Erkenntnis

, 69:261

Too Naturalist and Not Naturalist Enough: Reply to Horsten

Original Article

DOI: 10.1007/s10670-008-9114-1

Cite this article as:
Incurvati, L. Erkenn (2008) 69: 261. doi:10.1007/s10670-008-9114-1
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Abstract

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.

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Faculty of Philosophy, University of Cambridge Cambridge UK

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