Re: Rosch: Categorisation

From: Harnad, Stevan (
Date: Sun Dec 31 1995 - 19:41:53 GMT

> From: "Smith, Wendy" <>
> Date: Mon, 4 Dec 1995 09:11:32 GMT
> The purpose of categorisation is to ease the cognitive burden for
> making decisions in the world, without reducing the information to
> the extent that wrong decisions are made.

Again, this critique is of Rosch, not Wendy:

The purpose of categorisation is to avoid the consequences of
miscategorisation. Categorisation means responding differentially to
certain KINDs (or classes, or categories) of input. The purpose of the
data-reduction is to get out of the Funes-problem of unique instances
with which you can do nothing. To reduce is to select what is invariant
in the inputs and will reliably allow them to be categorised correctly,
and to ignore the rest.

This is not just "processing economy": It is part to what it means to
learn and to generalise.

> By categorising,
> everything within a category can be treated in the same way, and
> different from everything in another category. Therefore, properties
> relevant to the task in hand must be used to define the category, and
> irrelevant properties ignored.

What the categoriser needs to do is categorise, not define. And
categorising (which can be thought of as sorting and labeling) is
responding in one way to some kinds of inputs and another way to others.
The moment one graduates from infinitely unique inputs (where Funes
is trapped, because of the Ugly Duckling Theorem) to treating different
inputs as being of the same KIND, one must become selective.

> The real world possesses structure,
> which can be used to this end. For example, certain properties tend
> to occur together, whereas other combinations are rare, eg scales are
> associated with fins, and feathers with wings.

Here's where the metaphysical/physical problem gets mixed up with the
psychological one. We don't "use" structure except inasmuch as it
correlates with what we must do with our inputs, as guided by the
consequences of doing the wrong thing. Co-occurring properties are in
and of themselves as useless as individual properties. The Ugly Duckling
Theorem is as true of pairs or triplets of properties as of single ones.
Correlations, after all, are just properties too!

What we are looking for is the properties that co-occur, not with one
another, but with the consequences of categorising one way or another
way. It's the ones that correlate with getting it RIGHT that we (or our
implicit category learning mechanism) need to find and use, ignoring the

It helps, of course, if nature is merciful, and makes the winning
features easy to find; one way to make them easy to find is to make them
redundant: two for the price of one. But such co-occurrence is useless
if it's not correlated with what the consequences of categorising this
way or that tell us.

Remember that the "intuition pump" to keep in mind when you think of
categorising is mushroom picking: The world is full of mushrooms; some
will nourish you; some will make you sick. At first you don't know which
kinds are which. So you try nibbling a bit and wait for the consequences
that signal whether you were right or wrong. Correlations between the
mushrooms won't help you: only the correlations between the mushrooms and
the consequences of eating them will. A lot of mushrooms may be both
green and round; but if some of them (the small ones) make you sick, and
some of them (the big ones) make you grow big and strong, THAT's the
correlation you should heed, not the other one...

> ER> ...our segmentation of a bird's body such that there is an
> ER> attribute called "wings" may be influenced not only by perceptual
> ER> factors...... but also by the fact that at present we already have a
> ER> cultural and linguistic category called "birds".
> I didn't quite follow this argument. Does she mean that because we have
> a category labelled "birds" we are more likely to consider wings as a
> relevant property? But don't the relevant properties determine the
> categories? Is it that there are naturally occurring categories in the
> real world, and the categories in the perceived world follow this
> structure? Is this the "carving at the joints" bit?

You caught the circularity, as well as the conflation between the
real-world structure and the task at hand: yes, sometimes we carve
nature at her joints, if that's what the consequences of sorting this
way or that dictate. But categorisation could also make us carve
elsewhere, CREATING the joints rather than following them. [I say
"creating," but of course all I mean is selecting from the vast
variation that there is out there, the hard-to-find invariants that
correlate with -- i.e., make you able to do -- successful categorisation.
Carving the "swan" out of the Ugly-Duckling noise, or "blooming,
buzzing confusion".]

