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The Philosophical Significance of Tennenbaum's Theorem (2012)

Button, T., Smith, P.

Oxford University Press

In: Philosophia Mathematica

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Publication Date: 2012-02-14

Description: Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a simpler model-theoretic result.

Print ISSN: 0031-8019

Electronic ISSN: 1744-6406

Topics: Mathematics , Philosophy

Published by Oxford University Press

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