Re: Sorry Godel - All Truths are Provable


Daryl McCullough wrote:
Charlie-Boo says...

Let w be any true sentence and v be any provable sentence. Now |-v
since v is provable, and |-(w^v) since w^v is logically equivalent to v
since w is true.

Two statements A and B are *logically* equivalent only if the statement

A <-> B

is provable. So w^v is not logically equivalent to v unless

w^v <-> v

is provable.

Whatever! So do you agree that w^v is true iff v is true? Then what
do you call that? Anyway, the same reasoning applies. If |-P then
|-~~P and if |-P then |-P^P etc. Get it? So if two wffs have the same
truth value, then they obviously would have the same provability. Why
not?

C-B

--
Daryl McCullough
Ithaca, NY

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