zhang@cogsci.ucsd.EDU (Jiajie Zhang) (01/10/89)
> 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. Paraphrasing is always a dangerous game, especially when the paraphrase is compared with its original by some formal system. I am not claiming what I wrote was an accurate paraphrase (I even couldn't paraphrase accurately an argument made by myself, let alone those by others:). I am just a reader of a couple of Lakoff's books, who happened to be excited by many arguments in the books. When I found what other people understood on Lakoff was different from mine, I tried to understand why. The result was what I wrote (or paraphrased). Regardless of whoever you commented on, some words should be avoided because they could sometimes be hot enough to explode a CRT terminal, especially when there was no evidence except of Nothing, Nowhere and Nothing which could never be served as fire extinguishers. Categorization, along with symbol grounding (and maybe some others), is fundamental in the study of human cognition. If there is some flaw in a theory of categorization, the adequacy of any other theory which is based on categorization theory should be questioned, especially when this theory is claimed to be a theory of human mind. Though classical theory of categorization was not killed, I think the challenge Lakoff gave and the questions he raised is profound.
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/10/89)
I'd like to take the discussion of the "classical" [vs. the "quantum"?] view of categories back a few steps to the original question: markh@@csd4.milw.wisc.edu (Mark William Hopkins) of the University of Wisconsin-Milwaukee wrote: " [Lakoff/Rosch's] 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 in such a class. " Forgetting about that magical word "or" is Lakoff's mistake. I think this original observation was quite correct, and the rest of the discussion diverged into red herrings and irrelevancies. The supposed argument against the so-called "classical view" is this: The classical view is wrong because (1) people do not use necessary/sufficient conditions to recognize categories and (2) necessary/sufficient conditions for categories do not exist. The evidence for (1) consisted of psychological experiments in which the dependent variable was (a) judgments of category goodness-of-fit, (b) reaction time, and (c) introspections about the features underlying categories. The data suggested that subjects (a') found some members more typical of a category than others, (b') took a longer time to categorize the less typical members, and (c') could not come up with necessary and sufficient conditions for the membership by introspection. The evidence for (2) consisted of (c') (the lack of introspective conditions) plus (d) the fact that some categories indeed lack necessary and sufficient conditions, either because membership is by nature and by definition not all-or-none (as in the category "big" vs "small") or because the boundary between membership and nonmembership is graded, fuzzy, approximate, arbitrary, unknown, or unknowable (as with "living" vs. "nonliving"). What should be apparent from this summary is that none of the conclusions were based on examining categorization itself -- i.e., our ability to categorize an X as an X and a non-X as a non-X for all those X's with which we can demonstrably do this in a reliable, successful, all-or-none fashion. Instead, the conclusions were based on typicality judgments and reaction time, and these were indeed found to be graded, unlike the membership judgments themselves, which were, of course, all-or-none. With experimenters and subjects then all suitably flabbergasted that not only was typicality graded, but no one could think of necessary and sufficient conditions, it was concluded that the underlying representations for categories must prototypes, exemplars, "family resemblances" or what have you, with graded degrees of membership governed by closeness to a prototype rather than all-or-none membership governed by necessary/sufficient conditions. A good enough illustration of this came in this very discussion, where bondc@@iuvax.cs.indiana.edu (Clay M Bond) of Indiana University CSCI, Bloomington wrote: " [My students] began the discussion [of the properties of cups vs " glasses] 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. rwojcik@@bcsaic.UUCP (Rick Wojcik) added: " [Lakoff's] 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... you need some metric " for calculating prototype effects off of such formulas... some " properties are more central than others to a category... it is now " thought biologically possible to grow babies in males. Would " such a male parent be considered the 'mother'? The problem is that this kind of research and this kind of conclusion simply changes the subject: Instead of trying to find (C) the representation that will allow us to perform X/non-X categorization in the myriad cases where we can indeed do it in a reliable, all-or-none fashion, it turns instead to (T) judgments of typicality and to introspections about how we categorize, and then offers T as if it were the mechanism for C, whereas T simply PRESUPPOSES a mechanism for C, without specifying it or even realizing that the question has been begged! Worse yet, a T-mechanism is put forward as a C-mechanism, a job it certainly can't do! To put it simply: The problem of categorization and its underlying representation is the problem of how categorizers like us are able to do what we can do, which includes an enormous core of successful, reliable, correct, all-or-none categorizations as well as a large number of categorizations that are graded to various degrees. I don't categorize a penguin as a bird "to a degree" -- it's a bird, all the way, and I get it right every time. I do find it a less typical bird than a robin. And if I introspect about HOW I manage to categorize it as a bird, I probably can't come up with a set of features that are necessary and sufficient to do so. But SOMETHING up there manages to do it in my head, and it's then my job, not as introspector but as empirical theorist, to try to come up with models for how that can be done. One thing is sure: