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Weinberg's Refutation of Nominalism

  • Fred Wilson (a1)


Professor Weinberg, in his recent Abstraction, Relation, and Induction, has critically discussed the nominalistic tradition stemming from Ockham and continuing in the work of Berkeley and Hume. In this tradition there is one fundamental principle, which however divides into two parts. The first is (α) Whatever is distinguishable is distinct, and conversely. The second is (β) Whatever is distinct is separable, and conversely. Weinberg argues that both (α) and (β) are mistaken.

In this paper I propose to explore the case against nominalism. I shall suggest that Weinberg's argument against (β), though not defective in the way some recent critics believe, depends upon a hidden premiss. I shall also suggest that the argument against (β), when the needed premiss is added, is but a special case of a more general argument. The latter in no way depends upon considerations concerning relational predicates, though Weinberg does in his discussion specifically introduce such considerations. Nor is that unreasonable on his part.



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1 University of Wisconsin Press, Madison and Milwaukee, 1965. (Hereafter referred to as “Weinberg.”)

2 Weinberg, pp. 54–56.

3 Weinberg, p. 54.

4 For Ockham, see Weinberg, p. 45, and for Hume, p. 35.

5 Weinberg, pp. 54–55.

6 The Journal of Philosophy, 64, 1967, pp. 539–540. See also Roma and Thomas, “Nominalism and the Distinguishable Is Separable Principle,” Philosophy and Phenomenological Research, 28, 1967, pp. 230–231.

7 Moody, p. 540.

8 Cf. H. Hochberg, “Eiementarism, Independence, and Universals,” Philosophical Studies, 12, 1961, pp. 36–43; reprinted in E. B. Allaire et al., Essays in Ontology, (Nijhoff, The Hague, 1963), pp. 22–29.

9 Cf. Weinberg's vigorous defence of logical atomism in his “Contrary-to-Fact Conditionals,” The Journal of Philosophy, 48, 1951, pp. 17—22.

10 Weinberg, p. 55.

11 It is only at the very end of this paragraph on p. 56 that Weinberg draws his discussion to a close: “Hence it follows that the dictum [(β)] cannot be maintained.”

12 Weinberg, p. 55.

13 Roma and Thomas, op. cit., p. 231, make this point. But they fail to see that this is precisely what Weinberg argues. They charge that it is hidden premiss for the argument which they along with Moody attribute to Weinberg.

14 Whether the entity is construed as some sort of individual or as some sort of character or property does not matter for what we are about.

15 Weinberg hints at this; see his fn. 127, p. 55.

16 Weinberg hints at the necessity of abandoning absolute time; see top of p. 56 where he speaks of individuals being temporally related, and at the bottom of p. 55 where he notes that the individuals involved must be momentary things. For more detailed discussions of this argument, see Bergmann, G., “Some Reflections on Time,” in his Meaning and Existence, (University of Wisconsin Press, Madison, 1960), pp. 225264; and P. Cummins, “Time for Change,” Analysis, 26, 1965, pp. 41–43.

17 Thus, Weinberg comments, p. 55 in the middle of his discussion of (β) and just following (C), that ‘Here it is plain that a dubious analysis of relations as well as the violation of a strict definition of numerical identity is responsible for the persistence of the doctrine [i.e., (β)].”

18 Weinberg also wants, of course, to make the point about “logical dependence” that we noted above.

19 This view of relations is roughly that of the early Meinong; see the second of his “Hume Studies” in Barber, K., Meinong's Hume Studies: Translation and Commentary, (University Microfilms, Ann Arbor, Michigan, 1966), pp. 195230, and also Barber's commentary, pp. 55–97. See also Bergmann, G., “The Problem of Relations in Classical Psychology,” in his The Metaphysics of Logical Positivism, (Longmans, Green, New York, 1954), pp. 277299.

20 Weinberg, p. 105 ff, argues that this is Ockham's view. Weinberg's discussion is blurred because he does not carefully distinguish between R and the foundations of R.

21 As Weinberg, p. 44 f, points out, Ockham continually argues from God's omnipotence.

22 Nor, one might note, is (I) violated for y in this case. Y's properties have not changed; rather, y and all the facts about y have simply been destroyed.

23 Cf. Bergmann, G., “The Ontology of Edmund Husserl,” in his Logic and Reality, (University of Wisconsin Press, Madison, 1964), pp. 193224.

