Too naturalist and not naturalist enough: Reply to Horsten

Erkenntnis 69 (2):261 - 274 (2008)
Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out of the objection which is in line with the naturalistic spirit of Horsten’s proposal but which further weakens the analogy with Isaacson’s Thesis. I conclude by evaluating the prospects for providing an analogue of Isaacson’s Thesis for ZFC.
Keywords Mathematical truth  Isaacson's Thesis  Mathematical naturalism
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References found in this work BETA
William Craig (1953). On Axiomatizability Within a System. Journal of Symbolic Logic 18 (1):30-32.
Michael Dummett (1994). Reply to McGuiness. In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer

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