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Re: CHAT: mathematics

From:Dennis Paul Himes <dennis@...>
Date:Tuesday, December 12, 2000, 2:24
John Cowan <jcowan@...> wrote:
> I am leaning here on, which provides > a lot more detail.
This discussion has gotten offtopic a while ago, so I'll skip the details and just make a few points, while leading back to conlanging at the end. 1) The above site seems to be saying that we can prove that there does not exist a proof of ~G in PA, we just can't prove in PA that there does not exist a proof of ~G. 2) The site goes on to give a late version of Goedel's theorem (Rosser's version) which exhibits a statement with the qualities I was using for the Goedel statement. I think our basic problem is that we have been referring to two different versions of the theorem. I spent several semesters in grad school studying Goedel, but that was over twenty years ago, and I'm a bit hazy on the details. 3) Throughout this discussion we've been referring to PA, but I'm not sure how many conlangers realize that this is short for Peano Arithmetic, named after Guiseppe Peano, the inventor of Latino sine Flexione. =========================================================================== Dennis Paul Himes <> Disclaimer: "True, I talk of dreams; which are the children of an idle brain, begot of nothing but vain fantasy; which is as thin of substance as the air." - Romeo & Juliet, Act I Scene iv Verse 96-99