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From: markh@csd4.milw.wisc.edu (Mark William Hopkins)
Newsgroups: comp.ai,talk.philosophy.misc,sci.lang
Subject: Categorization: Lakoff's mistake.
Keywords: Reference
Message-ID: <18@csd4.milw.wisc.edu>
Date: 21 Dec 88 00:16:10 GMT
References: <484@soleil.UUCP> <1654@hp-sdd.HP.COM> <1908@crete.cs.glasgow.ac.uk> <151@feedme.UUCP> <719@quintus.UUCP>
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In article <719@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) writes:
>To continue this rather constructive approach of suggesting good books
>to read that bear on the subject, may I recommend
>
>	Women, Fire, and Dangerous Things
>	-- what categories reveal about the mind
>	George Lakoff, 1987
>	U of Chicago Press, ISBN 0-226-46803-8
>
>I don't think the data he presents are quite as much of a challenge to
>the traditional view of what a category is as he thinks, provided you
>think of the traditional view as an attempt to characterise ``valid''
>categories rather than actual cognition, just as classical logic is
>an attempt to characterise valid arguments rather than what people
>actually do.  As an account of what people do, it is of very great
>interest for both AI camps, and

I don't think it is even a challenge to the traditional view, when the view
is taken as an attempt to characterize human cognition.

Lakoff's essential argument is that humans do not form categories whose
membership is based on necessary and sufficient conditions (the Classical view 
of Categorization).  As a basic fill-in-the-blank example consider a category,
whose members have a majority of the properties out of the three: A, B, C. 
Lakoff asserts that this kind of category defies the Classical view, because a
given member need not have ANY of the three properties, nor have them ALL 
though it would have most of them.  None of the criteria is necessary and
none sufficient.

Yet this kind of argument does not rule out the Classical view, because the
predicate:
		    (A and B) or (B and C) or (C and A)

*IS* a necessary and sufficient condition for membership to such a class.
Forgetting about that magical word "or" is Lakoff's mistake.  Or could it
be that the people who hold to the Classical view have also made the same
mistake of forgetting about that word?

As a more concrete example, Lakoff brings up the Motherhood Test problem.
The idea is that there as MANY criteria that determine whether a given
woman is your mother or not, none of which need be possessed by any given
mother:  she could have given you birth to you, she could have nurtured you,
he/she could be female, etc.  But it's really the same kind of class as that
mentioned above.