Re: Abstraction

From: S.Harnad (
Date: Tue Feb 10 1998 - 13:47:05 GMT

> From: "SAM HEIGHWAY" <>
> We were talking yesterday about our capacity for remembering
> things, and grouping them up in order to remember more. This we
> decided was a form of abstraction. I was just thinking, you could say
> that in their development, children actually do the complete opposite
> by means of assimilation and accommodation. For example, a child may
> categorise a dog as being anything with 4 legs and a tail. When they
> see a horse for the first time, they have to not only create a
> completely new category for horses, but they have to redefine the
> criteria which determine a dog, and this is accommodation. I know it's
> probably irrelevant to what we were doing in the session, but I just
> found it quite an interesting concept that in cognitive development,
> children use the complete opposite of abstraction in order to
> recognise more objects in the world around them, yet as they grow
> older, they actually simplify the categories in order to remember
> more. Sam

It's not irrelevant at all, but a good observation and connection!

First, you are absolutely right that categorisation is not always
abstraction towards bigger, more general kinds; sometimes it is toward
smaller, more minutely divided kinds.

Piaget's "assimilation/accommodation" has always struck me as a bit vague
and metaphorical, but maybe it does fit what we are talking about now. A
better and more self-explanatory way of describing the kinds of things
children do when they learn to sort and name the things in the world is
"overinclusion" (or "overextension") and "underinclusion" (or

If you show a child the picture of a bear in a story book and say it's a
"bear," and then you show the child a picture of a gorilla, and the child
says "bear," then it is overextending the category, putting things in it
that don't belong. That's probably because the features it has abstracted
are "brown" and "big" and "standing on 2 legs".

To get the category right, the child has to find some more specific features
of Bears and Gorillas so it can tell them apart. Probably the shape of the
head and face will do it, and then the category settles down into what looks
like just the right extension (membership).

But then you show it a panda bear, and it doesn't know it's a bear (because
it's black and white instead of brown). The child must again abstract,
recognising that the colour does not matter, only the shape of the head
and body does. And so on.

(The abstraction is often "implicit" rather than "implicit," which
means the child's perceptual system will detect and use features to do
the categorisation correctly, but the child will not know which features
it is using. We can often sort and name things without knowing HOW we
do it. But if someone points out to us what the features are, we can
usually make this "implicit" knowledge "explicit. Many of the things we do
with language consist of making implicit features explicit, especially when
we are teaching new categories to kid-sib...)

It is by these kinds of over and under extensions of categories and by
their corrections -- usually by changing (implicitly or explicitly) the
features used to decide what's what -- that we all form new

And you're right, that the direction of categorisation and abstraction
is not always "up" in the sense of including more and more kinds of
things in bigger and bigger categories, till the top is just "thing," or
"everything." Some categories are based on subdividing categories we
already have into smaller categories.

The child might learn "flower" first -- for those coloured things that grow
on green stems outdoors -- and only later subdivide them into roses, tulips,
and orchids. This is still abstraction, in that you base your categorisation
on "picking out" some features and ignoring others. (Selecting some features
and ignoring others is exactly what "abstracting" is.) But in this case, the
selection results in a more minute subdivision of a category you already
have, rather than a recombination of the categories you already have into
bigger ones that contain them (as it would be if we learned roses, tulips and
orchids are first, and then only later what a "flower" is).

Some people think there is a "basic level" of categories that we always
learn first (Rosch & Lloyd 1978). That basic level is not too high and
not too low. For example, we will learn "horse" before we learn
"thoroughbred" or "palomino". We also learn "horse" before we learn "mammal"
or "quadruped" (four-legged creature).

It may be true that we learn some levels of our category hierarchies
-- "entry levels" -- before others, because they are the common ones, or the
easy ones, or the more important ones for us. But there is nothing special
about any level. "Dog" may be good enough to describe a dog for you and me,
but for a dog breeder it is useless; what he wants is the breed's name,
say, "collie." And for collie specialists, there are probably more refined
categories. And for evolutionists specialising in "canids" there may be more
general categories, that include dogs, wolves and jackals.

But it's abstraction whether you go up or you go down, because what you are
always doing is picking out and using some of the features and ignoring
others. That's what abstraction is: Finding and naming new categories based
on some features and not others.

