[FOM] Godel's Theorems

[praatika@mappi.helsinki.fi]

Charlie Volkstorf wrote:

> Panu Raatikainen wrote 5/2/02:

> > (i) There is a sentence G of L(S) which is neither provable or
> > refutable in S.
> > (ii) moreover, G is true.

> ... since the proof of (i) => (ii) is much simpler than the proof 
> of (i), I doubt if many people believe (i) but don't believe (ii), unless 
> they are unaware of this proof of (i) => (ii).  

RE: Just two remarks. First, quite many people are familiar with (i) 
without knowing at all its proof. Second, my own experience is that some 
people with even a relatively good idea of how (i) is proved have rather 
confused ideas about why exactly (ii) holds. 

I am not really willing to participate to Wittgenstein exegesis, but I 
wanted to suggest that perhaps e.g. LW and others have had some 
difficulties with understanding the step (i) => (ii), and what (ii) could 
mean. On the other hand, it is quite easy to understand the meaing of (i), 
even if its detailed proof is quite laborious.   

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