Objective Probabilities in Number Theory

Philosophia Mathematica 19 (3):308-322 (2011)
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Abstract

Philosophers have explored objective interpretations of probability mainly by considering empirical probability statements. Because of this focus, it is widely believed that the logical interpretation and the actual-frequency interpretation are unsatisfactory and the hypothetical-frequency interpretation is not much better. Probabilistic assertions in pure mathematics present a new challenge. Mathematicians prove theorems in number theory that assign probabilities. The most natural interpretation of these probabilities is that they describe actual frequencies in finite sets and limits of actual frequencies in infinite sets. This interpretation vindicates part of what the logical interpretation of probability aimed to establish.

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2011-08-19

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Elliott Sober
University of Wisconsin, Madison

Citations of this work

Statistical Data and Mathematical Propositions.Cory Juhl - 2015 - Pacific Philosophical Quarterly 96 (1):100-115.

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References found in this work

The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
The Logic of Chance.John Venn - 1876 - Dover Publications.

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