Birds, by the way, are not cultural or linguistic categories:
artifacts and adjectives are...

"Bird" is the name of a set of things that we can identify when we see
them, and that we can also describe, and identify from a description.
How we see and "segment" a bird is no doubt influenced both by what
birds look like and are made of and by the fact that we have learned to
call them all "birds." But we have learned to call them all "birds" on
the basis of what they look like (by selecting -- presumably
unconsciously, since we can't say what they are -- the features that
will reliably allow us to sort "birds" from "nonbirds," etc.). So the
"influence" goes both ways: We categorise birds as birds by selecting
the winning features from among the many irrelevant ones, the features
that on the basis of which they can be sorted reliably and correctly.
But now that we have selected those features and ignored the rest, the
bird doesn't look the same as it did when we didn't know it was a bird,
and didn't know which features to select or ignore, so we sampled them
all. That's the influence in the other direction.

> Categories can be described in both the horizontal and vertical
> dimension. The vertical dimension gives increasing abstraction one way,
> and increasing specificity of properties the other way. The horizontal
> dimension gives equivalent categories, defined by prototypes.

See my response to Denise about "levels" and prototypes.

> There is a basic level in the vertical hierarchy, which has
> significantly more attributes than the superordinate category, but not
> significantly less than the subordinate category.

This strikes me as arbitrary and probably also not true. Yes,
abstracting means selecting on fewer and fewer (because more and more
general) features. But there is no "basic" level. You can step into the
category hierarchy at any point: Funes's "Fido-instant," which is just
one view of Fido for one instant -- unique and never recurring. Then
there is Fido, who is a collie, a dog, a canid, a carnivore, a mammal,
an animal, an organism, an object, something... You think "dog" is
"basic" here? Maybe, in the sense that we happen to talk more about and
be more around dogs than Fido's or collies or canids or carnivores, but
what about in a kennel, where almost everything is a dog? or in a pet
store? Would "dog" still be the "basic level" for a collie breeder?

I suspect that with "basic" levels the truth of the matter is revealed
by the old Maine joke (apologies for the sexism; it's not part of the
point) that went "How's your wife?" Answer: "Compared to What?"
Well, what your basic or default category level is is also a "compared
to what?" matter. And if it differs for a collie breeder and a pet store
owner then it might well differ for you and for me, which is to say that
there IS no basic level, just an informational context, consisting of a
set of confusable alternatives that you must somehow sort correctly
(as with the mushrooms, or the sandwich machine with the 6 numbers on

> The basic categories
> also had motor movements and shapes in common. Basic categories were
> also the most abstract level at which a representative image could be
> formed, and the one at which objects were perceived or recognised,
> learned and named.
> Again, I didn't quite follow this argument. Is she saying that the
> basic categories are the basic categories because our imagery,
> perceptions, language etc all converge at this level? Or is it because
> we learn these as a basic category that our perceptions, imagery,
> language etc use this as a base?

You've asked exactly the right question. No doubt there are some things
in the world that are just obviously more like one another than they are
like anything else. (Then the only question is: do any important
consequences for us ride on our distinguishing them from everything
else?) There are probably also other things that are not so obviously
distinct, but we happen to have been born with special detectors that
home in on and magnify their distinctness, and ignore their other
features. (Our color perception is probably like this.) Then there are
things, like dogs, that, because we all happen to live in roughly the
same kind of world, are predictably learned and named by us all. The
image of a "dog" for a comparative zoologist is probably different
from our own image of a dog. And we can perceive, recognise, learn and
name things at countless levels, depending on what we need to tell apart
from what. ("Compared to what?") Rosch is just caught up in typical
cases, whereas categorisation is all-purpose.

> Categories can be defined either by their centres (ie the most typical
> member) or by their boundaries. Prototypes can be agreed even when
> boundaries are hazy (can this also go the other way - ie hazy prototype
> and clear boundary? I'm thinking of "games" here). I thought a
> prototype was something like the "ideal" category member, but that
> doesn't seem the impression given here. So, what exactly is a
> prototype?

