Synthese 198 (4):3783-3799 (2019)

Authors
Alessio Persichetti
University of Aberdeen
Abstract
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, plus the Remarks on the Foundations of Mathematics. First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: a rejection of the debate about realism and anti-realism in mathematics; and 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.
Keywords Wittgenstein  Logic  Contradictions  Alan Turing  Mathematics  Paraconsistent Logic
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11229-019-02310-w
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,636
External links

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

In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
Beyond the Limits of Thought.Graham Priest - 1995 - Philosophy 71 (276):308-310.
Beyond the Limits of Thought.Graham Priest - 1999 - Philosophical Quarterly 49 (194):121-125.

View all 29 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Wittgenstein & Paraconsistência.João Marcos - 2010 - Principia: An International Journal of Epistemology 14 (1):135-173.
Wittgenstein & Paraconsistência.João Marcos - 2010 - Principia: An International Journal of Epistemology 14 (1):135-73.
Wittgenstein's Attitude Toward Contradiction.Seung-Chong Lee - 1992 - Dissertation, State University of New York at Buffalo
The Development of Wittgenstein's Views on Contradiction.Laurence Goldstein - 1986 - History and Philosophy of Logic 7 (1):43-56.
The Barber, Russell's Paradox, Catch-22, God, Contradiction, and More.Laurence Goldstein - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press. pp. 295--313.
Wittgenstein, Philosophy and Logic.Ilham Dilman - 1970 - Analysis 31 (2):33 - 42.
A Note on Saying Nothing and Saying More in the Tractatus.Pasquale Frascolla - 2018 - History and Philosophy of Logic 39 (2):135-139.
Wittgenstein's Later Logic.B. H. Slater - 1979 - Philosophy 54 (208):199 - 209.
Wittgenstein and the Status of Contradictions.Louis Caruana - 2004 - In A. Coliva & E. Picardi (eds.), Wittgenstein Today. Padova: Poligrafo. pp. 223-232.
A Dialectical Contradiction is Not "A and Not-A".Du Ruji - 1982 - Contemporary Chinese Thought 13 (4):3-8.

Analytics

Added to PP index
2019-07-04

Total views
67 ( #163,791 of 2,462,266 )

Recent downloads (6 months)
9 ( #78,486 of 2,462,266 )

How can I increase my downloads?

Downloads

My notes