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Topic: New essay on Goedel's Incompleteness Theorem
Replies: 123   Last Post: Oct 1, 2009 11:56 PM

 Messages: [ Previous | Next ]
 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.

Date Subject Author
9/21/09 Bill97
9/21/09 george
9/21/09 Frederick Williams
9/21/09 Aatu Koskensilta
9/21/09 LauLuna
9/21/09 Scott
9/24/09 Frederick Williams
9/24/09 Scott
9/21/09 Scott
9/22/09 Daryl McCullough
9/21/09 Newberry
9/22/09 Guest
9/22/09 Newberry
9/22/09 Scott
9/22/09 Scott
9/22/09 Newberry
9/22/09 Scott
9/22/09 Newberry
9/22/09 namducnguyen
9/22/09 Scott
9/22/09 namducnguyen
9/23/09 Daryl McCullough
9/24/09 LauLuna
9/24/09 Newberry
9/25/09 Scott
9/22/09 LauLuna
9/22/09 Scott
9/23/09 Scott
9/23/09 Scott
9/23/09 Scott
9/24/09 Scott
9/24/09 Newberry
9/24/09 namducnguyen
9/27/09 Newberry
9/26/09 Scott
9/26/09 David C. Ullrich
9/26/09 Scott
9/26/09 Frederick Williams
9/26/09 Scott
9/27/09 Frederick Williams
9/26/09 namducnguyen
9/26/09 namducnguyen
9/26/09 Marshall
9/26/09 namducnguyen
9/26/09 namducnguyen
9/26/09 Marshall
9/27/09 namducnguyen
9/27/09 Marshall
9/27/09 namducnguyen
9/27/09 namducnguyen
9/27/09 Marshall
9/27/09 Scott
9/27/09 Scott
9/27/09 Scott
9/28/09 Daryl McCullough
9/28/09 David C. Ullrich
9/29/09 Scott
9/29/09 Daryl McCullough
9/29/09 Aatu Koskensilta
9/29/09 Newberry
9/27/09 george
9/27/09 george
9/28/09 Scott
9/28/09 namducnguyen
9/29/09 Frederick Williams
9/29/09 Aatu Koskensilta
9/28/09 Scott
9/28/09 ross.finlayson@gmail.com
9/29/09 Marshall
9/29/09 Aatu Koskensilta
9/29/09 Marshall
9/30/09 Frederick Williams
9/30/09 Marshall
9/30/09 Marshall
10/1/09 Marshall
9/30/09 Marshall
9/30/09 Marshall
9/29/09 Scott
9/30/09 namducnguyen
9/30/09 Scott
9/30/09 Scott
9/30/09 Scott
9/30/09 Scott
9/30/09 Tim Little
10/1/09 Scott
10/1/09 Daryl McCullough
10/1/09 David C. Ullrich
10/1/09 Scott
10/1/09 David C. Ullrich
10/1/09 Marshall
10/1/09 Scott
10/1/09 Tim Little
9/30/09 Scott
9/30/09 Daryl McCullough
9/30/09 Scott
9/29/09 Newberry
9/23/09 Scott
9/23/09 Newberry
9/24/09 Frederick Williams
9/24/09 namducnguyen
9/24/09 Aatu Koskensilta
9/24/09 namducnguyen
9/24/09 namducnguyen
9/24/09 namducnguyen
9/24/09 namducnguyen
9/24/09 ross.finlayson@gmail.com
9/23/09 John Jones
9/24/09 LauLuna
9/24/09 Newberry
9/27/09 george
9/30/09 Scott
9/30/09 Scott
9/30/09 Daryl McCullough
9/30/09 Scott
9/30/09 Daryl McCullough
9/30/09 David Libert
9/30/09 Tim Little
9/30/09 ross.finlayson@gmail.com
9/30/09 Marshall
10/1/09 Marshall
10/1/09 Daryl McCullough
9/30/09 Scott
10/1/09 Daryl McCullough