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

[Jon Awbrey]

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

Don Mikulecky wrote:
> 
> Language is but one possible formal system in the system we are describing.

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.

> 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.

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

> 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!

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.

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.

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.

Many Regards,

Jon Awbrey

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