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In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered. |
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This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...) |
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In this chapter, I consider some problems with naturalizing mathematics. More specifically, I consider how the two leading kinds of approach to naturalizing mathematics, to wit, Quinean indispensability‐based approaches and Maddy's Second Philosophical approach, seem to run afoul of constraints that any satisfactory naturalistic mathematics must meet. I then suggest that the failure of these kinds of approach to meet the relevant constraints indicates a general problem with naturalistic mathematics meeting these constraints, and thus with the project of naturalizing mathematics (...) |
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Philip Kitcher's account of scientific progress incorporates a conception of explanatory unification that invites the so-called 'obsessive unifier' worry, to wit, that in our drive to unify the phenomena we might impose artificial structure on the world and consequently produce an incorrect view of how things, in fact, are. I argue that Kitcher's attempt to address this worry is unsatisfactory because it relies on an ability to choose between rival patterns of explanation which itself rests on the relevant choice having (...) |
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In this paper I return to the mid-20th-century debate between Quine and Carnap on the status of metaphysics questions with an eye toward advancing contemporary debates about whether naturalists can coherently undertake substantive metaphysical inquiry. Following Huw Price, I take the debate between Quine and Carnap to hinge, in part, on whether human inquiry is functionally unified. However, unlike Price, I suggest that this question is not best understood as a question about the function(s) of descriptive discourse. This goes along (...) |
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