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
Kurt Gödel (1986). Collected Works. Oxford University Press.
Vann McGee (1997). How We Learn Mathematical Language. Philosophical Review 106 (1):35-68.

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