Re: Panu Raatikainen's review of two of Chaitin's books.

From: *** T. Winter (***.Winter_at_cwi.nl)
Date: 05/19/04 

Date: Wed, 19 May 2004 02:05:05 GMT

I am sitting on the sideline and do not understand:

In article <fa69ae35.0405180608.34b19f82@posting.google.com> erayo@bilkent.edu.tr (Eray Ozkural exa) writes:
> Torkel Franzen <torkel@sm.luth.se> wrote in message news:<vcbiseu40ev.fsf@beta19.sm.ltu.se>...
...
> > Raatikainen doesn't attack any proofs. Why not comment on something
> > actually stated or argued by Raatikainen?
...
> ABSTRACT. The aim of this paper is to comprehensively question the
> validity of the standard way of interpreting Chaitin's famous
> incompleteness theorem, which says that for every formalized theory of
> arithmetic there is a finite constant c such that the theory in
> question cannot prove any particular number to have Kolmogorov
> complexity larger than c.

Where is the attack on the proof? As far as I see, there is an attack
on the *interpretation*.

> This abstract claims that Theorem LB in AIT is wrong (incompleteness
> of formal axiomatic systems).

Not as far as I can see. It only claims that the standard *interpretation*
is wrong.

> Don't tell me that he is just wrestling with an interpretation, he is
> not. The guy is openly saying that "I show that the limiting constants
> provided by the theorem do not in any way reflect the power of
> formalized theories, but that the values of these constants are
> actually determined by the chosen coding of Turing machines, and are
> thus quite accidental" which means that Theorem LB is wrong!

Eh? Does Chaitkin claim in LB that the constants are independent of
the Turing machines chosen? If so, where? I think that is the actual
question from Torkel Franzen. 

-- 
*** t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~***/