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Peirce: His Story of Information

From: Jon Awbrey <jawbrey@oakland.edu>
Date: Thu, 25 Jan 2001 14:36:03 -0500
Message-ID: <3A708023.71B72B26@oakland.edu>
To: Bernard Morand <morand@iutc3.unicaen.fr>, Joshi Mukul Madhukar <mukul@cse.iitb.ernet.in>, machine-learning@egroups.com
CC: Arisbe <arisbe@stderr.org>, RDF Logic <www-rdf-logic@w3.org>, SemioCom <semiocom@listbot.com>, Mary Keeler <mkeeler@u.washington.edu>, Jack Park <jackpark@VERTICALNET.COM>

Bernard Morand wrote:
> A 09:24 25/01/01 -0500, Jon Awbrey a 嶰rit:
> > The history of our ideas about information in relationship to
> > notions of entropy or uncertainty is really quite fascinating.
> > Most people are unaware that C.S. Peirce was lecturing on the
> > subject that he called the "Theory of Information" at Harvard
> > as early as 1865.
> Jon,
> I have to be counted among those who are unaware of this Peirce's Lecture.
> Then I would be very grateful if you could give the reference.  Is it in
> what is usually quoted as Harvard Lectures?  If so which one please?
> Thanks
> Bernard
> __________________________________________________________________
> Bernard Morand
> D廧artement Informatique
> Institut Universitaire de Technologie BP53 14123 Ifs Cedex France
> TEL (33) 02 31 52 55 34             FAX (33) 02 31 52 55 22
> e-mail: morand@iutc3.unicaen.fr
> http://www.iutc3.unicaen.fr/~moranb/
> __________________________________________________________________


Bernard, Mukul, & All,

Peirce's "Theory Of Information" (TOI) is a big part
of what my ever ongoing dissertation work is all about.
His most sublime phrases on the subject are now found in
the first volume of the 'Chronological Edition' (CE 1),
although he hints at the idea more sporadically even
earlier than the Harvard Lectures of 1865 and the
closely related Lowell Lectures of 1866.

The material where he moves from the familiar combinatorial business
of counting functions {f : X -> Y}, and the sorts of things that are
amenable to comparison with functions, to "detaching the exponent"
as a measure of "informed constraint", is stuff that I first saw in
the Microfilm Edition, way back at the end of my undergraduate years,
when I was doing my Senior Thesis on a problem that I noticed in his
way of "operationalizing" logical connectives -- a solid two years
work on a single paragraph, namely, CP 4.306! -- but I think that
a lot of this can be found in NEM ('New Elements of Mathematics').

Just in case you do not have the CE handy,
here is how I introduce a number of the
most enticing selections at the end of
the first part of my dissertation:

才~~~~~~~~才~~~~~~~~才DISSERTATION~才~~~~~~~~才~~~~~~~~  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.
Most 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 a 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 yet another contact point between the theory of signs
and the logic of inquiry.  As Charles Sanders Peirce aptly
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.
| (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.  (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.  (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'.  (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 early 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 to our ears 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
to measure the quantitative dimensions of information.
This is precisely the kind of linkage that I need in
this project to integrate the dynamic and the symbolic
aspects of inquiry.

Not by sheer coincidence, the task of understanding
symbolic action, working up gradually through icons
and indices to the point of tackling symbols, is
also one of the ultimate aims that the building
of interpretive and objective frameworks, as
being proposed in this work, is intended to

An OF ("objective framework") is a convenient stage for
those works that have progressed far enough to make use
of it, but in times of flux it must be remembered that
an OF is only a hypostatic projection, that is, the
virtual image, reified concept, or "phantom limb"
of the IF ("interpretive framework") that
tentatively extends it.

When the IF and the OF sketched here have been developed
far enough, I hope to tell wherein and whereof a sign
is able, by its very character, to address itself to
a purpose, one determined by its objective nature
and determining, in a measure, that of its
intended interpreter, to the extent that
it makes the other wiser than the other
would otherwise be.  C'est Moi

From the emblem unfurled on a tapestry to tease out
the working of its loom and spindle, a charge to bind
these frameworks together is drawn by necessity from
a single request:  "To whom is the sign addressed?"
The easy, all too easy answer comes "To whom it may concern",
but this works more to put off the question than it acts as a
genuine response.  To say that a sign relation is intended for
the use of its interpreter, unless one has ready an independent
account of that agent's conduct, only rephrases the initial
question about the end of interpretation.

The interpreter is an agency depicted over and above
the sign relation, but in a very real sense it is simply
identical with the whole of it.  And so one is led to examine
the relationship between the interpreter and the interpretant,
the element falling within the sign relation to which the sign
in actuality tends.  The catch is that the whole of the intended
sign relation is seldom known from the beginning of inquiry, and
so the aimed for interpretant is often just as unknown as the rest.

These eventualities call for the elaboration of interpretive
and objective frameworks in which not just the specious but
the speculative purpose of a sign can be contemplated,
permitting extensions of the initial data, through
error and retrial, to satisfy emergent and
recurring questions.

