This paper portrays the later Wittgenstein’s conception of contradictions and his therapeutic approach to them. I will focus on and give relevance to the Lectures on the Foundations of Mathematics (LFM 1976), plus the Remarks on the Foundations of Mathematics (RFM 2001). First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: (a) a rejection of the debate about realism and anti-realism in mathematics; and (b) Wittgenstein’s endorsement of logical pluralism. Then, I will explain Wittgenstein’s therapeutic approach towards contradictions, and why it means that a contradiction is not a problem for logic and mathematics. Rather, contradictions are problematic when we do not know what to infer from them. Once a meaning is established through a new rule of inference, the contradiction becomes a usable expression like many others in our inferential apparatus. Thus, the apparent problem is dissolved. Finally, I will take three examples of dissolved contradictions from Wittgenstein to clarify further his notion. I will conclude considering why his position on contradictions led him to clash with Alan Turing, and whether the latter was convinced by the Wittgensteinian proposal.
...MoreSimilar Citations
Article
Anderson Nakano;
(2021)
On Ramsey’s reason to amend Principia Mathematica’s logicism and Wittgenstein’s reaction
(/isis/citation/CBB314453813/)
Article
Köchy, Kristian;
(2010)
Vielfalt der Wissenschaften bei Carnap, Lewin und Fleck. Zur Entwicklung eines pluralen Wissenschaftskonzepts
(/isis/citation/CBB000933030/)
Book
Jack Copeland;
Jonathan Bowen;
Mark Sprevak;
Robin Wilson;
(2017)
The Turing Guide
(/isis/citation/CBB709222979/)
Book
Turing, Alan Mathison;
Appel, Andrew W.;
Feferman, Solomon;
(2012)
Alan Turing's Systems of Logic: The Princeton Thesis
(/isis/citation/CBB001213136/)
Book
Andrew Hodges;
Douglas Hofstadter;
(2014)
Alan Turing: The Enigma: The Book That Inspired the Film "The Imitation Game"
(/isis/citation/CBB485951446/)
Article
Stillwell, John;
(2004)
Emil Post and His Anticipation of Gödel and Turing
(/isis/citation/CBB000771953/)
Article
Aldrich, John;
(2009)
England and Continental Probability in the Inter-War Years
(/isis/citation/CBB001021431/)
Article
Paula Quinon;
(2021)
Can Church’s thesis be viewed as a Carnapian explication?
(/isis/citation/CBB401301232/)
Article
Cassou-Noguès, Pierre;
(2008)
Gödel et la thèse de Turing
(/isis/citation/CBB000930661/)
Book
Nedo, Michael;
(2013)
Wittgenstein: una biografia per immagini
(/isis/citation/CBB001213930/)
Article
David Loner;
(2020)
Alice Ambrose and the American Reception of Wittgenstein's Philosophy of Mathematics, 1935–75
(/isis/citation/CBB296871977/)
Article
Thomas McNally;
(2016)
More Than a Feeling: Wittgenstein and William James on Love and Other Emotions
(/isis/citation/CBB108623002/)
Book
Williams, Meredith;
(1999)
Wittgenstein, mind, and meaning: Toward a social conception of mind
(/isis/citation/CBB000111954/)
Article
Sayward, Charles;
(2005)
Steiner versus Wittgenstein: Remarks on Differing Views of Mathematical Truth
(/isis/citation/CBB000933620/)
Article
Lampert, Timm;
(2003)
Psychophysical and Tractarian Analysis
(/isis/citation/CBB000502675/)
Book
José L. Zalabardo;
(2015)
Representation and Reality in Wittgenstein's Tractatus
(/isis/citation/CBB726782024/)
Chapter
Susanna Zellini;
(2018)
Wittgenstein, Mach e il senso comune
(/isis/citation/CBB902592785/)
Essay Review
Nordmann, Alfred;
(2002)
Another New Wittgenstein: The Scientific and Engineering Background of the Tractatus
(/isis/citation/CBB000502666/)
Book
Halais, Emmanuel;
(2007)
Wittgenstein et l'énigme de l'existence: la forme et l'expression
(/isis/citation/CBB000772822/)
Book
Stern, David G.;
(2004)
Wittgenstein's Philosophical Investigations: An Introduction
(/isis/citation/CBB000550812/)
Be the first to comment!