[Arisbe] Re: Differential Logic & Dynamic Systems

Sat, 11 Aug 2001 10:54:01 -0400

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Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

HP: Clarification of Hertz's language:
    A "consequent" is not to be confused with a "consequence"

HP: Hertz's epistemological condition and limitation hold at all levels.  Para-Hertz:

PH: Organisms form images (or models) of external patterns;
    and the form which they give them is such that
    the consequents of the images
    are always
    the images of the necessary natural consequents 
    of the patterns pictured.

Okay, then I miserad that.

So let me back-track to your earlier diagram,
included for convenience here in a moderately
context-preserving sort of way:

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Subj:  Re: Inquiry Into Models
Date:  Sun, 05 Aug 2001 12:20:15 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Arisbe <arisbe@stderr.org>, Generic Ontology Group <ontology@ieee.org>
  CC:  Organization Complexity Autonomy <oca@cc.newcastle.edu.au>

HP: Your diagram is near enough to the way I meant it,
    but it was not meant as a formalization, but as a
    clarification, as in diagramming a sentence.

|   EXTERNAL OBJECTS ____ WE FORM FOR OURSELVES ____ IMAGES, SYMBOLS, OR PICTURES
|         |                                        / [SIGNS, BRAIN STATES, WHATEVER]
|         |                                       /                  |
|         |                                      /                   |
|   [NATURAL LAWS]        . . . SUCH THAT . . . /    [LOGICAL, MATHEMATICAL MODEL]
|         |              /                                           |
|         |             /                                            |
|         |            /                                             |
|   NECESSARY NATURAL /___ ARE THE SAME AS THE _____ LOGICALLY NECESSARY
|   CONSEQUENTS                                      CONSEQUENTS OF THE MODEL

HP: Let me elaborate.  The only formal part is in the right vertical column.
    All the rest is a kind of epistemological diagram indicating the necessary
    conditions for an empirically verifiable formal model to successfully represent
    our experience.  An important aspect of the Hertz's statement, emphasized by the
    diagram, is that the horizontal lines represent the observer's (or agent's) semantic
    interaction with the world (i.e., detection, pattern recognition, observation, measurement),
    the right vertical column represents the syntactic or formal (usually sequential) manipulations
    of the observer, and the left vertical column represents the part of the world (space, time, energy,
    and matter) that we choose to model.  The separation of semantics (measurement of particular events)
    from syntax (the formal model of universal laws) is essential for physical theory.

HP: I often quote von Neumann, although there is general consensus in physics:

    | That is, we must always divide the world into two parts, the one being the observed system,
    | the other the observer.  In the former, we can follow up all physical processes (in principle
    | at least) arbitrarily precisely.  In the latter, this is meaningless.  The boundary between
    | the two is arbitrary to a very large extent.  ...  -- but this does not change the fact
    | that in each method of description the boundary must be placed somewhere, if the method
    | is not to proceed vacuously, i.e., if a comparison with experiment is to be possible.
    |
    | John von Neumann,
    |'Mathematical Foundations of Quantum Mechanics',
    | Translated from the German edition by Robert T. Beyer,
    | Princeton University Press, Princeton, NJ, 1955, 1983.
    | Princeton Landmarks in Physics Series, 1996, page 420.

The paragraph concludes:

| Indeed experience only makes statements of this type:
| an observer has made a certain (subjective) observation;
| and never any like this:  a physical quantity has a certain value.
|
| JvN, MFOQM, page 420.

HP: The most difficult column is the middle vertical column that is often called
    the "epistemic cut" because it separates the subject and object, or better,
    the knower from the known.  This can never be formalized without losing
    its essential function which is to provide the initial conditions for
    the formal model.  As von Neumann has made clear, if you try to move
    the cut left to include the measurement process in the model, then
    you must create a new measurement for new initial condition for
    the new model now including the old measuring device as part
    of the model -- an infinite regress. 

HP: This is summary and consequently it is oversimplified.
    Before saying more, I would like to know if Peirce makes
    a clear distinction or defines an epistemic cut between
    the world and the inquirer.

JA: I think that it would be fair to say -- in fifty words or less, but who's counting? --
    that Peirce treats the lines that we draw between self and other as any other brand
    of hypothetical construction, to wit, lines of whose positions we are bound to draw
    the consequence of their supposed truth, whereon to abandon, defend, or redraw them.

JA: I have strung a few beads, reflective of
    this "particular line of thought" (PLOT),
    on the random sampler of threads from my
    dissertation that I e-nounced under that
    mot "Reflective Interpretive Frameworks".

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Now as to the various artists' "terms of art",
if I am being careful I am supposed to recall
that the 2-trope of "consequence"/"consequent"
disports many splintered nuances even beneath
the banner of the rag-tagmime pragmatic genre,
where Peirce, if I remember it smartly enough,
rimed the rheme of "antecedent"-<"consequent",
while Dewey facetated a parsèd "con-sequence".

All that aside, for the moment, then, what I need to find out about your own usage
is whether you intended the "LOGICALLY NECESSARY CONSEQUENTS OF THE MODEL" in your
diagram to indicate a logical relation, and then whether it is a "model-theoretic"
relation, or else a "proof-theoretic" relation, or both, at least, to the extent
that one can have both.

