British Journal for the Philosophy of Science 56 (4):727-747 (2005)
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.
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A Priori Knowledge: Debates and Developments.C. S. Jenkins - 2008 - Philosophy Compass 3 (3):436–450.
Concept Grounding and Knowledge of Set Theory.Jeffrey W. Roland - 2010 - Philosophia 38 (1):179-193.
Concepts, Experience and Modal Knowledge1.C. S. Jenkins - 2010 - Philosophical Perspectives 24 (1):255-279.
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