in all the cases where categorizers are demonstrably able to categorize their input in a reliable, correct all-or-none fashion, there NECESSARILY exists a set of features in the input that is jointly SUFFICIENT to generate the successful performance, and the internal mechanism will certainly detect and represent these, though not necessarily in a consciously accessible way. (As to "necessity": empirical science does not really specialize in this; psychology cannot really hope to discover or stipulate what is necessary for something to BE an X -- just what is sufficient to reliably detect it as an X, when it is indeed detectable.) Now let's move on to the last red herring: Disjunctive features. zhang@@cogsci.ucsd.EDU (Jiajie Zhang) of Institute for Cognitive Science, UC San Diego wrote: " 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... the example you gave is a disjunctive " concept and its existence is a powerful argument used by people against " the classical view, because the second assumption of the 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 exemplar " view, but these two views are also under criticism (Medin & Smith) What is a feature? Is being curved a feature? What about not being straight? Or not being curved? Or being straight or curved? Would a feature detector that looked for an even number of limbs be detecting a feature? How about an uneven number of limbs? Or a prime or uneven number of limbs? It should be apparent that in any nonarbitrary definition of "feature" (which, by the way, cannot be made independently of an implicit notion of a feature detector) any invariant property of an object, be it monadic, polyadic, relational, negative, conditional, or disjunctive qualifies as a feature. A feature is a detectable state of affairs, describable by a predicate; and some states of affairs are described by disjunctions, negations, conditionals, relational statements (or even quantitative statements of degree -- with or without a reliable all-or-none threshold feature). So I don't know who is the original owner of the "classical view," but whoever excluded disjunctions of features did so completely arbitrarily from the standpoint of any theory of categorization. Yet even prohibiting disjunctive features does not move us toward graded theories (except in cases where category membership is demonstrably graded too, as indicated by graded categorization judgments -- NOT graded typicality judgments). The ongoing rounds of criticism and counter-criticism that have been set off by the Roschian research (to which Zhang alludes at the end of the passage I quoted) are, in my view, simply symptoms of the incoherence of the views that set this whole bandwagon rolling in the first place. (For an alternative approach to categorization, see "Categorical Perception: The Groundwork of Cognition," Cambridge University Press 1987, S. Harnad, Ed., in which I offer a candidate solution to the symbol grounding problem.) -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/11/89)
From article <Jan.10.00.43.16.1989.3587@elbereth.rutgers.edu>, by harnad@elbereth.rutgers.edu (Stevan Harnad): " ... " The problem is that this kind of research and this kind of conclusion " simply changes the subject: Instead of trying to find (C) the " representation that will allow us to perform X/non-X categorization " in the myriad cases where we can indeed do it in a reliable, all-or-none " fashion, it turns instead to (T) judgments of typicality and to " introspections about how we categorize, and then offers T as if it " were the mechanism for C, whereas T simply PRESUPPOSES a mechanism for " C, without specifying it or even realizing that the question has been " begged! Why does T presuppose a mechanism for C? " Worse yet, a T-mechanism is put forward as a C-mechanism, a " job it certainly can't do! Why not? If 40%-X and 89%-X are grades, then so is 100%-X a grade. If you have T, C can be described as a special case of it. "... One thing is sure: in all the cases where categorizers are " demonstrably able to categorize their input in a reliable, correct " all-or-none fashion, there NECESSARILY exists a set of features in the input " that is jointly SUFFICIENT to generate the successful performance, and ... That's sure only if you adopt a notion of feature that is empirically empty. That is, if a feature is any function whatever of perceptible things in the input (past and present), including perhaps disjunctions, weightings, etc., then you could say that since someone performed a categorization, there must have been some things he noticed, a "feature", that allowed him to do so. This empty argument might reasonably be taken to be a reductio ad absurdum for allowing anything at all to count as a feature. Greg, lee@uhccux.uhcc.hawaii.edu
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/11/89)
In Article 3140 of comp.ai, lee@uhccux.uhcc.hawaii.edu (Greg Lee)
of University of Hawaii asks:
" Why does T presuppose a mechanism for C?
Because to judge how typical an X an X is I must first be able to judge
that it's an X.
" If 40%-X and 89%-X are grades, then so is 100%-X a grade.
" If you have T, C can be described as a special case of it.
40% what? 89% what? If you don't have a 100% category in the first
place for whatever you have a graded quantity of, you have an
incoherent concept or an infinite regress. Suppose gold was, by its
nature, an alloy, i.e., K% lead and (100 - k)% "gold." Now what was
that SECOND stuff I just mentioned? (Once you have C, T can be described
as a special case of it, not vice versa.)
" if a feature is any function whatever of perceptible things in the
" input (past and present), including perhaps disjunctions, weightings,
" etc., then you could say that since someone performed a categorization,
" there must have been some things he noticed, a "feature", that allowed
" him to do so. This empty argument might reasonably be taken to be a
" reductio ad absurdum for allowing anything at all to count as a feature.
On the contrary, I think it's a QED, and one that those who have been
caught up in the Roschian view ought to take a careful look at (when
the categorization is reliable rather than just a lucky guess).
