embracing, fact: the world. The world, however, is to be distinguished from the universe, the individual which is the sum of all (first-order) individuals, the things in space and time. The universe is no more than a constituent, the subject constituent, in the great fact, the world. I find this a very disconcerting position, and I suppose that many other naturalistically-minded philosophers do also. I agree with Grossmann about the need for universals. I do not think that it is really possible to deny that there is genuine, objective, mind-independent repetition in the universe. (And if not repetition, then at least genuine, objective, mindindependent, similarity.) At the same time I am strongly drawn to Naturalism, the view that the world of space and time is the sole reality at the price, the view that the world of space and time is the sole reality. If Grossmann is right, however, one can only have Naturalism at the price of Nominalism. The package-deal of Naturalism with universals is not on offer. (Which is no more than many Naturalists, and many Platonists, have thought, of course.) But while Grossmann accepts a bifurcation of reality, he does not accept a bifurcation of ways of knowing reality. He does not accept the Rationalist epistemology where spatio-temporal individuals are grasped by perception, and universals by the eye of the soul. As Anderson used to emphasize, and as I think Grossmann would agree, this epistemology leads to the apparently insuperable problem of what the faculty is which grasps the facts in which individuals and universals are united. Instead, Grossmann emphasizes that even perception is propositional, involving an awareness that things have properties and relations (Sec. 19). This, though I would not disagree with it, indeed applaud it, means that, on Grossmann’s view, even

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dogs have access to higher things. Is this carrying Animal Liberation too far? But let us come back to the question whether Naturalism could not be combined with an acceptance of universals in rebus. Grossmann calls this doctrine of “concrete universals” (no connection with the Absolute Idealist’ concrete universals) as opposed to his own “abstract” universals. He does not give the hypothesis of concrete universals much attention. Here is one line of thought that might lead us to make properties and relations abstract, lying outside the individual. Suppose that a has property F. It is a fact about a that it is F, but a is not identical with F. a is just a. So if a is to be a mere constituent of the fact, then F must stand outside a. Hence, unlike a, it is not concrete. One way out of this dilemma, a way that I favour and a way which was at one time taken by Bergmann (see Grossmann’s Sec. 30), is to identify a with all non-relational facts about a. It is helpful in taking this line if one distinguishes between what I have elsewhere called the “thin” and the “thick” particular. The thin particular is the particular considered in abstraction from all its properties, what a Scotist would think of as the thinness or bare particularity of the thing, the factor which makes it numerically different from other things. The thick particular is the thing along with its (non-relational) properties. Now it is the thick, not the thin, particular which it is plausible to identify with the totality of non-relational facts about a. If, as Grossmann does not, we admit conjunctive properties, then we can roll up all of a’s non-relational properties into one big property, super-F. The fact that a is super-F can then be identified with (thick) a. Grossmann (Sec. 30) criticizes this view as involving bare particulars. He says: When you see… two billiard balls, you see two individual things… and you see a number of properties and relations, but you do not see, in addition, either “bare places” or “bare particulars”.

This strikes me as quite unfair reasoning for one who has (1) refused to dissolve individuals into bundles of universals; yet (2) made their proper-

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ties “abstract”, that is, denizens of another realm. I think that Grossmann’s particulars look a good deal barer than Bergmann’s (or mine). Grossmann has another argument in reserve, however (private communication). It is that if things are facts, then it will be facts that have properties, stand in relations, etc., yet that this seems false. Thick a is white. But is the fact that a has super-F white? For myself, I am not clear that the fact is not white, although it is certainly linguistically awkward to say that it is. I suspect that what is needed is a translation of ordinary subject-predicate talk into fact talk, a move which does not look too difficult to make. But I think that Grossmann would stigmatize this ploy as an illegitimate contextual definition trying to palm off a mere complex equivalence as an identity. We would thus be led back to the old dispute again. Grossmann has another, perhaps more important, argument against “concrete” universals, universals brought downstairs. It is the problem of locating them. The problem about properties can perhaps be met by arguing that they are multiply located, located in each individual which exemplifies them. I do not think that Grossmann has any argument against this. Following McTaggart, he does raise a problem about relations, though. To use Leibniz’s example, if David is the father of Solomon, where is the relation of paternity located? It seems awkward to answer: the mereological whole whose parts are David and Solomon: though this answer may be possible. One sort of relation that can perhaps be dealt with satisfactorily by a “concrete” view is spatio-temporal relation. Those relations are “in” space-time because they constitute, or at least partially constitute, space-time. Causal relations are a problem, however, unless a Humean theory of causation is viable, as I think it is not. But the problem could be solved by a causal theory of time, or a causal theory of space-time. For then the causal system of nature would be identical, or partially identical, with the spatiotemporal system. It is arguable, and was argued in effect by Hume, that all external relations, “relations of matters of fact” in Hume’s terminology, can be classified as spatio-temporal and/or causal. Internal relations, “relations of ideas” in Hume’s very unsatisfactory terminology, do not appear to lend themselves to reductions to spatio-temporal relations. It is not clear to me, however, that they are genuine relations, although the predicates involved

