# [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
> 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/