Journal of Philosophical Logic 32 (2):139-177 (2003)

Hartry Field
New York University
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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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Logic of Provability.George S. Boolos - 1993 - Cambridge and New York: Cambridge University Press.

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Citations of this work BETA

Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
No Fact of the Matter.Hartry Field - 2003 - Australasian Journal of Philosophy 81 (4):457 – 480.

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