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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.

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A. Baker (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114, 223238.

M. Colyvan (2010). There is no easy road to nominalism. Mind, 119(474), 285306.

F. Correia (2007). Modality, quantification, and many Vlach-operators. Journal of Philosophical Logic, 36(4), 473488.

M. Fara , & T. Williamson (2005). Counterparts and actuality. Mind, 114(453), 130.

J. Friedman (2005). Modal platonism: An easy way to avoid ontological commitment to abstract entities. Journal of Philosophical Logic, 34(3), 227273.

A. Hazen (1976). Expressive completeness in modal language. Journal of Philosophical Logic, 5, 2546.

H. T Hodes . (1984a). On modal logics which enrich first-order S5. Journal of Philosophical Logic, 13(4), 423454.

H. T Hodes . (1984b). Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13, 1326.

J. Ketland (2005). More curious inferences. Analysis, 65(1), 1824.

J. Ketland (2011). Nominalistic adequacy. Proceedings of the Aristotelian Society, 111(2), 201217.

Ø Linnebo . (2003). Plural quantification exposed. Noûs, 37(1), 7192.

J. Melia (1995). On what there’s not. Analysis, 55(4), 223229.

J. Melia (2000). Weaseling away the indispensability argument. Mind, 109(435), 455479.

F. A. Muller , & M. P Seevinck . (2009). Discerning elementary particles. Philosophy of Science, 76, 179200.

C. Peacocke (1978). Necessity and truth theories. Journal of Philosophical Logic, 7, 473500.

C. Pincock (2007). A role for mathematics in the physical sciences. Noûs, 41(2), 253275.

M. Resnik (1983). Review of Science without Numbers by Hartry Field. Noûs, 17(3), 514519.

M. Resnik (1988). Second-order logic still wild. Journal of Philosophy, 85, 7587.

S. Saunders (2006). Are quantum particles objects? Analysis, 66, 5263.

B. van Fraassen (1980). The Scientific Image. Oxford, UK: Clarendon Press.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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