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=====1.2.1.3. Observation and Interpretation=====
=====1.2.1.3. Observation and Interpretation=====
The foregoing discussion of observation and observables seems like such a useless exercise in hair-splitting that a forward declaration of its eventual purpose is probably called for at this point. Section 2 will introduce a notation for propositional calculus, and Section 3 will describe a proposal for its differential extension. To anticipate that development a bit schematically, suppose that a symbol "x" stands for a proposition (true-false sentence) or a property (qualitative feature). Then a symbol "dx" will be introduced to stand for a primitive property of "change in x". Differential features like "dx", depending on the circumstances of interpretation, may be interpreted in several ways. Some of these interpretations are fairly simple and intuitive, 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
The foregoing discussion of observation and observables seems like such a
that its operational interpretation entails difficulties similar to that of assignment statements, I think this notation may provide an alternate way of relating the declarative and procedural semantics of computational state change.
useless exercise in hair-splitting that a forward declaration of its eventual
purpose is probably called for at this point. Section 2 will introduce a
notation for propositional calculus, and Section 3 will describe a proposal for
its differential extension. To anticipate that development a bit schematically,
suppose that a symbol "x" stands for a proposition (true-false sentence) or a
property (qualitative feature). Then a symbol "dx" will be introduced to stand
for a primitive property of "change in x". Differential features like "dx",
depending on the circumstances of interpretation, may be interpreted in several
ways. Some of these interpretations are fairly simple and intuitive, 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 similar to that of
assignment statements, I think this notation may provide an alternate way of
relating the declarative and procedural semantics of computational state change.
If a particular observer is taken as a standard, then discussion reduces to a
In one of its fuller senses the differential feature "dx" can mean something like this: The system under consideration will next be observed to have a different value for the property "x" than the value it has 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 another observer. 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 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.
universe of discourse about various two-place relations, that is, the relations
of a system's state to several designated properties. Relative to this frame, a
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 only an imaginary or 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 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 are 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.
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
If a particular observer is taken as a standard, then discussion reduces to a universe of discourse about various two-place relations, that is, the relations of a system's state to several 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 properties 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 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 in the synthesis of physical and intelligent dynamics.
becomes standardized by exhibiting properties 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 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 in the
synthesis of physical and intelligent dynamics.
====1.2.2. Symbolic Media====
====1.2.2. Symbolic Media====
