[Arisbe] Re: Language is but one possible formal system

[Jon Awbrey]

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Don,

When these dialogues get too complex,
as they often do, I sometimes resort
to using tags on the old stuff, and
inserting new comments unindented.

Jon

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DM:  Language is but one possible formal system in the system we are describing.

JA:  I guess I go along with those who say that the kinds of languages
     that we all know and love best, that form our human birthright,
     are "naturally evolved biological systems" (NEBS).  In accord
     with my own estimation of their complexity, I have given up
     trying to comprehend these NEBS in all their glory, and
     have retreated to trying to understand various species
     of artificial "formal languages" that lie within my
     power to study in some detail.  To the extent that
     these formal languages mimic some aspect of true
     natural languages, in their syntactic, semantic,
     and pragmatic facets, it may be possible to get
     a slight glimmer of what the real thing is like.

DM:  But it is a special system.  It becomes a model for other models
     of a similar type.  This is because of the self reference built
     into the situation.  The use of language is always self referential.
     This, I think, is what the triadic symbolism attempts to capture.

JA:  I do not see this, as sign relations are involved
     in perfectly straightforward types of reference.

DM:  That is what I surmised before I started this round
     of exposition.  My purpose is to get you to see it.
     Maybe I will fail.  It happened once before.

DM:  The modeling relation can model itself.  It can model the model of itself.
     It can model the model of the model of itself.  The triad can also be
     modeled by the modeling relation.  Yet the modeling relation is in
     itself a symbol.  Can you see where this goes?  As a symbol the
     modeling relation can be a member of a triad.  It is only by
     using some form of methodological reductionism that this
     gets untangled.  However, as in any complex system,
     the reduction of an entanglement *necessarily*
     looses something.  Not only that the thing
     lost *can not* be recaptured from the
     disentangled parts.  It has an
     ontology of its own.  That can
     only be seen in the context
     of the particular whole.
     The triadic system *must*
     be seen in that complex
     context or it becomes
     another reductionist
     trap.

This is mostly my fault for not reading more Rosen before I jump in.
So, for the present and immediate future, I can only be addressing
what I know about "modeling relations" in general, as they are
typically used by many other people.  Continuing apologies.

Some of the first few things that I need to know about any relation are:

   1.  Does it have a definite "arity"?
   2.  If so, is the arity finite?
   3.  If so, what is it?

Most other folks that I know about think of their modeling relations
as analogies, arrows, functions, maps, metaphors, transformations,
and so on, making them all very special relations of arity 2.
So the first thing that I would need to know about Rosen's
notion is how it compares with that.  It would probably
be futile for me to continue without getting clear
on this issue, so I will stop here.

DM:  The problem is that any triad exists in the context of a larger
     system and contributes to that larger system's definition while
     deriving its own meaning from the larger system.  Hence triads
     are a formal system into which particular aspects of the natural
     system are encoded.  The modeling relation represents the very
     act of using the triadic concept as a special case!

JA:  I have the feeling that we are using these words in very different ways.
     What exactly do you mean by a "triad"?  My current guess would be that
     it might be a 3-tuple of the form <object, sign, interpretant> that
     is an element of a particular type of 3-adic relation, L c OxSxI,
     where the sets O, S, I are the object domain, sign domain, and
     interpretant domain, respectively, of the sign relation L.

JA:  It is frequently useful to approach the concept
     of a full-fledged sign relation in three phases:

     1.  A "sign relation" simpliciter, L c OxSxI, could be just about any
         3-adic relation on the arbitrary domains O, S, I, so long as it
         satisfies one of the adequate definitions of a sign relation.
     
     2.  A "sign process" is a sign relation plus a significant sense of transition.
         This means that there is a definite, non-trivial sense in which a sign
         determines its interpretant signs with respect to its objects.
         We often find ourselves writing "<o, s, i>" as "<o, s, s'>
         in such cases, where the semiotic transition s ~> s'
         takes place in respect of the object o.

     3.  An "inquiry process" is a sign process that has value-directed transitions.
         This means that there is a property, a quality, or a scalar value that can
         be associated with a sign in relation to its objects, and that the transit
         from a sign to an interpretant in regard to an object occurs in such a way
         that the value is increased in the process.  For example, semiotic actions
         like inquiry and computation are directed in such a way as to increase the
         "alacrity", "brevity", or "clarity" of the signs on which they operate.

JA:  All in all, sign relations are not limited to purely linguistic types of systems.
     They encompass the data of the senses, natural signs, and plastic representation,
     just to name some randomly-chosen species of this very widely disseminated genus.

DM:  Jon, I think my use of triad is totally that of those in semiotics
     who are students of Pierce.  I have been embroiled in this stuff on
     another list which dwells on this.  That is why your appearance on
     this list was rather interesting to me.  You seem to be working in
     isolation from all this other activity.

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