Benacerraf, Field, and the agreement of mathematicians
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Hartry Field’s epistemological challenge to the mathematical platonist is often cast as an improvement on Paul Benacerraf’s original epistemological challenge. I disagree. While Field’s challenge is more difficult for the platonist to address than Benacerraf’s, I argue that this is because Field’s version is a special case of what I call the ‘sociological challenge’. The sociological challenge applies equally to platonists and fictionalists, and addressing it requires a serious examination of mathematical practice. I argue that the non-sociological part of Field’s challenge amounts to a minor reformulation of Benacerraf’s original challenge. So, I contend, Field’s challenge is not an improvement on Benacerraf’s. What is new to Field’s challenge is as much a problem for the fictionalist as it is for the platonist.
KeywordsBenacerraf Field Platonism Epistemological challenge
Thanks to Corinne Bloch-Mullins, Ben Caplan, Sam Cowling, Lina Janssen, Kathryn Lindeman, May Mei, Reed Solomon, Audrey Yap, three anonymous referees, my colleagues at the University of Kansas, and an audience at Denison University. Thanks also to audiences that heard an ancestor of this paper at the University of Missouri, the 2014 Midwest Epistemology Workshop, and a workshop at the University of Umeå.
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