Suppose we have several extremely large bags full of tiny marbles which have been taken from a very big heap of marbles of all sorts of colours. We draw one marble from bag A and find it is red. What is the probability that all the marbles in bag A are red? The answer is that it is not appreciably different from what it was before any drawing has been made, i.e. very, very small. When, however, we go on drawing marbles and they all turn out to be red, then if granted certain well-known assumptions, the probability of the hypothesis ‘All the marbles in A are red’ increases, and its value can be expressed with the aid of the inverse probability theorem. The way to establish the truth of the hypothesis that all the marbles in bag A are red, in case we are unable to check them all, is to check as many as we can, for the more we find to be red the higher the credibility of the generalization.
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- 1.C. G. Hempel, ‘Comments on Instantiation and Confirmation’, in Boston Studies in the Philosophy of Science, Vol. II, New York 1964, p. 22.Google Scholar
- 2.G. Schlesinger, ‘Instantiation and Confirmation’, ibid., pp. 1–17.Google Scholar
- 3.The reader may, if he wishes, turn, without any loss of continuity, to Section IV.Google Scholar