Talk:Tarski's indefinability theorem

From Wikipedia, the free encyclopedia

[edit] Indefinability?

Not really an English word, even though for some odd reason it does get a fair number of Google hits. Should be moved to Tarski's undefinability theorem, or better, Tarski's theorem on the undefinability of truth, which I think is the standard name. --Trovatore 05:42, 9 March 2006 (UTC)

Looking it up in www.m-w.com, I find "indefinable" is an English word, which I suppose I knew. I still maintain it's not a mathematical English word. It's used for qualities like someone's indefinable charm, not for sets that have no definition of a specified form. --Trovatore 05:49, 9 March 2006 (UTC)

• JA: Personally, I prefer TIT to TUT. Jon Awbrey 07:06, 9 March 2006 (UTC)

[edit] References

I edited the article and addeda a references tag. The following points need to be addressed:

• I could swear I read (with my own eyes) a footnote by Tarski where he claims he independently proved the theorem, apart from Godel's work. The article right now is self-contradictory on this issue. I'll dig up my reference.
• The last paragraph says (or does it?) that negation is not necessary. The proof given clearly uses negation. A reference for the last paragraph would be helpful.

By the way, I agree with Trovatore that indefinability is not the right word. CMummert 03:37, 18 July 2006 (UTC)

I have verified to my satisfaction that Tarski did state in print that he developed his theorem independently of Gödel's work. By the way, my memory is that he believed, after seeing Gödel's paper, that he was only a few years short of proving the same thing. CMummert 03:54, 18 July 2006 (UTC)

[edit] Paraconsistency

I would really like a reference for this claim: "Although some have claimed otherwise, Tarski's Theorem is not restricted to bivalent classical logic. For example, it can be generalized to interpreted languages based on many-valued logic, such as fuzzy logic, and to dialetheism, paraconsistent logic, etc." I think this claim is incorrect and Tarski's theorem does not hold in a paraconsistent language, because the proof of the theorem uses reductio ad absurdum, and absurdities are allowed in paraconsistent logics. (Analogously for Gödel's incompletess theorem.) 130.37.20.20 15:58, 11 January 2007 (UTC)

Although some have claimed otherwise, Tarski's Theorem is not restricted to bivalent [[classical logic]]. For example, it can be generalized to interpreted languages based on [[many-valued logic]], such as [[fuzzy logic]], and to [[dialetheism]], [[paraconsistent logic]], etc

I never liked that sentence anyway, so I will move it here. I left the rest of the paragraph, which is correct. CMummert · talk 16:55, 11 January 2007 (UTC)