, Volume 103, Issue 3, pp 303-325

A platonist epistemology

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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.

I would like to thank the following people for their helpful comments on earlier versions of this paper: Arnold Koslow, Hartry Field, Jerrold Katz, Michael Resnik, Elliott Mendelson, Charles Landesman, Stephen Schiffer, Adam Vinueza, David Pitt, Jody Azzouni, David MacCallum, Colin McLarty, Tom Slaughter, Henry Mendell, Penelope Maddy, Michael Liston, Ricardo Gomez, Seth Crook, Stuart Cornwell, and various people at the University of Colorado, Boulder, where I read this paper in February, 1994. Much of the research for this paper was carried out under a City University of New York Dissertation Fellowship; I am grateful for this.