I kinda object to the use of "T" because it conflicts with
the extremely long history of dynamic systems, discrete time systems, even
electronics which is often spread out in a frequency v time plane. Wavelets,
Fourier analysis, control systems, optimal controls, discrete sampled systems,
and zillions of other engineering marvels use “T” and have for
centuries. It seems unnecessary to displace it now.
I can see your objection to using "Thing" also, and
considered “T_Thing” as a memorable symbol for it, but I guess
"Topmost" and "terminal" should do the job. I.e., a
node is topmost if it has no parent nodes in the lattice, and a node is terminal
when it can't be expanded into a child node collection within the lattice.
If I understand this right, the comprehension of a symbol-associated
is the Boolean product
that define all the condition of that symbol that discriminate it from the
topmost node. Perhaps the same product of fluents discriminates
descendent nodes of the designated node Desi as well, but does not
completely discriminate, because
these other nodes are lower in the lattice than the designated node Desi. I.e.,
it must be a complete path from the topmost node (in the lattice) to an Nth
terminal descendent of the topmost node after N fluents have been satisfied,
traversing the lattice edges from the symbol to the terminal node, i.e., the
But I see no rationale justifying the requirement that only attributive
properties (single argument fluents) be used to form the lattice. Why can’t
relational predicates be used, but descendants partitioned among true and false
values of the predicates? If the only rationale is tradition, (i.e., Aristotle
and Obama say so), that shouldn’t hold weight against a more effective
solution using the more general predicates instead of solely attributive property
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of John F. Sowa
Sent: Tuesday, August 17, 2010 8:17 AM
Subject: Re: [ontolog-forum] Triadic Sign Relations
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.
The terms 'comprehension' (or 'intension') vs. 'extension' are
technical terms, and the distinction is as old as Aristotle.
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'.
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
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.
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):
For every x, T(x).
But T also has the minimum possible comprehension (or intension):
zero. That single axiom, which is true of everything, says
about anything. T has no attributes or properties of any kind.
> I interpret "comprehension" in this passage as
referring to the
> degree of specialization of a "term", or symbol.
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.
RC> CSP seems to be saying that the more specialized a Thing is,
> the more "information" it's designation contains
> disambiguation from other Things.
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.
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.
The correct statement is that deleting differentiae from the
definition of a term has two effects:
1. It makes the definition less informative (i.e, smaller
comprehension or intension).
2. It makes the term more general (i.e., larger extension).
CSP>> Every addition to the comprehension of a term lessens its
>> extension up to a certain point, after that further
>> increase the information instead.
RC> What is that “certain point” which CSP eulogizes?
That point is where you have all the necessary and sufficient
conditions for a definition. (But he didn't eulogize it.)
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).
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