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## Re: [ontolog-forum] Context, at last!

 To: "[ontolog-forum]" Duane Nickull Fri, 17 Jun 2005 15:35:46 -0700 <42B35042.2060902@xxxxxxxxx>
 ```Chris:    (01) This entire thread highlights my basic assertion that the context of "perceiver" is really a core principle to qualify any assertion.    (02) When you state x=y, if I am only perceiving a two dimensional characters of an alphabet written on a paper, I disagree since x is clearly x and y is clearly y. From my point of perception, I can clearly see that an x looks different that a y and if I do not know they are variables for something else, I would have to perceive them as different.    (03) If x represents something else, as does y, then it may be true that x = y pending on the point of view. If x and y are different monikers for the same object, then it is true if I perceive only the object itself. However, if I perceive the object plus the distinction that one group of people refer to it as x and another refer to it as y, then I could (probably contentiously) argue that from their perception, x and y are not the same since x and y have different names.    (04) Nevertheless, your logic is equally infallable. Anyone perceiving ID_FOL: x = y.. will agree    (05) It would have been cool to have this knowledge to argue with algebra teachers in high school 25 years ago. I could have been (more) disruptive by challenging their assertions ;-)    (06) Duane    (07) Chris Menzel wrote:    (08) >On Fri, Jun 17, 2005 at 12:26:04PM -0700, Duane Nickull wrote: > > >>Chris Menzel wrote: >> >> >> >>>ID: if x = y, then anything true of x is true of y. >>> >>> >>> >>Disagree. >> >> > >Well, we haven't really fixed the context rigorously enough for there to >be anything to disagree about. In the context of standard first-order >logic with its usual extensional semantics, the above principle is >rendered schematically as follows: > > For any well-formed formula A not containing the variable y, the > following is an axiom: > > ID_FOL: x = y -> (A -> A'), > > where A' is the result of replacing every free occurrence of x in A > with an occurrence of y. > >And the fact is that, on the standard, extensional semantics for >first-order logic, every instance of ID_FOL is valid. That's not >something about which one can rationally disagree; it's just a >mathematical fact about first-order languages and their models. > >What one might disagree with is that the principle ID (properly >formalized) is valid in every logical context. And that is exactly what >the counterexamples I mentioned were designed to show -- ID fails, or at >least appears to fail, in contexts involving belief and necessity (among >others). > > > >>Most things may be the same but it is still instance y as opposed to >>instance x, therefore his axiom has a logic error. >> >> > >You lost me there, I'm afraid. > > > >>They are still two different things. It may be better to state: >> >>if x = y, then x is y and both should be called x. >> >> > >That rather seriously confuses the *value* of the variable "x" with "x" >itself. It also seems implausible -- Mark Twain is Sam Clemens, but I >don't see any particular reason why he *should* be called by either >handle. (And aside from these points, the development of theories that >include semantical notions like "called" are fraught with difficulty.) > > > >>Also - an important consideration of context is perceiver. >> >> > >Yes, that can be important. That is one reason there is a lot of active >research on formal theories of context at the moment. > > > >>To you and I, a coffee table is a solid item, to a neutrino, it is a >>lot of open space interspersed with a few bits of solid matter... >> >> > >True enough, so a neutrino's ontology of your front room will probably >look a lot different than your front room ontology! Note, though, that >the notion of context is often just assumed in the background of an >ontology -- we often create ontologies *from the perspective of a given >perceiver or set of perceivers*, e.g., domain experts in a mfg shop >floor. For these cases, the notion of context needn't play an explicit >role. More and more, though, we have a need to represent multiple >ontologies arising out of different contexts within a *single* >framework, and this requires explicit mechanisms that enable us to group >pieces of information according to context -- and that's exactly what >formal theories of context are attempting to provide. > >Cheers! > >Chris Menzel > >_________________________________________________________________ >Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ >Subscribe/Unsubscribe/Config: >http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ >Shared Files: http://ontolog.cim3.net/file/ >Community Wiki: http://ontolog.cim3.net/wiki/ >To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx > > > _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Unsubscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (09) ```
 Current Thread [ontolog-forum] Context, at last!, Nicolas F Rouquette Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Nicolas F Rouquette Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Duane Nickull Re: [ontolog-forum] Context, at last!, Duane Nickull Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Duane Nickull <= RE: [ontolog-forum] Context, at last!, Peter F Brown Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Nicolas F Rouquette Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Chris Menzel Re: [ontolog-forum] Context, at last!, Patrick Cassidy Re: [ontolog-forum] Context, at last!, Chris Menzel