--
Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu
srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp
BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net
(609)-921-7771reiter@babbage.harvard.edu (Ehud Reiter) (01/12/89)
Steve Harnad writes: >I don't categorize a penguin as a bird "to a degree" -- it's a bird, all the >way, and I get it right every time. I do find it a less typical bird >than a robin. And if I introspect about HOW I manage to categorize it >as a bird, I probably can't come up with a set of features that are >necessary and sufficient to do so. But SOMETHING up there manages to >do it in my head, and it's then my job, not as introspector but as >empirical theorist, to try to come up with models for how that can be done. Personally, the only reason *I* categorize a penguin as a bird is that I was taught this in school. I doubt I would have put penguins in the same category as robins if I had made up my own categories. Indeed, many tribal languages use the category "flying animal" (includes bats but not ostriches) instead of "bird", and Lakoff points out in his book that the biologists themselves are debating what the "correct" taxonomic categories should be. The point, then, is that "bird" is a culturally defined and perhaps somewhat artificial category, and may not have a simple definition as a set of features. I also doubt *I* have a definition of "penguin" as a set of perceptual features. All the penguins I have ever seen have been in zoos, with signs telling me that they were penguins. I doubt I could reliably identify an animal as a penguin without the presence of those handy signs - but that doesn't stop me from knowing that the category "penguin" exists, and from being able to make inferences from the classification (i.e. if someone tells me that animal X is a penguin, I will infer that X likes cold weather). So, I can still use categorization information, even if I cannot define that category in terms of perceptual features. This is even more true for abstract categories - what set of perceptual features identify Republicans? Lawyers? Widows? In short, the reason I categorize a penguin as a bird is that I have been taught this as a rule - and the reason I categorize an object as a penguin is that a nearby sign tells me that the object is a penguin. Features have very little to do with the process. I'm not trying to say that people never categorize objects solely from perceptual information, because of course they do this sometimes. What I am saying is that there is a lot more to how categories are defined and used than perceptual features. Ehud Reiter reiter@harvard (ARPA,BITNET,UUCP) reiter@harvard.harvard.EDU (new ARPA)
turney@svax.cs.cornell.edu (Jenn Turney) (01/12/89)
In article <Jan.11.01.00.51.1989.8990@elbereth.rutgers.edu> harnad@elbereth.rutgers.edu (Stevan Harnad) writes: > > >In Article 3140 of comp.ai, lee@uhccux.uhcc.hawaii.edu (Greg Lee) >of University of Hawaii asks: > >" Why does T presuppose a mechanism for C? > >Because to judge how typical an X an X is I must first be able to judge >that it's an X. > >" If 40%-X and 89%-X are grades, then so is 100%-X a grade. >" If you have T, C can be described as a special case of it. > >40% what? 89% what? If you don't have a 100% category in the first >place for whatever you have a graded quantity of, you have an >incoherent concept or an infinite regress. Suppose gold was, by its >nature, an alloy, i.e., K% lead and (100 - k)% "gold." Now what was >that SECOND stuff I just mentioned? (Once you have C, T can be described >as a special case of it, not vice versa.) > This argument is specious. Deriving concept membership (categorization) from typicality ratings is not automatic. It is entirely possible for something to receive a typicality rating for a category without any knowledge about whether it actually belongs to the category. Suppose you encounter a new creature in the wild which has wings and feathers, flies, and has a trunk. You don't know whether it's a bird or not but if you were asked to rate its typicality of the category "bird", it's very likely that you would give a non-zero rating. It may still be possible to derive C from typicality ratings; however, the dilemma now is determining where the dividing line is. Perhaps all instances with typicality ratings higher than 15% are members of the category. (Another case: wouldn't you say a panda was a pretty typical bear, even though pandas are in the raccoon family, not the bear family?) As regards the statement that categories are either 100% or incoherent, I'll remind you of the results of Armstrong, Gleitman and Gleitman. They asked subjects to give typicality ratings of numbers for the category "even number". Surprise -- 4 is a more typical (better exemplar) even number than 806. The obvious next question is, how relevant is "typicality"? Is it the right term to use -- would using another term improve the situation? Reference: Armstrong, S. L., L. R. Gleitman, H. Gleitman (1983). What some concepts might not be. _Cognition_, 13, 263-308. ________ | | Jenn | | turney@svax.cs.cornell.edu | let us all be born just one more time | | | Dept. of Computer Science | we may yet get it \_| | Cornell University | right
reiter@endor.harvard.edu (Ehud Reiter) (01/12/89)
In article <24080@cornell.UUCP> turney@svax.cs.cornell.edu (Jenn Turney) writes: >(Another case: wouldn't you say a panda was a pretty typical bear, even >though pandas are in the raccoon family, not the bear family?) This is a good example of the ambiguity of biological classifications. According to Stephen O'Brien, "The Ancestry of the Giant Panda", SCIENTIFIC AMERICAN, Nov 87, the biology of the situation is as follows: Physiology: - red pandas have some physiological similarities to racoons - giant pandas have physiological similarities to both racoons and bears Evolutionary History: - 35 million years ago, the common ancestor of red pandas and racoons split from the common ancestor of giant pandas and bears - 30 millions years ago, red pandas split from racoons - 20 million years ago, giant pandas split from bears This is the *biology*. Now, how about *language*. Should we define the class "racoon" to include giant pandas and red pandas, as Turney suggests? Or, should we define "racoon" to include red pandas, and "bear" to include giant pandas? Or should we should we put red pandas and giant pandas into their own class, "panda"? As language users, the choice is ours - but whatever choice we make, it will be something that has to be taught, not something that is intuitively obvious. And if another culture makes a different choice than we do, we would not be justified in saying they were "wrong" and we were "right". As one last caution, Lakoff points out that if we decide to classify strictly according to evolutionary history, we would have to put crocodiles in the class "bird", because crocodiles and robins are much closer in terms of evolutionary history than crocodiles and lizards. This would be a shame, because it seems to me that the class (crocodile, robin, hawk, penguin ...) is much less useful to a language user than the class (robin, hawk, penguin ...) - and I would be so bold as to argue that an even more useful class might be just (robin, hawk, ...) (i.e. leaving out penguins, ostriches, emus, etc). Ehud Reiter reiter@harvard (ARPA,BITNET,UUCP) reiter@harvard.harvard.EDU (new ARPA)
wlp@calmasd.GE.COM (Walter L. Peterson, Jr.) (01/12/89)
In article <965@husc6.harvard.edu>, reiter@babbage.harvard.edu (Ehud Reiter) writes: > Steve Harnad writes: > >I don't categorize a penguin as a bird "to a degree" -- it's a bird, all the > >way, and I get it right every time... > > Personally, the only reason *I* categorize a penguin as a bird is that I > was taught this in school... > Actually, the categorization of penguins and all other birds is quite easy. Unlike most other taxonomic categories, biologist are in agreement as to what creatures are members of the Class Aves. All animals that have feathers are birds and all birds have feathers. This is not just a "cultural bias" nor is it an arbitrary rule. -- Walt Peterson. Prime - Calma San Diego R&D (Object and Data Management Group) "The opinions expressed here are my own and do not necessarily reflect those Prime, Calma nor anyone else. ...{ucbvax|decvax}!sdcsvax!calmasd!wlp
bill@utastro.UUCP (William H. Jefferys) (01/12/89)
In article <24080@cornell.UUCP> turney@svax.cs.cornell.edu (Jenn Turney) writes:
#
#Suppose you encounter a new creature in the wild which has wings and feathers,
#flies, and has a trunk. You don't know whether it's a bird or not
#but if you were asked to rate its typicality of the category "bird", it's
#very likely that you would give a non-zero rating.
