On 11 Sep 2012, at 12:39, benjayk wrote:
Our discussion is going nowhere. You don't see my points and assume
I want to
attack you (and thus are defensive and not open to my criticism),
and I am
obviously frustrated by that, which is not conducive to a good
discussion.
We are not opertaing on the same level. You argue using rational,
"precise"
arguments, while I am precisely showing how these don't settle or even
adress the issue.
Like with Gödel, sure we can embed all the meta in arithmetic, but
then we
still need a super-meta (etc...).
I don't think so. We need the understanding of elementary arithmetic,
no need of meta for that.
You might confuse the simple truth "1+1=2", and the complex truth
"Paul understood that 1+1=2". Those are very different, but with comp,
both can be explained *entirely* in arithmetic. You have the right to
be astonished, as this is not obvious at all, and rather counter-
intuitive.
There is no proof that can change this,
and thus it is pointless to study proofs regarding this issue (as
they just
introduce new metas because their proof is not written in arithmetic).
But they are. I think sincerely that you miss Gödel's proof. There
will be opportunity I say more on this, here, or on the FOAR list. It
is hard to sum up on few lines. May just buy the book by Davis (now
print by Dover) "The undecidable", it contains all original papers by
Gödel, Post, Turing, Church, Kleene, and Rosser.
Bruno
http://iridia.ulb.ac.be/~marchal/
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