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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    References found in this work BETA
    Robert Merrihew Adams (1983). Divine Necessity. Journal of Philosophy 80 (11):741-752.
    George Bealer (2000). A Theory of the a Priori. Pacific Philosophical Quarterly 81 (1):1–30.
    Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
    Michael Bergmann (2005). Defeaters and Higher-Level Requirements. Philosophical Quarterly 55 (220):419–436.
    P. A. Boghossian (1997). Analyticity. In B. Hale & C. Wright (eds.), A Companion to the Philosophy of Language. Blackwell. 331-368.

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