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Re: [ontolog-forum] Triadic Sign Relations

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Thu, 19 Aug 2010 11:07:10 -0700
Message-id: <20100819180711.03890138CFD@xxxxxxxxxxxxxxxxx>

Hi John,

 

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 node, Desi, is the Boolean product of fluents 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 Individual.  

 

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 predicates.  

 

JMHO,

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

 

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Tuesday, August 17, 2010 8:17 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
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 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.

 

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 nothing

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 to ensure

 > 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 additions

 >> 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).

 

John

 

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