Re: Provable in T?


Rupert wrote:
Here you need to pause to divulge your professional understanding
of the DIFFERENCE between G_T and Con(T).
For civilians, G_T *is* Con(T).

G_T is the diagonalization of the predicate "the diagonalization of the
predicate with Goedel number x is unprovable".

Why you want to allege that this in some important sense might
DIFFER from Con(T) is mysterious, since ANY statement alleging the
unprovability of ANY other statement is equivalent to the consistency
of T,
since, by definition, "T is inconsistent" means that T proves
everything.
Whether you instantiate the unprovable statement to something simple
or something complicated is NOT the important point, at this
point. The important point is that it does NOT matter what you
instantiate it to.

.

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