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- Otávio Bueno & Edward N. Zalta (2005). A Nominalist's Dilemma and its Solution. Philosophia Mathematica 13 (3):297-307.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.In my reading list | Discuss this article | Edit | Categorize |My bibliography
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Yet, he also says that it is philosophically indeterminate which criterion for what exists is correct. Nominalism is the view that certain objects ( i.e ., abstract objects) do not exist, and not the view that it is philosophically indeterminate whether or not they do. I resolve the dilemma that Azzouni's claims pose: Azzouni is a non-factualist about what exists, but he is a factualist about which criterion for what exists our community of speakers has adopted. It is in the (...)
ln this paper I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logtcist approach from recent criticisms; in particular from the charge that a crucial principle in the logrcist reconstruction of arithmetic, I·Iume’s Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view I then indicate a way of extending the nominalist logzcist approach beyond arithmetic. Finally, I argue (...)
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