A revenge-immune solution to the semantic paradoxes

Journal of Philosophical Logic 32 (2):139-177 (2003)
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
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Reprint years 2004
DOI 10.1023/A:1023027808400
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Modalities in Substructural Logics.Greg Restall - 1992 - Logique Et Analyse 35:303-321.

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Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
On Artifacts and Truth-Preservation.Shawn Standefer - 2015 - Australasian Journal of Logic 12 (3):135-158.
The Inexpressibility of Validity.Julien Murzi - 2014 - Analysis 74 (1):65-81.
Revision Revisited.Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch - 2012 - Review of Symbolic Logic 5 (4):642-664.

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