[FOM] Inconsistency of P
panu.raatikainen at helsinki.fi
Mon Oct 3 02:47:08 EDT 2011
Lainaus "Monroe Eskew" <meskew at math.uci.edu>:
> I was not claiming "K(n)<c" is true in my example.
I guess I was too quick.
In any case, the essential point is that for all Sigma_1 complete
theories, (simple) consistency equals to Pi_1 soundness, i.e. that the
theory does not prove any false Pi_1 sentences.
If, as in our original example, a theory T is inconsistent, because it
proves "K(n)>c" for some n, it must be that it proves *some* false
Pi_1 sentence F as a consequence.
So if a subtheory S also proves "K(n)>c" but is consistent, it must
either be Sigma_1 incomplete, or somehow block the derivation of F
All the Best
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
More information about the FOM