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Synthese

, Volume 192, Issue 8, pp 2413–2436 | Cite as

On the concept of finitism

  • Luca IncurvatiEmail author
Article

Abstract

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 

Notes

Acknowledgments

Many thanks to Alex Oliver, Charles Parsons, Erich Reck, William Tait and two anonymous referees. An earlier version of this material was presented at the History and Philosophy of Infinity Conference at the University of Cambridge. I wish to thank Benedikt Löwe for inviting me to the conference and the members of the audience for their valuable feedback.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Philosophy, Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

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