Re: Sorry Godel - All Truths are Provable


Charlie-Boo wrote:
Rupert wrote:
Charlie-Boo wrote:
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.

No, that's not obvious at all. It's not true.

It is obvious and not true (as it was obvious to Hilbert.)

Well, it's not obvious to me. Why is it obvious?

That still
does not explain where logic fails us. Where is the "point of
disconnect"?

We all know from the outside that true does not mean provable (I have
developed at least a half dozen proofs of that myself.) But if your
car doesn't start, don't you look under the hood to see where the
problem is?

C-B

Why
not?

C-B

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Sorry Godel - All Truths are Provable
    ... Rupert wrote: ... Let w be any true sentence and v be any provable sentence. ... So w^v is not logically equivalent to v unless ... then they obviously would have the same provability. ...
    (sci.logic)
  • Re: Sorry Godel - All Truths are Provable
    ... Charlie-Boo wrote: ... Let w be any true sentence and v be any provable sentence. ... So w^v is not logically equivalent to v unless ... then they obviously would have the same provability. ...
    (sci.logic)
  • Re: Sorry Godel - All Truths are Provable
    ... So w^v is not logically equivalent to v unless ... So if two wffs have the same ... The idea that truth and provability are defined so differently because ...
    (sci.logic)
  • Re: Sorry Godel - All Truths are Provable
    ... Daryl McCullough wrote: ... Let w be any true sentence and v be any provable sentence. ... So w^v is not logically equivalent to v unless ... then they obviously would have the same provability. ...
    (sci.logic)
  • Re: Sorry Godel - All Truths are Provable
    ... So w^v is not logically equivalent to v unless ... So if two wffs have the same ... The idea that truth and provability are defined so differently because ...
    (sci.logic)