[FOM] On >>this sentence cannot be proven true<<

[Hartley Slater]

At 12:00 PM -0400 25/7/06, Laureano Luna Caba?ero wrote:
>Arnon Avron wrote on Aug 22 2003 04:41:43 in the thread [FOM] Godel 
>Sentence & The Liar :
>   
>>"This sentence cannot be proven true" immediately leads to a
>>paradox if we assume (wrongly, I am convinced) that it expresses
>>a meaningful proposition.
>   
>   This is not exactly so. Call "K" the sentence at issue. The 
>assumption that K expresses a proposition, and hence that K has a 
>truth value, leads to the conclusion that K is true. Only the 
>assumption that we know that K expresses a proposition leads to a 
>paradox.
>
>   Anyway, I'm inclined to agree with Arnon Avron on the essential. I 
>also think that most probably K expresses no proposition. My concern 
>here is: can this be proven?

It can be proven that it does not express a single proposition, but 
that allows it might express more than one.  Tarski's T-scheme 
presumes that the sentences it applies to are not ambiguous - or 
indexical, for instance.  So it should explicitly involve this 
condition, and read, with 'Sx*p' as 'x says that p', and 'r' ranging 
over referential phrases to propositions:
If  (r)(Sar iff r=*p) then Tx iff p.
I have several papers in central places explaining this further 
(details available on request); there is also a major paper along the 
same lines by Charles Parsons in The Paradox of the liar,  edited by 
Robert L. Martin, Reseda : Ridgeview, 1978.
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