[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

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