From p. 7:
"The
classical concept is defined 'by necessary and sufficient conditions'
-that is, by set theoretic definitions on properties. It is an
elementary theorem of logic that the whole of the operations of
sentential logic, for instance, may be
grounded solely in the primitive operations of intersection and
complement. More generally, logical sets and categories are defined on
presumed 'atomic properties' and are commensurable wholly based on the
set-theoretic possibilities of those sets –i.e. union, intersection,
complement, etc....
"This
classical categorization therefore expresses an absolute, rigid and
nested hierarchy of levels and containment. In Lakoff’s terms it
expresses a hierarchical 'container schema.' Ultimately, (because they
are nested), at the limits these processes specify (1) a largest
concept: 'something,' (defined by no atomic properties), whose extension
is 'everything,' and (2) a smallest concept: a particular 'object' in
reality, (or possible reality), defined by all its atomic properties.
Given the classical paradigm then, reason necessarily begins with
'something,' (the most general concept), and points, inexorably, to some
'thing,' i.e. a specific object."
"Prototype
theory was a radical departure from traditional necessary and
sufficient conditions as in Aristotelian logic, which led to
set-theoretic approaches."
From Women, Fire and Dangerous Things:
"The
psychologically most basic level was in the middle of the taxonomic
hierarchies....[and] is the only level at which categorization is
determined by overall gestalt perception....[which is] perception of
overall part-whole configuration" (46-7).
"The
ability to categorize at the basic level comes first....basic level
categories develop prior to classical taxonomic categories....classical
taxonomic categories are 'later achievements of the imagination" (49).
"It
is important to realize that these [basic categories] are not purely
objective and 'in the world,' rather they have to do with the world as
we interact with it.... 'It should be emphasized that we are talking
about a perceived world and not a metaphysical world without a knower
(Rosch 1978, p.29)" (50).
"The
classical theory of categories provides a link between objectivist
metaphysics and and set-theoretical models.... Objectivist metaphysics
goes beyond the metaphysics of basic realism...[which] merely assumes
that there is a reality of some sort.... It additionally assumes that
reality is correctly and completely structured in a way that can be
modeled by set-theoretic models" (159).
He argues that this arises from the correspondence-representation model.
So
our basic categories are embodied in image schemas that arise from our
interactions with the world. Recall that one characteristic of these
basic categories is the part-whole gestalt, aka hierarchy. Since image
schemas and basic categories operate below conscious attention we’ve
come to assume that they are inherent to the world themselves and thus
project this notion of “natural hierarchy,” with its most developed
forms in Aristotelian nested, categorical hierarchies. All of which
assumes a basic, particular and inherent “constituent” as foundation at
the bottom and/or a general and inherent “being” as foundation at the
top. Meanwhile the process actually begins in the middle of the
classical taxonomy and we get more specific “downward” and more general
“upward” from there on a useful but constructed hierarchy. This doesn’t
necessarily eliminate hierarchy per se, just contextualizes it is a more
naturalistic, nondual way and only eliminates its dualistic and
metaphysical elements.
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