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in attributing them are certainly many-placed. But the so-called relations seem to be supervenient upon, logically entailed by, the nature of their terms. This suggests to me that they are nothing over and above the conjunction of certain facts about their terms. It would not suggest this to Grossmann, of course. He would think that all one had here was a logical relation between the fact that the terms had certain properties and the holding of certain relations between the terms. But, for myself, I think that it is a reasonable inference from the supervenience of internal relations to the conclusion that they are not genuine relations. If so, perhaps, the spatio-temporal relations are the real relations. A believer in “concrete” universals would then have an answer to the difficulty of locating relations. V. Intentionality No review of Grossmann’s book would be in any way complete which failed to mention his doctrine of intentionality. What account is to be given of thinking about that golden mountain? Grossmann, taking the phenomenological facts at face value, thinks that what we have here is a relation: It seems to me to be an inescapable conclusion that the intentionality of mental acts is a relational feature of such acts. (Sec. 79)

Grossmann rejects Bergmann’s admission of mere possibilities as beings, and the early Russell’s category of subsistence. There is only one level of being: existence. He also rejects the later Russell view that the real terms of the relation are the thinker, goldenness and the mountain. He is thus driven towards Meinong’s view: that the golden mountain does not exist but that the thinker is related to it. With these “abnormal” relations, the second term does not exist. Grossmann does take issue with Meinong on one point. Meinong holds that, although the golden mountain does not exist, it does have properties, in particular being golden and being a mountain. Grossmann holds that the non-existent has no properties. It can only be thought of, or imagined to have, properties. This point against Meinong has obvious force, but I think that it also involves difficulties. If all non-existents things lack properties then, by the Identity of Indicernibles with Grossmann accepts in such a

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context, they are all the same thing. (Cf. the null-class.) Yet the Golden Mountain is not the Fountain of Youth. Grossmann does make an interesting attempt to generalize the problem of “abnormal” relations beyond the mental. He argues (Sec. 82) that the state of affairs P Q is a fact if P exists even where Q does not. Since facts exist independently of human minds, this shows that the existence of “abnormal” relations does not depend upon there being minds. This complex fact involves an abnormal relation, the disjunction relation, holding between the two constituents of the disjunctive fact, the existent P and the non-existent Q. But one can go even further than that. If it is a fact that neither P or Q exist, then the neither/nor relation, the stroke-function relation, holds between two constituents which are both non-existent. Such a relation is wholly abnormal: neither of its terms exist. The situation with negative facts may also be noted. Since Grossmann accepts negative facts, and takes them to have the basic form not-P, their constituent P is non-existent. In negative facts, the constituent of negation is always related to a non-existent constituent (Sec. 82). I think that there are still further prima facie cases of “abnormal” relations. As argued at various times by John Burnheim, C. B. Martin and myself, unmanisfested dispositions have a strong formal similarity to non-existent intentional objects. Martin has even argued recently that dispositionality is the true locus of intentionality, with the mental case no more than a particularly spectacular instance of the phenomenon. This brittle glass never breaks. But is not the glass related to a non-existent happening, its potential breaking? However, this generalization of the problem of abnormal relations does do two things. First, it takes away one important reason to think that the mental is a quite special thing in the universe, and so makes things easier for Materialism. Second, it raises hopes, in my mind at least, of solving the intentionality problem without resorting to what I find perfectly incredible: relations which genuinely have non-existents terms. I think that the correct strategy is to work on dispositions first, and somehow “reduce” the offending relation. If that can be done, as I have some reasonably solid hopes to

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think it can be done, I would then hope that the solution can be projected back on to the golden mountain problem. It would be necessary also to have a solution to the problem of disjunctive, negative, and stroke-function facts. A discussion would also be required of exclusion laws where the excluded state of affairs never exists. Grossmann’s sharp posing of the problem is certainly valuable, even if most of us are unable to accept his solution. VI. Classes, Structures and Numbers Besides properties and relations Grossmann, as might be expected, recognizes classes as a further category of “abstract” object. He is unworried by the teeming proliferation of classes which so disturbs Goodman. (But he does reject the null-class as anything but a convenient fiction.) I think the most interesting feature of his treatment of classes is his treatment of the class paradoxes. Grossmann’s plausible line on the paradoxes generally is that they are nothing but surprising non-existence proofs. The proofs healthily shock our intuitions about what can exist. For instance, the paradox about the sentence which says it is false is resolved by saying that what the argument proves is that, despite appearances, no proposition corresponds to the words “The sentence on this page is false”. Similarly for Russell’s paradox about the property F such that a property G has this property if and only if is not a G. There is no such property F, Grossmann argues. In the case of classes, the paradoxes of Cantor and Russell show, respectively, that there is no class of all classes, and no class of all classes not members of themselves. Grossmann, rather plausibly I think, considers and rejects other solutions, such as defining one’s way out of the difficulty by distinguishing between classes and sets. But Grossmann’s resolution of Cantor’s paradox leads to an interesting situation. Corresponding to each category, Grossmann holds, there is a categorical property. So being a class is a property. But Cantor’s paradox has shown that there is no class of all classes. So here is a property which, contrary to previously unchallenged assumption, does not determine a class.

