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## Re: [ontolog-forum] Inconsistent Theories

 To: cmenzel@xxxxxxxx, "[ontolog-forum]" "John F. Sowa" Mon, 08 Feb 2010 21:40:54 -0500 <4B70CB36.8050408@xxxxxxxxxxx>
 ```Chris M. and Pat C.,    (01) Here's another way to state the point:    (02) For two consistent theories T1 and T2 to be inconsistent, there must be something on which they disagree (e.g., some statement S is derivable from T1, and ~S is derivable from T2).    (03) If all the nonlogical symbols (names of predicates, entities, etc.) are different in T1 and T2, there is very little that they could disagree about. But Chris made the following point:    (04) CM> In first-order logic (with identity), it is possible to express > that there are only N things, for any natural number N.    (05) To illustrate Chris's point, suppose that a theory T1 says that there exists exactly one x. It can do so by the following statement in predicate calculus:    (06) (Ex)(Ay)(y=x).    (07) Literally, this says that there exists an x, and for all y, y is equal to x.    (08) The theory T2, however, might say that there exists an x and a y and they are not equal:    (09) (Ex)(Ey)~(x=y).    (010) These two theories are contradictory.    (011) One could quibble about whether the symbol "=" is a logical or a nonlogical symbol. I would claim that identity is part of the logical apparatus (partly because I agree with Wittgenstein that x=y is a statement about the names x and y, rather than a statement about the subject domain). In any case, I don't want to get into metaphysical arguments about the nature of identity.    (012) John    (013) _________________________________________________________________ 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    (014) ```
 Current Thread Re: [ontolog-forum] Inconsistent Theories, (continued) 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, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, John F. Sowa <= Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, John F. Sowa Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, John F. Sowa Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, Rich Cooper Re: [ontolog-forum] Inconsistent Theories, Christopher Menzel Re: [ontolog-forum] Inconsistent Theories, Rich Cooper