Re: Classical Categorisation

From: Harnad, Stevan (
Date: Sun Feb 04 1996 - 12:20:40 GMT

> From: "Harrison, Richard" <>
> Date: Wed, 24 Jan 1996 14:39:10 GMT
> The classical view of categorisation is that category membership is
> based on the invariant features we detect in different kinds of stimuli
> (where kinds is defined by requiring the same response).

To be fair, one should admit that the "classical" view was not as crisp
as this. It did not, like this, clearly focus on features of the sensory
projection that would allow you to respond differentially to (i.e.,
categorise) them. The view was entangled with the physical/metaphysical
question of the what features things REALLY have. So the
"necessary/sufficient" conditions for actually being in the category
were conflated with the features it was necessary/sufficient for an
input to have in order to be able to categorise it successfully. The
latter is the real psychological question, and it's the one you've
described, but, historically, the "classical" view was a willy-nilly
combination of the two.

> This view was thought to be wrong for a number of reasons. The main
> reason centers around the Vanishing Intersections objection. People
> cannot say which features they use to define each category and any
> attempt to define the features can be denied as examples of the
> category exist that do not have that feature.

For a reference, you might cite Fodor's "Language of Thought."

> However, the fact that we
> are not always conscious of the invariant features does not mean we are
> not using them to tell which category stimuli are in. Many other
> cognitive phenomena also operate at a subconscious level (e.g. implicit
> memory). Also, this criticism confuses the psychologist's epistemic
> problem "What can we do?" with the philosophers ontic problem "What is
> actually there?"

Not at all obvious to your kid brother how they've been confused, or
even what has been confused, from what you've written here.

> The claim that because we cannot name the features used to define a
> category we cannot be using invariant features is made especially of
> abstract categories such as "beauty" and "truth" for which it is
> especially hard to find features which the stimuli of category members
> share. Wittgenstein is cited as an authority on this as he pointed out
> no one can define "game" but we all know a game when we see one, hence
> membership is based on family resemblances not features. However,
> abstract categories can be achieved by combining more concrete stimuli
> that have been grounded in invariant features. For example, we could
> correctly categorise a zebra even if we had never seen one before if we
> had combined the previously grounded categories "horse" and "stripes".

All true, but a bit too quick -- and not apparent whether you are
really understanding or just repeating: Kid brother needs to know why
abstract categories are more of a problem than concrete ones (in fact,
what ARE abstract categories?). Also, "game" seems a lot more concrete
than "truth" or "beauty." And also games are mostly man-made artifacts,
so what counts as a game seems to be more up to us than what counts as,
say, true, or even triangular. So give the problem of a abstract
categories a bit more thought...

> An alternative approach has been to suggest that membership of a
> category is due to how close an object resembles a prototype of its
> category (e.g. Rosch and Lloyd, 19??). This view is based on
> experimental evidence that supposedly opposes a classical position as
> well as the philosophical objection already outlined.

The philosophical objection has not really been outlined: Which one? The
"vanishing intersections"? That needs a bit more fleshing out for
kid-brother purposes.

> Rosch and others
> found that people find some category members more typical than others
> and typical members of a category are learnt and categorised faster
> than nontypical members. She inferred that category membership is based
> on closeness to prototypes to explain this data. For example,
> nontypical members took longer to identify than typical ones due to the
> extra processing time required to fit stimuli to prototype.
> This approach has not been successful. It has some value when one is
> trying to explain continuous categories such as "big" as the family
> resemblance of "bigness" has relevance to even the smallest thing.
> Everything is big to some extent. However, talk of family resemblance
> breaks down when considering noncontinuous categories, for example, is
> a game more like "blue" than like "chair"? This question clearly cannot
> be answered. Also, a big methodological problem with the evidence
> provided to support the prototype view is that in studies of typicality
> judgments typicality is not categorisation, in fact, it presupposes
> categorisation.

Fine, but again a bit fast. And prototype-nearness is not identical
to "family resemblance": The latter refers mainly to either/or features,
where family members don't all share one and the same set of features,
but they each have several of them, enough to give them all the
appearance of being in the same family. The notion is vague, and meant
to cover what Wittgenstein thinks are equally vague notions we have of
what belongs in a category. The point is that if we drop the metaphysics
and get down to the business of actually trying to explain how people
can, say, recognise many individuals as belonging to the same family (if
and when they can actually do so, and do so reliably!), then there is
still a set of features that is being used, even if it is of the form:
A & B, or, A & B, or B & not-C, ... etc. Together, this would amount to
a complicated set of features that generate our (correct)

Note that this is not the same as prototype-matching, where there is a
"prototype" or standard form, plus many degrees of deformation of it,
and category membership on whether a given deformation is closer to this
prototype or that one. This may explain relational categories like big
and small, or categories that may have innate templates, such as facial
expressions, but it is unlikely to be a general explanation of
categorisation capacity, for the reasons you mention, as well as the
fact that as a categorisation mechanism, template-matching has proved to
have only very limited success, compared to more general
feature-analytic mechanisms (of which it is merely a special case, as are
the either/or categories of "family resemblances). What is most
important to note is that the general feature-analytic approach to
categorisation is the classical view!

> Most importantly, the prototype approach has not led to a model being
> built that can categorise and, furthermore, even in theory one could
> not be built to categorise as we do. It is not clear, for example,
> where the prototypes would come from. In contrast, approaches adopting
> the classical view that detection of invariant features in stimuli is
> the basis of categorisation have had some success in modeling human
> categorisation.

You have not explained your repeated use of "invariant" to your kid
brother: Invariant under what? We normally thing of things as either
changing under certain transformations, or remaining invariant: The
distance between your eyebrows and your mouth is invariant under
rotation: It doesn't change if your head is upside down. What is on top,
however, is not invariant under rotation. The angles of a triangle are
invariant under a size transformation (they are the same if you make the
triangle bigger or smaller), but its area is not invariant.

A related sense of invariance comes from signal analysis: Remember the
description of the event-related potential (in, say, Libet's paper on
the "readiness potential"): If you measure a subject's EEG (brain waves)
while you sound a tone repeatedly, it looks like a different wiggly line
every time, but if you average those wiggly lines with one another,
though each is different, a specific wave (with an upward and downward
hump) gradually becomes apparent as you average in more and more
wiggles: The averaging is canceling out what is NOT invariant in the
signal -- otherwise known as the noise variance -- and bringing out what
is invariant: The signal buried in the noise.

It is this sense of variance/invariance among features in different
samples of members and nonmembers of a category during category
learning ("honest toil") that you must explain in the context of
categorisation, features, and the "classical" view.

> So, the philosophical and experimental objections to the classical view
> do not stand up to examination, the alternative approach has not been
> useful in modeling human capacities while approaches based on the
> classical premise have had some success. The more useful and
> satisfactory approach is therefore one that is based on the classical
> view.

The last paragraph is the kind you should avoid, one that contains no
information, just a song to the virtues of the punchline! All energy and
information should be focused on persuading kid brother of the truth of
the punchline, and why/how it is true. Assume, as usual, that he is
brilliant, highly motivated, but both uninformed in any of this and
highly critical and easily bored by unclear descriptions or uncompelling
arguments or evidence...

In general, though, I think you understand most of this: You just need
to put it in a form that will pass the kid-brother test!

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