Journal Article

Knowledge of Arithmetic

C. S. Jenkins

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 56, issue 4, pages 727-747
Published in print December 2005 | ISSN: 0007-0882
Published online October 2005 | e-ISSN: 1464-3537 | DOI: https://dx.doi.org/10.1093/bjps/axi142
Knowledge of Arithmetic

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The goal of the research programme I describe in this article is a realist epistemology for arithmetic which respects arithmetic's special epistemic status (the status usually described as a prioricity) yet accommodates naturalistic concerns by remaining fundamentally empiricist. I argue that the central claims which would allow us to develop such an epistemology are (i) that arithmetical truths are known through an examination of our arithmetical concepts; (ii) that (at least our basic) arithmetical concepts are accurate mental representations of elements of the arithmetical structure of the independent world; (iii) that (ii) obtains in virtue of the normal functioning of our sensory apparatus. The first of these claims protects arithmetic's special epistemic status relative, for example, to the laws of physics, the second preserves the independence of arithmetical truth, and the third ensures that we remain empiricists.

Preliminaries

Justifying and grounding concepts

Cameras and filters

An epistemology for arithmetic

Concluding remarks

Journal Article.  9623 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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