[FOM] inconsistency of P and extreme formalism
Panu Raatikainen
panu.raatikainen at helsinki.fi
Tue Oct 11 02:05:07 EDT 2011
Lainaus "Richard Heck" <rgheck at brown.edu>:
> What's the weakest natural theory in which you can "do syntax" to a
> reasonable degree? And here, so far as I understand, the consensus
> answer is something like:
> I\Delta_0 + \omega_1 or Buss's S^1_2. Both of these are adequate for
> talk about interpretations (in the syntactic sense) of one theory in
> another and to prove things like: If B can be interpreted in T, then, if
> Con(T), then Con(B)---assuming T and B have "nice" axiomatizations, at
> least.
It would be interesting to know whether this holds for Nelson's Q_0^*
too, and in particular, whether Q_0^* can "know" that a subtheory of
it, with only bounded rank-and-level proofs, is contained in it.
It seems to me that this would make all the difference for the correct
analysis of Nelson's attempted inconsistency proof...
All the Best
Panu
--
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
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/
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