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## Re: [ontolog-forum] Axiomatic ontology

 To: "[ontolog-forum] " Chris Menzel Thu, 7 Feb 2008 10:18:11 -0600 (CST)
 ```On Wed, 6 Feb 2008, John F. Sowa wrote: > Avril, > ... > On the other hand, I would not recommend the following approach > for number theory:    (01) To say the least.    (02) > > Axiom 9. can be maintained, but the meaning of 'every' has to be > > interpreted to denote a totality of something around 10**120, > > or Ackermann(5 5), or something finite that can be written down > > or understood in some way.    (03) The view isn't even coherent. If Ackerman(5 5) exists, why not Ackerman(Ackerman(5 5) 5) -- a massively larger number? And of course if *that* number exists, well, you get the idea.    (04) > Many 19th century mathematicians strongly objected to that way of > talking, and I sympathize with them. But those mathematicians would > *never* agree to a fixed upper bound on the integers, such as 10**120, > Ackermann(5 5), or any other finite integer.    (05) Indeed -- which of course means that there are infinitely many finite integers, and hence that there is a set that contains them, hence a power set of that set, and off we go down the Cantorian bunny trail! :-) You may not like where that leads, but it is very hard to argue that there is a nonarbitrary point at which you can stop that line of reasoning.    (06) -chris    (07) _________________________________________________________________ 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    (08) ```
 Current Thread Re: [ontolog-forum] Axiomatic ontology, (continued) Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Christopher Menzel Re: [ontolog-forum] Axiomatic ontology, Barker, Sean (UK) Re: [ontolog-forum] Axiomatic ontology, paola . dimaio Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Avril Styrman Re: [ontolog-forum] Axiomatic ontology, Christopher Menzel Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Chris Menzel <= Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Ed Barkmeyer Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, John F. Sowa [ontolog-forum] Visualization of ontologies for business, Mills Davis Re: [ontolog-forum] Visualization of ontologies for business, matthew.west Re: [ontolog-forum] Visualization of ontologies for business, Mills Davis Re: [ontolog-forum] Visualization of ontologies for business, Adrian Walker Re: [ontolog-forum] Visualization of ontologies for business, Elisa F. Kendall