Changes

=====1.1.3.1.  Levels of Analysis=====

=====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).

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  

<p>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.</p>

| complex of abstract structures is given an interpretation in actual linguistic  

| material.

To summarize the main points:  A system of analytic levels is a theoretical

<p>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.</p>

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

The language of category theory preserves a certain idiom to express this aspect  

of facticity in phenomena (MacLane, 1971), which incidentally has impacted the  

 

applied world in the notions of a database view (Kerschberg, 1986) and a  

The language of category theory preserves a certain idiom to express this aspect of facticity in phenomena (MacLane, 1971), which incidentally has impacted the applied world in the notions of a database view (Kerschberg, 1986) and a simulation viewpoint (Widman, Loparo, & Nielsen, 1989).  In this usage a level constitutes a functor, that is, 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 to relational calculi is developed in (Freyd & Scedrov, 1990).

simulation viewpoint (Widman, Loparo, & Nielsen, 1989).  In this usage a level  

constitutes a functor, that is, 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 to relational calculi is developed in (Freyd &  

Scedrov, 1990).

=====1.1.3.2.  Base Space and Free Space=====

=====1.1.3.2.  Base Space and Free Space=====