Re: Roles and dependence

sowa@west.poly.edu (John F. Sowa)
Date: Sat, 23 Sep 1995 22:33:34 +0500
From: sowa@west.poly.edu (John F. Sowa)
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To: cg@cs.umn.edu, phayes@ai.uiuc.edu, srkb@cs.umbc.edu
Subject: Re: Roles and dependence
Cc: p.m.simons@leeds.ac.uk, phayes@cs.uiuc.edu, phismith@ubvms.cc.buffalo.edu
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Pat Hayes:

>Very, very little is *logically* necessary.

True.  Nothing but tautologies and anything that follows from explicit
axioms and definitions.  But that was my point:  Firstness, Secondness,
and Thirdness do not depend on physical properties of the world, but
on the conceptions that we use for classifying and talking about it.
Following is one of Peirce's shortest and simplest statements of the
distinction:

   First is the conception of being or existing independent of anything
   else.  Second is the conception of being relative to, the conception
   of reaction with, something else.  Third is the conception of mediation,
   whereby a first and a second are brought into relation.

Note that the distinction depends on "conceptions".  It does not depend
on the way the world is, but on the way that we think about it, classify
things in it, talk about them, and define the words or predicates we use.

>Side remark: discussions of counterfactual conditionals often, it seems to
>me, fail to appreciate the need for consistency with the entire mass of our
>knowledge. Eg its one thing to say, if Hannibal hadnt crossed the alps,
>then...; but I find it impossible to imagine Putnam's 'twinearth' world in
>which H2O is replacedf by XYZ....

Peirce's distinction does not depend on counterfactual conditionals.
I agree with you about the problems of such discussions, and I have never
found Putnam's twin earth examples very convincing.  But I wasn't using
such arguments.  I was giving examples of beliefs that some people
sincerely believe and have presumably reconciled to the entire mass of
their knowledge.  In any case, those examples were for illustrative
purposes and were not central to my point.

I will try once more to state my understanding of what Peirce
was trying to say:

 1. Firstness classifies an entity by its intrinsic structure, pattern,
    or form, independent of any relationships it may have to any external
    entity.  In logic, Firstness can be represented by monadic predicates
    such as circle(x), potato(x), or elephant(x), which describe the form
    of an entity x without taking into account any other entities external
    to x.

 2. Secondness classifies an entity according to some relationship it may
    have to some external entity.  Despite their structural differences,
    a potato and a steak can both be food for some human being; a horse,
    a bicycle, and a jet plane can be a mode of transportation for somebody;
    and a human being and a business organization can be classified as
    legal persons in some contract.  Each of these entities can be described
    by its own form (Firstness).  But by its relationship to some external
    entity, it is classified as a type of Secondness:  Food, ModeOfTransport,
    or LegalPerson.  In logic, these types may be represented by explicit
    dyadic predicates or by monadic predicates food(x) or legalPerson(x),
    whose definitions involve an implicit dyadic relation to something
    else:  x is food only if it is suitable for eating by some animal y;
    x is a legal person only if x can be a party to some contract y.

 3. Thirdness classifies an entity by its mediating effect in bringing
    other entities into relation.  As an example, the Firstness of an
    architectural drawing is its form as pencil marks on paper.  It can
    be described by a monadic predicate whose truth or falsity is
    determined by the pattern of marks without regard to their meaning.
    As Secondness, the pattern of the drawing reflects the structure of
    some building (let's assume one that already exists to avoid any
    distractions about hypotheticals).  The Secondness depends on a dyadic
    predicate that relates the pencil marks y to the physical structure z.
    As Thirdness, the drawing is a guide for a contractor or builder who
    translates (or has translated) the pattern of marks to a structure of
    wood, steel, and concrete.  It would be defined by a triadic predicate
    that involves the builder x who maps the drawing y to the structure z.

I hope that this statement is "crisp" and "clear" enough.  As stated, 
it doesn't really sound like a very important distinction.  But its
importance comes from the applications, especially to some of the 
purposes that Peirce used it for:  his three-way distinction of signs
as icon, index, and symbol (his words); and his three-way division of
semiotics as syntax, semantics, and pragmatics (those terms were introduced
by Charles Morris in 1938 when he was trying to explain Peirce's semiotics;
CSP's actual terms were "pure grammar" for syntax, "logic proper" for
semantics; and "rhetoric" for pragmatics.)  He also applied it to a
three-way classification of logical contexts as actuality, modality,
and intensionality.  That is an application that I plan to discuss more
fully in my talk at the AAAI Fall Symposium on Context in November.

John