Categories are "defined" by the consequences of MIScategorising things.
If you've got to sort a bunch of things into two piles (correctly!) in
order to eat (say, mushrooms vs. toadstools), it has little to do with
"centres" and everything to do with boundaries: There is an all-or-none
boundary between edible mushrooms and toxic mushrooms. If instead
of asking whether a particular mushroom is edible, you ask how TYPICAL
it is of an edible mushroom, you are changing the subject. Typicality
may have centres and hazy boundaries, but categories need not; they can
be anything.

One model of categorisation had been this: We have a prototype or
the ideal or central member in our heads. When we see a
particular instance, our brain deforms the prototype to try to fit it
to that instance. It also tries to deform other prototypes. The one
that's closest to it, i.e., the one that's easiest to deform into it, is
the category it belongs too.

That's a reasonable first guess at a pattern recognition theory, and
it's been tried, and it works for some kinds of patterns (the ones that
really are deformations of prototypes), but not for most patterns, which
are better thought of us sets of features, a few of which are relevant to
correct categorisation, most of which are not. So the trick is not to
deform a prototype but to find the right features. In fact, deformations
on a prototype are probably best thought of as a special kind of dynamic
feature analysis.

There are "categories" like "big" and "small" for which matching to the
closest prototype works. I would say that these categories are not very
categorical! Even the smallest thing is big to some degree, and vice
versa. But is a bird a fish to some degree? And what about "game":
Maybe we can't define "game," hence can't list its relevant features,
but can we sort games and nongames correctly? If there is a criterion
for "correctness" (say, that we all agree whether it is a game or not),
and we can sort correctly, then, whether or not we can say what it is,
there must be a basis on which we are sorting. Is it that everything is
"gamey" to some degree? I doubt it. (Is a bird "gamey"? [I refer, of
course, being a vegetarian, to the "ludic" sense of "gamey," not
the olfactory sense. How "gamey" is the number three?] No, I think
our ability to reliably agree on whether most things are or are not
games, in an all-or-none way, suggests that there ARE features that
games share, and that something in our heads detects them. It's
cognitive psychology's task to find out what they are, and explain how
our mind learns to detect them. Unfortunately, Rosch's "prototype"
notion does not tell us; it does tell us how we decide how typical a
game a game might be, but that wasn't the question...

> The more properties a member shares with the prototype, or other
> members of the same category, the more prototypical it is. Conversely,
> prototypicality is negatively correlated with the number of properties
> it shares with member of different categories. It is also related to
> various psychological measurements, eg reaction time, speed of learning
> etc. However, prototypes alone are not enough to provide a model of
> categorisation or an explanation of how categories are represented.
> Furthermore, "a" prototype is only possible with artificially designed
> categories (because it can be specified, property by property, by the
> experimenter), and hence in the real world a prototype may be somewhat
> abstract.

I'm sure ANYTHING can be rated for for how typical it is of a category
(given that we can readily see clouds as looking like camels, weasels
and whales), be it natural or artificial, concrete or abstract. The
trouble is that typicality judgment is not categorisation! In fact, it
PRESUPPOSES categorisation, for before you can say how typical an X
this thing is, you must know what an X is and that this thing's an X!
Yes, given that you know what a bird is, it is also true that you find
some birds more typical birds than others, that you can both learn and
recognise that the more typical birds are birds quickly than you can
learn or recognise the less typical ones. And probably you can name
more "bird-features" in typical birds than atypical birds, and fewer
features they share with typical fish. But alas none of this explains
how we categorise! One thing's sure: It's not the NUMBER of features
it has that that decides whether or not something is in a category, but
WHICH features it has.

> There are problems. Some of the properties, rather than establishing a
> prototype for a category, can only be assigned after the category
> system has been developed - eg large for piano. Yes, it's large for a
> piece of furniture, but that implies that the category "furniture" has
> already been established. When participants were rating prototypicality
> of category members, their judgement appeared affected by their
> knowledge of the categories. In other words, they were demonstrating
> C.P.! Prototypes will also be context dependent, in that if the
> prototype is for the category "bird", it will differ depending upon
> whether the context is "African" or "English". If a context is not
> specified, people will supply their own - possibly the most usual
> context for them.

