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Professor Darlington and the Confirmation of Laws

Published online by Cambridge University Press:  14 March 2022

Hugues Leblanc
Hugues Leblanc*
Affiliation:
Bryn Mawr College
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Abstract

The author discusses Professor Darlington's recent paper “On the Confirmation of Laws.” He criticizes Professor Darlington for not writing out in full the evidence sentence in formula III of his paper, and expresses doubts as to whether Professor Darlington's solution to the problem of the confirmation of laws follows from the complete version of that formula.

Type
Discussion
Information
Philosophy of Science , Volume 26 , Issue 4 , October 1959 , pp. 364 - 366
Copyright
Copyright © 1959 by Philosophy of Science Association

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References

1 See J. Darlington, “On the Confirmation of Laws,” Philosophy of Science, vol. 26 (1959), no. 1, pp. 14-24. Concerning Carnap's theory of the symmetrical c-functions, see R. Carnap, Logical Foundations of Probability, Chicago, 1950, chapter VIII.

2 Professor Darlington uses ‘A’ where I have ‘P’ and ‘B’ where I have ‘A’.

3 Note that the evidence sentence e in Professor Darlington's formula III must include the population sentence 'Rf(A,P) = p' or some analogue thereof if III is to constitute, as Professor Darlington intends it to be, a theorem of direct probability, that is, a theorem which, in Professor Darlington's own words, page 19, “concerns an inference from a population to an included sample.” The evidence sentence e in Carnap's +T96—1c (2), loc. cit., page 505, which Professor Darlington quotes (footnote 26, page 20) as his source for formula III, is a statistical distribution for n given individuals with respect to the division formed by the two predicates 'A' and ‘ ~ A’, with the cardinal numbers n 1 for ‘A’ and n-n 1 for ‘ ~ A’, and hence implicitly contains the data 'Rf(A,P) = n 1|n'. Note also that the evidence sentence e in formula III must not contain the sample sentence 'Af(A,S) = s′' [a sentence which occurs in (3) below], for if it did, e would then imply either the hypothesis in formula III or the denial of that hypothesis and formula III would of course be disprovable.

4 See J. Neyman: Lectures and Conferences on Mathematical Statistics and Probability, Washington, 1952.

5 For a definition of the equivalence of two sentences with respect to a third one, see Carnap, loc. cit., p. 85, D20-2a.