A revenge-immune solution to the semantic paradoxes

Journal of Philosophical Logic 32 (2):139-177 (2003)
Abstract
The paper offers a solution to the semantic paradoxes, one in which we keep the unrestricted truth schema "True ↔ A", and the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in "ordinary" contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True with A within the language. The logic is also shown to have the resources required to represent the way in which sentences that lead to paradox in classical logic are "defective". We can in fact define a hierarchy of "defectiveness" predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various "levels of defectiveness" can all be made coherent together within a single object language
Keywords conditionals  Curry paradox  determinateness  Liar paradox  truth
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 12,697
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

No references found.

Citations of this work BETA
Vann McGee (2010). Field's Logic of Truth. [REVIEW] Philosophical Studies 147 (3):421 - 432.
Lionel Shapiro (2011). Expressibility and the Liar's Revenge. Australasian Journal of Philosophy 89 (2):297-314.
Philippe Schlenker (2010). Super Liars. Review of Symbolic Logic 3 (3):374-414.

View all 12 citations

Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

33 ( #59,577 of 1,413,138 )

Recent downloads (6 months)

3 ( #66,796 of 1,413,138 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.