David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 105 (2):141 - 176 (1995)
In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Montgomery Link (2009). Wittgenstein and Logic. Synthese 166 (1):41 - 54.
Similar books and articles
David G. Stern (2001). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Dialogue 40 (03):624-626.
Stig Børsen Hansen (2010). The Later Wittgenstein and the Philosophy of Religion. Philosophy Compass 5 (11):1013–22.
Mathieu Marion (2003). Wittgenstein and Brouwer. Synthese 137 (1-2):103 - 127.
Eric Winsberg (2000). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Philosophy of Science 67 (3):533-.
Marc A. Joseph (2001). Review of M. Marion, Wittgenstein, Finitism, and the Foundations of Mathematics. [REVIEW] Mind 110 (438):501-504.
Steve Gerrard (1991). Wittgenstein's Philosophies of Mathematics. Synthese 87 (1):125-142.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.
Added to index2009-01-28
Total downloads27 ( #65,603 of 1,102,812 )
Recent downloads (6 months)4 ( #84,523 of 1,102,812 )
How can I increase my downloads?