All your observations are spot-on: Typicality rating is not
categorisation; it is a similarity judgment, and as such, it can be
influenced by the categorisation (categorical perception). And outcomes
are indeed often context-dependent, with Rosch assuming as universal
facts about categories (e.g. basic levels, prototypes) "facts" that are
merely default contexts most people happen to share.

> It would also appear that events over the course of time can be chunked
> into basic units, which are fairly consistent across people, and also
> across distant and recent memories. The units tend to be those which
> have a script. Again, I was confused here - couldn't this mean that the
> unit may have a cultural basis, which could explain the consistency?
> Anyway, one of the ways in which a boundary was defined in these events
> was by the objects that a person was interacting with. So, for example,
> there were "getting dressed" objects - jeans, t-shirt, socks, in one
> event, and "having breakfast" objects in the next event - coffee,
> cereal, kettle.

All these "categories" are a bit to ad hoc and arbitrary for me: Let's
solve "bird" first, then worry about "getting dressed objects"...

> The objects which are most prototypical for these categories are those
> which fit best into the scripts for the categories, eg cereal is a
> better fit and more prototypical for "having breakfast" than steak and
> chips. Again, I'm not sure of the point here - if both are learned
> within a culture, then the more prototypical will fit into the script
> better than the less prototypical, won't they? Also, if the change in
> categories appears to signal a change in behaviour, ie heralds a
> different event, then doesn't this make the boundaries important?

The fact is that this is all such soft, impressionistic stuff that it's
hard to say what it boils down to. Not to a theory of categorisation,
I'll warrant...

> Anyway, within a narrative for an event, basic level objects are
> usually used, and provide the best understanding. Superordinate levels
> are too abstract, and subordinate levels are uneconomical and appear
> pretentious.

Compared to what? And that applies both to the narrative and the level:
I bet you I could provide a context for any narrative that shifts to
different levels of abstraction. Rosch has simply explored the everyday
default context.

> I found the emphasis on introspective evidence in this article
> confusing, because I couldn't disentangle which came first - a bit
> chicken and egg! However, in summary, each category is typified by a
> prototype, and inclusion in the category depends upon the number of
> properties an item shares with the prototype. The properties are those
> relevant to a particular context, or there would be an ugly duckling
> situation. The boundaries of the categories do not have to be clear cut
> to define and maintain the category. Prototypes may also be involved in
> the learning of categories. Although in real life the prototype is
> considered to be rather abstract, the examples given in the article
> were concrete, and prototypes didn't seem to work as well for the more
> abstract, superordinate levels.

The mechanism of categorisation is much more likely to be feature
detection than prototype matching. Prototype matching only explains
typicality judgment, which is trivial (whereas categorisation is very
NONtrivial). Nor is the "number of features shared with a
prototype" relevant to categorisation: categorisation requires finding
the RIGHT features, the one that will allow reliable, correct, and
in most cases ALL-OR-NONE (i.e. categorical) sorting; there may be fuzzy
categories, with cases where we cannot say what's what, or where there
is not even a fact of the matter about what's what. Those are not the
cases we need to model, because those are the cases where we CANNOT
categorise. Think again of mushroom-sorting: We want to know how we can
do the correct sorting that we can do, not the incorrect sorting that we
can't do (or where the mushroom is neither nourishing nor toxic). We can
worry about the frills after we have delivered the main goods.

There is only one way to go higher in a hierarchy of abstraction: from
the bottom up. The category "carnivore" is of no use for someone who
cannot yet tell apart living and nonliving things, or predator and
prey. No point talking about "colour" if you don't yet know "red" and
"green" (and even "round"). It all starts with concrete sensory stimuli,
and every absolute response you make to them, i.e. every categorical
response, will be based on having abstracted some feature or other.
That's what Funes and the mnemonist had so much trouble doing.


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