Re: Roles and dependence (John F. Sowa)
Date: Thu, 28 Sep 1995 07:43:38 +0500
From: (John F. Sowa)
Message-id: <9509281143.AA19781@west>
Subject: Re: Roles and dependence
Content-Length: 5275
Precedence: bulk

I think that we are talking past one another.  We agreed long ago
that all these variations of notations, including CGs, KIF, predicate
calculus, etc., are equivalent in their expressive power, with formal
translations from one to the other and back again.  So of course there
is nothing that I can represent that you cannot represent in an
equivalent way.

What I have been working on are some basic distinctions in ontology,
which can be multiplied together to generate a starting set of categories.
At the ontology workshop in Montreal, my primary point was that the
distinctions are more fundamental than the categories and that once
you agree on an appropriate collection of distinctions, a type lattice
can be generated just by taking combinations.  I also made the point
that not all combinations may make sense, and you must state certain
constraints (or axioms) that rule out the ones you don't like.

As my two starting dimensions, I suggested the two-way distinction
of Physical vs. Abtract and Peirce's three-way distinction of
Firstness, Secondness, and Thirdness.  The product of these two
generates six categories, which happen to correspond very neatly
to the first six of Whitehead's "categories of existence":

 P1. Physical Firstness corresponds to Whitehead's "actual entities",
     which include both physical objects and processes.

 P2. Physical Secondness = W's "prehensions", which he said are
     "concrete facts of relatedness".

 P3. Physical Thirdness = W's "nexus", which he said are "individual
     facts of togetherness".

 A1. Abstract Firstness = W's "eternal objects", which he related to
     Plato's "forms", but with Aristotle's "correction" that the forms
     are derived by abstraction from physical reality.

 A2. Abstract Secondness = W's "propositions", which both he and Peirce
     defined in almost exactly equivalent terms:  a proposition is the
     predication of a form to some entity.  The forms may include simple
     forms or arbitrarily complex ones, which are made up of logical
     combinations of simpler forms.

 A3. Abstract Thirdness = W's "subjective forms", which correspond to
     Peirce's mediating intentions.

Besides these six, Whitehead had a Category 7 of "multiplicities" and
a Category 8 of "contrasts", which he said were mechanisms for generating
and combining categories.

As a starting point for defining the top level of an ontology, I find
these six categories to be cleaner, simpler, and more comprehensive
than anything else I've seen in the AI literature.  I certainly don't
deny that there is an enormous amount of work necessary to bridge the gap
between these half dozen very general categories and the thousands of
very detailed types in natural languages and systems like Cyc.  But as
I have said in many notes to these lists, we need both top-down theoretical
work and bottom-up empirical work.  They complement one another.

Some comments on your note:

>As I said above, it is the CONCEPT of being....

I wasn't talking about "the concept of being" or about the existential
quatifier.  I was talking about the predicates or relations that one
would use to classify or describe things.

> ... I can scent
>a hint here of what I suspect to be a fundamental limit of Peirce's
>thinking, which is that he really couldn't believe in both things and

Comments like that are what incites flamage.  You were irritated at
my deprecating attitude towards Bertrand R. and much of 20th century
logic.  Comments like yours about Peirce are just as uncalled for.  If
you would take the trouble to read his 1885 paper on logic, then we
might have some basis for talking about such "fundamental limits".
What I have been trying to say with my citations from Peirce is that
his conception of relations and reified relations, etc., is just as
up to date, if not more so, than anything being written in the literature
of AI, logic, and philosophy today.  You may dispute that claim, if you
like, but ONLY IF you show specific quotes from his writings that exhibit
those limitations.

>Oh, give me a break. So 'Thirdness' is just denotation! What was all the
>fuss about? We seem to be back on Fregean ground rather firmly.

No.  I was delighted that you chose the word "representation", which is
one that Peirce used as a prime example of Thirdness.  But denotation
is not the same as representation.  Denotation happens to be an example
of Secondness.

>>Please remember that Peirce invented predicate calculus in its modern

>All credit to him, then. However, this is not a very good argument
>*against* modern logic ;-)

I have never been arguing against modern logic.  My citation of Peirce's
writings was to point out that his logic is IDENTICAL to modern logic.
What I have been arguing against is the impoverished ontology that
Bertrand R. bequeathed to the community.  And I have been trying to say
that CSP and Bertie's colleague ANW had found a better way.

In any case, the most important aspect of the ontology that has been
ignored in the current literature is Category A3 = Abstract Thirdness
= Whitehead's "subjective forms".  I believe that this category is
essential to clarifying the semantics of contexts, but that's a
story for another day.