Non-standard numbers: a semantic obstacle for modelling arithmetical reasoning

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Logic Journal of the IGPL 20 (2):477-485 (2012)
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Abstract

The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines

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10.1093/jigpal/jzq051

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The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Computability and recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Computational Structuralism &dagger.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.

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