On the Concept of Finitism

Synthese 192 (8):2413-2436 (2015)

Luca Incurvati
University of Amsterdam
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.
Keywords Finitism  Hilbert  Infinite totality  Intuition
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DOI 10.1007/s11229-014-0639-3
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Collected Papers.Colin McGinn & Gareth Evans - 1988 - Philosophical Review 97 (2):278.
Mathematical Thought and its Objects.Charles Parsons - 2007 - Cambridge University Press.
Absolute Generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - Oxford University Press.

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