We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...

These essays are intended to illustrate various ways in which ideas about language may be used to clarify philosophic problems. They contain careful interpretations and criticisms of theories of language.

A common type of inductive problem is to predict the nature of an unobserved finite sample of a given population on the basis of an observed finite sample of the same population. More precisely, given a class of events A, we examine a sample Sn having n members, of which mi belong to the class Bi. On the basis of our knowledge that mi/n of Sn have been Bi, we attempt to predict the ratio of members of Bi to members (...) of A in a sample Sr containing r unobserved members of A. This type of inference has been called “predictive inference” by Carnap. It is not necessary to argue that all inductive problems reduce to this form; we merely observe that such problems frequently arise, and that they have practical and theoretical importance. In The Short Run I suggested that this kind of problem could be handled by first determining the long run probability P of Bi, relative to A of Bi, to A in the observed sample Sn) and then predicting that the relative frequency of Bi within the unobserved sample Sr will approximate P sufficiently for practical purposes. The foregoing procedure requires a rule of each of two types: a rule for the ascertainment of the values of long run probabilities, and a rule for the application of knowledge of long run probabilities to predictions in the short run. The Short Run was not concerned with the nature and justification of rules of the first type, but rather sought to justify a rule of the second type on the assumption that we already possess knowledge of long run probabilities. (shrink)

1. The Problem. In spite of the vast discussion which has been devoted to the theory of probability, the problem of the short run has received surprisingly little attention. Yet, the whole significance of the theory depends upon a solution of this problem, for without an answer to it we cannot say why it is useful to have knowledge of probabilities or why we should take account of this knowledge in making practical decisions. As far as I know, Charles Peirce (...) was the first to appreciate the importance and difficulty of the question, and his characteristically vivid formulation serves as an excellent starting point for its consideration. He says:According to what has been said, the idea of probability essentially belongs to a kind of inference which is repeated indefinitely. An individual inference must be either true or false and can show no effect of probability; and therefore, in reference to a single case considered in itself, probability can have no meaning. Yet if a man had to choose between drawing a card from a pack containing twenty-five red cards and a black one, or from a pack containing twenty-five black cards and a red one, and that of a red one were destined to transport him to eternal felicity, and that of a black one to consign him to everlasting woe, it would be folly to deny that he ought to prefer the pack containing the larger proportion of red cards, although from the nature of the risk, it cannot be repeated. [Collected Papers, 2.652]. (shrink)