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## Re: [ontolog-forum] The class of the planet Venus

 To: "[ontolog-forum]" Ed Barkmeyer Thu, 12 Jul 2012 12:03:57 -0400 <4FFEF56D.2070201@xxxxxxxx>
 ``` John F Sowa wrote: > 4. The distinction between intensions and extensions can be used > for individuals as well as for sets, relations, functions, and > classes. The basic point is that the extension is something > in the world (or a model of the world), and the intension is > a definition that is used to characterize and identify the > thing or things in the world (or some model of the world). >    (01) IMO, this is the most important point.    (02) As John says, the fundamental idea is that the extension is the thing itself; the intension is a characterization of the thing. And the same unique extensional thing can have multiple unrelated characterizations whose only relationship is that they happen to describe the same thing. E.g., the Vice President of the US in 2004 and the man who shot his friend on a hunting trip in 2009. With respect to intension v. extension, there is nothing special about "unitary intensions", other than that we presume that the extension of a unitary intension has cardinality 1.    (03) The problem with the morning star and the evening star is that it causes us to talk about the relationships between the intensions, on the basis of knowing that there is a common extension. It is probably better to ask about the relationship between the morning star and the Roman fertility goddess -- the Romans (and their predecessors at least back to Homer) thought the two not-clearly-related intensions were coextensive, that the star was the perceptible goddess.    (04) The most important use of the distinction is when we don't know whether, or how, two "unitary conceptualizations" are related, rather than when we do. I am reminded of the tale of the young mathematician whose pursuit of a Ph.D. led him to study vector spaces that combined the features of two unrelated interesting categories. After several months of work, he obtained some impressive theoretical results. After several more months, he obtained an astounding theoretical result. And finally, about a year in, he obtained one final result -- the only such vector space is {0}! That bit of additional knowledge made all the prior results trivial. The mathematics of the intension was exciting only because he didn't know the extension.    (05) I do wish John had avoided the insertion of the parenthetical expressions in the above, because they weaken, perhaps to the point of confusing, his thesis.    (06) The reason I object to John's parenthetical references to "models of the world" is that most "models" in this sense are intrinsically intensional. The artefacts in models are /constructed from/ the intensions, and two such artefacts may indeed be different even when the thing they are models of is the same. A model of a building is not a building. Two different models of the same building are different things, each conforming to a particular characterization of the building, whether the building itself exists or not, and in fact, whether or not the building in being actually possesses those characteristics. (This is a critical idea in Herbert Simon's famous work "The Sciences of the Artificial", and in some of Ted Goranson's work.) So it is in fact very difficult to argue that two conceptualizations of model elements are 'coextensive'. The model element is a manifestation of the conceptualization, not the extension of it. I would go so far as to say that a model element is a Frege Zeichen -- a sign/symbol for the intension (Sinn).    (07) -Ed    (08) > Please note that Frege used the example of the morning star > vs the evening star to illustrate his distinction between Sinn > vs Bedeutung. > > The terms Sinn and Bedeutung name two points on the meaning triangle. > In German, they are Zeichen, Sinn, Bedeutung -- usually translated > as sign, sense, and reference. > > Those terms are related to intensions & extensions, but they > are not quite the same. For other terms used to label the > three vertices of the meaning triangle, see Slides 88 to 90 > of http://www.jfsowa.com/talks/kdptut.pdf > > John > > _________________________________________________________________ > 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 > >    (09) -- Edward J. Barkmeyer Email: edbark@xxxxxxxx National Institute of Standards & Technology Manufacturing Systems Integration Division 100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528 Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800    (010) "The opinions expressed above do not reflect consensus of NIST, and have not been reviewed by any Government authority."    (011) _________________________________________________________________ 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    (012) ```
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