Graduate studies at Western
|Abstract||Decision under conditions of uncertainty is an unavoidable fact of life. The available evidence rarely suffices to establish a claim with complete confidence, and as a result a good deal of our reasoning about the world must employ criteria of probable judgment. Such criteria specify the conditions under which rational agents are justified in accepting or acting upon propositions whose truth cannot be ascertained with certainty. Since the seventeenth century philosophers and mathematicians have been accustomed to consider belief under uncertainty from the standpoint of the mathematical theory of probability. In 1654, Blaise Pascal entered into correspondence with Pierre de Fermat on two problems in the theory of probability that had been posed by the Chevalier De Méré – the first involved the just division of the stakes in a game of chance that has been interrupted, the second is the likelihood of throwing a given number in a fixed number of throws using fair dice. This correspondence resulted in fundamental results that are now regarded as the foundation of the mathematical approach to probability, and historical studies of probabilistic reasoning almost invariably begin with the Pascal-Fermat correspondence. Franklin has no interest in denying the significance of the mathematical treatment of probability – he is, after all, a professional mathematician – but the principal theme in his book is the gradual “coming to consciousness” of canons of inference governing uncertain cases.|
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