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Grossmann has earlier argued for the less startling but still unorthodox thesis that there are classes to which no property corresponds. Not every class determines a property. (Contrary to what, e. g. Frege assumes.) I think that this contention of Grossmann’s must be right, unless one is prepared, as some philosophers are, to let the range of the word “property” expand indefinitely. Consider, for instance, one of those utterly heterogeneous classes, having members belonging to all sorts of different categories, which philosophers and set-theorists love to give as examples (The King’s College Chapel, the square root of 2, …). To make matters even more difficult for orthodoxy, give the class an infinity of members. This class might well be a mere class, with no property in common to its members. So not every class determines a property. But can we say that not every property determines a class? I confess that even I shrink from this Grossmannian boldness. The following intuition, at least, seems to me to be worth hanging on to: every genuine universal determines a class. Combined with Grossmann’s treatment of Cantor’s paradox this would have the consequence, not unwelcome to me, that there is no universal of being a class. Rather, it is an irreducibly heterogeneous notion. The logically successful, paradox free, conception of classes is the iterative view, with higher-order classes formed out of a substratum of lower-order classes acting as their members. This iterative procedure suggests that the notion of being of a class is a heterogeneous one. In any case, it is noteworthy that being a class is the only case given by Grossmann of a property which does not determine a class. After classes comes the category of wholes, or, to use the term of Grossmann’s which I much prefer, structures. Structures are structures of elements in relation. But, as Grossmann points out, their criterion of identity is not mere identity of content. The love of A for B, and the love of B for A, are structures with identical content, relational and non relational. Yet they are not identical structures. To get identical structures, the same non-relational elements must be related by the same relations in the same way. Many of the things that Grossmann would treat as mere structures, I would say are structural properties. But Grossmann’s idea that all properties are simple (his hyper-atomism of properties, as it were) prevents him treating any structures as properties. The category of structure does enable him to

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deal with miscellaneous portions of facts which are not themselves facts, such as is F (which he distinguishes from the property F), A is, is R to an F, having R to b, and so on. Numbers Grossmann takes to fall under the category of quantifier, a not implausible view for a metaphysic which takes fact to be the allembracing, unifying, category. All, some, no, etc, are said to be indefinite quantifiers. I have perhaps given too jejune, too dry and stringy, an impression of Grossmann’s whole argument. In his discussion of number, for instance, as in his discussion of all the other categories, the argument is enriched and given great depth by the criticism of alternative philosophical views of number. The criticism are acute, straightforward, and in case after case rather devastating. The book is presented in a very clear typescript with justified margins. However it lacks a subject index, a shortcoming not entirely made up for by an excellent analytical table of contents. David M. Armstrong

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2. Comments on Armstrong’s “Universals” I shall not bother to praise once again your clarity, fairness, and insight.

Chapter I (The Problem) Introduction 1. It seems to me that your introduction to the problem is prejudiced.

The very example with which you start (two inscriptions of the same word) cannot but prejudice the issue. Take instead Stout’s two billiard balls which are white, round, etc. Not for a moment is there any doubt about these two balls (a) that they are not identical (the same), (b) that they are not even partially identical. All that can be said is that they have the same color, the same shape, the same size, the same weight, etc. The visit with Bishop Butler is totally misleading: There is simply no question of partial identity. The two balls are not the same; the only question is: Do they have the same color, shape, size, etc. Yes or no? This is obscured by your very expressions: p. 2, line 15: There is something about the two “the’s that is identical (my italics). No, there is nothing about them that is identical! But is their color identical? (The same, line 20). Also: line 12 from Bootom: the two tokens are not totally separate. Yes, the two billiard balls are totally separate! Pp. 4-5: … they are also in a way the same. No: They are in no way, no way, no way the same: What is (perhaps) the same is the color of the one and the color of the other. (same word; you could not do this with the balls: same balls?) Next line: There is something (strictly) identical about the two “the”. Not in a thousand years: what may be identical is their color, their shape, etc. Lines 8-9: Perhaps the two tokens are said to be the same… . No way: the two balls are said go be the same? Never. Only because you loaded the dice by using this example. Later on: The two different tokens have something strictly identical: No,

