Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Scott

Posts: 66
Registered: 2/2/07
Re: New essay on Goedel's Incompleteness Theorem
Posted: Sep 30, 2009 5:19 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sep 30, 4:26 pm, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
> Scott H says...
> > If
> > statements can be about Goedel numbers, then Goedel numbers can be
> > about Goedel numbers.

>
> I can't make any sense of that.


I'll try to simplify it:

1. Every statement has a Goedel number.
2. If a statement is 'about' a number, then its Goedel number is also
'about' that number.
3. Some statements are about Goedel numbers.
4. Therefore, there are Goedel numbers that are about Goedel numbers.

[...]

> 3. There is a provability predicate Pr for Peano Arithmetic with the
> property that for any formula Phi,
> If Phi is provable from the axioms of Peano Arithmetic
> then
> Pr(#Phi) is true
> Conversely, if Phi is not provable from the axioms of
> Peano Arithmetic, then
> ~Pr(#Phi) is true.


More accurately, if x proves Phi, then the formula Pr(x, Phi) is
provable, and if x doesn't prove Phi, then the formula ~Pr(x, Phi) is
provable.

[...]

> 5. Applying 4 to the formula ~Pr, we have
>
> G <-> ~Pr(#G)
>
> So, what is the G', G'', etc. that you are talking about?


I have called #G, G'. G'' comes in when we transform #G into the
Goedel number of an equivalent statement.


Date Subject Author
9/21/09
Read New essay on Goedel's Incompleteness Theorem
Bill97
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
george
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
Aatu Koskensilta
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
LauLuna
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/21/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/22/09
Read Goedel's Incompleteness Theorem Found to be Complete
Guest
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
LauLuna
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/25/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
LauLuna
9/22/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
David C. Ullrich
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/26/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
David C. Ullrich
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Aatu Koskensilta
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
george
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
george
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Aatu Koskensilta
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/28/09
Read Re: New essay on Goedel's Incompleteness Theorem
ross.finlayson@gmail.com
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Aatu Koskensilta
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
bogus address
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Tim Little
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
David C. Ullrich
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
David C. Ullrich
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Tim Little
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/29/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Frederick Williams
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Aatu Koskensilta
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
namducnguyen
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
ross.finlayson@gmail.com
9/23/09
Read Re: New essay on Goedel's Incompleteness Theorem
John Jones
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
LauLuna
9/24/09
Read Re: New essay on Goedel's Incompleteness Theorem
Newberry
9/27/09
Read Re: New essay on Goedel's Incompleteness Theorem
george
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
David Libert
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Tim Little
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
ross.finlayson@gmail.com
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Marshall
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough
9/30/09
Read Re: New essay on Goedel's Incompleteness Theorem
Scott
10/1/09
Read Re: New essay on Goedel's Incompleteness Theorem
Daryl McCullough

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.