ONT Re: Inquiry Into Models
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Jon Awbrey wrote (JA):
Howard Pattee wrote (HP):
Heinrich Hertz wrote (HH):
Jon Awbrey did not write (~JA):
Charles Sanders Peirce wrote (CSP):
HP: I would like to wind up a hanging tail or thread
that Jon finds "too long to pursue now."
JA: Doleful experience has taught me that it is best to expand our focus a bit
to compass "sign relations", taken as wholes, over and above just isolated
signs, and taken at least at first in extension as sets of 3-tuples of the
form <o, s, i>, with o, s, i the "object", "sign", "interpretant sign" of
the "elementary sign relation" (ESR) <o, s, i>.
JA: At this point, I personally find the comparsion with group theory to be compelling.
A "group" is another sort of set of 3-tuples that is subject to a terse definition,
and yet the theory of groups encompasses a wealth of imaginative possibilities and
utilitarian potentials that can scarcely be con-&-sur-veyed in any finite lifetime.
JA: As it happens, one of my many "returns" to mathematics,
after a time in the wilds of philosophy and psychology,
was through the slits of "group representation theory",
but the tale thereby hanging is too long to pursue now.
~JA: defining sign as a triad: of 3-tuples of the form <o, s, i>,
with o, s, i the "object", "sign", "interpretant sign"
HP: Let me pursue it briefly because it relates closely to what science is
all about. Group representation theory is a theory of homomorphisms, or
how one formal structure can be mapped into another formal structure so
that interesting or significant properties are preserved. If the mapping
(image, observation, projection, coding, measurement) is from a physical
system (i.e., matter and energy in space and time) to a formal system
then we have a physical model. Here is Hertz's statement of this
epistemic homomorphism (formally a commutation relation):
HH: | We form for ourselves images or symbols of external objects;
| and the form which we give them is such that the logically
| necessary (denknotwendigen) consequents of the images in
| thought are always the images of the necessary natural
| (naturnotwendigen) consequents of the thing pictured.
|
| For our purpose it is not necessary that they [the images] should be
| in conformity with the [external] things in any other respect whatever.
| As a matter of fact, we do not know, nor have we any means of knowing,
| whether our conception of things [our models] are in conformity with
| them [external things] in any other than this one fundamental respect.
|
| H. Hertz (1857-1894),
|'The Principles of Mechanics', Dover, NY, 1984, pp. 1-2;
| orig. German ed., 'Prinzipien Mechanik', 1894.
HP: This is a terse statement. A commutation diagram makes it clearer:
Howard, this diagram seems to have been messed up by your line wrap.
> EXTERNAL _____ WE FORM FOR _____ IMAGES OR SYMBOLS, PICTURES
> OBJECTS OURSELVES . . . [SIGNS, BRAIN STATES, WHATEVER]
> | /
> |
> | /
> |
> [NATURAL LAWS] . . . SUCH THAT . . . [LOGIC, MATHEMATICAL MODEL]
> | /
> |
> NECESSARY / |
> NATURAL /
> |
> CONSEQUENTS ____ARE THE SAME AS____THE LOGICALLY NECESSARY CONSEQUENTS OF THE MODEL
HP: "WE FORM FOR OURSELVES ..." includes all forms of sensing, perception,
observation, measurement, coding, etc. which must be initiated by an
agent or organism. In physics, this is the essential cut between the
world and the observer that is necessary whenever a measurement is made.
It cannot be considered as resulting from natural laws. That is why there
is a "measurement problem" in physics.
HP: Jon's (Peirce's?) definition of sign as a triad, <o, s, i>, with
o, s, i the "object", "sign", "interpretant sign" might correspond
to the first line of the above diagram, but there is no model or
homomorphism, which is why I find it epistemologically inadequate.
Peirce's definition of sign is too vague and ambiguous for me to
unravel. When he has more time, perhaps Jon could diagram it,
and say what "determined or created by" constructively entails.
And what implements the "sort of correspondence" that Peirce
has in mind? Peirce's definition:
CSP: | A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm
Howard, please excuse me if I wax a bit tetchy at this point --
as nobody knows the troubles I've seen over this one scruple --
and not all of the obscurities that one finds being credited
to Peirce are really the obscurities of Peirce, nor even due
to his way of writing, which I think is admirably clear here.
This is a perfectly good -- ok, a nearly perfectly good -- mathematical definition
of a particular family of combinatorial structures, that I know as "sign relations".
A sign relation L is a SET of 3-tuples of the form <o, s, i>,
where o is an element of the set O, called the "object domain",
where s is an element of the set S, called the "sign domain", and
where i is an element of the set I, called the "interpretant domain".
In other words, a sign relation L is a SUBSET of the cartesian product OxSxI,
a circumstance which Asciians write as "L c OxSxI".
Thus CSP did not say, and JA will not say, assertively, what JA mentions here
in the form of a statement that says "a sign is a triad of the form <o, s, i>",
nor any such thing as that.
Many of these further issues are tackled in the running accumulation of links
that I have already posted, but I will admit that the dialogical organization
of some of these sub-sutras is not always the best for finding quick answers,
and so I will work on extracting some more caustically focused e-lucidations.
The link-o-rama that I started on the topic of "Determination" is meant to begin
addressing what Peirce meant by "determined or created" in this sign definition,
and also elsewhere, in general.
To make a long story short, what Peirce means by "correspondence" in this definition
is just the whole 3-adic sign relation itself, which he occasionally describes as
a "triple correspondence". He does not mean to suggest any sort of pallid 2-adic
"imaging" or "mirrortying" as implicated in a "correspondence notion of truth".
The issues that you raise at the end of your note are related to those
that I tried to raise once in the SUO Forum, without much success, but
hope springs eternal and all that, so here is how I tried to spring it:
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Computable Manifolds & Discrete Topologies
http://suo.ieee.org/ontology/msg01383.html
http://suo.ieee.org/ontology/msg01405.html
http://suo.ieee.org/ontology/msg01440.html
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Manifolds Of Sensuous Impressions (MOSI's)
http://suo.ieee.org/ontology/msg01392.html
http://suo.ieee.org/ontology/msg01397.html
http://suo.ieee.org/ontology/msg01399.html
http://suo.ieee.org/ontology/msg01422.html
http://suo.ieee.org/ontology/msg01461.html
http://suo.ieee.org/ontology/msg01476.html
http://suo.ieee.org/ontology/msg01490.html
http://suo.ieee.org/ontology/msg01579.html
Alternates --
http://stderr.org/pipermail/arisbe/2001-March/000341.html
http://stderr.org/pipermail/arisbe/2001-March/000342.html
http://stderr.org/pipermail/arisbe/2001-March/000343.html
http://stderr.org/pipermail/arisbe/2001-March/000344.html
http://stderr.org/pipermail/arisbe/2001-March/000349.html
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Reference Material --
Sign Relations, Extensional Style
http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg01224.html
http://suo.ieee.org/email/msg01233.html
http://suo.ieee.org/email/msg03111.html
http://suo.ieee.org/email/msg04807.html
Higher Order Sign Relations, Quotation, Reflection
http://suo.ieee.org/ontology/msg00625.html
http://suo.ieee.org/ontology/msg00703.html
http://suo.ieee.org/ontology/msg00973.html
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