[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 15

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1.1.3.1.  Levels of Analysis

The primary factorization is typically only the first in a series of analytic
decompositions that are needed to fully describe a complex domain of phenomena.
The question about proper factorization that this discussion has been at pains
to point out becomes compounded into a question about the reality of all the
various distinctions of analytic order.  Do the postulated levels really exist
in nature, or do they arise only as the artifacts of our attempts to mine the
ore of nature?  An early appreciation of the hypothetical character of these
distinctions and the post hoc manner of their validation is recorded in
(Chomsky, 1975, p. 100).

| In linguistic theory, we face the problem of constructing this system
| of levels in an abstract manner, in such a way that a simple grammar
| will result when this complex of abstract structures is given an
| interpretation in actual linguistic material.
|
| Since higher levels are not literally constructed out of lower ones,
| in this view, we are quite free to construct levels of a high degree
| of interdependence, i.e., with heavy conditions of compatibility
| between them, without the fear of circularity that has been so
| widely stressed in recent theoretical work in linguistics.

To summarize the main points:  A system of analytic levels is
a theoretical unity, to be judged as a whole for the insight it
provides into a whole body of empirical data mediately gathered.
A level within such a system is really a perspective taken up by
the beholder, not a cross-section slicing through the phenomenon
itself.  Although there remains an ideal of locating natural
articulations, the theory is an artificial device in relation
to the nature it explains.  Facts are made, not born, and
already a bit factitious in being grasped as facts.

The language of category theory preserves a certain idiom to express this aspect
of facticity in phenomena (MacLane, 1971), and which incidentally has impacted
the applied world by way of the notions of a database view (Kerschberg, 1986)
and a simulation viewpoint (Widman, Loparo, & Nielsen, 1989).  In this usage
a level of analysis constitutes a functor, in effect, a particular way of
viewing a whole category of objects under study.  For direct applications
of category theory to abstract data structures, computable functions, and
machine dynamics see (Arbib & Manes, 1975), (Barr & Wells, 1985, 1990),
(Ehrig, et al., 1985), (Lambek & Scott, 1986), and (Manes & Arbib, 1986).
A proposal to extend the machinery of category theory from functional
calculi to relational calculi is developed in (Freyd & Scedrov, 1990).

Jon Awbrey

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