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Published online by Cambridge University Press: 14 March 2022
Mr. E. J. Nelson, in “The Inductive Argument for an External World,” treats of fundamental topics with erudition and urbanity, but his essay remains inconclusive, I believe, with respect to its purpose of discrediting the argument. He agrees with Mr. Savery, Mr. Pratt, and me, as against the positivists, that the question of the existence of an external world is meaningful (249) and indeed of paramount importance for both metaphysics and logic. But he argues against us that it cannot be inductively established by its supposed power of “saving the appearances.” He is not sure that any induction is valid; but even if other inductions are valid, he thinks this one can not be (240, 245, 247), for the following reasons. (1) By the multiplicative axiom of probability-theory, evidence for a hypothesis can only multiply its antecedent probability, and can increase the probability only when the latter is finite, while the hypothesis of an external world has and can have no finite antecedent probability (241, 245). (2) By the same axiom, even granted an antecedent probability for the hypothesis itself, no experience can act as evidence to increase the probability of a hypothesis except in so far as the hypothesis implies, makes probable, or “explains” the evidence, and this the hypothesis of an external world cannot do (244, 245, 247).
1 Philosophy of Science, Vol. III, July, 1936, pp. 237-249. Numbers in parentheses in the body of the following text refer to pages of this essay.
2 Mr. Nelson charitably surmises that the realists have not heard of the need for a finite antecedent probability (247). I cannot accept such absolution. Cf. “The Argument for Realism,” The Monist, Vol. XLIV, 1934, p. 193.
3 C. D. Broad, Mind and Its Place in Nature, and Scientific Thought; J. M. Keynes A Treatise on Probability, p. 238 ff. In ordinary cases the multiplicative axiom is used to appraise an increment of probability from evidence which is late and supplementary, and the antecedent probability of the hypothesis is its probability on the rest of the evidence, i.e., previous evidence. The realistic hypothesis seems to be in a different situation just because the evidence which the realist adduces for it is, so to speak, all the evidence in the world. In its case, therefore, we cannot overlook what we usually overlook in other cases, namely, that the axiom requires eventually a strictly a priori probability.
Incidentally, Keynes believes in the applicability of inductive method to the problem of the external world. Cf. op. cit., p. 240. Throughout the following discussion I follow Mr. Nelson's example in taking Keynes's Treatise as standard reference. It is a good example, but we should remark that the whole question takes on a different aspect, not to the advantage of Mr. Nelson's argument, when considered in the frames of the probability-theories of von Mises, Popper, and Reichenbach, for instance.
4 Treatise, p. 61, etc.
5 Cf. Keynes, op. cit., p. 238.
6 Cf. Keynes, op. cit., pp. 253 ff.
7 Keynes, op. cit., p. 139, expresses the law: a/h + ā/A = 1.
8 Op. cit., pp. 239, 253.
9 Op. cit., p. 256.
10 Keynes makes virtually this point, when he defends the analogical argument to other minds by maintaining the irrelevance of the myness which is common and peculiar to one member of that analogy. Op. cit., 258.
11 Cf. V. F. Lenzen, “Physical Causality,” e.g., Univ. of California Publications in Philosophy, Vol. XV, 1932, pp. 80-84.
12 J. Nicod, Le Problème Logique de l'Induction, p. 19 n.
13 Keynes, op. cit., 239, 247 n.
14 Op. cit., pp. 259-260.