Re: Classical Categorisation

From: Harnad, Stevan (
Date: Sun Feb 04 1996 - 18:06:26 GMT

> From: "Baden, Denise" <>
> Date: Sun, 4 Feb 1996 17:36:41 GMT
> The classical view of categorization was that we sort things into
> categories based on feature detection i.e by those features that are
> necessary and sufficient to sort them.
> Rosch had several objections to the classical view. She pointed out
> that subjects are unable to say which features they are using when
> they sort items into categories, but they can tell you which they
> believe to be most typical. Rosch also draws on Wittgenstein's
> arguments, using the oft quoted example of our inability to define a
> game based on its necessary and sufficient features. Different games
> share family resemblances, but have no common invariant feature.
> This led Rosch to build categories around prototypes.

Fine until the last bit: You need to define family resemblances.
Also what does "building categories around prototypes" mean?

> Rosch and Mervis (1975) found that the more prototypical of a
> category a member is rated, the more attributes it has in common
> with other members of a category and the fewer attributes in common
> with members of contrasting categories. This may be explained in 2
> ways. 1. that such structure is given by the correlated clusters of
> attributes in the real world. 2. the structure may be the result of
> the human tendency, once a contrast exists, to define attributes for
> contrasting categories so that the categories will be maximally
> distinctive.

The finding is that some things are easier to categorise than others,
and these seem to have more features in common. The rest is just
conjecture. Discuss the distinction between what kinds of things there
are and how we can tell which is which (the "ontic" vs. the "epistemic"

> Rosch also presented evidence that prototypes of categories are
> related to the major dependent variables with which psychological
> processes are usually measured. These include things like speed of
> processing, where subjects decide whether x is a member of category
> y, speed of learning of artificial categories, order and probability
> of item output, i.e. when subjects list examples of a category.
> However prototypes do not specify representation and process models.
> For example, in pattern recognition, prototypes can be described as
> well by feature lists, structural descriptions or templates. Also
> prototypes can be represented by both propositional and image
> systems.

Not sure about what you mean by "representation and process models," but
what's clear is that "prototypes" don't tell us how the brain (or any
categorisation system) manages to categorise successfully -- except for
special cases such as "big" and perhaps "happy face" involving relative
magnitudes or the genuine deformation of idealised templates. Prototypes
are a special case of feature theories, hence the opposition is rather
like "apple" vs. "fruit."

I'm not sure what you mean by "represented," but propositional systems
are better for some things than others, and pattern recognition
(category learning) from concrete sensory input is not their strong
point. Not sure what you mean by "image systems."

> Pattern matching theorists argued against the prototype theory,
> maintaining that categories are based on feature detection as there
> is a correlation between features and outcomes.

Kid brother doesn't quite get what you are saying here, particularly as
distance-from-a-template is merely a special kind of feature.

> In addition, many of
> Rosch's criticisms of the feature detection model do not bear
> careful analysis. Firstly, it is not a valid argument to claim that
> because subjects can't pick out the features they use to categorise,
> they are not using features. Most of our methods of doing cognitive
> tasks are not evident by introspection. Also Rosch confuses ontic
> metaphysical questions with epistemic questions. The psychologist is
> interested in how we actually categorize, and so there is little
> point focusing on the grey areas, where people are not sure which
> category to put an item in, as this leads on to questions about what
> things really are.

And those ontic questions need to be settled by physicists, biologists
and philosophers, not psychologists, who need only explain what people
can successfully sort, and how.

> Rosch's prototype idea can also be criticised on the basis that it
> doesn't really give any thoughts to the mechanisms that lie behind
> our ability to categorize. Any mechanism has to ignore irrelevant
> features and pay attention to relevant, invariant features. This can
> be illustrated by the ugly duckling theorem, which proves that 7
> white geese and 1 black swan are all equally different if every
> feature is equally weighted. If every feature is equally weighted,
> then (like Funes) we would not be able to abstract the relevant
> invariant features - everything would be infinitely unique.
> Categories enable cognitive economy - `to reduce the infinite
> differences among stimuli to behaviourally and cognitively usable
> proportions'.

Fine, but kid-bro does no know who Funes is, and couldn't quite figure
out from what you said what the ugly duckling theorem is: Everything is
equally similar to (or different from) everything else unless you favour
some features over others (give an example). The relation to Funes, who
remembered every instant as infinitely unique, is that he could not
selectively weight features, hence could not learn to categorise
anything, because he could not selectively forget and ignore anything;
everything was preserved in its infinite uniqueness, hence there were no
"kinds" of things (indeed, there should have been no "things" either,
just a series of unique instants).

It is not clear, though, whether this has any bearing on what Rosch
actually did and said, for, as you wrote, she was not really explaining
categorisation at all. It does, however, bear on the classical model,
which, again, has nothing wrong with it.

> Computationalists think we categorize on the basis of rules.
> Connectionists think its done by strength of weights - i.e
> invariance extraction eg neural nets can take input, get feedback
> and find what input is correlated with what feedback - leads to
> weighting of relevant features. With unsupervised learning, neural
> nets will sort items into categories without feedback; this really
> just enhances natural contours. With supervised learning, neural nets
> use the feedback signal to pick out the invariant or salient
> features. This results in the formation of categories, which we then
> label/symbol.

Kid-bro doesn't understand what you mean by "natural contours": Explain.
Also, what is the relation between category labels and symbols?

> The categorization that we have enables us to ground symbols in our
> capacity to use them.

Kid-bro doesn't get this at all: Sounds like some sort of ecclesiastical
formula, but what does it MEAN, really?

> If we distinguish between inputs, we are
> categorizing.

Kid-bro: Oh ya? So if I distinguish between two inputs, saying whether
they're identical or not identical, where's the category? (Explain
Miller's absolute discrimination [= categorisation] and relative
discrimination [not categorisation].)

> Funes and mnemonist provide examples of the problems
> that arise from an inability in abstracting the invariant features
> of categories.

Yes, but you'll have to expand on that, of course, not just mention the
key words, so kid-bro understands what you're talking about (and so I know
you do too!)

> A philosophic objection, known as the vanishing intersections
> objection claims that the neural net could not be detecting
> invariant features of categories relative to other categories as the
> invariant feature doesn't exist. But this leads to metaphysics-
> psychologists are interested in how we sort stuff out ( eg not
> interested in what apples really are, or if its still an apple if
> its square and blue).

You mixed up two issues here. First, though you love 'em, this is not
particularly about neural nets! It's about ANY categorisation mechanism;
neural nets are just one possible candidate. Second, vanishing
intersections is not just a metaphysical objection: The objection is
that even among the actual inputs we encounter, those that belong to one
category, especially if it is a very abstract one, such as "goodness,"
"truth" or "beauty", if you look for the features all members share,
there are none! The reply is that if there is nothing the members have
in common, then it is not at all clear how we could sort them correctly!
Even inborn feature detectors wouldn't work if there were no features
distinguishing the members from the nonmembers!

Remember that you are supposed to be weighing the evidence for and
against the "classical" view of categorisation: That it is based on
invariant features. If none exist (and we set aside silly alternatives
such as closeness-to-prototype or either/or features, both of which ARE
features and perfectly classical) then the only alternative to the
classical view is magic. (Ungrounded inborn symbols designating abstract
categories certainly won't do the trick, because they have to be
connected to the world, and that brings in the problem of bottom-up
categorisation and features all over again.)

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