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## Re: [ontolog-forum] Visual Complexity

 To: "[ontolog-forum] " Chris Menzel Thu, 8 Feb 2007 04:09:48 -0600 <20070208100948.GB82844@xxxxxxxx>
 ```On Thu, Feb 08, 2007 at 01:52:57AM -0500, John Sowa wrote: > Chris, > > I was just trying to express, not very clearly, that there > is just one mereological totality of Bill + Chuck: > > JFS>> In mereology, Bill and Chuck are each parts of the collection > >> that consists of Bill and Chuck. You can call that pair C, but C > >> is not a new entity. It is just Bill and Chuck. > > CM> John, that is not correct. The mereological sum of Bill > > and Chuck -- call it Bill+Chuck -- is typically defined in > > mereology as the smallest thing that has Bill and Chuck as > > parts. (Equivalently, it is the unique thing X such that > > anything that overlaps X either overlaps Bill or overlaps > > Chuck.) It is not "just Bill and Chuck". It is a third > > thing distinct from the two of them. > > The crucial issue is how many potential "entities" exist. > > > And in mereology you have Bill, Chuck, and Bill+Chuck. > > No. The totality consists of just the sum of Bill & Chuck.    (01) No? John, your own assertion betrays you. "The sum of Bill & Chuck" (in mereology) refers to something, namely, the sum of Bill & Chuck. It is neither Bill nor Chuck -- for, unlike Bill and Chuck, it has both Bill and Chuck as parts. It is a third thing. You are trying to have your mereological cake and it eat it, too.    (02) > A better example is to consider France, which was subdivided into > provinces and later subdivided into departments. There is only one > totality, which is France, and the different ways of subdividing it > are potential parts.    (03) Right, just as there is the one totality Bill+Chuck and many ways to divide it into potential parts -- notably, into its Bill part and its Chuck part, each a totality in its own right. Similarly, you can divide France by a line running through Paris and Dunkirk into two separate land masses. So we can distinguish three land masses -- France, "western" France, and "eastern" France. The analogy is less than perfect, of course, because Bill and Chuck are autonomous organisms, so the division of of Bill+Chuck into its Bill and Chuck parts is a more "natural" one than my division of France. But mereologically the principle is the same -- non-overlapping entities are distinct from their sum.    (04) > With mereology, there is no clear answer to how many parts there are > if you have a continuous area or solid.    (05) Sure 'nuff. Not relevant to my point, of course.    (06) > > By contrast, in mereology, the sum of Bill and Bill+Chuck is just > > Bill+Chuck; likewise, the sum of Bill's left arm and Bill is just > > Bill. In set theory, as you note, you get the distinct entities > > {Bill, {Bill, Chuck}} and {BillsLeftArm, Bill}. But in mereology > > and set theory alike, the sum/set of Bill and Chuck is a third > > thing distinct from Bill and Chuck. > > I agree with this,    (07) Oh, well, then, great! (Somehow I thought you didn't agree...like when you said "No" above. :-)    (08) -chris    (09) _________________________________________________________________ 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    (010) ```
 Current Thread Re: [ontolog-forum] Visual Complexity, (continued) Re: [ontolog-forum] Visual Complexity, Christopher Menzel Re: [ontolog-forum] Visual Complexity, Pat Hayes Re: [ontolog-forum] Visual Complexity, tom beckman Re: [ontolog-forum] Visual Complexity, Charles D Turnitsa Message not availableRe: [ontolog-forum] Visual Complexity, andersen Re: [ontolog-forum] Visual Complexity, Sergei Nirenburg Re: [ontolog-forum] Visual Complexity, andersen Re: [ontolog-forum] Visual Complexity, John F. Sowa Re: [ontolog-forum] Visual Complexity, Christopher Menzel Re: [ontolog-forum] Visual Complexity, John F. Sowa Re: [ontolog-forum] Visual Complexity, Chris Menzel <= Re: [ontolog-forum] Visual Complexity, John F. Sowa [ontolog-forum] UNSUBSCRIBE, jdelre Re: [ontolog-forum] UNSUBSCRIBE, Horning, Jim Re: [ontolog-forum] UNSUBSCRIBE, Christopher Menzel Re: [ontolog-forum] Visual Complexity, Cassidy, Patrick J. Re: [ontolog-forum] Visual Complexity, Christopher Menzel Re: [ontolog-forum] Visual Complexity, Pat Hayes Re: [ontolog-forum] Visual Complexity, Pat Hayes Re: [ontolog-forum] Visual Complexity, Pat Hayes Re: [ontolog-forum] Visual Complexity, Pat Hayes