Re: Roles, again (Fritz Lehmann)
Date: Sun, 10 Sep 95 04:53:24 CDT
From: (Fritz Lehmann)
Message-id: <>
Subject: Re: Roles, again
Precedence: bulk
     Pat Hayes has responded to Sowa and Guarino disapproving of
using the Peircean notions of Firstness, Secondness and Thirdness as
major ontological distinctions.  I am favorably impressed with Sowa's
use of these categories, though I have some reservations, so I would like
Pat to be much more cogent and specific in asking us to dismiss them.
(Also, Pat, the fact that Husserl once thought of something is not wholly
sufficient grounds to dismiss it as nonsense.)

     Hayes wrote:
-----begin quote----
>>Oh, thats a GREAT help. There were three incomprehensible words and now
>>there are four. Could I put in a plea for good old Fregean extensionality
>>here? In spite of its evident ability to intellectually seduce, I cant see
>>a single practical reason why we should take any of this Peircian mysticism
>>seriously: it belongs with Freemasonry.
>I don't know whether it's Freemasonry, what is certainly true is that these
>words are incomprehensible but at the same time stimulating.

Not to me. They seem simply confused. Every attempt to make them precise
has failed.
----end quote---

     I would be impressed to learn that Pat has read "every attempt to
make them precise".  Other than the book of Robert Burch, "A Peircean
Reduction Thesis", which I'm supposing Pat has reviewed negatively
(I would still like to see that review), what other sources have "failed"?

     There are three rather different issues here, A, B and C:

     A. There is the formal algebraic version of Peircean Firstness,
Secondness and Thirdness -- which John Sowa has not even mentioned in
any of his speeches and papers to date.  This was in Burch's book, and
consists of the fact that some concepts cannot be properly defined using
only monadic predicates, and some cannot be properly defined using
only monadic and dyadic predicates, but require at least one truly
triadic predicate.  At this very deep and formal level, one must opine
with great caution since there are traps for the unwary.  A monad here
is like a univalent ion, a dyad is like a bivalent ion, and a triad is
like a trivalent ion -- these can be thought of as logical Tinker-Toys.
     Monad:  O---     Dyad:  ----O----    Triad:   -----O
For reasons unknown to me, Pat Hayes objects to this treatment of logic.
What I SUSPECT Pat has done in negatively reviewing Burch, is to shift
the fundamental graph-theoretic junctions from the RELATIONs over to
the OBJECTs, using conjunction.  Since a logical "complex" (to use
Whitehead's, Russell's and Wittgenstein's apt word) is a bipartite
directed hypergraph (as in Conceptual Graphs), in which one class of
junctions is Individuals and the other is Relations, it is possible to
shift graph-theoretic junctions from one class to the other using a technical
trick.  But doing so does not avoid the main (hyper)graph-theoretical
point, which is that you can't ever make a triad (as shown above) by
joining up a lot of dyads.  This relates to Tarski & Givant's famous
result that all of logic can be carried out using only three variables,
but no fewer.  The three variables are the three spokes of a triad.
(Note that a triad cannot be "reified" into an object and three dyads, unless
you have a way of insuring that the new dyads are unary functions rather
than general dyadic relations.  Maurizio Lenzerini pointed this out.)

     B. The above having _not_ been used by Sowa for his ontological
distinctions, we turn to what he did use Firstness, Secondness and 
Thirdness for.  Here I support Sowa part way, even most of the way.  Sowa
acknowledges that the words Firstness, etc. don't 'grab' people, but
still he gets them in.  What Sowa means by Firstness is what Peirce
meant _at_the_gross_level_ , something which is identifiable by its
own features, regardless of its relations to any other object.  Secondness
refers to a predicate which is determined only by the relationship of
an object to other objects.  This is a perfectly clear distinction and
is, as Guarino said, closely related to Bolzano/Husserl/Simons/Guarino 
"foundation" or existential dependency, which Guarino formally defined
in his message (no mush-headedness there, Pat).  So "dot" is a Firstness
and "corner" is a Secondness.  Cheshire Cat is a Firstness, its smile
is a Secondness -- etc.

     The more difficult concept is Thirdness.  Peirce in his writings
called this a number of things, but "mediation" is the version Sowa has
(wisely, I think) used.  When Adam named the beasts of Eden, that involved
Thirdness -- the name-to-beast relation has no existence without some
Adam or some other RepresentingThing (to use Doug Lenat's phrase for this);
Peirce found that no amount of theorizing could reduce this to a Secondness
or Firstness as described.  The third argument (the "Interpretant") is
fundamentally needed; all "sign" relations are instances of Thirdness.
Sowa has called the 3 categories Form, Role and Mediation (and if he'd stuck
to that, I bet Pat Hayes would probably never have spotted the Peirce trinity
lurking within).

     I agree that the sign-relation is inherently triadic (no thing A
"represents" any thing B in a yet-unexplored cave), but I feel that Sowa
has sometimes been too quick in assigning other things to Thirdness (I can't
remember specific examples now, but I shook my head in disapproval);  if you
are going to put something in the (properly somewhat rare) category of
Thirdness, you need to be very specific about why.

    C. To conclude, the third separate issue is whether, as Peirce himself
believed, the gross-level distinctions mentioned in B. above can, by very
careful analysis, be reduced to the purely mathematical algebraic notions
in point A. above.  That is, in a definitional treatment reducing Form,
Role and Mediation to deeper, more primitive notions, will it turn out that
only Mediation will require logical triads, and only Role and Mediation (not
Form) will require logical dyads?  Although I accept the Form/Role/Mediation
distinction as a pragmatic one, and I know the algebraic point (which is
at Kindergarten level really), I have not yet seen a conclusive grounding
of one level in the other.  For example the "form" of an object includes
shape, which involves dyadic relations among its parts, so this cannot
simply be a true Firstness in the algebraic sense.  Peirce reserved "pure
qualities of feeling" for this deeper Firstness -- e.g. the sensation
experienced by a newborn baby the first time it sees blue light.  As soon
as this "blue" is assimilated in the brain and associated with other things
(like the sky) low-level Secondness and Thirdness have become involved. There's
a long road of analysis from the categories in one level to the lower level.
At the lowest, algebraic, level, Firstnes, Secondness and Thirdness are mere
issues of (hyper)graph theory; the basic "reduction thesis" (all higher-
arity relations can be reduced to triads, but not triads to dyads nor
either one to monads) was also noted in the field of Invariant Theory
independently by J. J. Sylvester -- and it has correponding analogues in
Tarski & Givant, Tensor nets, and satisfiability theory (3SAT \neq 2SAT 
but 3+nSAT = 3SAT).   Maybe Pat Hayes will dissuade me of this belief
in his review of Burch (if he ever sends me a copy ...).

     So I ask that, in further evaluations of the three-way distinction,
the critics be very clear about what it is they mean to criticize, and
don't mix up levels A., B. and C. listed above.  As far as I know, Sowa has
only used the pragmatic distinctions of level B, and most people should
judge that on its own merits.  It's only because Pat Hayes has recently
reviewed a book about level A that these other aspects have come up here.

     (By the way there's an even deeper level, D, namely my own theory of
course.  It does not recognize "individuals" as such, and treats every
inherence (trope) as a Secondness, Firstness being relegated to _unattached_ 
monadic predicates, and triads are treated as in Rudolf Wille's and my 
"Trilattice theory" paper in ICCS-95 --- but the World will have to keep
waiting a little longer for the ultimate revelation....)

                          Yours truly,   Fritz Lehmann
GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
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