On Quine and Putnam's Indispensibility Argument

Posted by Unknown on Thursday, November 01, 2007 with No comments
Confirmation and the Indispensability of Mathematics to Science

Susan Vineberg
Philosophy of Science, Vol. 63, No. 3, Supplement. Proceedings of the 1996 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers (Sep., 1996), pp. S256-S263

Abstract: Quine and Putnam argued for mathematical realism on the basis of the indispensability of mathematics to science. They claimed that the mathematics that is used in physical theories is confirmed along with those theories and that scientific realism entails mathematical realism. I argue here that current theories of confirmation suggest that mathematics does not receive empirical support simply in virtue of being a part of well confirmed scientific theories and that the reasons for adopting a realist view of scientific theories do not support realism about mathematical entities, despite the use of mathematics in formulating scientific theory.

Quine, Putnam, and the ‘Quine-Putnam’ indispensability argument

David Liggins

Abstract: Much recent discussion in the philosophy of mathematics has concerned the
indispensability argument – an argument which aims to establish the existence of
abstract mathematical objects through appealing to the role that mathematics plays in
empirical science. The indispensability argument is standardly attributed to W.V. Quine
and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine’s
argument for the existence of abstract mathematical objects differs from the argument
which many philosophers of mathematics ascribe to him. Contrary to appearances,
Putnam did not argue for the existence of abstract mathematical objects at all. I close by
suggesting that attention to Quine and Putnam’s writings reveals some neglected
arguments for platonism which may be superior to the indispensability argument.