To:  Avril Styrman <Avril.Styrman@xxxxxxxxxxx> 

Cc:  ontologforum@xxxxxxxxxxxxxxxx 
From:  Pat Hayes <phayes@xxxxxxx> 
Date:  Thu, 31 Jan 2008 17:03:00 0600 
Messageid:  <p0623090ec3c7ffeb0076@[10.100.0.14]> 
At 11:12 PM +0200 1/31/08, Avril Styrman wrote:
> > Gödel specifically used this scheme at two levels: first, Yes, it strongly seems that it does. As it does not, in fact, I am at a loss to explain how you get
this impression. The passage is referring to goedel numbering, which
is a fairly elaborate algorithm for associating each _expression_ and
each formal proof with a unique number, in such a way that statements
about proofs and sentences (such as that this sentence is the
conclusion of that proof) can be made exactly equivalent to statements
about numbers, statements which can be stated and proved in formal
arithmetic. Nothing there about SELF reference.
I'm not being arrogant, but there comes a point when the level of
mutual comprehension is so utterly beyond what is necessary for a
rational conversation to take place, that no normal response is
possible. It's not that I disagree with you: I believe, from the
evidence so far, that your grasp of the topic is so weak that there is
nothing in what you say to agree or disagree with. And there are no
'issues' connected with the Goedel proof: it is a thoroughly
investigated piece of modern mathematics, now over half a century
old.
> I see where you are coming from (that in Well, first, that as stated is clearly false, as one could reason
logically without even knowing anything about arithmetic at
all. (I have written programs which satisfy this description.) But
more to the point, what is the relevance of this simple arithmetic
fact? You introduced it into the discussion, but I cannot see
why.
but this is NOT selfreference. No, it isn't. Read it again, or read any of the popular books
about Goedel's theorem. It has nothing whatever to do with
selfreference (or with proofs being trivial or circular, see below.)
And it does not refer to the provability of simple facts: it
establishes the NONprovability of some rather complex arithmetic
facts.
It is the _same_ as that it cannot be proved at all. Not in the sense of 'prove' that is used in the Goedel proof (and
throughout mathematics.)
If a proof of X requires self You mean, if the conclusion of a proof is one of its own
premises, it is not a proof at all. I agree with the spirit of this,
although I'd prefer to say it is a trivial or circular or vacuous
proof. But that is not the same topic as selfreference.
Pat
 
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