Chapter

Quantification and Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print August 2008 | ISBN: 9780199550470
Published online September 2011 | e-ISBN: 9780191701559 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199550470.003.0004
Quantification and Finitism

More Like This

Show all results sharing these subjects:

  • History of Western Philosophy
  • Philosophy of Mathematics and Logic

GO

Show Summary Details

Preview

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

Chapter.  11016 words. 

Subjects: History of Western Philosophy ; Philosophy of Mathematics and Logic

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.