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the two balls have (?) nothing strictly identical. Their color may be and that is the issue. 2. No wonder, then, that on bottom of p. 5 you describe a view and

imply that it is nominalistic, when in reality it is realistic. This is “class nominalism” as opposed to property realism: a Property

b

a Class

c

b c

Lines 4-5 from bootom: The realist does not hold that the “sameness of the tokens is not loose and popular”. Rather, he holds that there is no sameness at all, not at all. What is the same is the property (white, round), just as what is the same here is the class. No difference. The difference between realist and nominalist is not to be drawn as you do on page 6, lines 9-11., in terms of “loose and popular identity”. No thoughtful realist would ever hold that there is any sort of identity (loose and popular or otherwise) between the two billiard balls. At best, he may say that they are qualitatively the same. But this means that they have the same quality, and it is has nothing to do with the sameness of a river, or an elephant. Chapter III (Resemblance Nominalism) The Resemblance Regress 3. Pp. 53…108… The regress argument. I think that you are mis-

taken if you think that the argument can be applied to the property realist. But, then, I am not sure at all what you have in mind when you talk about this argument. I am suspicious that you are confusing two quite different arguments with each other: (a) the argument against nominalism and (b) (Bradley’s) argument against relations in general. Russell’s is (a). It is vicious, but only holds against nominalism (not, for example, against your class realism). One avoids the vicious regress as soon as one admits there to be a relation which is a

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universal. Just take another look at Russell’s argument: It clearly implies that as soon as you admit that the same relation of resemblance can obtain between different pairs of things, the regress ceases. Compare your version of the argument (p. 108) with Russell’s: These are totally different arguments. However, I am not sure that I understand your version of the argument. As it stands, it seems to reply on there being a property, instantiation, which certain states of affairs have. For example, A is F has this property. But this means that this state of affairs stands in the instantiation relation to that property; and the fact it does, does also have this property, etc. I have just changed my mind: This is neither Russell nor Bradley, but pure Armstrong! I do not see anything vicious about the regress, though: There exists the fact that A is F, the fact that this fact, P, has a certain property G (instantiation): (P); the fact that G (O) has G: G (G(P)), etc.: an infinite series of facts. But this is not vicious. But I think that the argument is not sound to begin with, because there is no such property as instantiation. When a fact contains the nexus of exemplification, then it is one of many facts that contain this relation, but it does not have, for that reason, a certain property, namely, instantiation (or better: “the property of containing exemplification as a constituent”.) And since there is no such property, the fact cannot, in turn, exemplify it. This is one of the important places where your axiom holds that there need not correspond a property to every phrase we can turn! 4. The notion of supervenience. This is a long story and I cannot go

into it here. Let me just say that I suspect that it is a swindle: One does not want to say that the thing is not there at all, but one wants to minimize its importance, its way of existing, its causal efficacy, or what have you. Your explanation is not helpful to me, since I want to distinguish between logically possibly worlds, ontologically possible worlds, biologically possible worlds, etc.

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Chapter V (Universals as Attributes) State of Affairs However, something more specific, connected with supervenience, caught my eye. P. 90: how precisely does it follow that the Class Nominalist needs no states of affairs? Are you assuming that it follows logically from the existence of a and class C that it is a member of C? I deny this! You may think it does because you give the following description of C: the class whose members are a, b, c, … . But what if I give the following description of the property F: the property exemplified by a, b, c, … . Is it then a logical consequence that a is F? If not, why is it one in the class case? But even if we assume that it follows from the existence of a and C that a is a member of C, this does not show that the Class Nominalist needs no state of affairs. All it shows is that a certain state of affairs (a is a member of C) logically follows from another state of affairs (a exists, and C exists). (Question: p. 92, according to what you now say about conjunctive universals, why are they not supervenient to conjunctive facts?) Chapter VII (Summing Up) 5. I find it peculiar that, as an end result, you should conclude that

realism’s fate depends to a large extent on resemblance between universals (p. 138). I find no intuitive difficulty whatsoever in believing that color shades, for example, are ordered by primitive, unanalysable, resemblance relations, so that they form the familiar three dimensions. These relations are not analyzable in terms of partial identity. But so what? Perhaps, the word “resemblance” as at fault! Some shades are more saturated than others. Some shades are lighter than others. (Some numbers are “closer” to each other? (3 and 5 vs. 3 and 200)). But it is possibly that I have totally misunderstood you on this point. Let me thank you again for sending me your book. I hope I have shown my appreciation by writing these comments. Reinhardt Grossmann

