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The mathematical theory of probability had its origin, in S. D. Poisson’s words, “in a problem about a game of chance proposed to an austere Jansenist by a man of the world.” The austere Jansenist was, of course, Pascal, and the man of the world the Chevalier de Méré. The simple rules of the probability calculus rapidly acquired a greater significance, and by the end of the seventeenth century James Bernoulli announced, in his Ars Conjectandi, that probability was to be understood as measuring degrees of certainty, and as such constituted the foundation of a new species of logic, the logic of uncertain, or, in modern terminology, of ampliative or inductive inference. Its principal application was to be in effect decision theory, to assist in determining prudent courses of action. Carnap was to say much the same thing two and a half centuries later (in Carnap and Jeffrey  p. 7, for example).
KeywordsPrior Distribution Subjective Probability Inductive Inference Dutch Book Subjective Distribution
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