At last, even with the needed frameworks only partly shored up,
I can finally ravel up and tighten one thread of this rambling
investigation.  All this time, steadily rising to answer the
challenge about the identity of the interpreter, "Who's there?",
and the role of the interpretant, "Stand and unfold yourself",
has been the ready and the abiding state of a certain system
of interpretation, developing its character and gradually
evolving its meaning through a series of imputations and
extensions.  Namely, the MOI (the SOI experienced as object)
can answer for the interpreter, to whatever extent that the
called for conduct can be formalized, and the IM (the SOI
experienced in act, in statu nascendi) can serve as a proxy
for the momentary thrust of interpretive dynamics, to whatever
degree that the called for process can be explicated.

To put a finer point on this result I can do no better at this
stage of discussion than to recount the "metaphorical argument"
that Peirce persistently uses to illustrate the same conclusion.

| I think we need to reflect upon the circumstance that every word
| implies some proposition or, what is the same thing, every word,
| concept, symbol has an equivalent term -- or one which has become
| identified with it, -- in short, has an 'interpretant'.
| Consider, what a word or symbol is;  it is a sort
| of representation.  Now a representation is something
| which stands for something.  ...  A thing cannot stand for
| something without standing 'to' something 'for' that something.
| Now, what is this that a word stands 'to'?  Is it a person?
| We usually say that the word 'homme' stands to a Frenchman for 'man'.
| It would be a little more precise to say that it stands 'to' the
| Frenchman's mind -- to his memory.  It is still more accurate
| to say that it addresses a particular remembrance or image
| in that memory.  And what 'image', what remembrance?
| Plainly, the one which is the mental equivalent of
| the word 'homme' -- in short, its interpretant.
| Whatever a word addresses then or 'stands to',
| is its interpretant or identified symbol.  ...
| The interpretant of a term, then, and that which it stands to
| are identical.  Hence, since it is of the very essence of a symbol
| that it should stand 'to' something, every symbol -- every word and
| every 'conception' -- must have an interpretant -- or what is the
| same thing, must have information or implication.  (CE 1, 466-467).

It will take a while to develop the wealth of information that
a suitably perspicacious and persistent IF would find implicit
in this unassuming homily.  The main innovations that this
project can hope to add to the story are as follows:

1.  To prescribe a "context of effective systems theory" (C'EST),
    one that can provide for the computational formalization
    of each intuitively given interpreter as a determinate
    "model of interpretation" (MOI).  An optimal array of
    concepts and methods would deal with the generic constitutions
    of interpreters, converting paraphrastic and periphrastic
    descriptions of their interpretive practice into relatively
    complete specifications of concrete, implementable, and
    reliable sign relations.

2.  To prepare a fully dynamic basis for actualizing interpretants.
    This means that an interpretant addressed by the interpretation
    of a sign would not be left in the form of a detached token or
    an abstract memory image to be processed by a hypothetical but
    largely nondescript interpreter, but realized as a definite
    brand of state configuration in a qualitatively explicit
    dynamic system.  To fathom what should be the symbolic
    analogue of a "state with momentum" has presented this
    project with difficulties both conceptual and terminological.
    So far in this project, I have attempted to approach the
    character of an active sign-theoretic state in terms of
    an "interpretive moment" (IM), an "information state" (IS),
    an "attended token" (AT), a "situation of use" (SOU), or
    an "instance of use" (IOU).  A successful concept would
    capture the transient dispositions that drive interpreters
    to engage in specific forms of inquiry, defining their ongoing
    state of uncertainty with regard to the practical objects and
    the topical questions of their immediate concern.  Entr'acte

Have I pointed at this problem from enough different
directions to convey an idea of its location and extent?
Here is one more variation on the theme.  I believe that
our theoretical empire is bare in spots.  There does not
exist yet in the field a suitably comprehensive concept
of a dynamic system moving through a variable state of
information.  This conceptual gap apparently forces
investigators to focus on one aspect or the other,
on the dynamic bearing or the information borne,
but leaves their studies unable to integrate their
several perspectives into a full-dimensioned picture
of the evolving knowledge system.

It is always possible that the dual aspects of transformation and
information are conceptually complementary and even non-orientable.
That is, there may be no way to arrange our mental apparatus to grasp
both sides at the same time, and the whole appearance that there are
two sides may be an illusion of overly local and myopic perspectives.
However, none of this should be taken for granted without proof.

Whatever the case, to constantly focus on the restricted aspects
of dynamics adequately covered by currently available concepts leads
one to ignore the growing body of symbolic knowledge that the states
of systems potentially carry.  Conversely, to leap from the relatively
secure grounds of physically based dynamics into the briar patch of
formally defined symbol systems often marks the last time that one
has sufficient footing on the dynamic landscape to contemplate any
form of overarching law, or any rule to prospectively govern the
evolution of reflective knowledge.  This is one of the reasons
why I continue to strive after the key ideas here.  If straw
is all that one has in reach, then ships and shelters will
have to be built from straw.

Peirce citations from:

| Charles Sanders Peirce,
|  'Writings of Charles S. Peirce: A Chronological Edition',
|   'Volume 1, 1857-1866', Peirce Edition Project,
|    Indiana University Press, Bloomington, IN, 1982.
| Cited in:
|  Jon Awbrey,
|   "Inquiry Driven Systems: An Inquiry Into Inquiry",
| http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm


With regard to what Peirce says here:

I think that it stands to reason.

I hope that you find these e-citations as e-citing as I do!

Jon Awbrey

Received on Thursday, 25 January 2001 14:36:31 UTC

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