[Arisbe] Re: Inquiry Into Isms -- k-adic versus k-tomic

[Jon Awbrey]

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At 12:34 AM 8/21/01 -0400, Jon wrote:

JA: Here is an old note I've been looking for since we started on this bit about isms,
    as I feel like I managed to express in it somewhere my point of view that the key
    to integrating variant persepectives is to treat their contrasting values as axes
    or dimensions rather than so many points on a line to be selected among, each in
    exclusion of all the others.  To express it briefly, it is the difference between
    k-tomic decisions among terminal values and k-adic dimensions of extended variation.

(snip)

JA: But I think that it is safe to say, for whatever else
    it might be good, tomic thinking is of limited use in
    trying to understand Peirce's thought. 

HP: The way I understood Peirce's -adic thinking depended on
    irreducibility.  This would distinguish them from, say, the
    three binary relations that make up the sides of a triangle,
    or a linear operator on three (or n) elements.  I also assumed
    that this was a conceptual irreducibility or even an ontological
    irreducibility.  Using normal language (since I can't follow Peirce's
    many variations), I would call "sign/interpreter/referent" such an
    irreducible triadic relation, since it is easy to see that no single
    member or pair of the three make any sense without all three. 

HP: Am I too far off base here?  I am not at all sure I understand what else
    Peirce includes in "irreducible".  Could you find some examples or quotes
    that would explain his concept of irreducible?

OK, YAFI (you asked for it).  As it happens, this is precisely what I just used up
one of the better years of my life trying to explain in the SUO discussion group,
and so I have a whole lot of material on this, most of it hardly scathed by any
dint of popular assimilation or external use.

I see a couple of separate questions in what you are asking:

1.  What is the qualitative character of the 3-adic sign relation?  In particular,
    is it better to comprehend it in the form <object, sign, interpretive agent>,
    or is it best to understand it in the form <object, sign, interpretant sign>?

2.  What is reducible to what in what way, and what not?

The answer to the first question is writ
in what we who speak in Peircean tongues
dub the "Parable of the Sop to Cerberus".
Peirce would often start out explaining
his idea of the sign relation, for the
sake of a gentle exposition, in terms
of Object, Sign, and Interpreter, and
then follow with a partial retraction
of the Agent to the Interpretant Sign
that occupies the alleged agent's mind.
Here is the locus classicus for this bit:

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There is a critical passage where Peirce explains the relationship
between his popular illustrations and his technical theory of signs.

| It is clearly indispensable to start with an accurate
| and broad analysis of the nature of a Sign.  I define
| a Sign as anything which is so determined by something
| else, called its Object, and so determines an effect
| upon a person, which effect I call its Interpretant,
| that the latter is thereby mediately determined by
| the former.  My insertion of "upon a person" is
| a sop to Cerberus, because I despair of making
| my own broader conception understood.
|
| CSP, 'Selected Writings', page 404.
|
| Charles Sanders Peirce, "Letters to Lady Welby", Chapter 24, pages 380-432,
| in 'Charles S. Peirce: Selected Writings (Values in a Universe of Chance)',
| Edited with Introduction and Notes by Philip P. Wiener, Dover Publications,
| New York, NY, 1966.

http://suo.ieee.org/ontology/msg02683.html

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Peirce's truer technical conception can be garnered
from another legendary bit of narrative exposition,
the story of the "French Interpretant's Memory":

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Here is a passage from Peirce that is decisive in clearing up
the relationship between the interpreter and the interpretant,
and, not by coincidence, has some bearing on the placement of
concepts as symbols, as their principal aspects are refracted
across the spectrum of sign modalities.

| 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).
|
| Charles Sanders Peirce, 'Chronological Edition', Volume 1, pages 466-467.

http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html

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As it happens, this is exactly the sort of conception of semiosis
that I need in my own work for building bridges between the typical
brands of tokens that are commonly treated in abstract semiotics and
the kinds of states in the configuration spaces of dynamic systems
that are the actual carriers of these signals.  Which explains
why I discuss this passage toward the end of the introduction
to my dissertation and make critical use of it throughout.

HP: I would say the triad "DNA (sign) / code or cell (interpreter) / protein (referent)"
    is the primeval case.  This apparently ontological irreducibility is one reason
    the origin of life is so mysterious, but that is another problem.

I am not sure about this, since I do not know for certain what the object of life is.
It would be just as easy to say that the protein is yet another interpretant sign in
a process whose main object is to simply to continue itself in the form to which it
would like to become accustomed.  The only way I know to decide would be to check
my favorite definition, but there is always a bit of play in the way that it can
be made to fit any particular concrete process.

HP: There are many other types of more or less epistemological  irreducible triads or n-adics,
    popularly known as non-linear systems.  The classical physics case is the three-body problem
    (three masses accelerated by Newton's 2nd law and attracting each other by Newton's law of
    gravitation).  By "more or less epistemological" I just mean that it is unsolvable by any
    closed exact integration, but we can still compute approximate orbits by numerical methods.
    Still, it is easy to see the irreducibility is built into the laws.  However, to a physicist,
    calling this a sign/interpreter/referent relation would be entirely gratuitous ("What can be
    done with fewer assumptions is done in vain with more." -- Ockham). 

HP: What intrigues me as a hierarchy theorist is that the irreducible "sign/interpreter/referent"
    triad at the cognitive level requires an interpreting brain that is some kind of irreducible
    n-adic network (where n >>3).  The brain is initially constructed from cells organized largely
    by the genes.  At that lower level, the "DNA/code/protein irreducibility" works only because
    "coding" itself requires an irreducible triad: "messengerRNA/ribosomes/polypeptides."  At a
    lower level still, all this depends on enzymes which are defined by, and only function as,
    an irreducible triad:  "substrate/enzyme/product".  Furthermore, the function of the enzyme
    depends on its folding into the right shape which is an irreducible n-body problem.  So, it's
    irreducible n-adics all the way down.

It looks like my brain's eyes are too blurry right now
to get to the irreducibility question, so I will save
it for the morrow.

Jon Awbrey

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