Re: Vanishing Intersections

From: HARNAD Stevan (
Date: Tue May 28 1996 - 18:25:45 BST

> From: "Lee, Liz" <>
> Date: Tue, 21 May 1996 09:32:14 GMT
> What is the problem of vanishing intersections?
> An intersection is the overlapping of features which two categories
> have in common, a shared feature.

It need not be two categories; it could be many. And it's really the
shared members of many sets: what the sets could me, among other things,
is sensory shadows, and what their shared overlap could be, would be the
features that all the shadows of a given KIND (category) had in common.
You have the basic idea, though, as your following example shows:

> Compare a rickshaw to a milk
> float, they seem to have little in common, but both are means of
> transport, both have wheels, both require people to make them move,
> the rickshaw needs somebody to pull it, the milk float somebody to
> drive it. They share these features.

Note that some of these features are sensory ones, but some are
functional ones (you need to DO something to them to perceive the
feature); other features might be more abstract still.

> Now compare the rickshaw to a
> bottle of milk, the intersection is certainly smaller, they may both
> be said to be containers - one of passengers, the other of milk, and
> both need sombody to move them, there is still an intersection. But
> consider comparing a rickshaw to milk itself, the intersection has
> vanished, there are no features that rickshaws and milk share.

Well, not entirely empty; the both occupy a finite space, for example.
But certainly their immediate sensory shadows look to have nothing in

> "Vanishing intersections" was a concept used by Fodor (amoung
> others) to explain why children cannot learn language by association
> alone. The intersections being referred to are the examples of
> language which the child hears from those around and bases his or
> her knowledge on, Skinner's theory of language acquisition suggests
> that all language is learned by a series of stimulus - response
> bonds. The intersections "vanish" because the examples have
> nothing in common, each thing the child hears is original.

This is rather vague. Remember that the vanishing-intersections argument
is not the same as the poverty-of-the-stimulus argument. The latter
applies to the learning of grammar; the former applies to the learning
of perceptual categories and word meaning.

> The
> concept was misapplied by Fodor because there is something these
> examples share, and that is they are all examples of language, they
> are all syntactically correct being governed by the rules of
> Universal Grammar (Chomsky), so the intersection is not vanishing.

Here I'm afraid you've missed the point, and confused the grammar and
word meaning issues: The vanishing-intersections argument does not apply
to grammar. It applies to perceptual and conceptual categories,
which are supposedly not based on shared features, because the shared
features supposedly do not exist.

The counterargument is that if people can categorise inputs correctly,
they either do it on the basis of magic, or on the basis of shared
features that make the successful categorisation possible. The fact
that we cannot introspect what those features are is just the usual
fact of cognitive life: We don't know HOW we do things, including how
we categorise. We have to wait for cognitive theory to discover how we
do it, and tell us! But the fact that intersections are INVISIBLE to
introspection certainly does not mean that they are non-existent...

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