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3. Comments on Grossmann’s “The Existence of the World” Chapter I (The Discovery of the World: Timeless Being) Individual things change, properties do not. Ok. But why assume that properties are in another realm? Why not start with facts —this object has this property, this object is related to that, and then see any realms there are —the space-time realm and any other— as constructions out of facts. Within facts, individuals and properties are kept together. Does this mean, then, that the properties (and relations) of spatio-temporal things are spatially and temporally located? I do not really think so. Spacetime and its locations should rather be taken to be a vast conjunction of facts, so that, e. g., location is constituted by certain facts —just with facts they are may be more of a scientific than a philosophical question. If the universe is kept separate from properties and relations then in itself, in its intrinsic nature, the universe is a shapeless, formless, thing. It is a bare particular with a vengeance! So let us have a compromise between the gods and giants. There is only one realm, but it is a realm of facts, involving both things and universals (properties and relations). Or if there is more than one realm, will not it also be a realm of facts? In particular, the naturalist who accepts universals does not have to locate properties, still less relations. All he needs assert is that different individuals may have the same property, different pairs, etc., may be related by the same relation, and take these to be facts. Locations, etc., are subsequent to (constituted by) facts. Chapter II (The Battle over the World: Universals) P. 23: I do not think that the nominalist should agree that there is something common to all human beings. Thus, for instance, step (4) —that individual essences have something in common will be strongly resisted by

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any sensible nominalist. He will say that our talk of sameness is not to be taken with full seriousness —it is “loose and popular” identity. P. 27 ff: I cannot understand you here, in your argument against me. If I assert that spatio-temporal relations help to constitute space-time, how does that involve me in asserting that these relations are not part of spacetime? On the contrary, if the relations help to constitute space-time, in some sense they are part of space-time. (But not by being located in spacetime.) You seem to think that if relations cannot be got into space-time by being located in it, they cannot be got into it at all. I deny your major! Chapter III (The Structure of the World: The Categories) Structures P. 47 ff: I am totally amazed that you can think the square is spatially simple. Can I be told “look (aim) at the left side of the square” without nonsense of drawing lines in my imagination? Is not space divisible? (not in the sense you can cut it —only that it has proper parts.) P. 49: I think that you structures are two or more entities related in a certain way —and that they are therefore a subspecies of fact. You say that, unlike facts, the conjunction of structures is not a structure. Well, I think that this is just definitional. I would not object to a conjunction of (joint existence) of structures constituting a structure. Not much, but a bare conjunction of facts is not much either. (Both supervene on the conjuncts.) Relations P. 52 ff: I think that Plato’s case for tallness (but not Leibniz’s case for paternity) is reasonably plausible. “Taller than” is a matter of comparison of height —and height is a matter of spatial distance of a stretched out person from sole to crown. We have here spatial quantities which it is plausible to think are non-relational properties of the persons involved. And then it is plausible to think that these properties are the sole truth-makers for the relations. What we have is an internal relation which flows from the nature of its terms. The same can be said of the numerical relations that you instance. In general, order can be generated by quantitative property as much as external relations.

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P. 57: It seems to me to be immensely plausible that Tom is the spouse of Jane, and Jane is the spouse of Tom, are the same fact differently expressed. Sets P. 58 ff: The view I now take of sets is that they are facts (state of affairs, in my terminology). Following Lewis I take plural sets to be mereological wholes whose parts are their unit-sets. What then is the difference between a and {a}? I think the later is the fact that a has certain property of an abstract sort —the property of having some unit-making property— unithood for short. You may like to see a paper I have on this subject. P. 59: The introduction of aggregates, in my case, did not spring from any hostility to sets. P. 60: Goodman quote. It is interesting to note that Goodman’s principle would also ban facts: A loves A, and B loves A are different facts formed from exactly the same constituents. P. 61 ff: It is not at all clear to me how these quotations support the idea that the existence of sets demands corresponding properties. Do you just mean that there are properties that do not determine sets? P. 63: There must be a property of being a set. Ok. But I wonder if this property is a universal? It seems a plausible assumption that every universal determines a set. Numbers P. 68: “An aggregate, that is, a spatio-temporal whole”. This is too confined a view of aggregates. I favour a totally permissive mereology: e.g. there is an aggregate of √-1 and the Sydney opera house. P. 69: I do not wholly reject the view that numbers are quantifiers because I think that a relational account of the quantifiers looks hopeful. Consider what it is to be All the A’s. Does not this aggregate (or class) have a certain relation to being an A?

