markh@csd4.milw.wisc.edu (Mark William Hopkins) (12/21/88)
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.
zhang@cogsci.ucsd.EDU (Jiajie Zhang) (12/22/88)
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.
rwojcik@bcsaic.UUCP (Rick Wojcik) (12/23/88)
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
bondc@iuvax.cs.indiana.edu (Clay M Bond) (12/25/88)
A classroom anecdote, inspired by the recent discussion of prototypes:
My students, all being quite as brainwashed as anyone else by our
educational system, were quite fond of the idea that everything could
be packaged up in nice, discrete little units and manipulated mathe-
matically. They liked the idea that everything was rule-governed, and
when we started talking about cognition, I asked for a show of hands
for the "Classical" theory of categorization.
The vote "for" was unanimous, so I asked them to give me:
a. The properties that all members of the category
GLASS share;
b. The properties that all members of the category
CUP share;
c. The properties which differentiate CUP from GLASS
(courtesy of Labov.)
They all seemed to think this was a brain-damaged idea, as simple as
it seemed to them, and as they gave me properties, I wrote them on the
board under their appropriate category labels.
By the time five properties had been listed they were arguing about
them and giving not only counter-examples, but alternative properties.
By the time another four properties had been listed, we had to put up
yet another category, MUG. And the argument could have lasted for
days.
They began the discussion thinking not only that the "Classical" system
was correct, but also by logical extension, the more defining properties
they gave, the more discrete and well-defined the categories would be.
They left the classroom realizing that the categories were anything but
discrete, and that the more properties they listed, the less discrete
the categories became.
Something else to put into the Classical pipe and smoke.
--
<< **********************DO***WHAT***THOU***WILT********************** >>
<< Clay Bond Indiana University Department of Leather, uh, Linguistics >>
<< bondc@iuvax.cs.indiana.edu AKA: Le Nouveau Marquis de Sade >>
<< {pur-ee,rutgers,pyramid,ames}!iuvax!bondc ************************* >>lee@uhccux.uhcc.hawaii.edu (Greg Lee) (12/30/88)
From article <671@cogsci.ucsd.EDU>, by zhang@cogsci.ucsd.EDU (Jiajie Zhang): "[paraphrasing G. Lakoff] " (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). Isn't this a straw man (or men)? What do formal systems have to do with modules? Take, for instance, Montague grammar. Where is there any assumption made about language being a module separate from the rest of cognition? (Answer: nowhere.) Where are categories assumed to be classical? (Nowhere.) What do distinctive features have to do with the possibility of formal operations? (Nothing.) This stuff is just an unwarranted slander against formalism. Even a modularist would not take language to be *independent* of the rest of cognition -- rather a system with some *principles* that are independent. Greg, lee@uhccux.uhcc.hawaii.edu
zhang@cogsci.ucsd.EDU (Jiajie Zhang) (01/02/89)
In article <2897@uhccux.uhcc.hawaii.edu>, lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: > Isn't this a straw man (or men)? What do formal systems have to do with > modules? Take, for instance, Montague grammar. Where is there any > assumption made about language being a module separate from the rest of > cognition? (Answer: nowhere.) Where are categories assumed to be > classical? (Nowhere.) What do distinctive features have to do with the > possibility of formal operations? (Nothing.) Sounds like a religious proof? Nowhere + Nowhere + Nothing = nothing Formal system (in the sense of Hilbert's formalism) has been well justified in mathematics, but there is no a priori warrant that the underlying principle of natural language in particular and human cognition in general is just such a formal system. In the study of natural language and human cognition, using formal system as methodology is one issue, treating it as truth is another. In generative linguistics, there are two important assumptions: (1) syntax of language is independent of other aspects of language (such as semantics and pragmatics) and (2) language is independent of other mental organs. Obviously, these are modularity assumptions. There is nothing wrong if these assumptions are only used for methodology purpose, but they are fundamentally flawed if they are taken as truth. Formal system approach to semantics (including Montague grammar) shows same formal elegance as what we can find in Chomsky's syntactic discussions, but it fails to account for many empirical data, too. Model-theoretic semantics, one branch of formal system approach to semantics, is even logically inconsistent (see Putnam's proof). The core of classical theory of categorization is set-theoretical model, which consists of nothing but abstract entities and sets, and sets of sets, and sets of sets of sets, etc. Linguists (especially those in generative linguistics) simply take for granted the classical theory of categorization. This is true of every aspect of generative linguistics. In generative phonology, distinctive features are those such as +voiced and -aspirated; sets are those such as segments marked +F. In generative syntax, a language is defined as a set of sentences which are sequences of phonological feature matrices, and a grammar as a set of rules which characterizes the set of sentences. Generative semantics is almost entirely based on classical theory of categorization, which is set-theoretical. Classical theory of categorization is clearly a basic assumption for formal system approach (at least generative linguistics) to language. Without features, sets, sets of sets, etc., formal system doesn't exist, let alone formal operation. > This stuff is just an unwarranted slander against formalism. I don't think any system built on formalism can make sense of this sentence:-) > Even a modularist would not take language to be *independent* of the > rest of cognition -- rather a system with some *principles* that are > independent. "Independent" doesn't mean "Isolated". Take generative linguistics as an example: syntax is viewed as a module independent of semantics, but syntax is not isolated from semantics. Actually, semantics is a another independent module which takes syntax as input.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/02/89)
