Different senses of finitude: An inquiry into Hilbert's finitism

Synthese 185 (3):335-363 (2012)

Sören Stenlund
Uppsala University
This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting concrete things, and a third sense is linked up with the immediate intuitive experience of multitudes of concrete things. Hilbert's fìnitism is examined with respect to these differences, and it will be shown that there is a tendency to conflate the different senses of number and fìnitude, a tendency which has been a source of problems in the discussion of the foundations of mathematics and in the philosophy of logic and language
Keywords Husserl  Hilbert  Life-word  Finitism  Metamathematics  Kant  Perceptual intuition  Number  Counting  Concrete objects  Surveyable  Foundations of mathematics
Categories (categorize this paper)
DOI 10.1007/s11229-010-9823-2
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,164
Through your library

References found in this work BETA

Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press.
Critique of Pure Reason.I. KANT - 1787/1998 - Philosophy 59 (230):555-557.
Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..

View all 23 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Gödel on Intuition and on Hilbert's Finitism.W. W. Tait - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
A Defense of Strict Finitism.J. P. Bendegem - 2012 - Constructivist Foundations 7 (2):141-149.
Extensions of the Finitist Point of View.Matthias Schirn & Karl-Georg Niebergall - 2001 - History and Philosophy of Logic 22 (3):135-161.
Hilbert's Programs: 1917–1922.Wilfried Sieg - 1999 - Bulletin of Symbolic Logic 5 (1):1-44.
Strict Finitism and the Happy Sorites.Ofra Magidor - 2012 - Journal of Philosophical Logic 41 (2):471-491.
Taxonomising the Senses.Fiona Macpherson - 2011 - Philosophical Studies 153 (1):123-142.
The Significance of the Senses.Matthew Nudds - 2004 - Proceedings of the Aristotelian Society 104 (1):31-51.
Mourning My Future Death.J. Jeremy Wisnewski - 2008 - Philosophy in the Contemporary World 15 (2):54-61.
Aspekte der frege–hilbert-korrespondenz.Kai F. Wehmeier - 1997 - History and Philosophy of Logic 18 (4):201-209.
Strict Finitism Refuted?Ofra Magidor - 2007 - Proceedings of the Aristotelian Society 107 (1pt3):403-411.


Added to PP index

Total views
45 ( #172,161 of 2,237,424 )

Recent downloads (6 months)
2 ( #792,748 of 2,237,424 )

How can I increase my downloads?


My notes

Sign in to use this feature