praatika at mappi.helsinki.fi
Mon Feb 10 06:54:02 EST 2003
I got recently very interested in the notion of
"synonymity" between theories (in the sense of
Karel de Bouvere). This notion was discussed in
FOM a little bit by Alasdair Urquhart, Allen Hazen
and Harvey Friedman some two years ago.
I would now like to return to it. It seems to
be a rather little known and incompletely
The notion apparently derives from Richard
Montague's unpublished dissertation, where
synonymous theories were called bilaterally
interpretable. Anyone familiar with Montague's
dissertation? Did Montague prove any interesting
results concerning this notion?
Does anyone know any interesting pairs of
theories, say, from arithmetic or set theory,
which are synonymous?
- the standard examples are just different
formulations of Boolean algerbra, or axioms for
Harvey wrote (27 Mar 2001):
> But I also proved some results about showing that
> different notions of interpretability in this context
> are the same. I believe I can show that under very
> general conditions, mutually interpretable is equivalent
> to synonymity. More later, if you are interested.
I would be very interested in hearing more...
PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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