Why anti-realists and classical mathematicians cannot get along

Topoi 20 (1):53-63 (2001)
Authors
Stewart Shapiro
Ohio State University
Abstract
Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails.
Keywords Philosophy   Philosophy   Philosophy of Science   Philosophy of Technology
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Reprint years 2004
DOI 10.1023/A:1010656826667
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The Objectivity of Mathematics.Stewart Shapiro - 2007 - Synthese 156 (2):337-381.

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