David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 87 (1):125-142 (1991)
Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period. The goal of my article is to provide a new framework for examining Wittgenstein's philosophies of mathematics and the evolution of his career as a whole. I posit the Hardyian Picture, modelled on the Augustinian Picture, to provide a structure for Wittgenstein's work on the philosophy of mathematics. Wittgenstein's calculus period has not been properly recognized, so I give a detailed account of the tenets of that stage in Wittgenstein's career. Wittgenstein's notorious remarks on contradiction are the test case for my theory of his transition. I show that the bizarreness of those remarks is largely due to the calculus conception, but that Wittgenstein's later language-game account of mathematics keeps the rejection of the Hardyian Picture while correcting the calculus conception's mistakes.
|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
Christian Greiffenhagen & Wes Sharrock (2006). Mathematical Relativism: Logic, Grammar, and Arithmetic in Cultural Comparison. Journal for the Theory of Social Behaviour 36 (2):97–117.
William W. Tait (1993). Some Recent Essays in the History of the Philosophy of Mathematics: A Critical Review. [REVIEW] Synthese 96 (2):293 - 331.
Toshio Irie (2012). On an Important Aspect of Relations Between a Problem and Its Solution in Mathematics and the Concept of Proof. Kagaku Tetsugaku 45 (2):115-129.
Similar books and articles
Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
Daesuk Han (2011). Wittgenstein and the Real Numbers. History and Philosophy of Logic 31 (3):219-245.
Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.
Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
Ludwig Wittgenstein (1975/1980). Philosophical Remarks. University of Chicago Press.
Mathieu Marion (1995). Wittgenstein and Finitism. Synthese 105 (2):141 - 176.
Cyrus Panjvani (2006). Wittgenstein and Strong Mathematical Verificationism. Philosophical Quarterly 56 (224):406–425.
Wenceslao J. Gonzalez (1991). Intuitionistic Mathematics and Wittgenstein. History and Philosophy of Logic 12 (2):167-183.
Added to index2009-01-28
Total downloads60 ( #69,059 of 1,792,149 )
Recent downloads (6 months)7 ( #120,088 of 1,792,149 )
How can I increase my downloads?