Mathematicians and Mathematical Objects

Abstract

The paper indicates why it is possible and even reasonable for mathematicians to be unconcerned with ontology of mathematical objects. Rather than such objects, mathematics is about `relations between objects' or `types of relation', in the words of Poincare and Russell, the so-called objects being mere pronouns. No ontological position is taken up, and doubt is cast on the meaningfulness of deciding whether a pronoun exists as distinct from the existence of what the pronoun may be used to refer to in applied mathematics. Talking about what may or may not exist is made acceptable to philosophers, perhaps, by the pretence proposed by Mark Crimmins for semantics, based on that proposed by Kendall Walton for aesthetics.