Synthese 103 (3):303 - 325 (1995)
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.
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References found in this work BETA
Philosophical and Mathematical Correspondence.Gottlob Frege, Gottfried Gabriel, Brian Mcguinness & Hans Kaal - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
Citations of this work BETA
Fictionalism, Theft, and the Story of Mathematics.Mark Balaguer - 2008 - Philosophia Mathematica 17 (2):131-162.
Multiverse Conceptions in Set Theory.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo - 2015 - Synthese 192 (8):2463-2488.
A Fictionalist Account of the Indispensable Applications of Mathematics.Mark Balaguer - 1996 - Philosophical Studies 83 (3):291 - 314.
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