[Arisbe] Re: Inquiry Into Inquiry
Jon Awbrey
arisbe@stderr.org
Mon, 06 Aug 2001 15:02:11 -0400
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Howard Pattee wrote (HP):
HP: I have read the passages from Peirce you quote over and over,
but I doubt if I could elaborate sensibly on what it means.
I think a few specific examples might help me interpret
how Peirce's definition of a sign and use of logic might,
or might not, be related to any of the wide variety of
inquiry that produced great discoveries in physics.
Yes, it is a little bit like reading Galois on Group Theory.
If you have a hundred years or so to get a grasp on what
a group is, then you can read his work and realize that
everything he says is perfectly apt. Sadly, we are
not to that point yet, where the Theory of Signs
is a standard part of the undergrad curriculum.
My own advice would be to try and flesh out Peirce's intensional description
of a typical sign relation in the materials of concrete extensional examples.
Think of the theory of sign relations as a subject like algebra, or geometry,
or more concretely, group theory, or graph theory. Most concretely, perhaps,
you might think of it in terms of relational databases, where sign relations
would be represented as a particular variety of three-column relation tables.
| No. 12. 'On the Definition of Logic'.
|
| Logic is 'formal semiotic'. A sign is something, 'A', which brings
| something, 'B', its 'interpretant' sign, determined or created by it,
| into the same sort of correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in which itself stands to 'C'.
| This definition no more involves any reference to human thought than
| does the definition of a line as the place within which a particle lies
| during a lapse of time. It is from this definition that I deduce the
| principles of logic by mathematical reasoning, and by mathematical
| reasoning that, I aver, will support criticism of Weierstrassian
| severity, and that is perfectly evident. The word "formal" in
| the definition is also defined. (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics',
| Four Volumes In Five Books,
| Edited by Carolyn Eisele,
| Mouton, The Hague, 1976.
HP: Simplifying:
A brings B to correspond with C as A corresponds to C.
So we can diagram it as a triangle:
| A (sign)
| / \
| / \
| / \
| / \
| C - - - - - B
| (object) (interpretant sign)
HP: So, A creates B and also brings B into the relation BC which is
the same (or lower?) relation as AC. (Have I got that right?
No, the "correspondence" that is indicated here is a "triple correspondence",
what might be called a "3-place transaction" in database terms. Let us name
this 3-place relation L. Accordingly, to say that "A brings B to correspond
with C as A corresponds to C" is simply to say that A brings B into the same
3-place relation L with something else B' and C as A occupies in the 3-place
relation L with B and C. Posed as an analogy with related terms in the form
<Object, Sign, Interpretant>, one has the proportion <C, A, B> as <C, B, B'>.
This is just a terse way of specifying that L is preserved in the transition
from the triple <C, A, B> to the triple <C, B, B'>. People will often think
that this makes semiosis (the sign process) necessarily an infinite progress,
but this is a mistake, as nothing in this definition of a sign relation says
that an interpretant sign must be distinct from the initial sign of a triple.
| A (sign)
| / \
| / \
| / 1 \
| / \
| (object) C - - - - - B (sign')
| \ /
| \ 2 /
| \ /
| \ /
| B' (sign")
Because of the circumstance that rendering a 3-tuple <x, y, z> of any 3-adic relation
in the figure of a plane triangle will frequently mislead the viewer to imagine that
all 3-adic relations can be decomposed into 2-adic relations, in the way that the
triangle decomposes into its component line segments, I suppose, I will take the
liberty of redrawing your figure in the following fashion -- though it does not
prevent a really dedicated misreader of maps from rushing heedlessly on in this
form of misadventure, it at least e-quips the coarse of my account with e-nuff
of a caltrope to slow the worsted of the unthinking reeders down, just a bit.
| A (sign)
| /
| /
| (object) C ----@
| \
| \
| B (interpretant sign)
HP: To me, so far, this is all uninterpreted formalism.
This is a formalism that is intended to help us talk about, think about,
analyze, design, realize, and amend the very activity of interpretation.
Have to break here,
Will return later,
Jon Awbrey
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HP: It's hard for me to imagine an interpretation that relates
to a physical situation. What does "create" mean? By what
process or action does a sign create an interpretant sign
and a relation? Why is the interpretant called a sign?
HP: The next statement is a real puzzle, especially to a physicist:
| This definition [of sign] no more involves any reference
| to human thought than does the definition of a line as the
| place within which a particle lies during a lapse of time.
HP: Does "line" refer to the trajectory of particle? In which case the line
may be defined by the particle but it is created by forces (other particles)
and therefore line, particle, and forces are inextricably related.
HP: In this comparison, he appears to mean that the sign corresponds to the line
and human thought to the particle. If so, then could he mean that human thought
and external forces (experience, environment) create or define the sign? That is
the only sense I could make of this metaphor, but why would he leave out external
forces and environments? These are the ultimate sources of both particles and
human thought.
HP: Finally, if he means by "deduce" what is normally meant,
and his definition is considered axiomatic, then he is
arriving at his logic by formal means.
| It is from this definition [axiom] that I deduce the
| principles of logic by mathematical reasoning . . .
HP: So I would agree it is a "formal semiotics".
What is lacking for me is an interpretation.
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