Talk:Metatheorem

This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles

Low

This article has been rated as Low-importance on the project's importance scale.

Associated task forces:
/
	Logic

The single example in this article seems atypical from the point of view of mathematical logic. In any case, there are probably many good examples that could be included. --Quux0r 08:29, 16 April 2007 (UTC)[reply]

Metalogic[edit]

Even under Arthur Rubin's conservative view that nothing belongs under the metalogic category, one would have to accept that a metatheorem of logic is a theorem of metalogic. It is appropriately in the category metalogic. Pontiff Greg Bard (talk) 18:59, 17 January 2008 (UTC)[reply]

Ah, but a "metatheorem" is not (at least necessarily) a "metatheorem of logic". I still don't think it fits, but I won't fight about it. — Arthur Rubin | (talk) 20:03, 17 January 2008 (UTC)[reply]

About theorems[edit]

Not all metatheorems are theorems "about theorems". For example, the theorem that T = "second-order Peano arithmetic" has only one model is certainly a metatheorem, since this is not provable in T but is a theorem about T provable in the metatheory. But this theorem does not refer in any way to provability in T, so it is not in any sense a theorem "about theorems". — Carl (CBM · talk) 22:39, 17 September 2009 (UTC)[reply]