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I call this the T relation, for totality. It may be said that the aggregate totals being an A, and in virtue of this relation the aggregate has the relational property of being the total of the A s, being all the A s. (This is expounded in A Combinatorial Theory of Possibility —not out yet.) An interesting feature of the T relation, the tallness relation, is that it is external. P. 71: I do not like “+ (2, 2, 4)” as a representation of 2 + 2 = 4. My reason is my dislike of the contemporary representation “R (a, b, c). Information is lost inside this symbolism. You do not know what is hooked up to what. I think that this is linked with the point that relations are abstractions from facts (states of affairs). Facts P. 74: Facts (state of affairs) —Not so much a category, I think, as a supercategory, in which all categories are involved. P. 75: “Some complex facts contain state of affairs which are not facts”, e. g. a disjunctive fact with one disjunct false, a neither-nor fact. This is where I go for Modus Tollens. I cannot come at “constructing” an existent from non-existents. I would say that there can be true disjunctive statements, and true neither-nor statements, but no such facts (in your terminology) —no such states of affairs, in mine. I therefore reject the “abnormal relations”. Some other account of connectives must be found (e. g. relations between statements.) P. 76: I think that you need one other part-whole relation: the mereological relation (Donald Williams called mereological relations the “partitive” relations). But I incline to think that structures are a species of facts, and so in both cases what we have are constituents. P. 77-78: “The naturalist must either deny the existence of facts or else hold that facts are temporal”. As usual, I seek to evade this by arguing that facts (state of affairs) are basic and time is constituted by the facts —in particular by temporal facts—

130

e. g., temporal relations between individuals. In your terms, I reduce the universe to the world. P. 79: As Russell pointed out, if you take all the positive facts, and add the totality fact —that these are all the facts there are— then the negative facts are all entailed. This suggests to me that we can get along without negative facts —they supervene and so are not ontologically something extra. P. 79 ff: I would, of course, think with Wittgenstein that (1) and (2) represent the same fact. Wittgenstein could defend (p. 55) his position by calling attention to the strangeness of constructing existence is best explained as identity. P. 82: I agree with you that Wittgenstein’s attempt to get rid of All fails. The Category of the World P. 84: In your list of categories I would (1) eliminate structures, sets, and quantifiers, (2) elevate facts to the status of supercategory. “The physical universe … is a spatio-temporal structure”. Is this ok. on your view? Being a spatio-temporal structure is a property of the universe. Properties are in another realm. Is not the physical universe really a bare particular? P. 84: “The world is a fact”, consisting of other facts.” Hooray! We are in agreement. And in that case is not your “universe” a mere constituent of a fact? P. 85: John Anderson tried to deduce his categories from “the form of the proposition” —for him, from the form of facts. Not unlike your enterprise. Necessity P. 88 ff: Surely what we can imaginate or not imaginate is a mere test of possibility or impossibility? (and, as you say, not a very reliable one.)

131

Chapter IV (The Substratum of the World: Existence) I agree with you that existence should not be taken to be a category, and, of course, I reject modes of being. P. 104: My position, of course, is that there are no “abnormal” relations. Solution: There must be some analysis (conceptual, empirical?) of intentionality. P. 104: No such thing as relational properties? Too harsh, in my opinion. We might want to appeal to such properties, for instance, in the theory of causality. (All F s that have R to G s become H’s as a result of having R to a G.) What we should say, I think, is that relational properties supervene on facts —facts involving relations. P. 105: I entirely agree that existence has nothing special to do with “the existential quantifier”. Chapter V (The Enigma of the World: Negation) P. 125 ff: One difficult about (non-inferential) perception of negative facts lies in the factor of causation. In non-inferential perception, the fact that a is F is, I think, causally responsible for the perceiver perceiving that a is F. Do we want to say that the fact that a is not F has causal powers? It seems uncomfortable to me. P. 132: All properties are positive, is this your view? Being invisible, therefore, is not a property? David M. Armstrong

132

Bibliography Aristotle, Categories. Armstrong, M. D, 1978, Universals and Scientific Realism, (2 Vols.: Nominalism and Realism; and A Theory of Universals). Cambridge University Press, 1978. ——, 1979, “Laws of Nature”. In Proceedings of the Russellian Society, Vol. IV, pp. 46-61. ——, 1983, What is a Law of Nature? Cambridge University Press, 1983. ——, 1984, “Reinhardt Grossmann's Ontology: Critical Notice of The Categorial Structure of the World, by Reinhardt Grossmann”. In Critical Philosophy, Vol. II, 1984, pp. 63-76. ——, 1987, (With Peter Forrest) “The Nature of Number”. In Philosophical Papers, Vol. XVI, 1987, pp. 165-86. ——, 1989, Universals: An Opinionated Introduction. Westview Press, 1989. ——, 1989. A Combinatorial Theory of Possibility. Cambridge University Press. Frege, G., 1969, “On Concept and Object”. In Geach, P & Black, M. (Eds.), Translations from the Philosophical Writings of Gottlob Frege, Oxford University Press, 1969, pp. 42-55. Grossmann, R., 1972, “Russell’s Paradox and Complex Properties”. In Noûs, Vol. VI, 1972, pp. 153-164. ——, 1973, Ontological Reduction. Indiana University Press, 1973. ——, 1974, Meinong. Routledge & Kegan Paul, 1974. ——, 1976, “Structures, Functions and Forms”. In Schirn, M. (Ed.), Studies on Frege: Logic and Philosophy of Language (2 Vols.), Fromman-Holzboog, Vol. II, 1976, pp. 11-32. ——, 1982, “The Nature of Universals: Armstrong’s Universals and Scientific Realism”. In Noûs, Vol. XVI, 1982, pp. 133-142. ——, 1983, The Categorial Structure of the World. Indiana University Press, 1983. ——, 1992, The Existence of the World: An Introduction to Ontology. Routledge & Kegan Paul, 1992. Plato, Sophist. Tooley, M., 1977, “The Nature of Laws”. In Canadian Journal of Philosophy, Vol. VII, 1977, pp. 667-698. Wittgenstein, L., 1961, Tractatus Logico-Philosophicus. McGuinness,1961.

