SUO: Re: Sign Relations & Communication
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
JA = Jon Awbrey
SR = Seth Russell
JA: Anyway, it seems that there are still a couple of things about
the basic concept of a sign relation that need to be clarified
before we can go any further.
JA: 1. The term "interpretant" in the pragmatic theory of signs is short
for "interpretant sign", so an interpretant has all of the other
properties that any sign might have, and is distinguished solely
by its role in the particular triples of the form <o, s, i> that
reside in the particular sign relation L c OxSxI in question.
SR: Well I would agree, except for your restraint of *solely* ...
for if there is no distinction, then why bother with the extra
element in your form? So that I agree that were we to analyze
separately the contents of either of the domains I or S formally,
then we contrive not to find any distinctions in the texture of
that analysis ... yet when we put them together in one analysis
(or picture) we will certainly be putting different things in each
domain the differences illustrating the various roles of three domains.
No, I mean that quite literally, and it is one of the most important aspects
of pragmatic semiotics that the interpretant sign really is a sign in relation
to its own interpretant sign, and so on, ad in/finitum, that is, achieving its
own form of closure in ways that are bounded or unbounded, finite or infinite.
Being an object, a sign, or an interpretant sign is not an essential attribute.
It is an accidental, contingent, incidental, pragmatic, relational role that
a thing happens to be playing at a particular moment of relation, expressed
as an "elementary relation" or a 3-tuple transaction of the form <o, s, i>.
At another moment, as embodied in <o', s', i'>, the very same things may
be playing entirely different roles. Don't bother trying to stop me if
you heard this one, but the "Daffy Duck Theory Of The Semiotic Universe"
(D^2 TOTSU) is a perfectly sensible, if somewhat mystical notion to the
Peircean way of thinking, to wit, the idea that the "Whole Universe" (WU)
is quite literally a sign of itself to itself, and thus that the ultimate
cosmic sign relation contains a triple <o, s, i> = <WU, WU, WU>. Really!
More generally speaking, this is what relational thinking is all about.
There need be nothing at all that distinguishes the relational domains
as sets. Think of the permutations of a set X = {1, 2, 3, 4, 5, 6}.
Such a permutation is a bijective function f : X -> X, in other words,
a special sort of relation F c X x X. There are 6! = 720 distinct such
functions f or relations F, but the functional or relational domains are
exactly the same X. Indeed, there are higher levels of abstraction that
are mounted in group theory where we forget all about X and just preserve
the structure of the group of 6! elements, Aut(X) = {automorphisms of X}
or Sym(6) = {symmetries of a set of 6 elements}.
JA: 2. Think of what I have been saying as a claim about
the "minimal adequate database" or the "minimal
adequate symbol parsing table" that one needs
either to model or to specify a significant
fragment of a real, not-excessively-trivial
communication process. Just by way of
a catchy title, let's call it the
Rosetta Stone Hypothesis.
SR: Perhaps I can get you to just blurt out this
Rosetta Stone ... huh? .... perhaps yes?
Been here, doing that.
JA: Applying this to the Computer question -- a section of
my dissertation is on this, and so I assure you that I
have been and will continue to take it quite seriously:
SR: Yes I did get the drift that you had been all over this territory ...
perhaps you can guide me ... bearing in mind of course that I am
not without my own intentions as to my final destination.
Gosh, I appreciate the vote of confidence, but my dissipation is still ongoing,
and I am probably the last person that you'd ever want to ask for guidance on
how to get it done. It's more of a tying together loose threads that nobody
would let me bundle or follow through the first three or four times around
kind of quest for me.
JA: There will be a sign relation L that can be said to capture a significant aspect
of what the "computer", that is, a physical system under the control of a program,
is doing with formal syntactic domain S. Here, S will be a formal language over
some alphabet A, that is to say, S c A* = the set of all finite strings over A.
SR: What (relation ?) does your sign 'c' stand for?
Mentally underscore it and read it as "subset of".
JA: Like I said once before, in these formal contexts we will almost always
have S = I, so the Sign and Interpretant columns will be filled with
elements from the very same formal language S = I c A*.
SR: Elements, yes perhaps, but content ... no, I don't think so ... not at least
if they are parts of the *same* picture and are analyzing *collectively*
some particular conundrum ... for then (as in my comment above) we would
not need the extra column at all. You have swept it away.
Pragmatic Agon: "The winning of our dis/content falls mainly in the O domain."
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