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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/1467-8284.00439
 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: 23,305
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
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Susan Haack (1978). Philosophy of Logics. Cambridge University Press.
J. L. Bell (1977). A Course in Mathematical Logic. Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..

View all 7 references / Add more references

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

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

101 ( #44,986 of 1,932,594 )

Recent downloads (6 months)

2 ( #333,233 of 1,932,594 )

How can I increase my downloads?

My notes
Sign in to use this feature

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