ONT Re: Information = Comprehension x Extension -- Discussion

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ICE.  Discussion Note 42

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HT = Hugh Trenchard

Re: ICE Discussion 38.  http://suo.ieee.org/ontology/msg05328.html

I continue to continue ...

HT: My second question relates to the analogy of particulars and properties to
    particles and waves, which question arises more at this point from a lack
    of a full appreciation of what is meant by particulars and properties.
    But despite my lack of understanding of properties and particulars,
    are you suggesting some sort of coexisting duality of particulars
    and properties -- or are you employing that analogy only to say
    that the implications of Peirce's formalisms are far beyond
    what people may have initially thought?

That's another one of those boldly-go types of abductive leaps that still
makes sense to me when I read it again, but I am moderately cognizant how
much hard trekking there is to do before the series converges on anything
conclusive.  My general sense from reading sundry old school philosophers
is that they always distinguished between "individuals" and "particulars",
taking the first to mean what it says:  atomic, indivisible, unsplittable.
We know what happened to 'that' fond notion -- of finding any such stuffs.
In contrast, a particular is a nominally smallest part in a given setting,
and the sort of thing that might easily be divided in the next discussion.

You can get the flavor of the brands of hairs that the Angelic Doctors
were adept at splitting in the Middle Ages, and Peirce's acquaintance
with them, by scanning the assortment of excerpts I gathered here:

DOI.  Doctrine of Individuals

01.  http://suo.ieee.org/ontology/msg04754.html
02.  http://suo.ieee.org/ontology/msg04756.html
03.  http://suo.ieee.org/ontology/msg04757.html
04.  http://suo.ieee.org/ontology/msg04758.html

DOI.  Doctrine of Individuals -- Commentary Notes

01.  http://suo.ieee.org/ontology/msg04755.html
02.  http://suo.ieee.org/ontology/msg04759.html
03.  http://suo.ieee.org/ontology/msg04760.html
04.  http://suo.ieee.org/ontology/msg04761.html

I'm not sure that non-angelic non-doctors like me can hope
to match this level of subtlety, but the basic distinction
between individuals and particulars seems clear enough and
actually comes up all the time in everyday applications of
computational logic to practical problems.

That's the individual/particular side of it.

The particular/property side of things is sometimes stated as a question
about "proper names" versus "common nouns", "generals", or "predicates".
This touches once again on the "limits of localization", simple or else.
Is there really a duality here?  And if so, why?  Or is this particular-
to-property dimension more like a homogeneous spectrum of peculiarities?

I don't know any kind of answer here,
but I'm only looking at various ways
that this aspect of reality has been
modeled in the past.

A couple of notes back, for instance, I was refreshing our collective
memories about the ways that these sorts of distinctions are commonly
handled in set theory.  In case you think I made all that up, there's
a collection of more or less relevant excerpts here:

SET.  Set Theory

01.  http://suo.ieee.org/ontology/msg04082.html

Appendix.  Elementary Set Theory

02.  http://suo.ieee.org/ontology/msg04083.html

A.1.  The Classification Axiom Scheme

03.  http://suo.ieee.org/ontology/msg04084.html
04.  http://suo.ieee.org/ontology/msg04086.html
05.  http://suo.ieee.org/ontology/msg04088.html

A.2.  Elementary Algebra of Classes

06.  http://suo.ieee.org/ontology/msg04089.html
07.  http://suo.ieee.org/ontology/msg04091.html
08.  http://suo.ieee.org/ontology/msg04092.html
09.  http://suo.ieee.org/ontology/msg04093.html
10.  http://suo.ieee.org/ontology/msg04094.html

A.3.  Existence of Sets

11.  http://suo.ieee.org/ontology/msg04095.html
12.  http://suo.ieee.org/ontology/msg04096.html
13.  http://suo.ieee.org/ontology/msg04097.html

A.4.  Ordered Pairs:  Relations

14.  http://suo.ieee.org/ontology/msg04098.html
15.  http://suo.ieee.org/ontology/msg04099.html

A.5.  Functions

16.  http://suo.ieee.org/ontology/msg04100.html

Links 2 through 16 of the above material are
selected and transcribed into plaintext from:

| John L. Kelley, 'General Topology',
| Van Nostrand Reinhold, New York, NY, 1955.

I'll bet we both need to take a break here.

Jon Awbrey

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