Re: Raatikainen's critique of Chaitin

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

Date: 4 Sep 2004 13:22:13 -0700

daryl@atc-nycorp.com (Daryl McCullough) wrote in message news:<chcg5r010g@drn.newsguy.com>...
> The correct statement of Chaitin's result is this:
>
> For any theory T, there is a constant real r such that
> for any Phi, T does not prove H(Phi) > r.
>

Oh my God! What real?

H : {0,1}* -> Z^+

Hello?

What do you mean by "Chaitin's result"? That is only the very first,
and the easiest theorem in the incompleteness chapter of AIT! I
suppose you did not read his work! Let's not talk about second hand
interpretations of his work (like done by the "master of logic"
Raatikainen who didn't read his work extensively, either)!

> It doesn't matter whether Phi is a theorem of T or not, T
> cannot prove that any particular statement has a very high
> entropy.
>
> The connection between entropy of a theory and strength of
> a theory (what it can prove) is very loose.

Please read Theorem C in incompleteness chapter of AIT! Here, page
210:
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cup.html

The theorem you are referring to above is Theorem LB, page 198. That
is the weakest incompleteness result that Chaitin gets! You don't even
know what Chaitin is talking about, and hence all this nonsense!!!!

What a shame!

When you are criticizing his philosophy of mathematics, you are
supposed to actually know the content of his theorems and proofs.
Otherwise, it's all small talk. 

--
Eray Ozkural