From: christo@psych.toronto.edu (Christopher Green)
Subject: Categories: bounded or graded?
Organization: Dept. of Psychology, University of Toronto
Date: Tue, 14 Apr 1992 14:38:22 GMT

A few days ago, I was debating with someone about the coherence of the
notion that categories are graded. I briefly refered to an argument by
Stevan Harnad disputing that it is (coherent). Whoever I was debating with
asked that I give Harnad's argument in more detail. What follows is an
excerpt of a discussion between Stevan Harnad and Herb Roitblat on this
issue. I think it lays things out pretty clearly.  It is long, so if anyone
wants to followup, please edit with extreme prejudice.
-christopher-


From: Stevan Harnad
Date: Sat, 21 Mar 92 03:14:43 EST
To: roitblat@uhunix.uhcc.Hawaii.Edu (Herb Roitblat)

[text deleted]

We disagree even more on categories. I think the Roschian view you
describe is all wrong, and that the "classical" view -- that categories
have invariant features that allow us to categorize in the all-or-none
way we clearly do -- is completely correct. Introspections about how
we categorize are irrelevant (did we expect introspection to do
our theoretical work for us, as cognitive theorists?), as are
reaction times and typicality judgments. The performance capacity
at issue is our capacity to learn to sort and label things as we do, not
how fast we do it, not how typical we find the members we can
correctly sort and label, not the cases we CANNOT sort and label,
not the metaphysical status of the "correctness" (just its relation
to the Skinnerian consequences of MIScategorization), and certainly
not how we happen to think we do it. And the categories of interest
are all-or-none categories like "bird," not graded ones like "big."

Cheers, Stevan

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> Date: Sun, 22 Mar 92 21:58:42 HST
> From: Herbert Roitblat  <roitblat@uhunix.uhcc.Hawaii.Edu>
> 
> This is a fundamental disagreement.  It seems to me that your intent
> to focus on the most clearly classical cases derives from your belief
> that classical cases are the paradigm.  Variability from the classical
> case is just "performance error" rather than competence.  Am I correct
> on this last point?  

[Stevan Harnad:]
Incorrect. I focus on categorical (all-or-none) categories because I
think they, rather than graded categories, form the core of our
conceptual repertoire as well as its foundations (grounding).

> Bird is no less trivial than mammal, but we are faced with the
> question of whether monotremes are mammals.  Living things are an all
> or none category.  Are viruses living things?  The question is not
> whether you believe viruses to be living things, you could be
> mistaken.  Are they living things in the Platonic sense that classical
> theory requires?  Bachelor is another classic category.  Is a priest a
> bachelor?  Is someone cohabiting (with POSSLQ) a bachelor?  Is an 18
> year old unmarried male living alone a bachelor?  Is a homosexual male
> a bachelor?  What are the essential features of a bachelor and can you
> prove that someone either does or does not have them?

[Stevan Harnad:]
Herb, I've trodden this ground many times before. You just said before
that you were a comparative psychologist. The ontology of the biosphere
is hence presumably not your data domain, but rather the actual
categorizing capacity and performance of human beings (and other
species). It does not matter a whit to the explanation of the mechanisms
of this performance capacity what the "truth" about montotremes, viruses
or priests is. Either we CAN categorize them correctly (with respect to
some Skinnerian consequence of MIScategorization, not with respect to
some Platonic reality that is none of our business as psychologists) or
we cannot. If we can, our success is all-or-none: We have not said that
cows are 99% mammals whereas monotremes are 80% mammals. We have said
that cows are mammals. And montotremes are whatever the biological
specialists (hewing to their OWN, more sophisticated consequences of
MIScategorization) tell us they are. And if we can't say whether a
priest is or is not a bachelor, that too does not make "bachelor" a
graded category. It just means we can't successfully categorize priests
as bachelors or otherwise!

We're modelling the cognitive mechanisms underlying our actual
categorization capacity; we're not trying to give an account of the
true ontology of categories. Nor is it relevant that we cannot
introspect and report the features (perfectly classical) that generate
our success in categorization: Who ever promised that the subject's
introspection would do the cognitive theorist's work for him? (These
are all lingering symptoms of the confused Roschian legacy I have been
inveighing against for years in my writings.)

> The classic conceptualization of concepts is tied closely to the
> notion of truth.  Truth can be transmitted syntactically, but not
> inductively.  If features X are the definition of bachelor, and if
> person Y has those features then person Y is a bachelor.  One problem
> is to prove the truth of the premises.  Do you agree that the symbol
> grounding problem has something to do with establishing the truth of
> the premises?

[Stevan Harnad:]
Nope. The symbol grounding problem is the problem that formal symbol
systems do not contain their own meanings. They must be projected onto
them by outside interpreters. My candidate solution is robotic grounding;
there may be others. Leave formal truth to the philosophers and worry
more about how organisms (and robots) actually manage to be able to do
what they can do.

> The truth of the premises cannot be proved because we have no
> infallible inductive logic. We cannot prove them true because such
> proof depends on proving the truth of the implicit ceteris paribus
> clause, and just established that proof of a premise is not possible.
> We cannot be sure that our concepts are correct.  We have no proof
> that any exemplar is a member of a category.  I think that these
> arguments are familiar to you.  The conclusion is that even classic
> categories have only variable-valued members, even they cannot truly
> be all-or-none.

[Stevan Harnad:]
The arguments are, unfortunately, familiar mumbo-jumbo to me. Forget
about truth and ontology and return to the way organisms actually
behave in the world (including what absolute discriminations they can
and do make, and under what conditions): Successful (TTT-scale) models
for THAT is what we're looking for. Induction and "ceteris paribus" has
nothing to do with it!

> I think, therefore, that we are not justified in limiting discussion
> to only those categories that seem most clear, but that we would be
> served by developing a theory of conceptual representation that did
> not depend on artificial demarcations.  I argue for a naturalistic
> theory of categories that depends on how people use conceptual labels
> (etc.).  I argue that such use depends on a certain kind of
> computation, that given enough time, people could endorse a wide range
> of categorizations.  The range of categorizations that they can
> endorse is the range of dimensions for which they represent the
> concept as having a value.  My hunch is that the number of these
> dimensions that can be used at any one time for performing a given
> task is small relative to the number of dimensions that they know
> about for the concept.  You seems more interested in characterizing
> the range of dimensions along which people can use their concept, I am
> more interested in the way in which they select those dimensions for
> use at the moment.  

[Stevan Harnad:]
I'm interested in what mechanisms will actually generate the
categorization capacity and performance of people (and animals). My own
models happen to use neural nets to learn the invariants in the sensory
projection of objects that will allow them to be categorized
"correctly" (i.e., with respect to feedback from the consequences of
MIScategorization). The "names" of these elementary sensorimotor
categories are then grounded elementary symbols that can enter into
higher-order combinations (symbolic representation), but inheriting the
analog constraints of their grounding.



-- 
Christopher D. Green                christo@psych.toronto.edu
Psychology Department               cgreen@lake.scar.utoronto.ca
University of Toronto
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