[FOM] Diagonalization Does Not Deliver Self-Reference

[praatika@mappi.helsinki.fi]

Dear Richard!

you wrote:

> However, as is obvious from quick consideration of the usual proofs of 
> the diagonal lemma, A is not a biconditional. It therefore has no rhs, 
> and since such syntactic facts are provable, A itself is refutable. The 
> case is, obviously, similar with (2).
> 
> The reason we fail to formalize (1) and (2) using diagonalization is 
> that diagonalization does not produce a self-referential sentence. 

I have not really thought this through properly, but the following occured 
to me: I wonder whether Vann McGee's trick which provides, for any 
sentence, a T-biconditional equivalent with the sentence, would help?

Best

Panu

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

E-mail: panu.raatikainen at helsinki.fi
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm