Crítica, Revista Hispanoamericana de Filosofía, Volume 13, number 38, August 1981
En torno a una revisión del logicismo
[On a Revision of Logicism]
Ricardo J. Gómez
Indiana University
Abstract: In Mathematical Knowledge, Mark Steiner discusses several schools
in the philosophy of mathematics; in the first two chapters he attempts
to criticize what he believes is a correct reconstruction of several
epistemic aspects of logicism and what he assumes are serious difficulties
of Quine’s philosophy of mathematics.
Our main claim is that his critical revision of logicism in incorrect
On the one hand, he gave an equivocal characterization of its central
problems and theses; as a result, he actuality has criticized
claims which were never supported by the logicist philosophers. On
the other hand, he wrongly evaluated Quine’s reduction of Arithmetic
into Theory of Sets. In fact, his criticism is based in an inadequate
conception of some features of Quine’s philosophy of mathematics.
Thus, Steiner wrongly understood Quine’s view about the reduction of
theories by assuming that such a reduction should satisfy such requirements
as clarity, certainty and an improvement in operativity. Finally,
he blamed Quine’s reduction for raising problems that, truly, do not
emerge.
As a consequence, logicism seems to stay beyond Steiner’s criticism.
[R.J.G.]
Keywords:
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