Abstract

Philosophy of mathematics demands a strong sense of necessity for mathematical truths. But this demand seems to collide with the existence of different but true and consistent mathematical beliefs. Following the works of Benacerraf, Field, Balaguer and Putnam, I argue that philosophers of mathematics can either accept the plurality of interpretations of mathematics, but deny that every interpretation corresponds to an object, or, they can claim that every theory isolates a unique and only object. Facing this quandary, the philosopher of mathematics submit their theories to several difficulties and are led to adopt either a coherence or a correspondence theory of truth. A series of questions are entailed and need an answer to provide an impressive and complete theory of mathematical objects.