[FOM] inconsistency of P
panu.raatikainen at helsinki.fi
Sat Oct 1 00:32:47 EDT 2011
> Basically, in order for Chaitin's theorem (10) to hold, the
> Kolmogorov complexity of the consistent theory T has to be less than
> So far as I know, the concept of the "Kolmogorov complexity of a
> theory", as opposed to the Kolmogorov complexity of a number, is
> 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.
Ph.D., University Lecturer
Docent in Theoretical Philosophy
Department of Philosophy, History, Culture and Art Studies
P.O. Box 24 (Unioninkatu 38 A)
FIN-00014 University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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