Synthese 103 (3):303 - 325 (1995)

Abstract
A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist.
Keywords platonism   mathematics   epistemology   toread
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DOI 10.1007/BF01089731
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References found in this work BETA

Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.
Language and Other Abstract Objects.Jerrold J. Katz - 1980 - Rowman & Littlefield Publishers.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.

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Citations of this work BETA

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