On the Coherence of Strict Finitism

Kriterion - Journal of Philosophy 33 (2):1-14 (2019)
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Abstract

Strict finitism is the position that only those natural numbers exist that we can represent in practice. Michael Dummett, in a paper called Wang’s Paradox, famously tried to show that strict finitism is an incoherent position. By using the Sorites paradox, he claimed that certain predicates the strict finitist is committed to are incoherent. More recently, Ofra Magidor objected to Dummett’s claims, arguing that Dummett fails to show the incoherence of strict finitism. In this paper, I shall investigate whether Magidor is successful in preventing Dummett from proving the incoherence of strict finitism. Though not all the counterarguments Magidor presents are successful, she does in the end manages to corner Dummett. There remains a small opportunity for Dummett to insist on the incoherence of strict finitism, but this is a very small opening. The final conclusion of this paper is that Dummett cannot logically prove the incoherence of strict finitism, even though not all hope is lost.

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Auke Montesano Montessori
Washington University in St. Louis

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References found in this work

Vagueness and Ignorance.Timothy Williamson & Peter Simons - 1992 - Aristotelian Society Supplementary Volume 66 (1):145-178.
Strict finitism.Crispin Wright - 1982 - Synthese 51 (2):203 - 282.
Vagueness and Ignorance.Timothy Williamson & Peter Simons - 1992 - Aristotelian Society Supplementary Volume 66 (1):145-178.
Strict Finitism and the Happy Sorites.Ofra Magidor - 2012 - Journal of Philosophical Logic 41 (2):471-491.
A Defense of Strict Finitism.J. P. Van Bendegem - 2012 - Constructivist Foundations 7 (2):141-149.

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