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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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Philosophy and Logical Foundations

Philosophy and Logical Foundations

(p.147) 6 Philosophy and Logical Foundations
Wittgenstein, Finitism, and the Foundations of Mathematics

Mathieu Marion (Contributor Webpage)

Oxford University Press

This chapter looks at some of the parallels and differences between intuitionism and Ludwig Wittgenstein's new logic. One good way to handle this topic is with the help of the notion of truth maker. This expression was introduced by Kevin Mulligan, Peter Simons, and Barry Smith in order to designate in a neutral fashion entities in virtue of which sentences and/or propositions are true. The basic intuitionist thesis is, on the other hand, that a mathematical proposition is made true by a proof of it. It is on the basis of this thesis that intuitionists developed a new interpretation of logical constants in the 1930s which has interesting affinities not with conceptions found in the Tractatus Logico-Philosophicus but with Wittgenstein's new form of analysis in the early 1930s.

Keywords:   intuitionism, Ludwig Wittgenstein, logic, Kevin Mulligan, Peter Simons, Barry Smith, philosophy, intentionality, rules

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