Philosophia Mathematica 9 (1):21-36 (2001)

William W. Tait
University of Chicago
This paper contains a defense against anti-realism in mathematics in the light both of incompleteness and of the fact that mathematics is a ‘cultural artifact.’. Anti-realism (here) is the view that theorems, say, of aritltmetic cannot be taken at face value to express true propositions about the system of numbers but must be reconstrued to be about somctliiiig else or about nothing at all. A ‘bite-the-bullet’ aspect of the defease is that, adopting new axioms, liitherto independent, is not. a matter of recognizing trutlis wliich had previoasly been unrecognized, but of extending the domain of what is true.
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DOI 10.1093/philmat/9.1.21
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Truth and Other Enigmas.Michael Dummett - 1980 - Revue Philosophique de la France Et de l'Etranger 170 (1):62-65.
Truth and Other Enigmas.Michael Dummett - 1981 - Philosophical Quarterly 31 (122):47-67.
What is Mathematics, Really?Reuben Hersh - 1997 - Oxford University Press.

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Citations of this work BETA

Mathematics and Fiction II: Analogy.Robert Thomas - 2002 - Logique Et Analyse 45:185-228.
Godel's Unpublished Papers on Foundations of Mathematics.W. W. Tatt - 2001 - Philosophia Mathematica 9 (1):87-126.

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