On the Concept of Finitism

Synthese 192 (8):2413-2436 (2015)
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At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. The paper investigates these conceptions and shows that they sanction different portions of mathematics as finitistic.



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Luca Incurvati
University of Amsterdam

Citations of this work

Ontology and Arbitrariness.David Builes - 2022 - Australasian Journal of Philosophy 100 (3):485-495.
In Defense of the Implicit Commitment Thesis.Ethan Brauer - 2022 - Ergo: An Open Access Journal of Philosophy 9.

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References found in this work

From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
Absolute generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - New York: Oxford University Press.
Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.

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