Re: Raatikainen's critique of Chaitin

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 09/12/04 

Date: 12 Sep 2004 14:37:24 -0700

Torkel Franzen <torkel@sm.luth.se> wrote in message news:<vcb8ybfiozm.fsf@beta19.sm.ltu.se>...
> cafeinst@msn.com (Craig Feinstein) writes:
>
> > Correction. I should have said "any FAS that is as powerful as PA or
> > more powerful than PA".
>
> No, you should have removed the unnecessary assumption that the
> system has only a finite number of axioms.

It has never been the suggestion that the number of axioms, hence the
axiom string is finite. Instead, the suggestion has been that the
Kolmogorov complexity of the axiom schema is finite, all along,
regardless of the length of the axiom string. Once more, you have
skipped upon the exact definition to arrive at a conclusion you would
prefer.

Take care, 

--
Eray Ozkural

Relevant Pages

  • Re: Set inclusion and membership
    ... even with an "anti-foundation" axiom) is perfectly workable. ... then de Bruijn's suggestion wouldn't be so bad. ... You can show the contradiction easily enough without the empty set. ...
    (sci.math)
  • Re: Raatikainens critique of Chaitin
    ... >> axiom string is finite. ... the suggestion has been that the ... earlier discussion that there are many valid axiom schema). ... But, perhaps you are right, insisting on a finite axiom string, we can ...
    (comp.theory)
  • Re: Raatikainens critique of Chaitin
    ... >> axiom string is finite. ... the suggestion has been that the ... earlier discussion that there are many valid axiom schema). ... But, perhaps you are right, insisting on a finite axiom string, we can ...
    (sci.math)
  • Re: Raatikainens critique of Chaitin
    ... > cafeinst@msn.com (Craig Feinstein) writes: ... It has never been the suggestion that the number of axioms, ... Kolmogorov complexity of the axiom schema is finite, all along, ... regardless of the length of the axiom string. ...
    (sci.math)
  • Re: Another Reason Why Collatz is Unprovable
    ... Craig Feinstein wrote: ... # An axiom that I am using in my Collatz paper could be stated: ... # Anyone who disputes this axiom is fooling himself or herself. ... Gerhard J. Woeginger http://www.win.tue.nl/~gwoegi/ ...
    (sci.math)