The Eleatic and the Indispensabilist

Abstract

The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe.  Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory.  Eleatics argue that only objects with causal properties exist.  Mark Colyvan's recent defenses of Quine's indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist's criterion.  I show that Colyvan's argument is not decisive against the eleatic and sketch a way to capture the important intuitions behind both views.