What Mathematical Truth Need Not Be

Abstract

I might have titled this paper “In Defense of Eidophobia”, eidophobes, in Belnapese, being those who, for one reason or another, find the idea of abstract entities distasteful. Since Nuel himself is an eidophile, I occasionally found myself at philosophical odds with him. But one of the best things about being a student of Nuel’s was that he had no need for eidological clones. So in a sense perhaps the greatest tribute I could render to his pedagogy is this paper, which makes it very clear that my eidophobia has remained intact. Studying with Nuel Belnap, one never had to fear that the spirit of independent (even eidocidal) inquiry might be compromised.

I would like to thank Michael D. Resnik for extensive comments and criticisms of an earlier draft. I would also like to thank Theodore Drange, Pieranna Garavaso, Stephen C. Hetherington, Lila Luce, and Michael Resnik for very helpful comments on this version.

This is not the only possible characterization of platonism. A more recent version claims only that what the statements of classical mathematics say is correct, without giving a referential account of “correct”. To these versions of mathematical platonism my remarks are irrelevant, but there is a long and continuing version of platonism in which mathematical statements refer to mathematical objects, and it is this version I am addressing here. In fact, I think it is highly debateable whether the term “platonism” is appropriate for disquotational views, or methodological platonism, but this is an issue I do not wish to debate here.

This is made very explicit by Paul Benacerraf in “Mathematical Truth”, Journal of Philosophy, Vol. LXX, No. 19;Nov. 8, 1973,pp. 662.