From article <674@cogsci.ucsd.EDU>, by zhang@cogsci.ucsd.EDU (Jiajie Zhang): " ... " The core of classical theory of categorization is set-theoretical " model, which consists of nothing but abstract entities and sets, and " sets of sets, and sets of sets of sets, etc. Most any sort of formal system can be constructed on a set theoretical foundation. Any functional relation can be represented as a set. So? Is everything that can be represented as a set a "classical category"? Hardly. " Linguists (especially " those in generative linguistics) simply take for granted the classical " theory of categorization. If this were so, it should be possible to examine a generative theory and point to where the assumption(s) of classical categories are introduced. I suggested that for the case of Montague grammar, one could not find such assumptions. You don't seem to have found any yet. Repeating the thesis won't pass for proof. " This is true of every aspect of generative " linguistics. In generative phonology, distinctive features are those " such as +voiced and -aspirated; sets are those such as segments marked " +F. Yes, sets everywhere we look. But classical categories? In generative phonology pronunciations are categorized by their underlying representations. Since an arbitrary number of arbitrary transformations express the relation between underlying and surface, there is no classical categorization. (One could contrast this with Daniel Jones' theory of the relation between phonemes and allophones, which does appear to be a classical categorization.) Greg, lee@uhccux.uhcc.hawaii.edu
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/05/89)
From article <2915@uhccux.uhcc.hawaii.edu>, by lee@uhccux.uhcc.hawaii.edu (Greg Lee): My attempt to defend formal systems from Jiajie Zhang's onslaught was not intended to be critical of George Lakoff's book, Women, Fire & Dangerous Things. I should have made it clear that I was commenting only on what Zhang wrote. Greg, lee@uhccux.uhcc.hawaii.edu
zhang@cogsci.ucsd.EDU (Jiajie Zhang) (01/06/89)
In article <2897@uhccux.uhcc.hawaii.edu>, lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: } From article <671@cogsci.ucsd.EDU}, by zhang@cogsci.ucsd.EDU (Jiajie Zhang): } "[paraphrasing G. Lakoff] } " (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). } } Isn't this a straw man (or men)? What do formal systems have to do with } modules? Take, for instance, Montague grammar. Where is there any } assumption made about language being a module separate from the rest of } cognition? (Answer: nowhere.) Where are categories assumed to be } classical? (Nowhere.) What do distinctive features have to do with the } possibility of formal operations? (Nothing.) } } This stuff is just an unwarranted slander against formalism. ... However, In article <2935@uhccux.uhcc.hawaii.edu}, lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: } } My attempt to defend formal systems from Jiajie Zhang's onslaught was } not intended to be critical of George Lakoff's book, Women, Fire & } Dangerous Things. I should have made it clear that I was commenting } only on what Zhang wrote. In the first article, Greg Lee acknowledged that what I wrote was just a paraphrase of one of the arguments George Lakoff made in his book. In the second article, however, Greg Lee denied what he acknowledged in the first article. This would be a perfect example of nonmonotonic reasoning if Greg Lee could show us the evidence which made his belief system changed and how this system changed. This kind of evidence or justification is important for the kind of nonmonotonic system like TMS, which may or may not be enjoyed by proponents of pure formalism, depending on how formalism is defined.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/07/89)
From article <681@cogsci.ucsd.EDU>, by zhang@cogsci.ucsd.EDU (Jiajie Zhang): " ... " In the first article, Greg Lee acknowledged that what I wrote was just " a paraphrase of one of the arguments George Lakoff made in his book. It may be an accurate paraphrase -- I don't know, since I haven't read Lakoff's book. If what you wrote is an accurate paraphrase, then my criticisms of what you said could be taken to be criticisms of what Lakoff said. If it's not, then they couldn't. " This would be a perfect example of nonmonotonic reasoning if Greg Lee " could show us the evidence which made his belief system changed and " how this system changed. My belief system didn't change. George sent me a note saying I ought not to slander a book that I obviously had not read. Hence my disclaimer. " This kind of evidence or justification is " important for the kind of nonmonotonic system like TMS, which may or " may not be enjoyed by proponents of pure formalism, depending on how " formalism is defined. This is neat. The discussion we have been having comes to serve as an example to further the inquiry. It's a pity that less is going on than you thought. I guess I'm still safely monotonic, whatever that means. An analogy between 'greater-than' and 'implies'? Greg, lee@uhccux.uhcc.hawaii.edu