David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Mark Balaguer (1995). A Platonist Epistemology. Synthese 103 (3):303 - 325.
Justin Clarke-Doane (forthcoming). What is the Benacerraf Problem? In Fabrice Pataut (ed.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity.
Audrey Yap (2009). Logical Structuralism and Benacerraf's Problem. Synthese 171 (1):157 - 173.
Maja Malec (2004). A Priori Knowledge Contextualised and Benacerraf's Dilemma. Acta Analytica 19 (33):31-44.
Michael Potter (2007). What is the Problem of Mathematical Knowledge? In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge.
Jeanne Peijnenburg & David Atkinson (2010). Lamps, Cubes, Balls and Walls: Zeno Problems and Solutions. Philosophical Studies 150 (1):49 - 59.
John R. Lucas (1968). Satan Stultified: A Rejoinder to Paul Benacerraf. The Monist 52 (1):145-58.
Dale Jacquette (2006). Applied Mathematics in the Sciences. Croatian Journal of Philosophy 6 (2):237-267.
Mark Balaguer (1998). Non-Uniqueness as a Non-Problem. Philosophia Mathematica 6 (1):63-84.
Terry F. Godlove (2011). Hanna, Kantian Non-Conceptualism, and Benacerraf's Dilemma. International Journal of Philosophical Studies 19 (3):447 - 464.
Thomas Hodgson (2012). Propositions, Structure and Representation. Proceedings of the Aristotelian Society 112 (3):339-349.
William H. Hanson (1971). Mechanism and Godel's Theorem. British Journal for the Philosophy of Science 22 (February):9-16.
Added to index2012-08-23
Total downloads57 ( #33,094 of 1,410,123 )
Recent downloads (6 months)10 ( #22,735 of 1,410,123 )
How can I increase my downloads?