JA: It hertz me to have to say it,
    But I'm afraid that I observe
    A defect in the picture given.
    Arrows of logical implication
    And arrows of cause to effect
    Need not of necessity commute
    These all too convenient ways.

HP: This is a misunderstanding, not a defect.  Hertz's "consequent" means 
    only "following" in a temporal sense.  It does not imply a "consequence" 
    which means two things.  Logically it means "derived from" and physically
    it means "caused by", often a source of confusion, as you warn us.

So you have "consequent" mean "temporal following" ("secular sequence"?)
on both sides of the commutative diagram?  I am afraid that the words
"LOGICALLY NECESSARY CONSEQUENTS OF THE MODEL" on the right side of
the picture are almost bound and determined to confuse folks about
this intention then.  Just a bit of observation, for all its warts.

PH: Para-Hertz:
    As a matter of fact, organisms do not know, nor have they any means of knowing,
    whether their images or models of external patterns are in conformity with them
    in any other than this one fundamental respect.

JA: I worry a little about that.

HP: I do too, but I can't think of a knock-down counterexample.

I guess that one of the things that worries me mea maximally about this dictum
is that it sounds nigh unto an echo of one of Ludovico Wittgenstein's chosiest
bits'o'wits, and one that's key to one of his oxymoronically "sharpest" points
of criticism that he directed against one of Bertrand Russell's most insipient
endeavors to get wiser, almost in spite of himself, than e'rr he later mangled
to become, to wit:

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Exhibit A:

| A proper theory of judgment must make it impossible to judge nonsense.
|
| Ludwig Witgenstein, 'Notebooks, 1914-1916',
| Edited by G.H. von Wright & G.E.M. Anscombe,
| With English translation by G.E.M. Anscombe,
| Harper & Row, New York, NY, 1969.  Page 97.

Exhibit B:

http://stderr.org/pipermail/arisbe/2001-June/000644.html

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By way of comparison, let us see
what the young C.S. Peirce has to
say on this subject of "nonsense":

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| But not to follow this subject too far, we have
| now established three species of representations:
| 'copies', 'signs', and 'symbols';  of the last of
| which only logic treats.  A second approximation to
| a definition of it then will be, the science of symbols
| in general and as such.  But this definition is still
| too broad;  this might, indeed, form the definition of
| a certain science which would be a branch of Semiotic
| or the general science of representations which might
| be called Symbolistic, and of this logic would be
| a species.  But logic only considers symbols
| from a particular point of view.
|
| A symbol in general and as such has three relations.
| The first is its relation to the pure Idea or Logos
| and this (from the analogy of the grammatical terms
| for the pronouns I, It, Thou) I call its relation
| of the first person, since it is its relation to
| its own essence.  The second is its relation to
| the Consciousness as being thinkable, or to any
| language as being translatable, which I call its
| relation to the second person, since it refers to
| its power of appealing to a mind.  The third is its
| relation to its object, which I call its relation to
| the third person or It.  Every symbol is subject to
| three distinct systems of formal law as conditions
| of its taking up these three relations.  If it
| violates either one of these three codes, the
| condition of its having either of the three
| relations, it ceases to be a symbol and makes
| 'nonsense'.  Nonsense is that which has a certain
| resemblance to a symbol without being a symbol.  But
| since it simulates the symbolic character it is usually
| only one of the three codes which it violates;  at any rate,
| flagrantly.  Hence there should be at least three different kinds
| of nonsense.  And accordingly we remark that that we call nonsense
| meaningless, absurd, or quibbling, in different cases.  If a symbol
| violates the conditions of its being a determination of the pure
| Idea or logos, it may be so nearly a determination thereof as
| to be perfectly intelligible.  If for instance instead
| of 'I am' one should say 'I is'.
| 'I is' is in itself meaningless,
| it violates the conditions of its
| relation to the form it is meant
| to embody.  Thus we see that the
| conditions of the relation of the
| first person are the laws of grammar.
|
| I will now take another example.  I know my opinion is false, still I hold it.
| This is grammatical, but the difficulty is that it violates the conditions
| of its having an object.  Observe that this is precisely the difficulty.
| It not only cannot be a determination of this or that object, but it
| cannot be a determination of any object, whatever.  This is the
| whole difficulty.  I say that, I receive contradictories into
| one opinion or symbolical representation;  now this implies
| that it is a symbol of nothing.  Here is another example:
| This very proposition is false.  This is a proposition to
| which the law of excluded middle namely that every symbol
| must be false or true, does not apply.  For if it is false it
| is thereby true.  And if not false it is thereby not true.  Now
| why does not this law apply to this proposition.  Simply because it
| does itself state that it has no object.  It talks of itself and only
| of itself and has no external relation whatever.  These examples show
| that logical laws only hold good, as conditions of a symbol's having
| an object.  The fact that it has often been called the science of
| truth confirms this view.
|
| I define logic therefore as the science of the conditions
| which enable symbols in general to refer to objects.
|
| At the same time 'symbolistic' in general gives a trivium consisting of
| Universal Grammar, Logic, and Universal Rhetoric, using this last term to
| signify the science of the formal conditions of intelligibility of symbols.
|
| CSP, CE 1, pages 174-175.
| 
| Charles Sanders Peirce, "Harvard Lecture I, 1865",
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

http://stderr.org/pipermail/arisbe/2001-May/000525.html

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Take your pick.
I've pict mine.

Jon Awbrey

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