David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Citations of this work BETA
Vann McGee (2010). Field's Logic of Truth. [REVIEW] Philosophical Studies 147 (3):421 - 432.
Harty Field (2004). The Consistency of the Naïve Theory of Properties. Philosophical Quarterly 54 (214):78 - 104.
Richard Heck (2012). More on 'A Liar Paradox'. Thought 1 (4):270-280.
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.
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