Opus has wings, feathers and a trunk. But he doesn't fly :-)
Bill Jefferys
--
Glend. I can call spirits from the vasty deep.
Hot. Why, so can I, or so can any man; But will they come when you
do call for them? -- Henry IV Pt. I, III, i, 53harnad@elbereth.rutgers.edu (Stevan Harnad) (01/12/89)
turney@svax.cs.cornell.edu (Jenn Turney) of Cornell Univ. CS Dept, Ithaca NY wrote: " Deriving concept membership (categorization) from typicality ratings is " not automatic. It is entirely possible for something to receive a " typicality rating for a category without any knowledge about whether it " actually belongs to the category. No one said it was automatically derivable. I even denied it was derivable at all. I said it was simply PRESUPPOSED (taken for granted) by the typicality theorist that there WERE categories that the typicality ratings reflected the typicality OF. I also denied that much can be learned about category representation from typicality ratings; it's simply a different problem. And of course I agree that there can be spurious typicality ratings, dissociated from knowledge about categories. That's why I think I think that typicality ratings are about as informative about category representation as Osgood's "semantic differential" is about meaning (and for just about the same reason)! " It may still be possible to derive C from typicality ratings... " Perhaps all instances with typicality ratings higher than 15% are " members of the category. "C" referred to how the category was represented in the head. I deny that you can derive (or infer or reconstruct) this from typicality ratings. All you can get out of typicality ratings is what goes into them, and they are not judgments about membership, they are judgments about "degree of membership." (Perhaps instances with typicality ratings higher than 15% ARE members of the category; perhaps not. So what? What we need to know is what the category-detecting representation that does the correct, reliable, all-or-none categorizing is.) " As regards the statement that categories are either 100% or incoherent... No one made such a statement. First, I said that, besides the reliable, all-or-none categories that we can sort correctly (virtually) 100% of the time (like bird), there are graded categories too (like big). What I said was incoherent was the idea that one could derive category representations (the ones that subserve our all-or-none categorization performance) from typicality judgments and nearness-to-prototype notions. (The reverse may well be possible.) -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/13/89)
reiter@babbage.harvard.edu (Ehud Reiter) of Aiken Computation Lab Harvard, Cambridge, MA wrote: " the only reason *I* categorize a penguin as a bird is that I was taught " this in school. I doubt I would have put penguins in the same category " as robins if I had made up my own categories... biologists themselves " are debating what the "correct" taxonomic categories should be... " "bird" is a culturally defined and perhaps somewhat artificial " category, and may not have a simple definition as a set of features. Some categories are indeed arbitrary (such as "things bigger than a breadbox," "things I like to wear on Tuesdays," "the three most similar grapheme strings on the prior line," or "things I call 'throg' because the spirit moves me") but not the interesting and important ones, such as penguin or bird. Our nonarbitrary categorizations are constrained by their consequences -- the consequences of MIScategorizing. In practical cases like (edible) mushroom vs. (poisonous) toadstool, the consequences are obvious. In empirical science the consequences are subtler, but there (e.g., electron vs positron). In taxonomy, too, there are consequences of miscategorizing (failed predictions), and to the extent that there are no empirical consequences, there might indeed be an element of arbitrariness in taxonomy. You were taught that a penguin is a bird for reasons that you must study zoology, morphology and evolution to understand fully. Perhaps at the fuzzy frontiers of taxonomy, as elsewhere in science, there is still uncertainty. It still makes no difference what your layman's inclinations are when it comes to sorting birds. In a prescientific culture, this, like sorting the "elements," may have been an arbitrary cultural matter, but not once one is better informed. Nor is a bird an artificial category (like walking-stick): It is a natural kind, whose nature is to be discovered, not stipulated. And that nature (insofar as it has palpable or measurable consequences) will always constrain our categorizations. " there is a lot more to how categories are defined and used than " perceptual features... I also doubt *I* have a definition of "penguin" " as a set of perceptual features. All the penguins I have ever seen have " been in zoos, with signs telling me that they were penguins. I doubt I " could reliably identify an animal as a penguin without the presence of " those handy signs... I can still use categorization information, even " if I cannot define that category in terms of perceptual features. This " is even more true for abstract categories - what set of perceptual " features identify Republicans? Lawyers? Widows? I think you (and most of us) could reliably identify a penguin without the help of a sign (though the sign might have been helpful feedback when we first learned to identify them). You may not have a DEFINITION, but you can certainly pick 'em out; it's hence reasonable to conclude that something in your head is successfully detecting them on the basis of reliable features in the sensory representation that you cannot verbalize (or have not yet learned to). Regarding abstract categories: As I suggested in my original posting, I think they are GROUNDED in concrete categories (and in the book I sketch a symbol grounding model that accomplishes this). The perceptual representations in which they are grounded, like their sensory features, may not be available to introspection. Moreover, there may be abstract, symbolic rules guiding our abstract categorizations that are likewise not introspectively obvious or accessible, yet reliably guiding our categorizations. That's just an inference, of course, but a pretty reasonable one; the alternative is either the incoherent Roschian view (which purports to get all-or-none categorization performance from models for graded typicality judgments) or else just plain magic. " should we put red pandas and giant pandas into their own " class, "panda"? As language users, the choice is ours - but whatever " choice we make, it will be something that has to be taught, not " something that is intuitively obvious. And if another culture makes a " different choice