Re: Vanishing Intersections

From: HARNAD Stevan (
Date: Thu Jun 06 1996 - 22:37:03 BST

> From: "O'Dell, Samantha" <>
> Date: Sun, 26 May 1996 17:46:16 +0100 (BST)
> The classical view of categorisation is that category membership is
> based on invariant features that we detect in different kinds of
> stimuli.

What does that mean, kid-sib style? What is categorisation? What are
invariant features?

> The idea of vanishing intersections is what the main objection
> to this classical view is based on. It is argued that people cannot say
> which features they use to define each category. Any attempt to define
> the features can be rejected because there are examples of the category
> that exist that do not have that feature.

Usually; not always. And what about AND features vs. OR features, or
even XOR features? Where is the invariant there? (Answer: being red
is a feature, being round is a feature, but being red OR round is
feature too.)

> The issue of vanishing intersections also arises when discussing the
> poverty of the stimulus. Chomsky argues that a child cannot learn the
> rules of Universal Grammar by trial and error with feedback because the
> stimulus is too impoverished. Fodor and others have generalised the
> problem of poverty of the stimulus from children's early grammar
> learning to concepts in general, and part of this generalisation was
> based on the vanishing intersections argument.

Yes, but the two arguments -- poverty and intersections -- are very
different: how?

> This states that it cannot be true that you learn a concept by trial
> and error and feedback because the examples don't have anything in
> common. For example, with concepts such as 'sensory quality' (which
> includes smell, colour, sound, shapes), where all the examples of them
> have nothing in common, it means the intersection vanishes. If this
> occurs then how are we to know what they mean at all? It is not
> possible that we learned it from sensory examples by trial and error
> and feedback. Wittgenstein made a similar argument with 'games'.

To raise this to an A, you should try to answer some of the good
questions you raise: Remember that in general we can't introspect HOW we
do things, so it's not surprising we don't know what features we use: It
doesn't follow that they don't exist; besides, they might be either/or
features, rather than both/and features. And more abstract features may
be grounded in more concrete sensory ones: the category "colour"
(compared to say "shape" or "size") is grounded in the category "red" or
"green" or ...

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