Strict Finitism and the Happy Sorites |
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Authors: | Ofra Magidor |
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Institution: | (1) University of Sheffield, Sheffield, S10 2TN, UK |
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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. |
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