ONT Re: Inquiry Into Inquiry
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Howard,
Here is a type of chart or diagram that I use
to keep track of the various sorts of domains
that I have to think about in my logical work.
To extent that most of this work derives from
basically Peircean ideas, maybe it will serve
to address your questions about the ways that
the various aspects of sign relations -- what
folks have come to call "syntax", "semantics,
"semiotics", and "pragmatics" -- are related
to one another.
--------------------------------///--------------------------------------
Objective Framework (OF) Interpretive Framework (IF)
--------------------------------///--------------------------------------
Formal or Mathematical Objects Formal or Mathematical Signs & Texts
--------------------------------///--------------------------------------
Propositions Expressions
(Logical) (Propositional)
o o
| |
| |
o o
/ \ / \
/ \ / \
o o o o
Sets Maps Set Names Map Names
(Geometric) (Functional) (Geometric) (Functional)
--------------------------------///--------------------------------------
I am always working within a suitable sign relation, say L c OxSxI, where O, S, I
are the pertinent domains of objects, signs, and interpretant signs, respectively.
The objects are the things that I have to mention, to talk and to think about.
The signs and the interpretants are what I use to talk and to think about them.
Let me restrict my attention for now to that part of my work where I spend most of my time
exploiting certain analogies between logic and real analysis, that is to say, between sets
of type B^k and (B^k -> B) and sets of type R^k and (R^k -> R), with B = {0, 1}, R = Reals.
The "formal objects" are the elements, sets, and functions that go with this set-up.
The "formal signs" are the expressions that are available to indicate these objects.
The word "formal" here means that I am concerned with their form,
and also that their place within the setting is formally declared.
It is considered "good form" to see how far you can get this way,
but everybody knows that you just can't have it all this way.
In computational work, which is what I am almost always working toward these days,
one is primarily concerned with public signs, and so it is convenient to let the
domain of signs and the domain of interpretant signs be the same domain, S = I.
In such a setting, I will typically refer to this as the "syntactic domain",
in part because it will always be formalized as a formal language, with
a formal grammar that defines its membership, and maybe a parser, too.
Now, at this point it may sound almost as if all we need to worry about is the
two sets O and S = I, plus the 2-adic relation of denotation that connects them.
But that would be ignoring the realities of computation, which can be described
as the job of taking obscure signs (like "5+7") for a formal object (a number)
and transforming it somehow into a clear sign (like "12") for the same object.
This process of passing from an initial sign s to an interpretant sign s' to
another interpretant sign s", ..., and eventually to a canonical or a normal
sign for the same object is a special case of a "sign process" or "semiosis".
The full pragmatic sign relation is L c OxSxI.
Syntax is the business of defining S as a set.
Semantics is the 2-dim projection of L on OxS.
Semiotic transitions are certain pairs in SxI.
When the setting is very rich, with many types of objects,
typically organized into an "ontological hierarchy" (OH),
along with all of their corresponding sign classes, then
I will try to organize the whole panoply of objects and
signs into an "objective framework" (OF), on one side,
and an "interpretive framework", on the other side.
Now this works well enough as long as these sides
do not overlap too much, but when you begin to
need to start talking and thinking about your
own syntax, that is, to make pieces of the
IF into objects of discussion and thought,
and thus to push them into the OF, then
you have to become more sophisticated,
and to need a structure that I call a
"reflective interpretive framework",
or a RIF.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