At 11:28 PM +0200 1/30/08, Avril Styrman wrote:
We do not need Gödel numbering to understand that 1+1=2
cannot be proved. It is so deeply tied with out cognitive
capabilities, that without understanding that 1+1=2, we could
not understand anything. If we try to prove that 1+1=2, we
have to use the same cognitive capabilities in the proof,
that we used when we understood that 1+1=2.
Nonsense.
This is the idea
of Gödel numbering: the things that are
to be proved have to
be used in their own proof.
Apparently you know very little about formal arithmetic or
Goedel's theorem.
a. 1+1=2 is provable in any formal arithmetic.
b. "the things that are to be proved have to be used in
their own proof" is not the idea of Goedel
numbering
c. Goedel's result has nothing at all to do with circularity in
proofs.
It is fine to be ignorant about a topic, of course, but to vent
your opinions in an authoritative way when you are so ignorant only
exhibits your ignorance to others. It is not persuasive.
Pat Hayes
Avril
-A little less formalization and a little bit of action
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