Intension/Sinn

fritz@rodin.wustl.edu (Fritz Lehmann)
Date: Fri, 11 Feb 94 03:02:19 CST
From: fritz@rodin.wustl.edu (Fritz Lehmann)
Message-id: <9402110902.AA05795@rodin.wustl.edu>
To: cg@cs.umn.edu, interlingua@ISI.EDU, phayes@cs.uiuc.edu
Subject: Intension/Sinn
Cc: wille@mathematik.th-darmstadt.de


      About KIF and Conceptual Graphs, I remarked earlier:

>>P.P.S. Must we totally neglect intension?  Sinn?  Two facts
>>are: A. There are too many different discordant notions of
>>what "intensions" are and many are hard to formalize neatly,
>>whereas everybody pretty much understands extensions as a formalism.
>>B. Notwithstanding fact A., intensions really matter more than
>>extensions.  Triangularity is the thing to know about, not the set of
>>triangles.  Same goes for Democracy, puffinhood and FAX machines.

     Pat Hayes replied:
>Well, yes, but....care is needed in discussions like this. For a
>start, it is notoriously difficult to say what intensions ARE:

     Yes, that's fact A.

>so difficult,
>in fact, that one begins to be suspicious that maybe the primal intuition is
>rather faulty.

     What's often faulty in formalizations is failure to "do justice to what
we know," in Hao Wang's words.  (Are _primal_ intuitions faulty?  Lesser
intuitions are faulty if in conflict with primal ones.)  Fact B.

>I have now reached the stage where I really have no idea what
>'triangularity' means, and suspect it means many different things in
>different philosopher's mouths.

     I'm still at the stage in which I have a better idea of what
"triangularity" means than what "the set of triangles" means.

...
     I said
>>Who really cares about arbitrary extensional sets of objects?

Pat Hayes>I do!  ...

     Pat, I don't believe it.  I think what you mean is that, as a logician,
you care about a logic's _ability_to_denote_ arbitrary extensional sets, but
do you really care about any arbitrary sets themselves?  Nah.  No-one does.
If I list arbitrary objects or entities with no pattern of common
qualities, you will be bored, not interested.  More essentially, such sets
are inherently useless.

     Except in the "What is a set?" section of a math book, or in
discussions like this one, no-one uses arbitrary sets at any time in
real life.  That's one reason why the set in "shoes--- and ships --- and
sealing wax --- Of cabbages --- and kings --- And why the sea is boiling
hot --- And whether pigs have wings." is funny.  Sets are interesting or
useful only when the (intensional) qualifications of membership are
interesting or useful.  Even math books use only intensional "set-builder"
notation rather than arbitrary lists, after the opening section.  The
operations of logic and set theory treat interesting and dull sets the same,
which is a both a merit and a limitation of logic and set theory. 
Extensional logic is a valid _constraint_ on the logic that matters, that
of meanings or "Sinn".  (That constraint is a Galois connection as I said
before.)

     From Aristotle through Leibniz and up to Frege, intensions
were considered more important.  Then, especially with the influence of young
Quine and a 40% chunk of Tarski, extensions became all the rage partly due to
ease of formalization.  There has always been a countercurrent, though.  More
recently a third view has emerged, that the basic concept is the _connection_
of intensions to extensions, in "trope theory", Wille's "formal concept
analysis", Russian "meronomy", and "fact-based ontology".

     To call something "knowledge representation" when it deals only with
sets is a bit misleading.  Knowledge is certainly about qualities.  An
amusing limitation of set-based (extensional) logic is that it is incapable
of distinguishing purely arbitrary sets from sets whose members do have some
quality in common.

     A knowledge representation which is entirely extensional will
necessarily fail to capture meaning, including even purely structural (i.e.
combinatorial) parts of meaning.  I think Bill Woods has often urged this
point.  This doesn't negate the value of current KIF, conceptual graphs or
extensional logic; it just means that there is more to the story.  The fact
that there is no consensus on formalizing the rest of the story doesn't mean
it isn't there and isn't important.

                                Fritz Lehmann
                            fritz@rodin.wustl.edu
4282 Sandburg, Irvine, CA 92715 USA    714-733-0566
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