[FOM] inconsistency of P
Monroe Eskew
meskew at math.uci.edu
Sat Oct 1 13:42:00 EDT 2011
Tao's claim is that the Chaitin machine must include a proof checker
for T, which is right. He then stipulated a definition of complexity
of a theory T as the length of the smallest machine that checks proofs
in T. Modulo some basic choices on coding Turing machines, which
seems to be necessary for Kolmogorov complexity to make sense, Tao's
notion seems well-defined. Furthermore, we can assume these choices
are held constant in the context of Nelson's argument, in which I see
no mention of variations on coding.
On Fri, Sep 30, 2011 at 9:32 PM, Panu Raatikainen
<panu.raatikainen at helsinki.fi> wrote:
>
> 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
>
>
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