Timeline for What assumptions and methodology do metaproofs of logic theorems use and employ?

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Dec 15, 2009 at 13:28	comment	added	user2529		Zev, I think you share some of the concerns you have, and I think it would be a good idea if you would post these explicity in a separate question for people to answer.
Dec 14, 2009 at 17:58	comment	added	Zev Chonoles		I have wondered this myself many times, as it seems like a glaring omission in what most people say is the statement of the incompleteness theorem. Indeed, for any theorem, in logic or otherwise, the correct statement is "Under the assumption of logic X, the result ____ is true." The problem with some results in logic is that, at least as it seems to me and Colin, we often appear to be using X = classical logic, and proving statements about other logics, in particular, logics which are inconsistent or stronger than classical logic - how does this make sense?
Dec 14, 2009 at 17:53	comment	added	Zev Chonoles		But (it seems to me) you haven't really gotten to the heart of Colin's question, which would ask in response "In which proof system do we "prove" Godel's incompleteness theorem, and how do we know our results in that system are correct?" For example, perhaps an intuitionist would not accept the proof of the incompleteness theorem - then in what sense have we really "proved" something about "all logics"?
Dec 14, 2009 at 13:16	vote	accept	CommunityBot
Dec 14, 2009 at 9:50	history	answered	Neel Krishnaswami	CC BY-SA 2.5