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Bayes rule takes the following familiar form: P(H/E) = P(E/H)P(H)/P(E).
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Peirce, C.S. holds a strikingly similar view: We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. Hence this initial scepticism will be a mere self-deception, and not real doubt; and no-one who follows the Cartesian method will ever be satisfied until he has formally recovered all those beliefs which in form he has given up. . . . A person may, it is true, in the course of his studies find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it and not because of the Cartesian maxim." Some Consequences of Four Incapacities, in Buchler, J. ed. Philosophical Writings of Peirce. New York: Dover Publications, 1955 pp. 228-229.
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