Chapter

Mathematical <i>Truth</i>?

Kitcher Philip

in Preludes to Pragmatism

Published in print November 2012 | ISBN: 9780199899555
Published online January 2013 | e-ISBN: 9780199980154 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199899555.003.0008
Mathematical Truth?

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This chapter takes up the idea that, in some domains, the functionalist account of truth as delineating the class of statements at which we aim might come apart from the structuralist machinery Tarski introduced to reduce truth to reference. Famously, it is hard to integrate a structuralist account of truth for mathematics with a well-articulated epistemology: if mathematical truth is to understand in terms of relations of reference to mathematical objects, the objects in question appear to possess properties that make knowledge of them impossible—at least on any naturalist account. Nor do those who desert the strictures of naturalism provide more than nebulous suggestions. The “epistemologies” they offer are so unclear and so devoid of evidence that they are scarcely worthy of the name. Naturalism can escape this dismal predicament by pursuing a strategy that is often useful in trying to understand human practices. Instead of trying to reconstruct mathematical knowledge in the present, one can try to understand its historical evolution.

Keywords: truth; Tarksi; structuralism; mathematics; naturalism

Chapter.  12188 words. 

Subjects: Philosophy

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