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The Philosophical Significance of Tennenbaum's Theorem

Button, T; Smith, P; (2012) The Philosophical Significance of Tennenbaum's Theorem. Philosophia Mathematica , 20 (1) pp. 114-121. 10.1093/philmat/nkr031. Green open access

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Abstract

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.

Type: Article
Title: The Philosophical Significance of Tennenbaum's Theorem
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/philmat/nkr031
Publisher version: https://doi.org/10.1093/philmat/nkr031
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10085883
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