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

[Hartley Slater]

At 12:00 PM -0400 27/7/06, laureano luna wrote:
>   >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.
>    ....
>   I cannot come to see how a sentence could express more than one 
>proposition; so, I'm highly interested in further details.


Forgive me, first of all: I was rather rushed, and there were a 
couple of errors in my FOM message before which should be corrected. 
First the Charles Parsons piece is in another book by Martin: Recent 
essays on truth and the liar paradox / edited by Robert L. Martin 
Oxford : Clarendon Press ; New York : Oxford University Press, 1984. 
Second the 'a' and the 'x' in the reformulated T-scheme should be the 
same, making it, for instance:
If (r)(Sxr iff r=*p) then Tx iff p.
Sentences which do not have just one meaning include indexical ones 
like 'that flower is pink', and semantically ambiguous ones like 
'There are flowers in the bank'.  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).  Of course, conditionalising the T-scheme in the 
manner above gives a reductio argument, which works in all 
paradoxical cases.  Papers of mine where this kind of thing is 
treated further include:

  'Prior's Analytic Revised' Analysis, 61 (2001), 86-90.

  'Syntactic Liars', Analysis 62 (2002), 107-9.

  'Namely-Riders: an Update' Electronic Journal of Analytic Philosophy 
(2002): (http://
ejap.louisiana.edu/EJAP/2002/Slater.html).

'Tarski's Hidden Assumption', Ratio, XVII (2004), 84-89.

'Ramseying Liars', Logic and Logical Philosophy, 13 (2004), 57-70.

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