The defeater version of Benacerraf's problem for a priori knowledge

Synthese 190 (9):1587-1603 (2013)
Abstract
Paul Benacerraf’s argument that mathematical realism is apparently incompatible with mathematical knowledge has been widely thought to also show that a priori knowledge in general is problematic. Although many philosophers have rejected Benacerraf’s argument because it assumes a causal theory of knowledge, some maintain that Benacerraf nevertheless put his finger on a genuine problem, even though he didn’t state the problem in its most challenging form. After diagnosing what went wrong with Benacerraf’s argument, I argue that a new, more challenging, version of Benacerraf’s problem can be constructed. The new version—what I call the Defeater Version—of Benacerraf’s problem makes use of a no-defeater condition on knowledge and justification. I conclude by arguing that the best way to avoid the problem is to construct a theory of how a priori judgments reliably track the facts. I also suggest four different kinds of theories worth pursuing
Keywords A priori  Rationalism  Benacerraf  Empiricism  Defeaters  Abstract objects
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DOI 10.1007/s11229-011-9894-8
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In Defense of Pure Reason.Laurence BonJour - 1998 - Cambridge University Press.
The Realm of Reason.Christopher Peacocke - 2003 - Oxford University Press.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Evidentialism.Richard Feldman & Earl Conee - 1985 - Philosophical Studies 48 (1):15 - 34.

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