[FOM] synonymity

[praatika@mappi.helsinki.fi]

Dear Colleagues

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 
understood notion.

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Montague's unpublished dissertation, where 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 
groups...

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...

Best


Panu  


Panu Raatikainen
PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki

Address: 
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Finland

E-mail: panu.raatikainen at helsinki.fi

http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm