Philosophia Mathematica 13 (2):174-186 (2005)

Authors
Leon Horsten
Universität Konstanz
Abstract
According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. On this account, the intended models of arithmetic are the notation systems with recursive operations on them satisfying the Peano axioms. [A]m Anfang […] ist das Zeichen.
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DOI 10.1093/philmat/nki021
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References found in this work BETA

How We Learn Mathematical Language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
First Published 1953.Ludvig Wittgenstein - forthcoming - Philosophical Investigations.
On the Complexity of Models of Arithmetic.Kenneth McAloon - 1982 - Journal of Symbolic Logic 47 (2):403-415.

View all 6 references / Add more references

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