Re: Roles, again (Pat Hayes)
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Date: Sun, 10 Sep 1995 15:29:32 -0600
To: (Fritz Lehmann),,,,,
From: (Pat Hayes)
Subject: Re: Roles, again
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At  4:53 AM 9/10/95 -0500, 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.

Well, could I make a counterrequest for a clear explanation what they are
supposed to mean which does not appeal to even more unclear ideas?

>(Also, Pat, the fact that Husserl once thought of something is not wholly
>sufficient grounds to dismiss it as nonsense.)

I said nothing as I left, did I? Husserl may be the greatest philosopher of
the 20th century; all I know is, I dont want to get involved with
Husserlian debates.

>     Hayes wrote:
>-----begin quote----
>>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)

Its about to be published in 'Minds and Machines', but I reproduce the
technical points later in this message. 

>....., what other sources have "failed"?

Forgive me, a slip. I should have written 'every attempt I have come
across..' or some such. Indeed, I do not claim total knowledge in this

>     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. 

No, it is to point out that these chemical metaphors (which, I am told,
influenced Peirce's thinking) are inappropriate, because an ionic bond is
'used up' by the bonding process, while there is no logical or ontological
objection to allowing one 'site' to attach itself to many 'ions'; or, what
is equivalent, to allow two such 'bonds' to merge into one:


In a more modern notation, this amounts merely to allowing a bound variable
to occur more than once in the body of the expression: 

                   |        |
(lambda x y z)(A(x,y) & B(z,y)) 

If we allow this it is trivial to create a Triad from Dyads. In case this
is going to be called a 'technical trick', let me point out that Burch uses
the *inverse* of this binding operation crucially in his proofs, which are
supposed to be essentially algebraic in nature, so what objection can there
be to this operation?

 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

Burch, and I believe Peirce before him, placed central importance on a very
particular class of mult-ads, the identities, which are true just when
their many arms denote the same object. Now, it seems to me, there is
something very peculiar in insisting that these things are essentially
relational in their nature, when the only way to explain what they mean is
to appeal to the existence of an individual (the thing called 'A', 'B' and
'C'). But if one admits the existence of the thing which the relation
refers to, all such multi-adic versions of identity collapse to a simple
conjunction of binary identities. The point can be illustrated by the
trinary case. Consider a tinkertoy graph using Triadic Identity:

  A ----3=

This is supposed to express the 'triadic identity' of A, B and C. Now, how
does this differ from the assertion that something exists which A, B and C
are all identical to, ie (exist x)(x=A & x=B & x=C)? To see how close they
are, just replace '3=' with 'x' and this becomes just a little semantic
network. Is this restatement a 'technical trick', or is it not a more
straighforward assertion of the very claim itself? How could one explain
the general notion of 'n-adic identity' without appealing to the idea of
something existing, and the binary notion of identity (eg consider doing it
recursively)? (For that matter, the very idea of bonding (or whatever one
calls sticking a tinkertoy peg into a tinkertoy hole) rather assumes this
idea, arguably: it amounts to an assertion that someTHING exists.)

Perhaps I might make the point using Peirican terminology: 3-identity is
not a Thirdness, but a collection of Secondnesses. Contrast it for example
with the trinary relation of 'collinear' between points. Here, if you take
away one of the three, the relation becomes trivial or meaningless. If I
were to show you the points only two at a time, you wouldnt be able to tell
if they were collinear. But 3-identity is quite different: here, one could
check the truth of the trinary relation by checking the truth of three
binary ones, and a reduction of 3-identity to any of its 2-identities still
carries propositional weight, ie even if I discard or hide the third
argument, telling you that 3-identity holds between A and B (and something
else) does tell you something about A and B (in fact, it is exactly the
assertion A = B).

>.... you can't ever make a triad (as shown above) by
>joining up a lot of dyads. 

You can if you join them up properly; see above.

>(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.

In the case of identity, the dyads are labelled with a dyadic relation, ie =.
Any Peircian graph built using these tinkertoys can be mechanically
relabelled to arrive at a perfectly coherent semantic network which
expresses the same proposition with the same graph: no special care is
needed. The 'new dyads' are all simple statements of identity. (Both need
some way of indicating quantifier scope. What works in one case also works
in the other, however. Details in the review.)

>     B. ......  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.

I find this completely unclear, in spite of the appeals to authority, for
more or less the reasons I gave in my reply to Nicola. I simply don't
believe in this explanation of Firstness. Nothing is 'identifiable'
entirely without reference to other things. (And by the way, what does
'identifiable' mean here? Visually recognisable? In a discussion of these
issues at IJCAI, I was told that a crucial aspect of Firstness was that
something was Firstish if you could define it only by reference to its own
'parts', which would seem to rule out dots.) How can you 'identify'
Cheshire Cat without reference to other objects (in this case, for example,
Lewis Carroll)? Let me repeat as clearly as I can: this notion is simply
incoherent. I challenge you to find me a single example of something which
can be described sufficiently well to 'identify' it without reference to
anything else. Even a mathematical point is something that has a position
but no extent (Euclid), so you have to be able to talk about
positions and extents.

But more to the present point, SO WHAT? What utility do these strange
concepts have, even if an account of them could be given in the terminology
of 20th century Western philosophy?


  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.

Glad you agree. 

 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. 

This stuff REALLY should be left to the historians. Not only, it seems, was
Peirce led into a logical mistake by an inappropriate chemical metaphor, he
also embraced a theory of perception (pure qualia) which has been
completely discredited for over half a century and which isn't consistent
with modern empirical psychology.

(Just by the way, how do you go about describing that Firstness without
reference to a baby, a light, a color and a time? Even the baby, it might
be argued, is experiencing a pure-blue-quale at a certain time, and this
indexicality is essential to the experience, which makes even that into
something binary.)

>     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.

I don't recall bringing them up in the present discussion: you are the
first to even mention level A. It was the B level that attracted my
attention. (If you mean to offer a psychoanalysis of my unconscious
motives, you may be right: who am I to say? However, you arent getting a
fee ;-)


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