[FOM] Inconsistency of P
meskew at math.uci.edu
Mon Oct 3 02:18:06 EDT 2011
I was not claiming "K(n)<c" is true in my example. I thought you were
inferring your claim about the failure of Sigma_1-completeness from
the proposition that the Chaitin machine for T will give a witness to
K(n)<c. I showed this is not the case because the Chaitin machine is
programmed to find the *first* witness in T, not S.
On Sun, Oct 2, 2011 at 9:49 PM, Panu Raatikainen
<panu.raatikainen at helsinki.fi> wrote:
> "K(n)<c" is a Sigma_1 sentence.
> If "K(n)<c" is true, and S is Sigma_1 complete, then S proves "K(n)<c".
> That is what Sigma_1 completeness is.
> I am afraid I fail to see how any involved Chaitin machine considerations
> (or whatever) could change that...
> 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
> E-mail: panu.raatikainen at helsinki.fi
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