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## Re: [ontolog-forum] Inconsistent Theories

 To: "[ontolog-forum]" Jawit Kien Mon, 8 Feb 2010 14:34:14 -0600 <9f9644bb1002081234j1543a534td41bc6b6e202b527@xxxxxxxxxxxxxx>
 So to be a bit pedantic but to show the confusion that can happen when trying to examine somethingthat is only loosely defined...On Mon, Feb 8, 2010 at 1:54 PM, Rich Cooper wrote: Example: Let the two theories be: TrueS(F,x) := ; FalseS(F,x)       := ; So that there are two theories: TrueS(F,x) is the set of Things which are believed (with current knowledge) to be in the set F for terminal vector x, while FalseS(F,x) is the set of Things which are believed NOT to be in F(x). Presumably "terminal vector" means something to Rich. Since it doesn't meananything to me, I'll make the assumption that if we have airplane terminals,it also makes sense to talk about boat or spaceship terminals, If an airplane terminal is a location that people arrive and depart from when they are traveling by airplane, then boat or spaceship terminals couldbe places that either float in water or float in space and allow transport by their corresponding mode of transportation.  If they float, then these terminals could move, and hence don't have to be anchored in place.It would then make sense to say these terminals have a vector,since a vector is made up of a direction and an angle.  When an object moves along a vector such as the unspecified terminals would move along, it would make sense to talk about the various positions or locations in 3-spaces which the terminal and group them as a set F. So the predicate TrueS() would map these sets and various vectorsand would hold when a particular terminal x and a particular set were observed.Presumably each observation would qualify as a "Thing", as you mentioned. I'm not sure what F(x) means. I guess it means a function that when given a direction and angle would produce a set of locations.  and your FalseS ()predicate would give you the infinite number of locations/positions which do not correspond to any vectors that the terminal moves along. Only a physicist can believe both true and false theories in a single situation and not think they need refining.  Then if there are any Things in both sets, something in expression1(x) is inconsistent with something in expression2(x).  The xor of the two sets (TrueS xor FalseS) identifies those Things which are over specified (true in the xor), or well specified with current knowledge (false in the xor). I agree this whole example feels incredibly underspecified.I have no idea how the FO ideas could clarify it, or even if they would even havean impact on these questions.I expect that if you have the terminal at any known point, there may be an infinite number of vectors it can move along, but there still will be plenty that it don't lieon those vectors.  When you are talking about xor'ing infinite sets, I expect youwill find that your intuitions don't guide you well. JK  Sincerely, Rich Cooper EnglishLogicKernel.com Rich AT EnglishLogicKernel DOT com -----Original Message----- From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Patrick Cassidy Sent: Monday, February 08, 2010 10:24 AM To: '[ontolog-forum] ' Subject: [ontolog-forum] Inconsistent Theories Changing the topic to reflect the narrow focus here: Query for Chris Menzel re: his reply to Cory C: > > On Feb 8, 2010, at 10:43 AM, Cory Casanave wrote: > > ... > > Considering the "Pat Axiom": That if 2 theories can be shown to be > incompatible they must share some concepts - intuitively obvious but I > have never seen it made explicit, thanks! > > Actually, the "Pat axiom" needs a couple small qualifications.  First, > each of the two theories in question has to be consistent.  An > inconsistent theory is incompatible with every theory, regardless of > any concept overlap.  Second, the theories must not put incompatible > conditions on the number of things that exist.  In first-order logic > (with identity), it is possible to express that there are only N things, > for any natural number N.  So if T1 says "There are exactly three > things" and T2 says "There are exactly four things", they will be > incompatible even if they share no concepts (though I suppose one could > say in this case that they share the concept of identity). > > Yours in excruciating correctness, > > Chris Menzel >   I'd like to get this right, so I could use some additional clarification:  If two theories assert that there are different numbers of "things" then it seems to me that these must refer to instances of the same category to be inconsistent.  Even though the category is not mentioned in the axioms, the implication of the (English language) interpretation is that the "thing" category is everything that could possible exist - and that would be the category of which the "things" are instances.  It seems that these assertions have to be made with respect to the same context, and if the context is the whole universe of all possible things that might exist, then that would specify the category intended.   As you can see, I am quite unfamiliar with this level of abstract thinking.  So, tell me, is there some way to avoid specifying at least implicitly the category of "things" referenced and still conclude that those theories are inconsistent? Pat Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 cassidy@xxxxxxxxx _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (01) ```
 Current Thread Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, (continued) Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Cory Casanave Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel [ontolog-forum] Inconsistent Theories, Patrick Cassidy Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Jawit Kien <= Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Jawit Kien Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel [ontolog-forum] White House "Challenge" call, Patrick Cassidy Re: [ontolog-forum] White House "Challenge" call, Pavithra Re: [ontolog-forum] White House "Challenge" call, Frank Olken Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Jawit Kien Re: [ontolog-forum] Inconsistent Theories, Rich Cooper