The Philosophical Significance of Tennenbaum's Theorem

Philosophia Mathematica 20 (1):114-121 (2011)
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
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DOI 10.1093/philmat/nkr031
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W. Dean (2013). Models and Computability. Philosophia Mathematica 22 (2):143-166.

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