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)
|