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:
Quantification and Finitism

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  • History of Western Philosophy
  • Philosophy of Mathematics and Logic


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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

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