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Ellenberg, J and Sober, E (2011)

Objective Probabilities in Number Theory

Philosophia Mathematica 19 (3): 308-322. doi: 10.1093/philmat/nkr022 First published online: August 17, 2011.

ISSN/ISBN: 0031-8019 DOI: 10.1093/phimat/nkr022

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.

@article {, AUTHOR = {Ellenberg, Jordan and Sober, Elliott}, TITLE = {Objective probabilities in number theory}, JOURNAL = {Philos. Math. (3)}, FJOURNAL = {Philosophia Mathematica. Series III}, VOLUME = {19}, YEAR = {2011}, NUMBER = {3}, PAGES = {308--322}, ISSN = {0031-8019}, MRCLASS = {00A30 (11B05)}, MRNUMBER = {2842922 (2012h:00015)}, DOI = {10.1093/philmat/nkr022}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Not specified