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Re: [ontolog-forum] Triadic Sign Relations

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 17 Aug 2010 11:17:22 -0400
Message-id: <4C6AA802.4020901@xxxxxxxxxxx>
On 8/17/2010 6:29 AM, Rich Cooper wrote:
> I interpret “comprehension” in this passage as referring to the degree
> of specialization of a “term”, or symbol.    (01)

The terms 'comprehension' (or 'intension') vs. 'extension' are
technical terms, and the distinction is as old as Aristotle.    (02)

The word 'comprehension' is the older term, and William Hamilton
replaced it with 'intension' to emphasize its relationship to
'extension'.  Unfortunately, he created more confusion than
enlightenment, because 'intension' sounds like 'intention'.    (03)

I'd also like to relate this discussion to the term used for the
top of a type hierarchy.  My preferred term is the symbol T for top,
because it avoids all possible confusion with words like 'thing'
or 'concept'.  If anybody wants a pronounceable word, I recommend
'entity' because it is a technical term that avoids all kinds of
pointless controversy about whether an event or a property is a thing.    (04)

The crucial point about T (or whatever else you want to call it) is
that it has maximum extension:  The corresponding predicate T(x)
is true of every and any x that anybody can imagine.  There is
one and only one axiom that defines the predicate T(x):    (05)

    For every x, T(x).    (06)

But T also has the minimum possible comprehension (or intension):
zero.  That single axiom, which is true of everything, says nothing
about anything.  T has no attributes or properties of any kind.    (07)

 > I interpret "comprehension" in this passage as referring to the
 > degree of specialization of a "term", or symbol.    (08)

It's better not to try to explain it.  Just think in terms of
the logic:  The comprehension (or intension) is determined by
the differentiae (monadic predicates) that define it:  adding
more differentiae makes a term more specialized, and deleting
differentiae makes it more generalized.  If you erase all the
differentiae, you get T.    (09)

RC> CSP seems to be saying that the more specialized a Thing is,
 > the more "information" it's designation contains to ensure
 > disambiguation from other Things.    (010)

That sentence shows why the word 'thing' should be banished
from any discussion of type hierarchies.  Its only effect is
to cause endless amounts of confusion.    (011)

There is no physical thing to which the words 'generalized'
and 'specialized' could apply.  You cannot find any animal
on planet earth that is more specialized or more generalized
than any other animal, plant, mineral, or event.  Things are
never general or special.  But terms can be.    (012)

The correct statement is that deleting differentiae from the
definition of a term has two effects:    (013)

  1. It makes the definition less informative (i.e, smaller
     comprehension or intension).    (014)

  2. It makes the term more general (i.e., larger extension).    (015)

CSP>> Every addition to the comprehension of a term lessens its
 >> extension up to a certain point, after that further additions
 >> increase the information instead.    (016)

RC> What is that “certain point” which CSP eulogizes?    (017)

That point is where you have all the necessary and sufficient
conditions for a definition.  (But he didn't eulogize it.)    (018)

Peirce was making the observation that adding more descriptive
information beyond what is necessary might be informative
(saying more about some subject) but that information wouldn't
reduce its range of applicability (making it more specialized).    (019)

John    (020)

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