David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 190 (9):1587-1603 (2013)
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
Laurence BonJour (1998). In Defense of Pure Reason. Cambridge University Press.
Christopher Peacocke (2004). The Realm of Reason. Oxford University Press.
Hartry Field (1989). Realism, Mathematics & Modality. Basil Blackwell.
Paul Boghossian (2003). Blind Reasoning. Aristotelian Society Supplementary Volume 77 (1):225–248.
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
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