Abstract

FERNANDEZ DE CASTRO, Max. De la posibilidad a la existencia matemática: los casos de Shapiro y de Balaguer. Sig. Fil [online]. 2009, vol.11, n.21, pp.73-101. ISSN 1665-1324.

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.

Keywords : Balaguer; Benacerraf; consistency; existence; Shapiro.

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