than we do, we would not be justified in saying they " were "wrong" and we were "right". As I suggested, the taxonomy of natural kinds -- to the extent that it is empirical (with testable consequences arising from MIScategorization) rather than hermeneutic (i.e., just a matter of interpretation, subjective similarity, or arbitrary convention) IS a matter of "right" vs. "wrong." I'd like to account for our ability to categorize birds, penguins and electrons reliably and correctly. I'll leave the hermeneutics to the Roschians. [I have made a distinction between two kinds of categorization and categorization task that might be instructive here: "ad lib" vs. "imposed" categorization. In an ad lib categorization task (as used by Tversky and others who investigate similarity), instances are presented to the subject, who is then to sort them as he sees fit. In "imposed" categorization, there is feedback as to whether the categorization is correct or incorrect (this is also called "supervised learning"): Miscategorization has consequences in imposed categorization, but not in ad lib categorization (which I just consider to be a form of impressionistic similarity judgment). Typicality judgments are really just similarity judgments too; similarity is, by nature, graded, continuous, and a matter of degree. Categorization, on the other hand, is discrete, categorical and all-or-none. I think that imposed categorization tasks are the right ones to look at in modeling categorization, along with their feedback from miscategorization. They are representative of reality and the constraints it imposes on how we sort things. Ad lib categorization is not really categorization AT ALL, but just subjective similarity judgments based on the default similarity structure of the set of inputs, as dictated either by our sensory systems, our prior (imposed) categories, or both.] -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
matt@nbires.nbi.com (Matthew Meighan) (01/13/89)
In article <179@calmasd.GE.COM> wlp@calmasd.GE.COM (Walter L. Peterson, Jr.) writes: > [ stuff deleted] >All animals that have feathers are birds and all birds have feathers. >This is not just a "cultural bias" nor is it an arbitrary rule. Just curious: exactly what makes this rule non-arbitrary and not culturally-based? Are you saying that if a different culture categorizes animals differently, then they are "wrong" and the above-mentioned categorization is "right", in some absolute sense? If so, please provide your proof. This categorization seems arbitrary on its face to me. -- Matt Meighan "The eighties are the fifties in color." - Cowtown matt@nbires.nbi.com (nbires\!matt)
reiter@endor.harvard.edu (Ehud Reiter) (01/13/89)
This is a long posting that discusses biological classifications. Be warned. Steve Harnad writes: >You were taught that a penguin is a bird for reasons that you must >study zoology, morphology and evolution to understand fully. Perhaps >at the fuzzy frontiers of taxonomy, as elsewhere in science, there is >still uncertainty. It still makes no difference what your layman's >inclinations are when it comes to sorting birds. In a prescientific >culture, this, like sorting the "elements," may have been an arbitrary >cultural matter, but not once one is better informed. Nor is a bird >an artificial category (like walking-stick): It is a natural kind, >whose nature is to be discovered, not stipulated. And that nature >(insofar as it has palpable or measurable consequences) will always >constrain our categorizations. Biological categories are a lot more arbitrary than many people seem to realize (this is one of the topics Lakoff discusses in his book). For anyone who is really interested in the topic, I highly recommend reading "Theories of Biological Classification and Their History", chapter 4 in Ernst Mayr, PRINCIPLES OF SYSTEMATIC ZOOLOGY, McGraw-Hill, 1969. Very roughly, the situation is as follows: The only things a biologist can directly observe or derive from direct observation are the composition of species and the phylogenetic tree (evolutionary history of species). A species is defined to be an interbreeding group of individuals. Given this definition, it is possible, at least in principle, to experimentally determine whether or not a group of animals belong to the same species. This CANNOT be done for higher classifications (families, generas, classes, etc) - there is no direct experimental test that determines whether or not a group of individuals belongs to the same genera, class, or whatever. At least in this sense, higher classifications (e.g. "bird", "penguin", "mammal", etc) are human inventions, not distinctions that are mandated by nature. To quote Mayr, pg 98 "...the major function of a classification [is] to be useful. A classification is a communication system, and the best one is that which combines greatest information content with greatest ease of information retrieval." Note that species have physiological properties that are shared by all members (e.g. all humans have two eyes), and also physiological properties which vary in the population (e.g. hair color in humans). The other thing that can be experimentally determined, at least in principle, is the the phylogenetic tree, that is the history of which species descended from which other species. The phylogenetic tree can be determined, for example, by examining differences in the DNA of different species. So, species and the phylogenetic tree are the only biological observables. Biologists have been debating for centuries how this data can be used to form higher-order categories like "bird" or "mammal". There are three main approaches: Phenetic: ignore the phylogenetic tree, and form higher-order categories by clustering species along their common physiological properties. So, for example, we might decide that one higher-order category is "all animals with feathers", and call this category "birds". Obviously, doing the clustering requires deciding which physiological properties are important, and we can well imagine a different culture deciding that "having feathers" was a less important property than "being able to fly", and thus using the alternate category "all animals that can fly". By necessity, all taxonomies created before the theory of evolution (including Linnaeus's classification and tribal classifications) are based on phenetic principles. Cladistic: ignore physiological properties, and create a higher-order category for each fork in the phylogenetic tree. In computer-science terms, each subtree of the complete phylogenetic tree would form a higher-order category. The advantage of cladism is that it is in some sense completely objective, since the cladistic taxonomy is completely determined by the phylogenetic