Anti-Realism in Mathematics

Abstract

This chapter discusses the implications of the modal theory developed in this book in terms of mathematics. It focuses on Mathematical Realism, because its own position regarding the ontology of mathematics can only be appreciated by way of contrast with the metaphysical doctrines it rejects. Mathematical Realism is the view that mathematical objects exist and that mathematical terms, such as five, and the null set, refer to these mathematical objects. It should be noted, however, that Mathematical Realists do not always insist that all the standard mathematical terms refer.