Philosophy of Science 60 (2):302-319 (1993)

Cory Juhl
University of Texas at Austin
The inductive reliability of Bayesian methods is explored. The first result presented shows that for any solvable inductive problem of a general type, there exists a subjective prior which yields a Bayesian inductive method that solves the problem, although not all subjective priors give rise to a successful inductive method for the problem. The second result shows that the same does not hold for computationally bounded agents, so that Bayesianism is "inductively incomplete" for such agents. Finally a consistency proof shows that inductive agents do not need to disregard inductive failure on sets of subjective probability 0 in order to be ideally rational. Together the results reveal the inadequacy of the subjective Bayesian norms for scientific methodology
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DOI 10.1086/289734
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Probabilities Over Rich Languages, Testing and Randomness.Haim Gaifman & Marc Snir - 1982 - Journal of Symbolic Logic 47 (3):495-548.

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