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## Re: [ontolog-forum] Terminology Question concerning WebArchitecture and

 To: "[ontolog-forum]" "Deborah MacPherson" Wed, 25 Jul 2007 21:16:19 -0400 <48f213f30707251816p17da2dedy5c08fe28fac32f2b@xxxxxxxxxxxxxx>
 ```What "is not there" can be just as important as what is there.    (01) What mathematical system works without zeros and placeholders?    (02) "Nothing" merits a catagory.    (03) Deborah MacPherson    (04) On 7/25/07, Waclaw Kusnierczyk wrote: > John F. Sowa wrote: > > Wacek, > > > > The question of how to or whether to represent a null value of > > some kind is a context-dependent issue about how to regularize > > the operators of some mathematical system. > > > > vQ> If you and me are just you and me, then nothing is nothing, > > > no entity at all, and not the empty set. You can well > > > interpret 'nothing' as a sheet of paper on which there is > > > no drawing, though there is the sheet -- how do such > > > interpretations help? > > > > The number 0, for example, simplifies the statements of many > > arithmetic principles. Similarly, the empty set simplifies > > many of the axioms of set theory. In lattices, the bottom > > symbol simplifies many axioms. In a Boolean lattice, the > > bottom corresponds to a proposition that is always false; > > such a proposition doesn't say anything useful, but it makes > > it possible to formulate the axioms more systematically. > > > > For some mathematical structures, a null value has no useful > > role. In most versions of mereology, for example, there is > > no empty part. An atom in mereology is defined to be something > > that has no part other than itself. In such systems, the word > > 'nothing' is just a way of saying 'no thing'. Unlike the empty > > set, which is assumed to exist in set theory, the word 'nothing' > > (or a formal symbol that represents it) would be a way of saying > > "It is false that there exists an x such that..." > > > > In short, the concept of 'nothing' or a 'null value' depends > > on the operations needed to regularize some system. > > No doubt here. I thought we were talking about ontology there, and > interpreting 'nothing' as denoting the empty set (an entity in itself) > does not seem correct to me. Of course, you may build a mathematical > model of reality in which nothing is modelled as the empty set (and the > empty set is modelled as the set composed of the empty set), and such a > model may be used to interpret sentences containing the word 'nothing'. > > But I do not see how "''nothing'', or > ''nonentity'' or ''nonbeing'', interpreted as the empty set, is another > ontological category." > > > vQ > > _________________________________________________________________ > 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 > >    (05) _________________________________________________________________ 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    (06) ```