tree. The problem with cladism is that it leads to a lot of categories which may not be very useful, e.g. "crocodiles and birds", "mammals and turtles", "primates and rodents". Evolutionary: use both physiological properties and the phylogenetic tree. Very roughly, the evolutionary taxonomist picks out certain phylogenetic subtrees (or possibly pruned subtrees, i.e. subtrees with some branches removed) that seem to correspond to species with shared physiological properties, and makes these (pruned) subtrees into his higher-order categories. For example, he might note that all descendants of the species Archaeopteryx share some physiological properties, and decide to call Archaeopteryx and all its descendants the class of "birds". This ends my 2-bit review of biological classification. I hope the reader takes away two points in particular: - higher-order classifications like "bird" are human creations, not directly observable distinctions that are mandated by nature. - biologists have differing views on what the "correct" higher-order classifications are, and how they should be defined. Besides the phenetic/cladistic/evolutionary split, note that both phenetic and evolutionary classifications require the taxonomist to exercise a good deal of judgement in deciding what the higher-order categories should be. Steve Harnad also writes: >I think you (and most of us) could reliably identify a penguin without >the help of a sign (though the sign might have been helpful feedback >when we first learned to identify them). You may not have a >DEFINITION, but you can certainly pick 'em out; it's hence reasonable to >conclude that something in your head is successfully detecting them >on the basis of reliable features in the sensory representation that >you cannot verbalize (or have not yet learned to). Perhaps I could identify a penguin from sight alone (I'm not sure), but I doubt I could identify, say, a platypus from sight alone. Yet, that doesn't stop me froming knowing things about platypuses (e.g. they lay eggs and live in Australia). As a human being, I'm not restricted to making categorization decisions from sense data alone - I have the capability to use language, and to know that object X is a platypus because I was explictly told that object X is a platypus. Walt Peterson writes >Actually, the categorization of penguins and all other birds is quite >easy. Unlike most other taxonomic categories, biologist are in >agreement as to what creatures are members of the Class Aves. All >animals that have feathers are birds and all birds have feathers. >This is not just a "cultural bias" nor is it an arbitrary rule. This is true. One definition of "bird" is all animals that have feathers (another is all descendants of Archaeopteryx). But the fact that the category is well-defined does not mean it is not arbitrary. Ehud Reiter reiter@harvard (ARPA,BITNET,UUCP) reiter@harvard.harvard.EDU (new ARPA)
zhang@cogsci.ucsd.EDU (Jiajie Zhang) (01/13/89)
In article <Jan.10.00.43.16.1989.3587@elbereth.rutgers.edu>, harnad@elbereth.rutgers.edu (Stevan Harnad) writes: > The problem is that this kind of research and this kind of conclusion > simply changes the subject: Instead of trying to find (C) the > representation that will allow us to perform X/non-X categorization > in the myriad cases where we can indeed do it in a reliable, all-or-none > fashion, it turns instead to (T) judgments of typicality and to > introspections about how we categorize, and then offers T as if it > were the mechanism for C, whereas T simply PRESUPPOSES a mechanism for > C, without specifying it or even realizing that the question has been > begged! Worse yet, a T-mechanism is put forward as a C-mechanism, a > job it certainly can't do! I agree that judgements of typicality can't provide us much information about the underlying mechanism of categorization. Prototypical effects are just effects, phenomena, and nothing more. They are just the outputs of some internal mechanisms underlying categorization. Early-Rosch did construct a prototype *theory*, which was intended to be a theory of the mechanism of categorization. However, late-Rosch gave up this kind of theory and only claimed that prototypical effect was just effect, not theory. This is an important point, and it was, for example, reiterated by Lakoff in his book. Though prototype *theory* didn't stand very long, the effect or phenomenon of prototypicality in categorization is real. Prototypical effect should be served as a constraint in the construction of a categorization theory, and any theory of categorization, if there is one, should be capable of explaining prototypical effect. > What should be apparent from this summary is that none of the > conclusions were based on examining categorization itself -- i.e., our > ability to categorize an X as an X and a non-X as a non-X for all > those X's with which we can demonstrably do this in a reliable, > successful, all-or-none fashion. I think our ability to perform categorization is just one of several important aspects of categorization. I think the following aspects are also important for the study of categorization. (1) Descriptive analyses of categories. These include intra- and inter-relationship of categories, characteristics of a category, taxonomy, etc. For example, biological taxonomy, Frank Keil's ontological categories. (2) Internal representations of categories. There are two parts: structure and process. Classical view, prototypical view, and examplar view are among many of the traditional approaches which tried to give a theory of how categories are represented in the mind. Lakoff's ICM is one of several recent approaches. Connectionism, in my opinion, might be the best tool (so far) to study categorization, though there hasn't been a connectionist theory of categorization yet. A theory of categorization should not only answer the question of what are the structures of internal representation of categories but also the question of HOW human beings actually DO the categorization. It should also be able to explain empirical data, such as prototypical effect. (3) Origin of categories, both ontogenetically and phylogenetically. Children's learning of categories and the evolution of categories are to some extent similar, but the difference between them is more important. Do categories exist objectively out there and wait for our human beings to find the regularities and pick them up? To what extent are categories artificial, that is, to what extent do human beings impose artificial categories on the nature? Learning categories through schooling is different from that through discovering, and that through creating. (4) Why do human beings categorize things? I think this might be related to what Harnad called miscategorization. Personally, I think this is a question about cognitive cost. (5) Borrowing from linguistics: relation between performance and competence of categorization, if this distinction makes any sense at all. > The ongoing rounds of criticism and > counter-criticism that have been set off by the Roschian research (to > which Zhang alludes at the end of the passage I quoted) are, in my > view, simply symptoms of the incoherence of the views that set this > whole bandwagon rolling in the first place. Prototypical effect is real. I don't think a theory which ignores prototypical effect is a reasonable and complete theory for categorization.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (01/14/89)
