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Hempel's Paradox

Published online by Cambridge University Press:  01 March 1966

D. Stove
D. Stove
Affiliation:
University of Sydney
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Extract

Many writers, and even Professor Hempel himself, have said that Hempel's definition of confirmation has the consequence that ‘AH ravens are black’ is confirmed by any non-black non-raven. This consequence is often referred to as the paradox of the ravens, and I will sometimes refer to it so. But I do not assume that this supposed consequence is paradoxical, and in fact I will not touch at all on the question whether it is. My object is just to show that in any case it is not a consequence of Hempel's definition and that its closest relative, among the genuine consequences of that definition, is not paradoxical, even superficially.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 4 , Issue 4 , March 1966 , pp. 444 - 455
Copyright
Copyright © Canadian Philosophical Association 1966

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References

1 See C. G. Hempel, ‘A Purely Syntactical Definition of Confirmation’, Journal of Symbolic Logic, vol. 8, 1943, p. 142 and passim. This basic article is referred to hereafter as ‘Definition’.

2 C. G. Hempel, ‘Studies in the Logic of Confirmation’, Mind, vol LIV, 1945, p. 14. This article is referred to hereafter as ‘Studies’.

3 ‘Definition’, p. 142.

4 ‘Studies’, p. 26. Cf. p. 22.

5 But, for Hempel, it is an unfortunate rule to have endorsed. For conjoined with his own charge, quoted earlier, that under his definition a green leaf confirms ‘All ravens are black’, it means nothing less than that under his definition ‘Green a Leaf a’ confirms that hypothesis; which is a charge far worse than anything that the definition's severest critics have ever alleged against it. It is needless to say that such a charge is false.

6 ‘Studies’, p. 26.

7 I owe this point to I. Scheffler, The Anatomy ofInquiry, pp. 58–59; though i s there made as an objection to treating explananda as objects, rather than to treating confirmantia so.

8 Not always; sometimes Ti is arrived at in the following way. ‘It is a consequence of Hempel's definition that’∼ Raven a' confirms ‘All ravens are black’; hence that any non-raven does so; hence that any non-black non-raven does so.’ But this derivation of Ti is open to just the same objections as the derivation from T2; and is less plausible as well as less common.

9 This theorem is a consequence of Hempel's definition, of course, because the definition satisfies the consistency condition 3.2, (‘Definition’, p. 127).

10 This theorem is a consequence of Hempel's definition because under that definition, if O I confirms h and O 2 is neutral to h, then O I. O 2 does not always confirm h; and it never does so, if h contains a universal quantifier and O 2 contains an individual constant which O 1 does not. Thus for example, while ‘Fa’, ‘Fa-Ga’, and ‘FaFb’ all confirm ‘(x)Fx’ under the definition, ‘FaGb’ does not. This rather peculiar ‘volatile’ quality which confirmation exhibits under his definition was briefly acknowledged by Hempel (‘Definition’, pp. 136–137); but I have never seen it discussed anywhere else.

11 See the preceding footnote.

12 See ‘Studies’, pp. 14–17.

13 See ‘Definition’, p. 123.

14 See ‘Definition’, pp. 123–124.

15 ‘Studies’, pp. 14–17.

16 See ‘Studies’, pp. 18–21.