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## Re: [ontolog-forum] Axiomatic ontology

 To: Pat Hayes , standard-upper-ontology@xxxxxxxxxxxxxxxxx, ontolog-forum@xxxxxxxxxxxxxxxx Avril Styrman Thu, 31 Jan 2008 21:04:45 +0200 <1201806285.47a21bcdd1608@xxxxxxxxxxxxxxxx>
 ```Pat,    (01) Lainaus Pat Hayes :    (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) ```
 Current Thread Re: [ontolog-forum] Axiomatic ontology, (continued) Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Ed Barkmeyer Re: [ontolog-forum] Axiomatic ontology, Sharma, Ravi Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Avril Styrman <= Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes