Theoria 84 (2):157-178 (2018)

Authors
Mark McEvoy
Hofstra University
Abstract
In this article, I present a novel account of a priori warrant, which I then use to examine the relationship between a priori and a posteriori warrant in mathematics. According to this account of a priori warrant, the reason that a posteriori warrant is subordinate to a priori warrant in mathematics is because processes that produce a priori warrant are reliable independent of the contexts in which they are used, whereas this is not true for processes that produce a posteriori warrant. Following this, I show how this difference explains why a priori warranting processes, such as proof (and mathematical intuition) can, and a posteriori warranting processes cannot, definitively establish mathematical results. I then show why, in the event of a conflict between a priori and a posteriori warranting processes, the former undermine, and cannot be undermined by, the latter. Finally, I explain the connection between apriority and mathematical necessity, but do so in a way that allows for the existence of contingent a priori knowledge.
Keywords Benacerraf problem  apriority  empirical warrant  mathematical knowledge  necessity  proof
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DOI 10.1111/theo.12145
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Naming and Necessity.Saul A. Kripke - 1985 - Critica 17 (49):69-71.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Naming and Necessity.Saul A. Kripke - 1980 - Philosophy 56 (217):431-433.
Content Preservation.Tyler Burge - 1993 - Philosophical Review 102 (4):457-488.

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