SUO: *Date 21 Jan 2002
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Subject. Abstract & Concrete
Problem. Getting a grip on the relation between abstract and concrete.
Stated like that, I almost forget why the whole thing was important.
But I know that some such issue keeps coming up in our discussions,
where I think to myself "it's that problem with abstractions again",
so let me try to remember some concrete moments when this happened.
1. While reading John Sowa on "abstract" versus "physical":
| The physical/abstract distinction is
| independent of the observer's viewpoint,
| but the continuant/occurrent distinction
| depends on the choice of time scale.
|
| John Sowa, 'Knowledge Representation', p. 71.
2. While talking to Matthew West about "adic" versus "tomic":
http://suo.ieee.org/email/msg07693.html
3. While trying to answer the questions of Seth Russell about programs:
http://suo.ieee.org/email/msg07697.html
http://suo.ieee.org/ontology/msg03654.html
4. While reading the things that some people write
about "extensions" versus "intensions", just
to pick a recent instance, the statements
that Ian Niles made in the SUO forum:
| First of all, the axiom isn't true, because not every formula
| specifying the intension of a class is true. For example, the
| intension of the class of unicorns is going to be something like
| 'an omnivorous quadruped with a horn sticking out of its forehead',
| and the formula specifying this intension will either be false or
| lack a truth value.
|
| http://suo.ieee.org/email/msg07704.html
| I'm not sure what "reality" you're referring to here.
| It's true that the same intension may have an extension
| in one context or possible world and another extension in
| another context or possible world. This fact is provided
| for in the SUMO, if we distinguish the intension of a class
| from its extension.
|
| http://suo.ieee.org/email/msg07713.html
Okay, that helps me to remember the practical context of the question.
From other discussions already in progress,
the topic of extensions and intensions is
the freshest in my mind, so let me start
by dealing off the bottom of the deck.
http://suo.ieee.org/ontology/msg03666.html
http://suo.ieee.org/ontology/msg03667.html
http://suo.ieee.org/ontology/msg03668.html
Question. What are the extensions and the intensions
of the term "The dwarves and the wizards that set out
with the hobbit over the misty mountains to repossess
the gold that the dragon stole"?
The intensions of the term, and thus of the corresponding concept,
assuming that one has by now conceived such a conception in one's
mind, would be the many "terms or corresponding concepts" (TOCC's)
that are "implied" by this one -- in olden days they were wont to
to say "contained" in this one, but we hardly comprehend that way
of toccing anymore -- for instance, "The company that came to tea
at Bilbo's under the Hill on Wednesday and appointed to meet with
him at the Green Dragon Inn, Bywater, at 11 a.m. sharp, Thursday".
Whether any among us has yet conceived a "comprehensive intension"
of this concept is something whereby would hang many another tale.
So let us do what is usually done when clarity is at premium, and
quickly about it, in a case like this, and shift to the extension.
What is the extension of the TOCC in question?
Exercise for the reader ...
Nah, just kidding. The extension of the concept in question,
as appropriate to the context in question, is just as follows,
presented in the order of the aforesaid Wednesday's appearance:
| Dwalin, Balin, Kili, Fili, Dori, Nori, Ori,
| Oin, Gloin, Bifur, Bofur, Bombur, Thorin, Gandalf.
We have the honour to remain
Yours deeply,
Awbrey & Co.
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