|To:||Avril Styrman <Avril.Styrman@xxxxxxxxxxx>|
|From:||Pat Hayes <phayes@xxxxxxx>|
|Date:||Thu, 31 Jan 2008 17:03:00 -0600|
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
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 self-reference (or with proofs being trivial or circular, see below.) And it does not refer to the provability of simple facts: it establishes the NON-provability 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 self-reference.
40 South Alcaniz St.
_________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|<Prev in Thread]||Current Thread||[Next in Thread>|
|Previous by Date:||Re: [ontolog-forum] Axiomatic ontology, Pat Hayes|
|Next by Date:||Re: [ontolog-forum] Axiomatic ontology, Pat Hayes|
|Previous by Thread:||Re: [ontolog-forum] Axiomatic ontology, Avril Styrman|
|Next by Thread:||Re: [ontolog-forum] [Fwd: Re: Axiomatic ontology], Pat Hayes|
|Indexes:||[Date] [Thread] [Top] [All Lists]|