[Top] [All Lists]

Re: [ontolog-forum] Axiomatic ontology

To: Pat Hayes <phayes@xxxxxxx>, standard-upper-ontology@xxxxxxxxxxxxxxxxx, ontolog-forum@xxxxxxxxxxxxxxxx
From: Avril Styrman <Avril.Styrman@xxxxxxxxxxx>
Date: Thu, 31 Jan 2008 21:04:45 +0200
Message-id: <1201806285.47a21bcdd1608@xxxxxxxxxxxxxxxx>
Pat,    (01)

Lainaus Pat Hayes <phayes@xxxxxxx>:    (02)

> 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.    (03)

So, prove it Pat! Prove it here. After that I'll prove that you 
used the very ability to distinguish between I and II.    (04)

> b. "the things that are to be proved have to be 
> used in their own proof"  is not the idea of 
> Goedel numbering    (05)

What else is the idea in the end, than to prove that
proving X requires self-reference?    (06)

This is copied from Wikipedia:    (07)

 Gödel specifically used this scheme at two levels: first, 
 to encode sequences of symbols representing formulas, and 
 second, to encode sequences of formulas representing proofs. 
 This allowed him to show a correspondence between 
 statements about natural numbers and statements about the 
 provability of theorems about natural numbers, the key 
 observation of the proof.    (08)

If the key idea is not self-reference, then what is it?    (09)

Suppose that I'm totally wrong. This does not change the fact 
that proving 1+1=2 requires understanding the difference of 
I and II. It does not change anything if Gödel took a longer 
road and included conventions used by modern mathematicians.
It is still the same old story: self-reference.    (010)

If you 'prove' something that is as obvious as can be like 
1+1=2, you only prove that you yourself feel more comfortable 
after having used some conventions. Tell me, do you need to 
prove that 1+1=2? Why do you? After you have proved it, do you 
feel more certain about 1+1=2?    (011)

Avril    (012)

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    (013)

<Prev in Thread] Current Thread [Next in Thread>