range theory of probability

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Laplace, Pierre-Simon, marquis de (1749—1827) French applied mathematician and theoretical physicist

Rudolf Carnap (1891—1970) German-born American philosopher

principle of indifference

Bertrand's paradox

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The range theory of probability holds that the probability of a proposition, relative to some evidence, is a proportion of the range of possibilities under which the proposition is true, compared to the total range of possibilities left open by the evidence. The theory was originally due to Laplace, and has guided confirmation theory, for example in the work of Carnap. The difficulty with the theory lies in identifying sets of possibilities so that they admit of measurement. Laplace appealed to the principle of indifference, supposing that possibilities have an equal probability unless there is reason for distinguishing them. However, unrestricted appeal to this principle introduces inconsistency (see Bertrand's paradox). Treating possibilities as equally probable may be regarded as depending upon metaphysical choices, or logical choices, as in the view of Keynes, or on semantic choices, as in the work of Carnap. In any event it is hard to find an objective source for the authority of such a choice, and this is one of the principal difficulties in front of formalizing the theory of confirmation.

Subjects: Philosophy.

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