[Arisbe] Re: Inquiry Into Inquiry
Jon Awbrey
arisbe@stderr.org
Tue, 07 Aug 2001 17:26:01 -0400
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Howard, I continue from where I left off last time.
Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):
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.
JA: 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.
JA: 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?
JA: 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")
JA: 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.
JA: This is a formalism that is intended to help us talk about, think about,
analyze, design, realize, and amend the very activity of interpretation.
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:
CSP: | 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.
Peirce is expressing what he calls his "non-psychological conception of logic".
Notice that he says "non", not "anti". The "non" in "non-psychological logic"
is like the "non" in "non-associative algebra" -- it generalizes the attached
subject by removing certain axioms, constraints, limitations, or restrictions.
Because psychology is a descriptive science and logic is a normative science,
they have different aims and ends, even on those domains where their surveys
of the phenomena of thinking overlap. That makes them independent sciences.
My guess is that Peirce's allusion to lines and particle motions is intended
to call to the minds of his readers the typical sort of definition of a line,
a geometric object, that readers of the time would have known from treatises
of "analytical mechanics", construed in terms of a relation between geometry
and physics. So I have two guesses about the purpose of the implied analogy:
Sign : Psyche :: Line : Physis.
Either he is saying that logic is independent of psychology
in the way that geometry is independent of dynamics, or he is
saying that logic is independent of psychology in the way that
both geometry and physics are independent of psychology.
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.
There is still this distinction between "being formal" and "being formalized".
The first is a question of "what it is", which we may never know for certain.
The second is a question of what particular agents have actually achieved.
You have to keep on trying to remember that Peirce was an admirer
of a blossoming sense of "form" that was still connected to its
living roots in the "philosophical history of science" (PHOS),
before the so-called "formalists" yanked it out of the ground
of its former meaningfulness, clipped it off, chopped it up,
and grafted it onto all the oddly-shaped, strangely-twisted,
and unnaturally-formed hedges of their own "formal gardens".
CSP: | 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.
I think that this definition is axiomatic in the way that
we say "a group is defined by the following three axioms".
Logic, as a formal and normative branch of the theory of signs,
can be studied, must be studied within the setting of semiotic.
This means that we have all of the resources of sign theory to
use in examining logic, having cast it as circumscribed domain,
and this resource may call on forms of organized phenomenology
that are generally known as "mathematical reasoning", and that
reach beyond normative science, involving as they do empirical
components. In order to see this clearly, it may be necessary
to drop a bit of our Western cultural mythology that says that
"Logic Or Rational Effability" (LORE) is identical with humane
consciousness itself. The apotropaic rationale of this belief
is manifestly obvious when one comes to think about it. Those
folks who still believe it have just not been paying attention.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