Berkeley y Benacerraf la aritmética es sólo un sistema de signos

Abstract

In this paper I point out that besides having made a proposal -with respect to arithmetic (and algebra)- which makes Berkeley an antecesor of Hartry Field -something which I do not elaborate more in this paper-, he also puts forth a nominalistic view which, in substantial points, is closely related to Benacerraf's in his "What Numbers Could Not Be". What I hold is that Berkeley's view, two hundred years before Benacerraf's, fullfils the latter's claim for numerical expressions to be meaningful and to make them useful in human practices.

I interpret sorne proposals by Berkeley which would ground the construction of a mathematical structure in which no use is made of sets or any type of entities -besides the structure itself, of which I give an example-, to give meaning to the expressions which constitute it. Such expressions get their meaning from the proposition they have in the said structure. I take it that a nominalistic position, at least at the level of elementary mathematics, avoids many theoretical problems which arise if we adopt a less econornical ontological position.