🚀 go-pugleaf

marty1@houdi.UUCP (M.BRILLIANT) of AT&T Bell Laboratories, Holmdel asks:

>	Why require 100% accuracy in all-or-none categorizing?... I learned
>	recently that I can't categorize chairs with 100% accuracy. 

This is a misunderstanding. The "100% accuracy" refers to the
all-or-none-ness of the kinds of categories in question. The rival
theories in the Roschian tradition have claimed that many categories
(including "bird" and "chair") do not have "defining" features. Instead,
membership is either fuzzy or a matter of degree (i.e., percent), being
based on degree of similarity to a prototype or to prior instances, or on
"family resemblances" (as in Wittgenstein on "games"), etc.. I am directly
challenging this family of theories as not really providing a model for
categorization at all. The "100% accuracy" refers to the fact that,
after all, we do succeed in performing all-or-none sorting and
labeling, and that membership assignment in these categories is not
graded or a matter of degree (although our speed and "typicality
ratings" may be).

I am not, of course, claiming that noise does not exist and that errors
may not occur under certain conditions. Perhaps I should have put it this way:
Categorization preformance (with all-or-none categories) is highly reliable
(close to 100%) and MEMBERSHIP is 100%. Only speed/ease of categorization and
typicality ratings are a matter of degree. The underlying representation must
hence account for all-or-none categorization capacity itself first,
then worry about its fine-tuning.

This is not to deny that even all-or-none categorization may encounter
regions of uncertainty. Since ALL category representations in my model are
provisional and approximate (relative to the context of confusable
alternatives that have been sampled to date), it is always possible that
the categorizer will encounter an anomalous instance that he cannot classify
according to his current representation. The representation must
hence be revised and updated under these conditions, if ~100% accuracy
is to be re-attained. This still does not imply that membership is
fuzzy or a matter of degree, however, only that the (provisional
"defining") features that will successfully sort the members must be revised
or extended. The approximation must be tightened. (Perhaps this is
what happened to you with your category "chair.") The models for the
true graded (non-all-or-none) and fuzzy categories are, respectively,
"big" and "beautiful."

>	The class ["chair," "bird"] is defined arbitrarily by inclusion
>	of specific members, not by features common to the class. It's not so
>	much a class of objects, as a class of classes.... If that is so,
>	then "bird" as a categorization of "penguin" is purely symbolic, and
>	hence is arbitrary, and once the arbitrariness is defined
>	out, that categorization is a logical, 100% accurate, deduction.
>	The class "penguin" is closer to the primitives that we infer
>	inductively [?] from sensory input... But the identification of
>	"penguin" in a picture, or in the field, is uncertain because the
>	outlines may be blurred, hidden, etc.  So there is no place in the
>	pre-symbolic processing of sensory input where 100% accuracy is
>	essential. (This being so, there is no requirement for invertibility.)

First, most categories are not arbitrary. Physical and ecological
contraints govern them. (In the case of "chair," this includes the
Gibsonian "affordance" of whether they're something that can be sat
upon.) One of the constraints may be social convention (as in
stipulations of what we call what, and why), but for a
categorizer that must learn to sort and label correctly, that's just
another constraint to be satisfied. Perhaps what counts as a "game" will
turn out to depend largely on social stipulation, but that does not make
its constraints on categorization arbitrary: Unless we stipulate that
"gameness" is a matter of degree, or that there are uncertain cases
that we have no way to classify as "game" or "nongame," this category
is still an all-or-none one, governed by the features we stipulate.
(And I must repeat: Whether or not we can introspectvely report the features
we are actually using is irrelevant. As long as reliable, consensual,
all-or-none categorization performance is going on, there must be a set of
underlying features governing it -- both with sensory and more
abstract categories. The categorization theorist's burden is to infer
or guess what those features really are.)

Nor is "symbolic" synonymous with arbitrary. In my grounding scheme,
for example, the primitive categories are sensory, based on
nonsymbolic representations. The primitive symbols are then the names
of sensory categories; these can then can go on to enter into combinations
in the form of symbolic descriptions. There is a very subtle "entry-point"
problem in investigating this bottom-up quasi-hierarchy, however:
Is a given input sensory or symbolic? And, somewhat independently, is
its categorization mediated by a sensory representation or a symbolic
one (or both, since there are complicated interrelations [especially
inclusion relations] between them, including redundancies and sometimes
even incoherencies)? The Roschian experimental and theoretical line of
work I am criticizing does not attempt to sort any of this out, and no
wonder, because it is not really modeling categorization performance
in the first place, just its fine tuning.

As to invertibility: I must again repeat, an iconic representation is
only analog in the properties of the sensory projection that it
preserves, not those it fails to preserve. Just as our successful
all-or-none categorization performance dictates that a reliable
feature set must have been selected, so our discrimination performance
dictates the minimal resolution capacity and invertibility there must be
in our iconic representations.
-- 

Stevan Harnad                                  (609) - 921 7771
{bellcore, psuvax1, seismo, rutgers, packard}  !princeton!mind!harnad
harnad%mind@princeton.csnet       harnad@mind.Princeton.EDU