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## Re: [ontolog-forum] Visual Complexity

 To: "[ontolog-forum]" "John F. Sowa" Wed, 07 Feb 2007 20:42:06 -0500 <45CA7FEE.5030006@xxxxxxxxxxx>
 ```Sergei and Bill,    (01) That is the distinction between set theory and mereology:    (02) > If sets are there in the world, then no - there's nothing > abstract going on. I'm real. Chuck is real. And the set > of me and Chuck is real.    (03) 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.    (04) But in set theory, if Bill and Chuck are members of the set S, then S is a third entity that is different from each of them. You have three things: Bill, Chuck, and {Bill,Chuck}. You can also construct a fourth thing, which is the set whose only member is the set whose members are Bill and Chuck: {{Bill,Chuck}}.    (05) You can form an infinite number of distinct sets whose starting elements are just Bill and Chuck:    (06) Bill, Chuck, {Bill}, {Chuck}, {Bill,Chuck}, {{Bill},Chuck}, {Bill,{Chuck}}, {{Bill},{Chuck}}, {{Bill}}, {{Chuck}}....    (07) You don't even need to start with anything. You can build up all of mathematics out of just the empty set: {}, {{}}, {{},{}}, {{{}}}, {{},{},{}}, {{{}},{{}},{{}}}...    (08) In that sense, sets are like lists in LISP. You can start with strings, such as "Bill" and "Chuck" and create lists out of dotted pairs ("Bill".("Chuck".())). But the dotted pair of two strings is not a string.    (09) String concatenation is similar to mereology. The concatenation of two strings is another string, such as "BillChuck", and there is no way to build up anything by concatenating the empty string to itself. No matter how many times you do so, you never get anything other than an empty string.    (010) To answer the question about concrete vs. abstract: the infinite number of sets you construct out of Bill and Chuck cannot be physical because they would have an infinite amount of matter and/or energy. Therefore, all but the bare atoms, Bill and Chuck, must be abstract.    (011) John    (012) _________________________________________________________________ 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    (013) ```
 Current Thread Re: [ontolog-forum] Visual Complexity, (continued) Re: [ontolog-forum] Visual Complexity, John F. Sowa Re: [ontolog-forum] Visual Complexity, Pat Hayes Re: [ontolog-forum] Visual Complexity, John F. Sowa 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