In the introduction to his Realism, mathematics and modality (1989), and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane (in: Fabrice Pataut (ed.) Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.
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Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy, 70, 661–679.
Clarke-Doane, J. (2016). What is the Benacerraf problem? In F. Pataut (Ed.), Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf. Dordrecht: Springer. www.columbia.edu/~jc4345/benacerraf%20with%20bib.pdf.
Field, H. (1989). Realism, mathematics and modality. Oxford: Blackwell.
Liggins, D. (2010). Epistemological objections to platonism. Philosophy Compass, 5, 67–77.
Thanks to Justin Clarke-Doane for discussion of an earlier draft; and anonymous referees.
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Liggins, D. The Reality of Field’s Epistemological Challenge to Platonism. Erkenn 83, 1027–1031 (2018). https://doi.org/10.1007/s10670-017-9925-z