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.independent

Topic: Godel Incompleteness Theorem
Replies: 172   Last Post: May 2, 2013 2:49 AM

Advanced Search

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

Posts: 6,964
Registered: 2/26/05
Re: Godel Incompleteness Theorem
Posted: Mar 25, 2009 5:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mar 25, 2:10 pm, barry barrett <barry3...@hotmail.com> wrote:

> There are two proofs here. 1. The incompleteness of P and 2. The General Incompleteness of P-like systems.
> I still don't see how you can call the proof of 2 (in Godel's original paper) "constructivist" by any
> definition of "constructivist" I've see.


Whether in the original paper or not, all we have to do is define 'P-
like system' (such as we do when we say such things as "a recursively
axiomatized theory adequate for a certain amount of
arithmetic" (where, 'a certain amount of arithmetic' may be given some
definition)), then, for any arbitrary consistent P-like system, we use
Godel's method to construct an undecidable sentence.

That is, GIVEN an arbitrary hypothetical consistent P-like system
talked about with the variable 'S', we can not only prove that there
is an undecidable sentence for S, but moreover we can DEFINE that
undecidable sentence with a definition that has no free variables
other than 'S'. What version of constructivism disallows that as
constructive?

> Maybe there are degrees of constructivism. I can imagine a certain type of constructivist accepting this.
> To put it succinctly: how could you accept this, but not accept proof by contradiction?


What does that have to do with constructivist rejection of non-
constructivist proof by contradiction?

> "Providing a constructive method" to prove x (in all cases where 1 & 2 apply) is not the same as providing
> a constructive proof of x for all those cases.


What does that have to do with the claim that Godel's proof (given
that we provide some formulations of 'P-like system') is constructive?
Given an arbitrary P-like system S, we construct an undecidable
sentence for S. Of course, there are infinitely many such systems S,
so we can't, as humans, perform this construction for each individual
such system. But constructivism doesn't require us to that. It is
sufficient that we prove for an arbitrary S and then apply "universal
generalization" to conclude that for ANY such system S there is an
undecidable sentence.

> So I half agree with you. It is somewhat constructive because it at least provides you with the method to
> construct the undecidable proposistion for a any P-like system.


I don't know what "other half" there is.

> Would you at least grant me that the proof that 1. ((P is incomplete)) is more constructive in nature then
> 2. ((the proof of general completeness))?


I don't know about DEGREES of constructivity (there very well could be
such a thing though I am not informed as to it), but the general proof
is constructive by ordinary constructivism such as by the BHK
interpretation.

