Formalism in mathematics: mathematical truth without commitment to abstract mathematical objects

Mathematical Platonism, with its commitment to ontology of abstract objects, is widely thought to be beset with insurmountable epistemological problems. Formalism is an anti-Platonist position which grounds the correctness of mathematical utterances in adherence to rules for transforming formal symbols. The simplest version of the view met with fatal criticism. The current project seeks to develop a variant which is immune to these and other objections. The resolution of these problems leads to a consideration of logic, as well as mathematics, and to an account of the nature of logical proof which revises the standard classical account.