[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 28

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1.2.1.3.  Observation and Interpretation

The foregoing discussion of observation and observables must have seemed
like such a useless exercise in hair-splitting that a forward declaration
of its eventual purpose is probably called for at this point.  Division 2
of the present text will introduce a notation for propositional calculus,
and Division 3 will describe a proposal for its differential extension.
To anticipate these developments, a bit schematically, suppose that the
symbol "x" stands for a proposition (a true-false statement) or a logical
property (a qualitative feature).  Then the symbol "dx" will be introduced
to stand for the primitive property of "change in x".  Differential features
like "dx", depending on the circumstances of interpretation, may be taken in
several ways.  Some of these interpretations are fairly simple and intuitive,
while other ways of assigning them meaning in the subject matter of systems
observations are more subtle.  In all of these senses the proposition "dx"
has properties analogous to assignment statements like "x := x + 1" and
"x := not x".  In spite of the fact that its operational interpretation
entails difficulties that are similar to those of assignment statements,
I have reason to believe that this notation may provide an alternate way
of relating the declarative and the procedural semantics of computational
state change.  In one of its fuller senses the differential feature "dx"
can mean something like this:

| The system in question will next be observed to have a different value
| for the property x than the value that it's just been observed to have.

As such, "dx" involves a three-place relationship among an observed object,
a signified property, and a specified observer.  Note that the truth of "dx"
depends on the relative behavior of the system and the observer, in a way that
cannot be analyzed into absolute properties of either without introducing other
observers.  If "dx" is interpreted as the expectation of a certain observer, then
its realization can be imagined to depend on both the orbit of the system and the
sampling scheme or the threshold level of the observer.  In general, differential
features can involve the dynamic behavior of an observed system, decisions about
a designated property, and the attention of a specified observer in ways that
are irreducibly triadic in their level of complexity.

For example, the system may "actually" have crossed the line between "x"
and "not x" several times while the observer was not looking, but without
additional oversight this is purely an imaginary or a virtual possibility.
And it is well understood that oversight committees, though they may serve
the purpose of a larger objectivity by converging in time on more broadly
warranted results, in the mean time only compound the complexity of the
question at issue.  Therefore, it should be clear that the relational
concept indicated by "dx" is a primitive notion, in the general case
irreducible to concepts of lower order.  The relational fact asserted
by "dx" is a more primary reality than the manifold ways of parceling
out responsibility for it to the interaction of separate agents that
may happen to constitute subsystems of the whole.  The question of
irreducibility in this three-place relation is formally equivalent
to that prevailing in the so-called "sign relation" that exists
among objects, signs, and interpreting signs or systems.

If a particular observer is taken as standard, then the discussion reduces
to a universe of discourse about various two-place relations, specifically,
the relations of a system's state to a number of pre-designated properties.
Relative to this frame, a system can be said to have a variety of objective
properties.  An observer may be taken as a standard for no good reason, but
usually a system of observation becomes standardized by exhibiting qualities
that make it suitable for use as such, like the fabled daily walks of Kant
through the streets of Konigsberg by which the people of that city were
said to be able to set their watches (Osborne, p. 101).  This reduction
is similar to the way that a pragmatic discussion of signs may reduce
to semantic and even syntactic accounts if the context of usage is
sufficiently constant or if a constant interpreter is assumed.
Close analogies between observation and interpretation will
no doubt continue to arise as we advance in the synthesis
of intelligent conduct with physical dynamics.

Jon Awbrey

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