From article <Jan.12.10.43.56.1989.23428@elbereth.rutgers.edu>, by harnad@elbereth.rutgers.edu (Stevan Harnad): " ... ""C" referred to how the category was represented in the head. ... Ah. Here's the problem. We have to assume Harnad is right to understand what he's saying. He proposes that all-or-none categories are in people's heads and that typicality judgements are made with reference to these. *If* that's so, then typicality judgements obviously presuppose all-or-none categories. (Someone on the other side of the fence would naturally take the view that all-or-none judgements presuppose graded categories.) We thought he was defending his theory when he was actually just reiterating it. Greg, lee@uhccux.uhcc.hawaii.edu
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/14/89)
reiter@harvard.UUCP (Ehud Reiter) Aiken Computation Lab Harvard,
Cambridge, MA wrote:
" Biological categories are a lot more arbitrary than many people seem to
" realize... there is no direct experimental test that determines whether
" or not a group of individuals belongs to the same genera, class, or
" whatever. At least in this sense, higher classifications (e.g. "bird",
" "penguin", "mammal", etc) are human inventions, not distinctions that
" are mandated by nature. To quote Mayr, pg 98
"
" "...the major function of a classification [is] to be useful.
" A classification is a communication system, and the best one is
" that which combines greatest information content with greatest
" ease of information retrieval."
"Information content" depends on resolving uncertainty. Objective
uncertainty is a function of objective consequences: It matters
whether this is a "mushroom" or a "toadstool," because if I miscategorize,
I may die. To the extent that categorization is guided by objective
consequences, it is nonarbitrary. Subjective uncertainty is another
matter. I may put some objects together purely because they look
prettier to me that way ("ad lib" categorization). That's truly
arbitrary. To the extent that taxonomy is constrained by the first kind
of uncertainty-reduction, it is empirical and informative. To the
extent that it is guided by the latter, it is arbitrary and subjective
(or "intersubjective," if most or all people happen to think things
look prettier that way).
" Obviously, doing the clustering requires deciding which physiological
" properties are important, and we can well imagine a different culture
" deciding that "having feathers" was a less important property than
" "being able to fly"
What does "important" mean? Again, if the decision is guided by
objective consequences, it is nonarbitrary; if subjective only, it's
arbitrary. Social constraints are a special case. Humans are, after
all, natural kinds. So the kinds of sanctions they impose on one
another are "natural" too. Hence if my speech community tells me that
"being able to fly" picks out an important category X, and they test me
on it in school, etc., then objective consequences dictate that I
better get it right. [Recall that the original issue here was whether
or not "classical" features underlie our categorizations, not whether
the features (or categories) are chosen for nonsocial or social
reasons; it is the objective, external existence of those features that
the classicist must be prepared to defend, not the basis for their
selection.]
" higher-order classifications like "bird" are human creations, not
" directly observable distinctions that are mandated by nature.
They may or may not be human creations, but they must be based on
objectively observable features if they are to be reliably picked out
(as they are).
" I doubt I could identify, say, a platypus from sight alone. Yet, that
" doesn't stop me from knowing things about platypuses... I'm not
" restricted to making categorization decisions from sense data alone - I
" have the capability to use language, and to know that object X is a
" platypus because I was explicitly told that object X is a platypus.
I'm nowhere suggesting that all categorization is restricted to "sense
data" alone but rather that it is GROUNDED in sensory features. Once
grounded, a symbol system is free to rise to ever higher levels of
abstraction. I need never have seen a platypus to know and speak about
them. But I do need to have grounded categories for "bills," "fur,"
"egg-laying," and whatever other features pick out the platypus (or
grounded categories for whatever features pick out those features,
or...etc.). That's exactly the capability that a grounded symbol system
for making propositions about category membership (language) gives
you. But this capability cannot be taken for granted either, any more
than the ability to categorize can; it must be explained (and my symbol
grounding theory is one candidate explanation).
" One definition of "bird" is all animals that have feathers (another is
" all descendants of Archaeopteryx). But the fact that the category is
" well-defined does not mean it is not arbitrary.
Two different senses of arbitrary seem to be at issue here, but only
one is relevant to the problem of the internal representation of
categories: The reason we single out a given feature and sort objects in
the world according to it may be arbitrary: A dictator may have decreed
that we must worship all creatures that exceed his own weight; if he
has the power to enforce his decree, then there are dire consequences
for us if we fail to detect and act according to this feature. Such a
category would be arbitrary in the sense that it did not really pick
out a natural kind (since there is nothing special about the dictator's
weight or about objects that exceed it), but it would nevertheless be
an all-or-none category with perfectly "classical" features (within the
limits of our senses and weighing instruments). [The dictator might also
have decreed that we must worship creatures that exceed his height OR
weight: This too would be a perfectly classical category, with all
members sharing the property of exceeding either the dictator's height
or his weight.]
