Strict Finitism Refuted?

Proceedings of the Aristotelian Society 107 (1pt3):403-411 (2007)
Abstract
In his paper ‘Wang’s Paradox’, Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett’s argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there are sets of natural numbers which are closed under the successor operation but nonetheless have an upper bound; (2) Such a commitment is inconsistent, even by finitistic standards. In this paper I claim that Dummett’s argument fails. I question both parts of Dummett’s argument, but most importantly I claim that Dummett’s argument in favour of the second claim crucially relies on an implicit assumption that Dummett does not acknowledge and that the strict finitist need not accept.
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DOI 10.1111/j.1467-9264.2007.00230.x
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References found in this work BETA
Elements of Intuitionism.Michael A. E. Dummett - 2000 - Oxford University Press.
Wang's Paradox.Michael Dummett - 1975 - Synthese 30 (3-4):201--32.

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Citations of this work BETA
Strict Finitism and the Happy Sorites.Ofra Magidor - 2012 - Journal of Philosophical Logic 41 (2):471-491.
On the Coherence of Wittgensteinian Constructivism.Amit Saad - 2016 - Acta Analytica 31 (4):455-462.

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