[FOM] inconsistency of P
Panu Raatikainen
panu.raatikainen at helsinki.fi
Sat Oct 1 00:32:47 EDT 2011
Tao wrote:
> Basically, in order for Chaitin's theorem (10) to hold, the
> Kolmogorov complexity of the consistent theory T has to be less than
> l.
Nelson wrote:
> So far as I know, the concept of the "Kolmogorov complexity of a
> theory", as opposed to the Kolmogorov complexity of a number, is
> undefined.
Diamondstone wrote:
> You can talk about the Kolmogorov complexity of anything that can be
> coded with a number, including any finitely axiomatizable theory
> (code the axioms with a number) or any computably axiomatizable
> theory (code the machine enumerating the axioms with a number).
Ihis is true - but it does not make sense to talk about *the*
Kolmogorov complexity of a theory, as this is totally relative to the
particular way of arithmetization, and the choice is arbitrary. You
can make the complexity of a theory T arbitrarily small, or large,
with different choices.
In particular, Tao's claim quoted above is false.
Read my:
http://www.mv.helsinki.fi/home/praatika/chaitinJPL.pdf
Best
Panu
--
Panu Raatikainen
Ph.D., University Lecturer
Docent in Theoretical Philosophy
Theoretical Philosophy
Department of Philosophy, History, Culture and Art Studies
P.O. Box 24 (Unioninkatu 38 A)
FIN-00014 University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/
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