The Nature of Mathematical Entities. Descartes and His Detractors: Gassendi and Mersenne

Abstract

The status of mathematical entities has been a recurrent philosophical problem in different times; here I explain how it was a key piece in the definition of ontological positions during Early Modernity. The touchstone for the foundation of scientific knowledge was the character assigned to mathematical entities —and, in general, to abstract entities, including logical ones— within the natural philosophy. I sketch two modern positions: on the one hand, the one defended by René Descartes, who assigned mathematical items a status of perennial entities, inherent to the very constitution and operation of the mind and, on the other, the one supported by authors such as Pierre Gassendi and Marin Mersenne, who defended the empirical and instrumental origin of those entities.