Indispensability arguments and instrumental nominalism

Review of Symbolic Logic 5 (4):687-709 (2012)
Abstract
In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that abstract mathematical objects exist. I wish to defend a particular objection to such arguments that has become increasingly popular recently. It is called instrumental nominalism. I consider the recent versions of this view and conclude that it has yet to be given an adequate formulation. I provide such a formulation and show that it can be used to answer the indispensability arguments. -/- There are two main indispensability arguments in the literature, though one has received nearly all of the attention. They correspond to two ways in which we use mathematics in science and in everyday life. We use mathematical language to help us describe non-mathematical reality; and we use mathematical reasoning to help us perform inferences concerning non-mathematical reality using only a feasible amount of cognitive power. The former use is the starting point of the Quine-Putnam indispensability argument ([Quine, 1980a], [Quine, 1980b], [Quine, 1981a], [Quine, 1981b], [Putnam, 1979a], [Putnam, 1979b]); the latter provides the basis for Ketland’s more recent argument ([Ketland, 2005]). I begin by considering the Quine-Putnam argument and introduce instrumental nominalism to defuse it. Then I show that Ketland’s argument can be defused in a similar way.
Keywords nominalism   Pettigrew   indispensability   WAYS   toread
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DOI 10.1017/S1755020312000044
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Discerning Elementary Particles.F. A. Muller & M. P. Seevinck - 2009 - Philosophy of Science 76 (2):179-200.
Second-Order Logic Still Wild.Michael D. Resnik - 1988 - Journal of Philosophy 85 (2):75-87.

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