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Platonism and Anti-Platonism in Mathematics
Philosophical Review 110 (1):79 (2001)
Abstract
Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and Quine, tells us there exist no numbers at all, and so no prime numbers. Nominalists are aware that the assertion of the existence of prime numbers is warranted by the standards of mathematical science; they simply reject scientific standards of warrant.Author's Profile
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Citations of this work
The Reliability Challenge and the Epistemology of Logic.Joshua Schechter - 2010 - Philosophical Perspectives 24 (1):437-464.
Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
Abstract Expressionism and the Communication Problem.David Liggins - 2014 - British Journal for the Philosophy of Science 65 (3):599-620.
Inference to the best explanation and mathematical realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
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