N.C.A. da Costa's Philosophy of Logic

Abstract

The failure of several attempts to achieve a paradox-free set theory led in time to the insight that contradiction in mathematics, far from being impossible, was at the root of every theory. But this insight could not, by itself, change the paradigm which required that every acceptable mathematical theory be consistent. It was necessary to create a logic which would allow the development of an inconsistent theory, and Newton C.A. da Costa took the first decisive step in that direction with his inconsistent set theory, in which he achieved, so to speak, a consistent inconsistency. The present paper exposes and discusses some of the main issues to be found in Da Costa’s recent Essay on the Foundations of Logic, and shows how the author, trapped between an historicist, conviction which his own development has grafted on him, and a strong need to reach an absolute foundation for reason, tries to achieve a compromise which is nevertheless favorable to historicism.