Journal of Applied Logic 11 (4):440-451 (2013)

Anubav Vasudevan
Columbia University
We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these constraints inform the analysis by fixing an a posteriori determinant of the probabilities, whereas, in the case of a priori reasoning, they imply certain claims which then serve as the basis for subsequent probabilistic deductions. In a given context of inquiry, the particular form which a priori or a posteriori reason may take depends, in large part, on the strength of the underlying symmetry assumed: the stronger the symmetry, the more information can be acquired a priori and the less information about the long-run behavior of the process is needed for an a posteriori assessment of the probabilities. In the context of this framework, frequency-based reasoning emerges as a limiting case of a posteriori reasoning, and reasoning about simple games of chance, as a limiting case of a priori reasoning. Between these two extremes, both a priori and a posteriori reasoning can take a variety of intermediate forms.
Keywords probability  a priori  a posteriori  symmetry  frequency
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DOI 10.1016/j.jal.2013.02.002
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References found in this work BETA

Generalizing the Lottery Paradox.Igor Douven & Timothy Williamson - 2006 - British Journal for the Philosophy of Science 57 (4):755-779.
Equipossibility Theories of Probability.Ian Hacking - 1971 - British Journal for the Philosophy of Science 22 (4):339-355.

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Citations of this work BETA

Entropy and Insufficient Reason: A Note on the Judy Benjamin Problem.Anubav Vasudevan - 2020 - British Journal for the Philosophy of Science 71 (3):1113-1141.

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