Journal of Philosophical Logic

, Volume 41, Issue 2, pp 471–491

Strict Finitism and the Happy Sorites


DOI: 10.1007/s10992-011-9180-8

Cite this article as:
Magidor, O. J Philos Logic (2012) 41: 471. doi:10.1007/s10992-011-9180-8


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.


Finitism Vagueness Sorites Sorites paradox Strict finitism Intuitionism Constructivism Cut Cut elimination Induction 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of Oxford (Balliol College)OxfordUK

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