Re: CHAT: mathematics

John Cowan <jcowan@...> wrote:
> I am leaning here on http://www.ltn.lv/~podnieks/gt5.html, 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    <>    dennis@himes.connix.com
                  http://www.connix.com/~dennis/dennis.htm

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