User talk:BuzzB
Hello and welcome! I just saw your message on my talk page. Sadly, I wasn't the person who created the Gödel's incompleteness theorem article. All I did was make a small formatting change but the old version of the Wikipedia software didn't keep all page versions, so there is no record of who created that page. But user:AxelBoldt is a prime suspect. --mav
Hi BuzzB, while I didn't initiate Gödel's incompleteness theorem, I wrote most of it, including the proof sketch.
Regarding the change of G(F) to G(F(x)): I guess one could argue it both ways; I'm afraid that the latter notation could mislead people into thinking that G(F(x)) is a statement form or a function, while indeed it is just a number. Also, further down in the proof one would have to write SU(G(SU(x))) and that is quite a mouthful.
Cheers, AxelBoldt 18:49 Apr 3, 2003 (UTC)
Your changes look good to me, please upload them to Gödel's incompleteness theorem; it's a load easier to modify things there than to send it back and forth on talk pages. I'll probably make a couple small edits, but that's the nature of the game. By the way, my Oxford English Dictionary lists "proven" as a synonym for "proved", but maybe that's a British vs. American thing.
I'd be interested to look at your paper. Do you have it on the web somewhere? Or you could send it to axelboldt at yahoo dot com. AxelBoldt 17:47 Apr 6, 2003 (UTC)
Hello,
I read Gödel's proof again, and I think I've come around to your position that G(F(x)) is clearer than G(F) after all. I guess initially I was thinking that only statement forms get Gödel numbers, but that's not true: all statements and statement forms get Gödel numbers.
Also, I believe now that my earlier statement
- This concept can be defined formally, and therefore we can construct a statement form SU(z) which embodies the concept: SU(z) is provable if and only if z is the Gödel number of a self-unprovable statement form.
is not correct. I think it should read "SU(z) means that z is the Gödel number of a self-unprovable statement from." The part about provability of SU(z) cannot be right: if the system is inconsistent, then SU(z) is provable for all z, even though there are no self-unprovable statement forms. What do you think? AxelBoldt 22:40 Apr 7, 2003 (UTC)
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