Scott
Posts:
66
Registered:
2/2/07


Re: New essay on Goedel's Incompleteness Theorem
Posted:
Sep 30, 2009 9:26 PM


On Sep 30, 5:23 pm, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > Scott H says... > > >1. Every statement has a Goedel number. > >2. If a statement is 'about' a number, then its Goedel number is also > >'about' that number. > > That doesn't make any sense. What is the number 4 about?
4 isn't the Goedel number of a statement that is about anything.
> >3. Some statements are about Goedel numbers. > >4. Therefore, there are Goedel numbers that are about Goedel numbers. > > I don't think it makes any sense to say that a Godel number is "about" > anything. In any case, I don't see where you are getting an infinite > sequence of G, G', G'', etc.
I say that a Goedel number is about something when its statement is about something. The infinite sequence arises when the substitution or 'arithmoquine' function is applied repeatedly.
> G could be said to be "about" its Godel number, since it says > that its Godel number is not the Godel number of a provable sentence. > But then G' is the Godel number of G, so G' is "about" whatever G is > about. So there is no G'', G''', etc.
I'll be more accurate: G' is about G'', the Goedel number of G', which G is about. As I told Aatu, I'll leave it open whether G, G', G'', ... are all basically the same statement.

