Xref: utzoo comp.ai:2951 talk.philosophy.misc:1755 sci.lang:3672
Path: utzoo!attcan!uunet!husc6!bbn!csd4.milw.wisc.edu!bionet!agate!ucbvax!ucsd!cogsci!zhang
From: zhang@cogsci.ucsd.EDU (Jiajie Zhang)
Newsgroups: comp.ai,talk.philosophy.misc,sci.lang
Subject: Re: Categorization: Lakoff's mistake.
Keywords: Reference
Message-ID: <671@cogsci.ucsd.EDU>
Date: 22 Dec 88 08:32:04 GMT
References: <484@soleil.UUCP> <1654@hp-sdd.HP.COM> <1908@crete.cs.glasgow.ac.uk> <18@csd4.milw.wisc.edu>
Organization: Institute for Cognitive Science, UC San Diego
Lines: 98


In article <18@csd4.milw.wisc.edu>, markh@csd4.milw.wisc.edu (Mark William Hopkins) writes:

> 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.

Well, I have to disagree with your claim.  On the contrary, I think it
is a challenge to the traditional view, especially when human
cognition is concerned.  
  
> 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?

By assuming that: (1) classical view of categorization is the view
that the membership of a category is based on necessary and sufficient
conditions, (2) Lakoff thought that classical view was just the one you
mentioned (actually he didn't), and (3) the ABC example you gave which
you think Lakoff used to defy the classical view can be stated in a
predicate which is a necessary and sufficient condition for the ABC
class, you made the following claim: classical categorization theory
CAN account for the phenomena which were considered as counter-examples for
classical view by Lakoff and that Lakoff made a mistake by ignoring the
magical word "or".

Before I make comments, I think it is important to clarify what the
classical view of categorization really is.

There are three basic assumptions of the classical view:

(1) summary representations: the representation of a concept is a
    summary description of an entire class, rather than a set of
    descriptions of various subsets or exemplars of the class.
(2) Necessary and sufficient features: the features that represent a
    concept are (a) singly necessary and (b) jointly sufficient to define
    that concept.
(3) Nesting of features in subset relations: if concept X is a subset
    of concept Y, the defining features of Y are nested in those of X.

(For an extensive review and discussion about different views of
categorization, see Medin & Smith's book Categories_and_Concepts.)

Here comes my comments on your critique on Lakoff.

(1) You assumed that the SECOND assumption of classical view is the one and
only one assumption of classical view.  This is a misunderstanding of
classical view.

(2) You even misunderstood the SECOND assumption of classical view.
Yes, the predicate (A and B)or(B and C)or(C and A) is a necessary and
sufficient CONDITION of the ABC class you gave, but it is NOT a
necessary and sufficient FEATURE of that class.  You confused
CONDITION with FEATURE.  Thus the predicate you gave is not relevant to the
problem of categorization. 

(3) In fact, the example you gave is a disjunctive concept and its
existence is a powerful argument used by people against classical
view, because the second assumption of classical view excludes any
disjunctive concept in classical categories.  Disjunctive concepts can
be accounted for by some alternative views of categorization such as
probabilistic (or prototypic) view and examplar view, but these
two views are also under criticism (Medin & Smith gave a good
discussion about this).

(4) As to the book, I think Women, Fire, and Dangerous Things is a
profound one.  Lakoff's critique on traditional view of language
(Chomskian) is especially worth mentioning (other arguments on 
cognition in general are also interesting).  His critique goes as follows
(hope it is not a misuderstanding):

    (a) Formal-system view of language assumes that (i) language is
        independent of the rest of cognition, that is, language is a separate
        modular system independent of the rest of cognition, and (ii)
        categories are classical (that is, can be characterized by distinctive
        features so that formal operations can be possible).

    (b) Lakoff argued that (i) language makes use of our general cognitive
        apparatus, that is, language is not a modular system, and (ii)
        classical view of categorization can't account for a large amount of
        empirical data and thus is not adequate to serve as a fundamental
        assumption for a general theory of language.

     (c) Combine (a) and (b), Lakoff argued that traditional (or
         formal-system) view of language is wrong.