[FOM] sentences which talk about themselves
Randall Holmes
holmes at diamond.boisestate.edu
Fri Oct 17 12:25:43 EDT 2003
Dear FOM colleagues,
The analysis of Godel sentences might benefit from following the
approach of Quine in _Mathematical Logic_ (in the last chapter on
"protosyntax", I seem to recall), where he suggests that the correct
approach is to develop a theory whose objects include the expressions
of its own language. This allows the use of the identity coding for
some purposes [:-)] and also makes it easier to talk inside the theory
about what codings in (e.g.) arithmetic might exist for expressioms of
the language.
A modest proposal: consider a higher-order logic or type theory in
which the base type (or one of the base types) is the type of
well-formed formulas of the language of the theory. In such a theory
one could discuss codings quite rigorously inside the theory itself.
--Randall Holmes
More information about the FOM
mailing list