[FOM] sentences talking about themselves

Randall Holmes holmes at diamond.boisestate.edu
Fri Oct 17 12:42:19 EDT 2003

Dear FOM Colleagues,

In particular, in a type theory one of whose base types is the
collection of expressions in its own language (or a supertype of this,
such as the collection of character strings), it is perfectly possible
to define exactly what is meant by a sentence A expressing the fact
that A itself is provable (with a given collection of proof rules),
since "A is provable (with a given set of rules)" can be expressed in
the language of this theory, and so can the function taking an
expression A to the expression meaning "A is provable".

--Randall Holmes

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