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Wittgenstein, Finitism, and the Foundations of Mathematics$
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Mathieu Marion

Print publication date: 2008

Print ISBN-13: 9780199550470

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199550470.001.0001

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Quantification and Finitism

Quantification and Finitism

Chapter:
(p.84) 4 Quantification and Finitism
Source:
Wittgenstein, Finitism, and the Foundations of Mathematics
Author(s):

Mathieu Marion (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199550470.003.0004

This chapter shows that Ludwig Wittgenstein's philosophy of mathematics has much less in common with intuitionism than is usually assumed, although some strategical moves are barely distinguishable. At least one such move cannot be overlooked because of its importance for the development of Wittgenstein's philosophy: it concerns quantification theory. This chapter shows that Wittgenstein's stance on quantification was, however, even more radical than that of intuitionists. This is a topic about which Wittgenstein changed his mind around 1929. The search for the source of Wittgenstein's new ideas on quantification leads directly to Hermann Weyl. He actually developed original ideas on topics such as quantification. According to him, propositions containing an existential quantifier ranging over the natural numbers do not possess the full status of judgement.

Keywords:   Ludwig Wittgenstein, intuitionism, mathematics, quantification theory, Hermann Weyl, quantification, finitism, David Hilbert, Frank Plumpton Ramsey

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