MoeBlee



Date Subject Author
7/21/08
Read Godel Incompleteness Theorem
thirdmerlin@hotmail.com
7/21/08
Read Re: Godel Incompleteness Theorem
Jesse F. Hughes
7/21/08
Read Re: Godel Incompleteness Theorem
G.E. Ivey
7/21/08
Read Re: Godel Incompleteness Theorem
Gerry Myerson
7/21/08
Read Re: Godel Incompleteness Theorem
Jesse F. Hughes
7/22/08
Read Re: Godel Incompleteness Theorem
Gc
7/22/08
Read Re: Godel Incompleteness Theorem
Paul Epstein
7/29/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
7/29/08
Read Re: Godel Incompleteness Theorem
Gerry Myerson
8/4/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
7/29/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/2/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/2/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/3/08
Read Re: Godel Incompleteness Theorem
Gerry Myerson
8/8/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/8/08
Read Re: Godel Incompleteness Theorem
Joshua Cranmer
8/9/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/9/08
Read Re: Godel Incompleteness Theorem
Joshua Cranmer
8/10/08
Read Re: Godel Incompleteness Theorem
Gerry Myerson
8/4/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/8/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/8/08
Read Re: Godel Incompleteness Theorem
Joshua Cranmer
8/9/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/12/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/12/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/18/08
Read Re: Godel Incompleteness Theorem
David R Tribble
8/19/08
Read Re: Godel Incompleteness Theorem
Jose Carlos Santos
8/19/08
Read Re: Godel Incompleteness Theorem
Gc
8/19/08
Read Re: Godel Incompleteness Theorem
Jose Carlos Santos
8/21/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/21/08
Read Re: Godel Incompleteness Theorem
Jose Carlos Santos
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
7/29/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
7/29/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
7/29/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/2/08
Read Re: Godel Incompleteness Theorem
Gc
8/3/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/3/08
Read Re: Godel Incompleteness Theorem
David Formosa (aka ? the Platypus)
8/12/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/3/08
Read Re: Godel Incompleteness Theorem
Gc
8/4/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/8/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/8/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/15/08
Read Re: Godel Incompleteness Theorem
thirdmerlin@hotmail.com
8/15/08
Read Re: Godel Incompleteness Theorem
Joshua Cranmer
8/15/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/18/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/18/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/18/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/19/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
5/2/13
Read Re: Godel Incompleteness Theorem
b9704084@hotmail.com
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/20/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/21/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/20/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/21/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/21/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/21/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/19/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
Jesse F. Hughes
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/20/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/22/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/22/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/28/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/29/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/18/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/18/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Herman Jurjus
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Herman Jurjus
8/18/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/18/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/18/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
LauLuna
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/20/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/20/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/20/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/21/08
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
8/21/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/19/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/19/08
Read Re: Godel Incompleteness Theorem
Mike Kelly
8/19/08
Read Re: Godel Incompleteness Theorem
LauLuna
8/19/08
Read Re: Godel Incompleteness Theorem
LauLuna
8/19/08
Read Re: Godel Incompleteness Theorem
LauLuna
8/19/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/19/08
Read Re: Godel Incompleteness Theorem
Gc
8/19/08
Read Re: Godel Incompleteness Theorem
puppet_sock@hotmail.com
8/28/08
Read Re: Godel Incompleteness Theorem
Jack Markan
8/29/08
Read Re: Godel Incompleteness Theorem
Zim Olson
8/29/08
Read Re: Godel Incompleteness Theorem
Zim Olson
8/30/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
8/30/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
9/1/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/2/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
9/5/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/5/08
Read Re: Godel Incompleteness Theorem
Jesse F. Hughes
9/5/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
9/7/08
Read Re: Godel Incompleteness Theorem
tchow@lsa.umich.edu
8/30/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/4/08
Read Re: Godel Incompleteness Theorem
Jack Markan
9/5/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/5/08
Read Re: Godel Incompleteness Theorem
Jack Markan
9/7/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/7/08
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
9/8/08
Read Re: Godel Incompleteness Theorem
Jack Markan
9/8/08
Read Re: Godel Incompleteness Theorem
Jack Markan
2/27/09
Read Re: Godel Incompleteness Theorem
contact080501@jamesrmeyer.com
2/27/09
Read Re: Godel Incompleteness Theorem
A N Niel
3/17/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/17/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/17/09
Read Re: Godel Incompleteness Theorem
Jesse F. Hughes
3/23/09
Read Re: Godel Incompleteness Theorem
barr barrett
3/23/09
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
3/24/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/24/09
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
3/24/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/25/09
Read Re: Godel Incompleteness Theorem
Aatu Koskensilta
3/25/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/25/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/25/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/25/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/25/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/25/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/26/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/26/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/26/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/27/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/27/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/27/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/27/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/28/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/30/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/30/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/31/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/31/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/31/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/31/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/31/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/31/09
Read Re: Godel Incompleteness Theorem
Jack Markan
3/31/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/31/09
Read Re: Godel Incompleteness Theorem
barry barrett
3/31/09
Read Re: Godel Incompleteness Theorem
Jack Markan
4/1/09
Read Re: Godel Incompleteness Theorem
barry barrett
4/1/09
Read Re: Godel Incompleteness Theorem
barry barrett

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.