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From: rwojcik@bcsaic.UUCP (Rick Wojcik)
Newsgroups: comp.ai,talk.philosophy.misc,sci.lang
Subject: Re: Categorization: Lakoff's mistake.
Keywords: Reference
Message-ID: <9402@bcsaic.UUCP>
Date: 22 Dec 88 18:40:03 GMT
References: <484@soleil.UUCP> <1654@hp-sdd.HP.COM> <1908@crete.cs.glasgow.ac.uk> <151@feedme.UUCP> <719@quintus.UUCP> <18@csd4.milw.wisc.edu>
Reply-To: rwojcik@bcsaic.UUCP (Rick Wojcik)
Organization: Boeing Computer Services AI Center, Seattle
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In article <18@csd4.milw.wisc.edu> markh@csd4.milw.wisc.edu (Mark William Hopkins) writes:
[On Lakoff's _Women, Fire, and Dangerous Things]

>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.

It's hard to summarize Lakoff's ideas in just a few words.  One should look at
his extensive discussions of examples before formulating an opinion on his
criticism of classical category theory.  Note that his thinking is strongly
influenced by Rosch's psychological theory of prototypes.  Classical
categorization does not explain prototype effects--the impression that some
entities belong more strongly to a category than other entities do.

>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?

You seem to be saying that, given three possible properties, an entity is
classifiable as a member of the category if it has at least two out of three
properties.  Note that this is hardly the 'classical view', which you seem to
be realizing in your afterthought.  Anyway, to be consistent with what you
said about Lakoff's views above, you would have to chain some more OR's on: or
A or B or C or (A and B and C) or nil.  Then you need some metric for
calculating prototype effects off of such formulas.  In constructing your
metric, take care to reread the chapter on radially structured categories,
where it is noted that some properties are more central than others to a
category.  Work that concept into your metric, and good luck as you drift
further away from the 'classical view' of categories.  :-)

>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.

Not really.  Womanhood is more central to the category than the properties of
nurturing or doing housework.  On the other hand, it is now thought
biologically possible to grow babies in males.  Would such a male parent be
considered the 'mother'?  Put that in your classical pipe and smoke it.
-- 
Rick Wojcik   csnet:  rwojcik@atc.boeing.com	   
              uucp:   uw-beaver!ssc-vax!bcsaic!rwojcik