Re: Raatikainen's critique of Chaitin

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 09/06/04 

Date: 6 Sep 2004 09:59:33 -0700

Robin Chapman <rjc@ivorynospamtower.freeserve.co.uk> wrote in message news:<chh5tg$grp$1@south.jnrs.ja.net>...
> >> The fact is that mathematicians read Chaitin and see no striking, deep
> >> nor relevant (to their work) conclusions.
> >
> > Not necessarily because there are no striking deep nor relevant
> > conclusions but more because they don't understand them.
>
> Because his theorems are exactly the results you would
> expect in the context; footnotes to Godel, Church and Turing.

Footnotes. You call his AIT monograph a collection of footnotes? There
are some quite serious and elegant theorems there. I wonder what you
are working on that you would not call "footnotes to X" then.

I can call all of 20th century mathematics as footnotes to Pythagoras,
or all philosophy as footnotes to Plato and Aristotle... How accurate
would that be except being an amusing reflection of the intricate
relations to history? As I detected before, this thread has
degenerated into a mudfest. Maybe you need another version of Peter
Olcott to busy yourselves with! You are too accustomed to flamewars,
rather than conducting sincere investigation of X's work.

Besides, I think Chaitin has shown a great deal of effort in humility,
he attributes the fundamental ideas to such great minds as Leibniz and
Borel in his book "Omega". His work indeed seems like formalization of
Leibniz's statements, and has relevance also to questions asked by
Godel.

In some philosophy papers, much less rigorous and "intuitive"
arguments about epistemology were given. For instance Putnam's
somewhat horrid arguments about any computation being anywhere. It's
always funny to watch how people resist to strong arguments, and have
no difficulty with weak arguments when it suits them.

Your posts made me realize that my task is much more difficult than it
seems. I want to erase Platonist tendencies from mathematics, e.g.
decisively eliminate the idea of God and heaven. If you can't
understand that Chaitin's results elaborately show that there is
randomness in the heart of mathematics and idealized reasoning in
general, *then* it would be impossible for folks like you to
appreciate that mathematical realism is bankrupt. Chaitin's work is
not just a collection of footnotes, I think.

Regards, 

--
Eray Ozkural

Relevant Pages

  • Re: Raatikainens critique of Chaitin
    ... You call his AIT monograph a collection of footnotes? ... > are some quite serious and elegant theorems there. ... I want to erase Platonist tendencies from mathematics, ... > decisively eliminate the idea of God and heaven. ...
    (sci.math)
  • Re: Raatikainens critique of Chaitin
    ... You call his AIT monograph a collection of footnotes? ... > are some quite serious and elegant theorems there. ... I want to erase Platonist tendencies from mathematics, ... eliminate the idea of God and heaven, then we're not on the same team. ...
    (sci.math)
  • Re: Raatikainens critique of Chaitin
    ... >> Footnotes to Godel indeed. ... > In my mind it has something to do. ... It remains the case that god/heaven has nothing to do with mathematics. ...
    (sci.math)
  • Re: Package Fancythm: tester & texperts wanted
    ... there any reason for adding one more package for theorems? ... great to have enhanced framed package instead which deals correctly ... footnotes in them are close to impossible. ... For this problem, a trick is to separate to \footnotemark, that you place in the theorem, and the corresponding \footnotetext, that you place right after. ...
    (comp.text.tex)