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Taking it Easy: A Response to Colyvan

Mind 121 (484):983-995 (2012)

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  1. Weaseling away the indispensability argument.Joseph Melia - 2000 - Mind 109 (435):455-480.
    According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of (...)
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  • There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
    Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...)
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  • Mathematics and aesthetic considerations in science.Mark Colyvan - 2002 - Mind 111 (441):69-74.