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INDISPENSABILITY ARGUMENTS AND INSTRUMENTAL NOMINALISM

Published online by Cambridge University Press:  06 March 2012

RICHARD PETTIGREW
RICHARD PETTIGREW*
Affiliation:
Department of Philosophy, University of Bristol
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF BRISTOL, 43 WOODLAND ROAD, BRISTOL BS8 1TB, UK. E-mail: [email protected]
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Abstract

In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that mathematical objects exist on the grounds that we make indispensable reference to such objects in our best scientific theories (Quine, 1981a; Putnam, 1979a) and in our everyday reasoning (Ketland, 2005). I wish to defend a particular objection to such arguments called instrumental nominalism. Existing formulations of this objection are either insufficiently precise or themselves make reference to mathematical objects or possible worlds. I show how to formulate the position precisely without making any such reference. To do so, it is necessary to supplement the standard modal operators with two new operators that allow us to shift the locus of evaluation for a subformula. I motivate this move and give a semantics for the new operators.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 687 - 709
Copyright
Copyright © Association for Symbolic Logic 2012

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