ONT Re: Inquiry Into Inquiry
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Howard Pattee wrote (HP):
Sungchul Ji wrote (SJ):
Jon Awbrey wrote (JA):
HP: Thanks for your Peirce exegesis. It helps. I'll try to read Turrisi.
Meanwhile, I'll lay off Peirce and think about the modelling relation
and causality.
HP: Sung asks:
SJ: What is the essential difference, if any, between the Hertz's and Rosen's
theories of modeling? If they are different in some essential ways, what
was the influence, if any, of Hertz's theory on Rosen's?
HP: A "modelling relation" and its limitations as used here
in an empiricist's sense (not in the formal mathematical
or logical sense) is in reality exceedingly complex and
can be viewed with several perspectives, and at many levels
of detail or abstraction. Hertz's statements are just the
simplest, earliest, precise, and cleverest expressions that
I know. As I said earlier to Jon, Hertz's opening four words,
"We form for ourselves images ..." evades, probably intentionally,
the really important perceptive, abductive, heuristic, imaginative
processes in creative inquiry.
I cannot help but to hear in these fourwords an an ominous echo of Aristotle:
| But since apparently nothing has a separate existence, except sensible magnitudes,
| the objects of thought -- both the so-called abstractions of mathematics and all
| states and affections of sensible things -- reside in the sensible forms. And for
| this reason as no one could ever learn or understand anything without the exercise
| of perception, so even when we think speculatively, we must have some mental picture
| of which to think; for mental images are similar to objects perceived except that
| they are without matter. But imagination is not the same thing as assertion and
| denial; for truth and falsehood involve a combination of notions. How then will
| the simplest notions differ from mental pictures? Surely neither these simple
| notions nor any others are mental pictures, but they cannot occur without such
| mental pictures. (Aristotle, 'Peri Psyche', 3.8).
|
| Aristotle, "On The Soul", in 'Aristotle (Volume 8)',
| W.S. Hett (trans.), William Heinemann, London, UK, 1986.
HP: I would say Hertz's statement is only the minimum necessary,
but by no means sufficient, condition for an empirically
acceptable model (theory, hypothesis). As Maxwell noted
later, such an austere condition may be correct, but it
is "deficient in both the vividness of its conceptions
and the fertility of its method." In other words,
Hertz's statement is no help in creating models.
It is not a description of inquiry; it is only
a necessary final test.
If I interpret "model" as "effective simulation", "iconic representation",
or "homomorphic image", then I can see your picture of Hertz's statement
as a rough sketch of the right idea, modulo a fair amount of hand-waving
that has left a precipitate residue yet to be cleared up, especially in
and around the current ambiguities of the word "consequent".
But if I try to set this species of iconic models within the context
of a larger question, about the ways that symbol systems facilitate
our adaptation to the realities of our objective world, then I can
only estimate such models as a convenient first approximation to
the genus in question, by no means necessary or even sufficient
in practical terms, nor anywhere near the gold standard when
it comes to the prospects of "analytic understanding" (AU).
HP: To answer Sung's first question, as a minimal necessary condition, I would say
Rosen's modelling relation is essentially the same as Hertz's. However, in my
discussions on OCA the basic relation has been elaborated beyond what Hertz and
Rosen expressed. My elaborations were often developed in collaboration with my
students, Peter Cariani, Luis Rocha, and Cliff Joslyn who have all independently
continued to refine and extend the modeling relation in different contexts. [e.g.,
see Cariani, "Some epistemological implications of devices that construct their
own sensors and effectors" in Varela and Bourgine, eds., "Towards a Practice of
Autonomous Systems" MIT, 1992. pp. 484-493. See also papers by Cariani, Rocha,
and Joslyn in BioSystems 60, April-May, 2001 available at:
HP: http://www.c3.lanl.gov/~rocha/pattee/
HP: To answer Sung's second question, as far as I can remember, Rosen's concept
of the modeling relation was developed without knowledge of Hertz's statement.
It was during one of our discussions that Rosen's figure of speech describing
one of his commuting mappings reminded me of Hertz's statement simply because
of the same figure of speech ("The consequent of the image is the image of the
consequent"), not because we were discussing modeling. That is when I thought
of representing Hertz by a commutation diagram. Since Rosen already had his
modelling relation in mind, I don't think he felt referencing Hertz was
necessary, although I thought it would have added some weight if he had.
HP: For you semioticians, the figure of speech is called "epanados",
a kind of whole-word palindrome or the repetition of a sentence
in reverse order. It is a common figure often used by Shakespeare
(e.g., "Fair is foul and foul is fair" Mac. 1.1.12") and the Bible
(e.g., "The sabbath was made for man, not man for the sabbath. Mk 2:27)
To be really fussy, this latter is an "antimetabole" which is an epanados
that is also an antithesis.
I have always called this the figure of "chiasmus" -- Webster gives the line
from Goldsmith "to stop too fearful, and too faint to go" -- and have called
any operator of the form [P, Q] = P(Q) - Q(P) a "chiasmatic commutator".
Jon Awbrey
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