[Inquiry] Re: Differential Logic A -- Discussion

Jon Awbrey jawbrey at att.net
Mon Feb 16 09:10:04 CST 2004


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DLOG A.  Discussion Note 13

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HT = Hugh Trenchard
JA = Jon Awbrey

Re: DLOG A Discussion 12.  http://suo.ieee.org/ontology/msg05421.html

Copied with corrections here:

JA: The way I see it, we have a reality, say x, and then we have a representation
    of that reality, say y.  If the representation y is "analytic" or "articulate"
    in any sense of those words, then it will analyze or articulate the reality x
    in terms of y's components, say, for example, y_1, y_2, y_3, just for a start.
    So we have a picture like this:

                         x              y
                         o------------->o
                                       /|\
                                      / | \
                                     /  |  \
                                    /   |   \
                                   o    o    o
                                  y_1  y_2  y_3

JA: Let me now draw what I consider to be a critical distinction with respect
    to the question of emergence, that is, to put it in the roughest possible
    terms, the issue of whether "the whole is more than the sum of its parts".

JA: If by "whole" we mean the object reality x, and if by "parts" we mean the
    parts of speech, so to speak, of the representation y, then the emergence
    of x beyond the y_j is hardly surprising, indeed, it's a corollary of the
    fact that the representation y is approximate, and thus it proves nothing
    about the potential emergence of y beyond its own components on the plane
    of the given representation.  Of course, this issue will only be confused
    still more by the unreflective reification of representational components.

JA: On the representational plane, however, the utility of the representation
    generally depends on each representation being determined by its components.
    What results from this requirement of useful representations is an obligation
    to render more explicit what we mean by "parts" and by "sum" in a given setting.
    For example, if y is simply the set {y_1, y_2, y_3}, then y is something that can
    be said to exist "over and above" its elements, at least, in some sense, even in
    the case of a singleton set, say, z = {z_1}.  But any claim of "emergence" for
    the relationship of a set to its elements would most likely be discounted as
    trivial, since the set is defined as something that is fully determined by
    its elements.

HT responds:

HT: I haven't given as much thought to this topic
    as I might have liked this weekend.  However,
    let me just throw another scenario out for
    discussion.

HT: It looks to me you've described a static scenario in which the components of
    reality x do not interact with one another -- they are simply properties of
    reality x.  This would be akin to describing an apple as consisting of the
    following properties:  it is roughly spherical, it is red, and it is juicy.

Hugh,

One of the things that I'm trying to convey here is just
how self-conscious we need to be about the gap between
the reality and the many alternative representations.

Notice how empty the space under x in my picture is.

I have not said anything positive about the components of x,
and only emphasized how cautious we have to be about imputing
the structure of the representation to the reality.  Now it's
true that a representation is always kind of static in a way,
verbs as words are not more fluid than nouns, and a program
is a fixed code even if we run it to simulate some process.
But that is a property of representations, and I have not
projected any of it onto the unknown x.

HT: I'm not clear what you mean by "parts of speech" as being the
    components which comprise the whole of reality x, but if they
    are linguistic/semiotic elements which represent properties
    of reality x, then the apple analogy seems to apply.

That was a figure of speech.  My intent was to stress
the fact that the y_j are parts of y, not parts of x.

HT: However, what happens when you complicate
    the scenario so as to describe components
    which interact?

As things stand, it would be complicating the
scenario a bit just to posit components for x,
for example, as depicted in the following way:

                         x              y
                         o------------->o
                        ...            /|\
                       . . .          / | \
                      .  .  .        /  |  \
                     .   .   .      /   |   \
                    .    .    .    o    o    o
                   x_1  x_2  x_3  y_1  y_2  y_3

Now, even if I were so bold to as to risk such a step
at this point in the development of my representation,
what would that really mean?  Fiat Lux?  Not my apple.
In fact, I never deplaned the plane of representation,
much less in a way that would harm any realities with
my filmy images.  Yes, it is probably a safe bet that
that everyone in this theatre has already bought into
the "physical symbol system thesis" (PSST), and so we
can admit that even our imaginings are bound by surly
bounds of earthly constraints, but talking about that
is still another matter, logically speaking, from the
matter of reality x that I chase in the present frame.

So I continue to recommend a great deal of caution with respect to this step,
to advise that we consider very carefully just what it means to take it, and
to suggest that there may be more ways to take it than are dreamt of til now.

A fast break for breakfast ...

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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