Naturalism, fiction and mathematical objects

Abstract

Quine's platonism regarding mathematical objects has been countered by fictionalist interpretations of mathematical discourse. Some of these interpretations are revisionist, while others are hermeneutic. In this essay I argue that all three of the philosophical positions mentioned are tenable, as the choice between them comes down to very fundamental philosophical intuitions concerning naturalism. To show this, I closely examine these positions, paying special attention the hermeneutic fictionalism, in account of it being the most novel of the three. I also suggest that this position is compatible with —and can become stronger if it is inserted in— a pluralistic conception of reality like the one advocated by William James.