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## Re: [ontolog-forum] Axiomatic ontology

 To: "[ontolog-forum]" "John F. Sowa" Sun, 28 Sep 2008 11:47:46 -0400 <48DFA722.2000608@xxxxxxxxxxx>
 ```Rob,    (01) This discussion leads to many issues about mappings:    (02) RF>> The work of Schmidhuber and Hutter avoid these "pitfalls" >>> [of logic] by ignoring formal logic and seeking a basis for >>> meaning in prediction/probability.    (03) JFS>> That's like a carpenter who struck his thumb with a hammer and >> later avoids the pitfalls of hammers by using nothing but saws.    (04) RF> I think of it in terms of a different metaphor. I think of it > as a cartographer who finds projections to a plane are always > distorted, and so decides not to limit herself to flat maps.    (05) Interesting comparison. It just so happens that C. S. Peirce was not only the person who invented the algebraic notation for FOL (in 1880-85), he also invented the quincuncial projection of the earth to a plane (1879). See the Wikipedia entry:    (06) http://en.wikipedia.org/wiki/Quincuncial_map    (07) Unlike the common Mercator projection, which exaggerates the areas of Canada, Alaska, and Greenland, the Q. projection preserves relative areas. Although it has some distortions, it has the very important property that great circle routes (for shipping and airlines) can be drawn with a straight edge on that map (to an approximation with negligible error for navigational purposes).    (08) This example shows why a person who rejects flat maps would overlook an important application. By that, I do *not* claim that people should limit themselves to flat maps, but that they should "never say never" to any point of view.    (09) As for category theory, its basic focus is on maps of all possible kinds. There are an infinity of ways of mapping one shape to another with many different kinds of distortions, some of which highlight different aspects of the things that are being mapped.    (010) Similarly, there are many different ways of mapping language to logic or logic to language. The English words 'and', 'or', 'not', 'some', and 'every' are landmarks that a mapping might preserve, highlight, or distort. But many different ways of mapping the content words of language will also preserve, highlight, or distort other aspects for various purposes.    (011) Instead of "ignoring logic", I suggest that people keep in mind that it shows up as those ubiquitous landmarks in English and other natural languages. Languages wouldn't have those words if people didn't find logical aspects important.    (012) John    (013) _________________________________________________________________ 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    (014) ```
 Current Thread Re: [ontolog-forum] Axiomatic ontology, (continued) Re: [ontolog-forum] Axiomatic ontology, Antoinette Arsic Re: [ontolog-forum] Axiomatic ontology, Christopher Menzel Re: [ontolog-forum] Axiomatic ontology, Antoinette Arsic Re: [ontolog-forum] Axiomatic ontology, Schiffel, Jeffrey A Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Antoinette Arsic Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Rick Murphy Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa <= Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Antoinette Arsic Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, Pat Hayes Re: [ontolog-forum] Axiomatic ontology, Randall R Schulz Re: [ontolog-forum] Axiomatic ontology, John F. Sowa Re: [ontolog-forum] Axiomatic ontology, Rob Freeman Re: [ontolog-forum] Axiomatic ontology, John F. Sowa