[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 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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