The commitment between identity and individuation in classical formal theories

Abstract

In this article, we advocate the view that classical formal theories (here understood as classical logic, usual set theory and mathematics) seem to be committed to the individuality of their ‘objects’ by assuming the identity of these objects. We begin by showing how identity is assumed in these disciplines and the problems that exist in such frameworks, which philosophers are typically unaware of. Throughout the text, we show several arguments that can make us believe that the classical formal theories really understand their objects as having an identity and are, therefore, individuals.

Keywords: classical logic, classical mathematics, classical set theory, identity, individuality.