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Epistemological Challenges to Mathematical Platonism

Øystein Linnebo
Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition
Vol. 129, No. 3 (Jun., 2006), pp. 545-574
Published by: Springer
Stable URL: http://www.jstor.org/stable/4321774
Page Count: 30
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Epistemological Challenges to Mathematical Platonism
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Abstract

Since Benacerraf's "Mathematical Truth" a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people's mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly turns out to be logical space for a response to the improved challenge where no such space appeared to exist.

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