Can a many-valued language functionally represent its own semantics?

Analysis 63 (4):292–297 (2003)
Tarski’s Indefinability Theorem can be generalized so that it applies to many-valued languages. We introduce a notion of strong semantic self-representation applicable to any (sufficiently rich) interpreted many-valued language L. A sufficiently rich interpreted many-valued language L is SSSR just in case it has a function symbol n(x) such that, for any f Sent(L), the denotation of the term n(“f”) in L is precisely ||f||L, the semantic value of f in L. By a simple diagonal construction (finding a sentence l such that l is equivalent to n(“l”) T), it is shown that no such language strongly represents itself semantically. Hence, no such language can be its own metalanguage
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References found in this work BETA
Susan Haack (1978). Philosophy of Logics. Cambridge University Press.
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Hannes Leitgeb (1999). Truth and the Liar in De Morgan-Valued Models. Notre Dame Journal of Formal Logic 40 (4):496-514.

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Citations of this work BETA
Lionel Shapiro (2011). Expressibility and the Liar's Revenge. Australasian Journal of Philosophy 89 (2):297-314.
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