About Reinhardt Grossmann (1931, Germany) Emeritus Professor at Indiana University. He is a leading member of the Iowa School founded by Gustav Bergmann. Grossmann brought his robust epistemological realism and his interest in Phenomenology into the School which was still moulded by Logical Positivism. He developed a comprehensive and sophisticated metaphysical system and advocated a radical empiricism according to which abstract objects can be perceived. His books include The Structure of Mind (1965), Reflections on Frege’s Philosophy (1969), and Phenomenology and Existentialism: An Introduction (1984).

About David M. Armstrong (1926, Australia) Emeritus Professor at the University of Sydney, a leading member of the School of Australian Realism and of Australian Materialism. He became known by his materialist philosophy of mind and later by his combination of universal realism and scientific realism. Without doubt one of the most influential metaphysicians of our time. His many books include A Materialist Theory of the Mind (eri1968), A World of States of Affairs (1997), The Mind-Body Problem: An Opinionated Introduction (1999), and Truth and Truthmakers (2004).

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About the Editors Erwin Tegtmeier Prof. of philosophy at the University of Mannheim. His areas of research are ontology, theory of knowledge, philosophy of science, philosophy of time, medieval philosophy, early phenomenology (Brentano and Meinong) and the philosophy of Gustav Bergmann. His books include Komparative Begriffe: Eine Kritik an der Lehre von Carnap und Hempel (1981), Grundzüge einer katergorialen Ontologie: Dinge, Eigenschaften, Beziehingen, Sachverhalte (1992), Zeit und Existenz: Parmenideische Meditationen (1997), and (ed.) Ontologie (2000), (co-ed.) Neue Ontologie and Metaphysik (2000), (co-ed.) Ontology and Analysis: Essays and Recollections about Gustav Bergmann (Ontos Verlag, 2007) and (ed.) Gustav Bergmann’s Collected Works (Ontos Verlag). Moreover he is co-editor of Metaphysica: International Journal for Ontology and Metaphysics. Currently, he is working on book on realism and intentionality . [email protected] Javier Cumpa (1983, Spain) is a researcher for Complutense University of Madrid. He is working on his Ph.D. on the Fact Ontologies of Reinhardt Grossmann and Gustav Bergmann, and on the Formal Ontologies of Meinong, Edmund Husserl, Adolf Reinach and Roman Ingarden. His main areas of research include the ontology of categories, the theory of universals, mereology, philosophy of science, and theory of knowledge. His papers include A Defense of Realism: The Physicalist Deconstruction of the World, (2009), Against Absurdity as Criterion of Categorial Sameness: Ryle’s Temptation (2010), Categoriality: Three Disputes over The Structure of the World (2010), and La naturaleza de las categorías: crítica del neutralismo metafísico de Gracia (2010). His forthcoming books include (ed.) Studies on the Ontology of Reinhardt Grossmann (Ontos Verlag, 2009), (ed.) Reinhardt Grossmann’s Collected Works (Ontos Verlag, 2010), (ed.) (with Erwin Tegtmeier) The Ontologist and the Task of Ontology: A Letter from Gustav Bergmann to Reinhardt Grossmann (Ontos Verlag, 2010). Currently, he is editing together with Erwin Tegtmeier a volume on Ontological Categories which will include contributions of the most important specialist in the topic (Ontos Verlag, 2010). [email protected]

136

Author Index Anderson, J. 1, 8, 11, 30, 109, 110, 115, 131.

Leibniz, W. G. 66, 107, 117, 128.

Alexander, S. 8.

Lewis, K. D. 129.

Aristotle. 107, 108, 115, 133.

Martin, B. C. 119.

