A nominalist's dilemma and its solution

Philosophia Mathematica 13 (3):297-307 (2005)
Abstract
Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with the cost of not taking mathematical theories literally. Jody Azzouni's Deflating Existential Consequence has recently challenged this conclusion by formulating a nominalist view that lacks this cost. In this paper, we argue that, as it stands, Azzouni's proposal does not yet succeed. It faces a dilemma to the effect that either the view is not nominalist or it fails to take mathematics literally. After presenting the dilemma, we suggest a possible solution for the nominalist.
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Jody Azzouni (2009). Empty de Re Attitudes About Numbers. Philosophia Mathematica 17 (2):163-188.
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