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Jenkins-Ichikawa, Carrie, , . Knowledge of Arithmetic
2005, British Journal for the Philosophy of Science 56: 727-747.
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Abstract: 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 funda- mentally 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 inde- pendent 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.

Comment: Useful as a primary or secondary reading in an advanced undergraduate course epistemology (in a section on a priori knowledge) or an advanced undergraduate course on philosophy of mathematics. This is not an easy paper, but it is clear. It is also useful within a teaching context, as it provides a summary of the influential neo-Fregean approach to mathematical knowledge.

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