What Numbers Are Real?

PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:253 - 269 (1986)
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Abstract

We suggest that there can be epistemologically significant reasons why certain mathematical structures - such as the Real numbers - are more important than others. We explore several contexts in which considerations bearing on the choice of a fundamental numerical domain might arise. 1) Set theory. 2) Historical cases of extension of mathematical domains - why were negative numbers resisted, and why should we accept them as part of our fundamental numerical domain? 3) Using fewer reals in physics, without really noticing.

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Kenneth Manders
University of Pittsburgh

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