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  1. Amos Nathan (2006). Probability Dynamics. Synthese 148 (1):229 - 256.
    ‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of PD. PD applies to (...)
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  2. Amos Nathan (1986). How Not to Solve It. Philosophy of Science 53 (1):114-119.
    Six recently discussed problems in discrete probabilistic sample space, which have been found puzzling and even paradoxical, are reexamined. The importance is stressed of a sharp distinction between the formalization of mathematical problems and their formal solution that, applied to probability theory, must lead through the explicit partitioning of a sample space. If this approach is consistently followed, such problems reveal themselves to be either inherently ambiguous, and therefore without solution, or quite straightforward. In both cases nothing remains of any (...)
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  3. Amos Nathan (1984). False Expectations. Philosophy of Science 51 (1):128-136.
    Common probabilistic fallacies and putative paradoxes are surveyed, including those arising from distribution repartitioning, from the reordering of expectation series, and from misconceptions regarding expected and almost certain gains in games of chance. Conditions are given for such games to be well-posed. By way of example, Bernoulli's "Petersburg Paradox" and Hacking's "Strange Expectations" are discussed and the latter are resolved. Feller's generalized "fair price, in the classical sense" is critically reviewed.
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  4. Amos Nathan (1984). The Fallacy of Intrinsic Distributions. Philosophy of Science 51 (4):677-684.
    Jaynes contends that in many statistical problems a seemingly indeterminate probability distribution is made unique by the transformation group of necessarily implied invariance properties, thereby justifying the principle of indifference. To illustrate and substantiate his claims he considers Bertrand's Paradox. These assertions are here refuted and the traditional attitude is vindicated.
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