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Non-standard numbers: a semantic obstacle for modelling arithmetical reasoning
Logic Journal of the IGPL 20 (2):477-485 (2012)
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 machinesAuthor Profiles
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Citations of this work
The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.
The Ontology of Digital Physics.Anderson Beraldo-de-Araújo & Lorenzo Baravalle - 2017 - Erkenntnis 82 (6):1211-1231.
References found in this work
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
Computational Structuralism &dagger.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.
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