Re: Roles, again

"Kenneth D. Forbus" <>
Date: Sun, 10 Sep 95 13:11:20 CDT
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To: (Fritz Lehmann),,,,,
From: "Kenneth D. Forbus" <>
Subject: Re: Roles, again
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I guess I am surprised that Pat should be asked to "more cogent and
specific"; I think the burden is in the other direction.  I have talked to a
number of
Peirce fans over the years, and I have yet to hear any convining argument
that I should bother reading him.  Specifically, I don't see any leverage in
the ideas I have heard attributed to Peirce in this list with regard to
representing knowledge or using it for reasoning.

BTW, the issue of formality is, I think, orthogonal in this discussion.  It
is possible to be both mystical and formal, i.e., spin out some piece of
mathematics that is syntactically and semantically correct, but at best
irrelevant to the what it is claimed to be in service of.


At 04:53 AM 9/10/95 CDT, Fritz Lehmann wrote:
>     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.
>Tel:(714)-856-0671               email: