[FOM] Inconsistency of P
Monroe Eskew
meskew at math.uci.edu
Sat Oct 8 16:11:10 EDT 2011
On Thu, Oct 6, 2011 at 8:59 PM, Panu Raatikainen
<panu.raatikainen at helsinki.fi> wrote:
>
>> Now T proves S is consistent and Sigma_1 complete.
>> So T proves S does not prove K(n) > c(T).
>
> I understand that we now assume again that T really is inconsistent. Then it
> is not very informative that it can prove these things - because it can
> prove any claim whatsoever.
>
Sorry if I was unclear, but no, we are not assuming T is inconsistent
here. The example where T is inconsistent serves to illustrate what
can be deduced in T, even when T is consistent. Because when working
in T, the consistency of T is always an open question. Working within
T you cannot refute the possibility that there is a consistent S
subtheory of T, extending Q, which proves K(n)>c(T) for some n.
Best,
Monroe
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