Now as to how that is related to the kind of "recoding" and
"rechunking" we are discussing in connection with Miller's Magical
Number 7 paper: The purpose of recoding is to be able to handle more
items of information within the limits of our perceptual capacity, memory,
and available time. A biologist would have to spend a very long time
making lists of particular mammals if he did not have the word "mammal" that
designated them all. Recoding all mammals into that one "chunk" allows
the biologist to contrast, say, reptiles and mammals, without having to
specify which reptiles and which mammals he is talking about. But for a
vertebrate biologist, that's all still too low level. He wants to talk
about vertebrates and invertebrates, and both mammals and reptiles are
vertebrates (they have backbones). The "chunk" he needs for his use is
bigger than the chunk the mammals-specialist needs.

By the same token, a herpetologist (who studies reptiles) needs the "chunks"
corresponding to chameleons, Gecko lizards and Gila monsters. In all these
cases, whether abstracting more finely into smaller categories or more
coarsely into bigger ones, we are always abstracting. And an abstraction, by
basing itself on some features and not others, is always recoding or
rechunking information into the kinds of units needed for the kind of use
you will put them to. If your units are too small, you'll have to spend a lot
of time giving lists instead of just naming the category that they all
belong to. If your units are too big, you'll have to use all kinds of extra
adjectives -- the "black and white spotted kind of dog," the "short-legged,
sausage-shaped kind of dog": rechunking them as "dalmations" and
"dachshunds" respectively makes it much easier to use, understand and
remember those categories.

This also touches on one of the important functions of language, something
that is changing all the time, namely, "lexicalisation". "Lexicon" is
another word for vocabulary. If we invent a word for "short-legged,
sausage-shaped kind of dog" -- namely, "dachshund," we have "lexicalised"
what would otherwise have been a long, awkward phrase to keep saying over
and over.

But we don't lexicalise everything. We only invent words for the "chunks"
that we will need to use over and over again. We don't have a word for
"things that are bigger than a breadbox," or "things that have an odd number
of legs". But if we did need those categories, we could lexicalise them. And
needs change. That's what a growing body of knowledge is all about.

Think of lexicalising -- turning something into a word in your vocabulary --
as a form of rechunking. Our vocabulary is our repertoire of "chunks," just
the size and level in our abstraction hierarchy (from "Mama" all the way
down to electrons and all the way up to galaxies and "things") that we need
for the time being. Language has the resources to add to that vocabulary
whatever we need, whenever we need it.

Rosch, E. & Lloyd, B. B. (1978) Cognition and categorisation.
Hillsdale NJ: Erlbaum Associates

One last point, only for the really careful philosophers and lexicologists
among you:

"Abstraction" is ordinarily thought of as a continuum from the most
"concrete" on one end to the most "abstract" on the other. In general,
"chair" is considered more concrete than "furniture," "dog" more
concrete than "animal," "red apple" more concrete than "redness," and
so on. "Concrete" things are the kinds that you can touch and see with
your senses: you can touch an apple, but not "redness" (let alone
"goodness" or "truth").

If this is so, then why do I say you are "abstracting" whether you move up
or down in your category hierarchy? whether you go from dog to animal or
from dog to dalmation?

The reason is that for a cognitive psychologist, abstraction is
something your brain does that allows you to name things. The way it
does it (whether implicitly or explicitly, and whether moving up or
down) always has to do with using (abstracting) some features rather
than others. In that sense, I must "abstract" whether I am trying to
find something more "concrete" or something more "abstract."

One way of resolving this difference in useage is to remind yourself (or
make explicit for yourself what was already implicit in what I have been
saying) that FEATURES can be categories too. They are not just things you
USE to name something else (an "apple" is a round, red fruit); you
can also name features (and that's what you do when you use them explicitly
rather than implicitly): "round" and "red" are also in our lexicon,
along with "apple" and "fruit."

But, in general, features are bound to be more abstract than objects,
because they are the things we use to pick out the objects; we abstract
features in order to categorise objects. A dog is concrete; a leg is
concrete, but "having four legs" is much more abstract. You can point
at a dog and at a leg, but you cannot point at a "having four legs."
You can point at a "quadruped," which is "an animal that has four
legs," but you can't point at the feature itself, really, just at the
legs. (This is even clearer when instead of a "part"-feature, like
"having four legs", you consider non-part-features like "red" or "round"
or "true" or "good.")

It is probably the object/feature distinction, rather than the
specific/general distinction that underlies some of the uses of the
word "abstract." -- But do not worry about this. It is well beyond
1st-year level cognitive psychology and the Magical Miller paper.

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