Revolutionary fictionalism: A call to arms

Philosophia Mathematica 13 (3):277-293 (2005)
Abstract
This paper responds to John Burgess's ‘Mathematics and Bleak House’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of metaphysical existence claims has no force against a naturalized version of fictionalism, according to which our ordinary standards of scientific evidence may show that we have no reason to believe the mathematical existence claims made within the context of our mathematical and scientific theories.
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    Frederick Kroon (2011). Fictionalism in Metaphysics. Philosophy Compass 6 (11):786-803.
    M. Balaguer (2011). Reply to Armour-Garb. Philosophia Mathematica 19 (3):345-348.

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