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

[laureano luna]

On Fri, 28 Jul 2006 08:29:00 Hartley Slater wrote:
   
  >Common examples of self-referential 
>sentences, such as 'this (very) sentence is false' fall directly into 
>the first category, since the referent of the 'this (very) sentence' 
>has to be determined with a gesture, and might be to some other 
>sentence.  If one gives names to sentences there is the same problem, 
>since it is not in 'sentence 1001 is false' itself that it is 
>sentence 1001, if it is, and that very same sentence might be given a 
>different meaning using a different numbering system.  In fact it can 
>be proved that there cannot be syntactic self-reference (see the 
>second paper below).  
   
  If I have understood, you mean that the indexical term "this" in "this sentence cannot be proven true" cannot be disambiguated within the sentence itself, so that the sentence remains, as other indexical do, a kind of propositional function that will only yield a propositional value by means of contextual disambiguation.
   
  I suppose this is what you mean by "there cannot be syntactic self-reference"; For this I will examine the paper indicated. 
   
  But assume "this very sentence cannot be proven true" or "the current sentence cannot be proven true" (ad lib) succeeds in achieving self-reference. Let us call it "K". Under that condition K seems to express no proposition. I have recently devised the following argument:
   
  1st. K cannot be proven true: if K were proven true it would be simultaneously true and false.
   
  2nd. If K expresses a proposition, then what K says has been proven true in 1st, so that K must be both true and false.
   
  Thanks again,
   
  Laureano Luna Cabañero 

 		
---------------------------------

LLama Gratis a cualquier PC del Mundo.
Llamadas a fijos y móviles desde 1 céntimo por minuto.
http://es.voice.yahoo.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: /pipermail/fom/attachments/20060729/453a46b0/attachment.html