24 Compare Meinong's discussion of similarity as an “ideal relation” in his Über Gegenstände höherer Ordnung und deren Verhältnis zur inneren Wahrnehmung, in his Gesammelte Abhandlungen, vol. II, (Barth, Leipzig, 1919), p. 395 ff. Cf. Findlay, J. N., Meinong's Theory of Objects and Values, Second Edition, (The University Press, Oxford, 1963), p. 35 ff, and Chapter Five, p. 113 ff. In certain respects Meinong's account of relational states of affairs in this work has changed from that given in the earlier Hume Studies; while still holding to the view that relations have foundations, r 1 and r 2, the relation R so founded is no longer contributed by the mind but is treated as a (subsistent) object of higher order. However, it still remains true that r 1 and r 2 are, and R is not, predicated in the strict sense of the relata. Cf. Findlay, p. 132 ff and also the excellent discussion of Meinong's development in Bergmann, G., Realism, (University of Wisconsin Press, Madison, Wise, 1967), Part IV, and especially p. 402 ff.

25 Cf. Russell, B., Introduction to Mathematical Philosophy, (Allen and Unwin, London, 1919), p. 44.

26 Cf. Russell, B., The Principles of Mathematics, Second Edition, (Allen and Unwin, London, 1937), p. 218 f

27 This is, of course, the basic fact presupposed in our ability to measure. Cf. G. Bergmann, “The Logic of Measurement,” in Proceedings of the Sixth Hydraulics Conference, (State University of Iowa Publications, Iowa City, 1956), pp. 19–34.

28 Cf. the discussion of certain of Goodman's views in A. Hausman, “Goodman's Ontology,” Chapter VI, in A. Hausman and F. Wilson, Carnap and Goodman: Two Formalists, (Nijhoff, T h e Hague, 1967).

29 Cf. Russell, The Principles of Mathematics, p. 218 ff.

One might also note the heroic efforts of Meinong to reduce dyadic relations to monadic properties; quality order is defined in terms of properties having “equal numbers of equal constituents” (cf. the Barber commentary, op. cit., p. 82 ff). On phenomenological grounds, which would seem on the basis of other things which he says to be acceptable to Meinong, the result must be condemned as absurd. Moreover, it is ultimately inadequate, for, while order among properties is defined in terms of the order among the numbers which number the constituents of these properties, the asymmetrical arithmetical relation remains unreduced to non-relations, a point which Russell (p. 223) makes in connection with views of this sort.

30 Weinberg, p. 63, cites the proof in Lewis, and Langford, , Symbolic Logic, Second Edition, (Dover, New York, 1959), pp. 387388.

One could, of course, construe the ‘and' in ‘r 1(x) and r 2(y)’ as non-truth-functional (a suggestion made by Roma and Thomas, op. cit., p. 233), but that would merely smuggle in at a slightly different point the descriptive relation one wants to analyze away: again, nothing is achieved.

31 Weinberg, p. 56.

32 This assumes the Axiom of Extensionality. If one rejects it, then one requires in the definition of ‘identity' for properties, that for two properties to be identical they must be both true of the same individuals (co-extensive) and also every second order property true of the one must be true of the other. Extensionality implies that coextensivity implies identity in this stronger sense.

33 As we have seen, for the nominalists, all predications in the strict sense will attribute a non-relational property to an individual. Ockham, of course, has properties in his ontology; cf. Moody, , The Logic of William of Ockham, (Russell and Russell, New York, 1965), p. 162 ff. Hume waffles on the issue of the ontological status of properties, introducing his obscure “distinction of reason”; cf. Treatise of Human Nature, Book I, Part I, sec. 7, (Everyman Edition, Dent, London, 1911, vol. I, p. 32). For a discussion of Hume's views, see Weinberg, p. 38 ff., and Meinong in Barber, op. cit., p. 137 ff.

34 Cf. Moody, The Logic of William of Ockham, p. 79 f., p. 162 f.; and G. Bergmann, “Some Remarks on the Ontology of Ockham,” in his Meaning and Existence, pp. 144–154.

35 Cf. G. E. Moore's discussion of G. F. Stout's position: “Are the Characteristics of Particular Things Universal or Particular?” in Moore's Philosophical Papers, (Allen and Unwin, London, 1959), pp. 17–31.

36 Cf. Bergmann, G., “Inclusion, Exemplification, and Inherence in G. E. Moore,” in his Logic and Reality, pp. 158170.

Weinberg's Refutation of Nominalism

  • Fred Wilson (a1)


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