Crítica, Revista Hispanoamericana de Filosofía, Volume 23, number 68, agosto 1991
Berkeley y Benacerraf
la aritmética es sólo un sistema de signos
[]
José A. Robles
Instituto de Investigacines Filosóficas
Universidad Nacional Autónoma de México
jrobles@servidor.unam.mx
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.
Keywords:
 PDF en Spanish (257 Kb)
