[FOM] Godel, Wittgenstein etc.

[praatika@mappi.helsinki.fi]

[The following remarks, which I first presented in a private 
correspondence, may perhaps clarify what I said in my earlier posting.]


My point was that we can apply Godel's theorem also to a theory S about 
whose consistency we are less confident (e.g. ZFC + some new strong axiom) 
and prove the conditional:

If S is consistent, then there is a true but unprovable-in-S sentence G (in 
L(S).

So what can we then say about the truth of G (for S). I think that the 
right conclusion is that we have exactly as much (or little) reason to 
believe in the truth of G as we have reason to believe in the consistency 
of S. 

(An amusing historical example is Quine's orginal version of ML (1940) - in 
the end of the book he presented a proof of Godel's theorem for his system. 
But ML was later proved to be inconsistent. Hence his G (for ML) was 
false!) 

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