Mathematical apriorism and warrant: A reliabilist-platonist account

Philosophical Forum 36 (4):399–417 (2005)
Mathematical apriorism holds that mathematical truths must be established using a priori processes. Against this, it has been argued that apparently a priori mathematical processes can, under certain circumstances, fail to warrant the beliefs they produce; this shows that these warrants depend on contingent features of the contexts in which they are used. They thus cannot be a priori. In this paper I develop a position that combines a reliabilist version of mathematical apriorism with a platonistic view of mathematical ontology. I argue that this view both withstands the above objection and explains the reliability of a priori mathematical warrant.
Keywords Reliabilism  Mathematical platonism  Apriority
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DOI 10.1111/j.1467-9191.2005.00211.x
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Linda Wetzel (1989). That Numbers Could Be Objects. Philosophical Studies 56 (3):273--92.

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