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Philosophia Mathematica Advance Access published online on June 23, 2007
Philosophia Mathematica, doi:10.1093/philmat/nkm029
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Copyright © The Author 2007. Published by Oxford University Press on behalf of the Business History Conference.

The Conceivability of Platonism{dagger}

Benjamin Callard*

Department of Philosophy, Lehman College, City University of New York, 360 Carman Hall, 250 Bedford Park Blvd West, Bronx, N.Y. 10468, U.S.A.

Correspondence: benjamin.callard{at}lehman.cuny.edu

It is widely believed that platonists face a formidable problem: that of providing an intelligible account of mathematical knowledge. The problem is that we seem unable, if the platonist is right, to have the causal relationships with the objects of mathematics without which knowledge of these objects seems unintelligible. The standard platonist response to this challenge is either to deny that knowledge without causation is unintelligible, or to make room for causal interactions by softening the platonism at issue. In this essay I argue that the idea of causal relations with fully platonist objects is unproblematic.

{dagger} I would like to thank Agnes Gellen Callard, Josh Sheptow, and Palle Yourgrau for helpful discussions of the ideas presented here.


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