Strict Finitism and the Happy Sorites

Journal of Philosophical Logic 41 (2):471-491 (2012)
Abstract
Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments
Keywords Finitism  Vagueness  Sorites  Sorites paradox  Strict finitism   Intuitionism  Constructivism  Cut elimination  Induction
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References found in this work BETA
George Boolos (1984). Don't Eliminate Cut. Journal of Philosophical Logic 13 (4):373 - 378.
Ofra Magidor (2007). Strict Finitism Refuted? Proceedings of the Aristotelian Society 107 (1pt3):403-411.

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