Austin, J. L. 59.

McTaggart, E. M. J. 107, 117.

Ayer, J. A. 7.

Meinong, A. 33, 35, 107, 118,

Bennett, J. 77. Bergmann, G. 1, 7, 8, 10, 29, 32, 48, 107, 108, 116, 117, 118, 135, 136.

133, 136. Newton, I. 24, 101. Occam, W. 45, 52, 57.

Berkeley, G. 107.

Plato. 58, 115, 128, 133.

Black, M. 36, 70.

Popkin, R. 8.

Bolzano, B. 107.

Popper, R. K. 77.

Bradley, H. F. 8, 34, 35, 60, 78, 124, 125.

Quine, O. W. 111.

Brentano, F. 33, 107, 136.

Ramsey, P. F. 51.

Burnheim, J. 119.

Ryle, G. 7, 60, 136.

Butler, B. 123.

Tegtmeier, E. 1, 5, 14, 136.

Cantor, G. 42, 120, 121. Castañeda, N. H. 31. Cumpa, J. 1, 5, 14, 136. Dretske, I. F. 77. Forrest, P. 13, 90, 91, 97, 133. Frege, G. 36, 42, 107, 121, 133, 135. Geach, P. 36, 133. Goodman, N. 120, 129. Hall, Everett. 8. Hochberg, H. 7, 8. Hume, D. 12, 77, 79, 81, 113, 114, 117. Husserl, E. 33, 82, 83, 107. Kant, I. 82.

137

Subject Index Acquaintance, 108.

126, 127, 130-131, 132, 136, conjunctive

Categories, 3, 7, 13, 32, 33, 35, 36,

facts, 39, 40, 63, 126; and disjunctive

38, 43, 56 91, 94, 95, 96, 97, 99,

facts, 119, 129, 130; and negative facts,

101, 107, 108, 109, 113, 114, 118,

119, 131, 132; see also Negation.

120, 121, 122, 128, 130, 131, 132,

Intentionality, 118-120, 132, 136; and ab-

136.

normal relations, 118-120, 130, 132; see

Empiricism, 32, 37, 52, 107, 108,

dispositions, 119; and non-existent ob-

109, 111, 113, 114, 132.

jects, 118-20.

Equivalence and identity, 108-112,

Laws of Nature, 2, 12-13, 112-114; and

113, 117.

causation, 2, 58, 84-85; and connections

Exemplification/Instantiation, 1, 2,

between universals, 2, 77-78, and in-

11, 12, 13, 33-37, 48-51, 60-61,

duction, 82, 84; and quantified facts, 2,

65-66, 68, 114-118, 124-125; and

76; and lawful and accidental generali-

co-instantiation, 52, 53.

ties, 83; and synthetic a priori truths, 2,

Existence, 12, 45, 56, 108, 118, 120, 127, 131, 132.

82-83. Naturalism, 43-45, 57, 115-116.

Individuals/Particulars, 11, 12, 32, 33, 43, 44, 45, 53, 55-58, 64, 108, 114, 127; and bare particulars, 56,

Necessity, 33, 76, 112, 113, 131. Negation, 108, 119, 132, see also Negative facts.

116, 127, 131; and bundles of pro- Nominalism, 32, 36, 61, 115, 125. perties, 33, 116; and complex indi-

Numbers, 3, 13-14, 120-122; and aggre-

viduals, 64; and structures, 14, 22-

gates, 3, 90-97, 129-130; and mereolo-

fn, 60, 91-93, 94, 99, 104, 108, 120-

gical sums, 3, 93, 94, 97, 99-102; and

122; and thick particulars, 43, 45,

quantifiers, 108, 120-122, 129-130.

116; and thin particulars, 43, 58, 116. Perception, see Intentionality; and propoFacts/States of Affairs, 11, 12, 33, 43-45 sitional mental acts, 115. 48-51, 55-58, 60, 63-67, 108, 115,

138

Physical Universe, 1, 43-45, 55-58,

63-64, 131; see also World. Properties/Universals, 1-2, 9-12; and simplicity, 21; and phenomenological criterion for simplicity, 23, 26-28; and complexity, 22; and scientific criterion for complexity, 24-25, 27-28; and conjunctive properties, 1, 37-40, 51-54, 6163, 66; and structural properties, 1, 4042, 54-55, 61-63, 66-67. Realism, 9, 24, 32, 45, 57, 61, 108, 124, 135, 136; see also Nominalism. Reduction, 10, 11, 22, 29; see also Criteria of simplicity and complexity for properties. Relations, 114-118, 128-129; and regress argument, see Exemplification; see also Intentionality. Sets/Classes, 2, 68-72, 120-122, 129, see also Aggregates. Supervenience, 125-126. World, 1, 11-12, see also Physical Universe.

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