hg17 at columbia.edu
Wed Oct 15 17:41:03 EDT 2003
I wrote in my last message that the best way
to say what a sentence says is to repeat the sentence.
This was meant for cases that in which the semantics
is give in a straightforward way, with the usual form
of truth conditions, as in the case of the Peano language.
Cases that involve tacit presuppositions, indexicals and
demonstratives are another matter. The same goes
for liar sentences and their like, where a different token
of the same sentence can express what the original token
fails to express, as in my pointer semantics.
The Goedel sentence is a sentence in Peano, which involves connectives
and quantifiers over natural numbers; to say what it says
is to translate it literally, following, so to speak, its
structure. For this purpose, one can of course introduce shorthand
notation: auxiliary predicates that, by definition, stand
for various wffs. In no way can such a process show that
the sentence says of itself that it is not provable.
More information about the FOM