From possibility to mathematical existence: The cases of Shapiro and Balaguer

Abstract

In this article, I shall concentrate on a way of dealing with the classic Benacerraf's problem concerning the inaccessibility of abstract objects. It is the principle (called FBP by Balaguer) that the objects characterized by the axioms of a consistent theory exist. I explore Shapiro and Balaguer's arguments in favor of this principle and I conclude that they are not strong enough to convince their rivals. I compare this principle with Quine's argument of indispensability, as a way of contrast.