SUO: Re: Semiotics Formalization
Semiotic SIG,
Submitted for your approval: A number of passages from some
of Peirce's earliest work that are critical to understanding
many aspects of his pragmatic semiotics, or theory of signs,
in particular, its integral relation to the ground-breaking
studies of inference, information, and inquiry that Peirce
was already presenting in his university lectures at the
time in question.
If you will excuse my appending yet another self-quotation,
I will cite here the way that I broach this subject in my
ever-ongoing dissertation work.
<http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm>
Note: To understand the quotations from Peirce you need to know
that he used the term "comprehension" for what we more often call
the "intension", that is, all of the properties of a subject that
are comprehended in a given term for it or implied by a specified
predicate of it. (My memory may be fuzzy here.)
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
1.3.4.17 Recapitulation: A Brush with Symbols
A common goal of work in artificial intelligence
and cognitive simulation is to understand how it
is possible for intelligent life to evolve from
elements available in the primordial sea.
Simply put, the question is:
"What's in the brine that ink may character?"
Pursuant to this particular way of setting out
on the long-term quest, a more immediate goal
of the current project is to understand the
action of full-fledged symbols, insofar as
they conduct themselves through the media of
minds and quasi-minds. At this very point the
quest is joined by the pragmatic investigations
of signs and inquiry, which share this interest
in chasing down symbols to their precursive lairs.
In the pragmatic theory of signs a "symbol" is a
strangely insistent yet curiously indirect type
of sign, one whose accordance with its object
depends sheerly on the real possibility that
it will be so interpreted.
Taking on the nature of a bet, a symbol's prospective
value trades on nothing more than the chance of acquiring
the desired interpretant, and thus it can capitalize on
the simple fact that what it proposes is not impossible.
In this way it is possible to see that a formal principle
is involved in the success of symbols. The elementary
conceivability of a particular sign relation, the pure
circumstance that renders it logically or mathematically
possible, means that the formal constraint it places on
its domains is always really and potentially there,
awaiting its discovery and exploitation for the
purposes of representation and communication.
In this question about the symbol's capacity for meaning,
then, is found another contact between the theory of signs
and the logic of inquiry. As C.S. Peirce expressed it:
| Now, I ask, how is it that anything can be done with a symbol,
| without reflecting upon the conception, much less imagining the
| object that belongs to it? It is simply because the symbol has
| acquired a nature, which may be described thus, that when it is
| brought before the mind certain principles of its use -- whether
| reflected on or not -- by association immediately regulate the
| action of the mind; and these may be regarded as laws of the
| symbol itself which it cannot as a symbol transgress.
| (Peirce, CE 1, 173).
|
| Inference in general obviously supposes symbolization;
| and all symbolization is inference. For every symbol
| as we have seen contains information. And ... all
| kinds of information involve inference. Inference,
| then, is symbolization. They are the same notions.
| Now we have already analyzed the notion of a symbol,
| and we have found that it depends upon the possibility
| of representations acquiring a nature, that is to say
| an immediate representative power. This principle is
| therefore the ground of inference in general.
| (Peirce, CE 1, 280).
|
| A symbol which has connotation and denotation
| contains information. Whatever symbol contains
| information contains more connotation than is
| necessary to limit its possible denotation to
| those things which it may denote. That is,
| every symbol contains more than is sufficient
| for a principle of selection.
| (Peirce, CE 1, 282).
|
| The information of a term is the measure of its
| superfluous comprehension. That is to say that
| the proper office of the comprehension is to
| determine the extension of the term. ...
|
| Every addition to the comprehension of a term,
| lessens its extension up to a certain point,
| after that further additions increase the
| information instead. ...
|
| And therefore as every term must have information,
| every term has superfluous comprehension. And, hence,
| whenever we make a symbol to express any thing or any
| attribute we cannot make it so empty that it shall
| have no superfluous comprehension.
|
| I am going, next, to show that inference is symbolization
| and that the puzzle of the validity of scientific inference
| lies merely in this superfluous comprehension and is therefore
| entirely removed by a consideration of the laws of information.
| (Peirce, CE 1, 467).
A full explanation of these statements, linking scientific
inference, symbolization, and information together in such
an integral fashion, would require an excursion into the
pragmatic theory of information that Peirce was already
presenting in lectures at Harvard as early as 1865.
For now, let it suffice to say that this anticipation of
the information concept, fully recognizing the reality of
its dimension, would not sound too remote from the varieties
of "law abiding constraint exploitation" that have become
increasingly familiar since the dawn of cybernetics.
But more than this, Peirce's notion of information supplies
an array of missing links that joins together in one scheme
the logical roles of terms, propositions, and arguments,
the semantic functions of denotation and connotation,
and the practical methodology needed to address and
measure the quantitative dimensions of information.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