Synthese 87 (1):125-142 (1991)
|Abstract||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)|
|Through your library||Configure|
Similar books and articles
Anthony Birch (2007). Waismann's Critique of Wittgenstein. Analysis and Metaphysics 6 (2007):263-272.
Cyrus Panjvani (2006). Wittgenstein and Strong Mathematical Verificationism. Philosophical Quarterly 56 (224):406–425.
Mathieu Marion (1995). Wittgenstein and Finitism. Synthese 105 (2):141 - 176.
Ludwig Wittgenstein (1975/1980). Philosophical Remarks. University of Chicago Press.
Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
Mathieu Marion (1998). Wittgenstein, Finitism, and the Foundations of Mathematics. Oxford University Press.
Daesuk Han (2011). Wittgenstein and the Real Numbers. History and Philosophy of Logic 31 (3):219-245.
Wenceslao J. Gonzalez (1991). Intuitionistic Mathematics and Wittgenstein. History and Philosophy of Logic 12 (2):167-183.
Added to index2009-01-28
Total downloads36 ( #33,071 of 549,753 )
Recent downloads (6 months)4 ( #19,337 of 549,753 )
How can I increase my downloads?