With nonarbitrary categories, nature is the dictator. Apart from that,
there is no difference between categories that are "arbitrary" and
"nonarbitrary" in this first sense (at least not for the cognitive
theorist concerned with explaining how categorization is accomplished
by the head; there may be a difference for the ontologist or the
physicist, but their concerns should not be conflated with the
epistemic concerns of the cognitive theorist).
The second sense of arbitrary would be one in which there really were
no objective features subserving an all-or-none distinction -- no
objective consequences whatsoever arising from miscategorization: Humpty
Dumpty's dictum that words mean what I want them to mean. Or an "X" is
whatever I say is an X. It is only arbitrary subjective categories of
the latter kind (what I've called "ad lib" categories) that might truly
lack classical features. And although it is not their intention, I
believe that the incoherent sort of category representation recommended
to us by those who think categories are represented nonclassically
would be arbitrary in this second sense.
--
Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu
srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp
BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net
(609)-921-7771harnad@elbereth.rutgers.edu (Stevan Harnad) (01/14/89)
zhang@cogsci.ucsd.EDU (Jiajie Zhang) of Institute for Cognitive Science,
UC San Diego writes:
" I agree that judgements of typicality can't provide us much
" information about the underlying mechanism of categorization...
" [but] our ability to perform categorization is just one of several
" important aspects of categorization...
In this passage Zhang agrees with most of the points I have been making
in these postings, so I cannot disagree, but I would say that our
ability to perform categorizations is by far the most important aspect
of categorization; the rest is little more than fine tuning once you
solve that problem.
Among the other aspects of categorization Zhang cites:
" (1) Descriptive analyses of categories... (e.g., biological taxonomy,
" Keil's ontological categories.)
Biological taxonomy is probably best left to biologists. What can
psychologists and computer scientists offer to the specialists here?
The same is true for ontology. (And Keil, by the way, is not doing
ontology, even if he says so: He is studying the development of
ontological concepts -- concepts of what there is.) On the other hand,
one is free to gather one's insights where one may, and if biology or
ontology gives someone an idea about how we manage to categorize, fine.
And, human categorization PERFORMANCE in any domain, including biology
and ontology, certainly counts as data.
" (2) Internal representations of categories... A theory of
" categorization should not only answer the question of what are the
" structures of internal representation of categories but also the
" question of HOW human beings actually DO the categorization. It should
" also be able to explain empirical data, such as prototypical effects.
" Connectionism, in my opinion, might be the best tool (so far) to study
" categorization...
For me, the question of how categories are internally represented and
the question of how we do categorization are the same question (the
basic question mentioned at the outset). The internal representation is
the mechanism subserving the categorization performance. I agree that
connectionism might be a candidate mechanism, particularly for category
learning and feature detection.
Prototype effects should certainly be explained, but categorization
itself must be explained first; once it is, I predict that prototype
effects will turn out to be a minor side-effect. I certainly wouldn't
"constrain" my categorization models at this stage to conform to
prototype effects -- any more than I would constrain them to conform to
reaction time, brain-damage effects or our foggy knowledge of brain
function. Let models achieve success at lifesize categorization
any-which-way first and then let's worry about fine-tuning them to
exhibit those extra frills. On the other hand, as suggested before, we
are free to gather INSIGHT wherever we may; so if prototype effects,
brain-damage data or neurobiological data inspire anyone to a working
categorization model, bravo! But the only CONSTRAINT we need on the
project is provided by the evidence of our actual categorization
performance capacity itself.
" (3) Origin of categories, both ontogenetically and phylogenetically.
" Do categories exist objectively out there and wait for
" human beings to find the regularities and pick them up? To what
" extent are categories artificial, that is, to what extent do human
" beings impose artificial categories on nature? Learning
" categories through schooling is different from that through
" discovering, and that through creating.
Developmental data on categorization performance are of course
important, because they provide some insight into the all-important
process of the acquisition of categories (including MIScategorization
and the input needed to correct it). Comparative data on other species
are of course relevant too. On the other hand, as I suggested, I think
cognitive scientists would do better to avoid the minefields of
ontology -- at least if they are not prepared first to arm themselves with
two millenia of philosophy. This much, however, looks as if it can be
said with some confidence: Objective categories -- i.e., those for which
there are objective consequences arising from miscategorizations -- must
have a basis in objective, discernible external features. Why we PICK
OUT those categories and those features may sometimes be socially
determined, but that does not make the features any less external.
I agree that learning categories from cases is importantly different
from learning them through instruction; and that the "creation" of
categories is yet another relevant aspect of performance. My own theory
addresses all of these cases explicitly.
" (4) Why do human beings categorize things? I think this might be
" related to what Harnad called miscategorization. Personally, I think
" this is a question about cognitive cost.
Categorization is merely a special form of differential responding to
input. Differential responding is guided by its consequences. We
must categorize things because there is a cost (in survival or
well-being) to miscategorizing them. I don't know what "cognitive
cost" means, but I think miscategorization is all-important because
that is what provides the feedback that allows us to converge on the
features that eventually allow us to get the categorization right. And
if there is no right or wrong to a category, as I said in another
posting, then all we have is subjective similarity judgment.
" (5) Relation between performance and competence of categorization
Our category competence is our capacity to categorize as we do, given
the inputs we get, and the feedback from the consequences of our
attempts. And just as in the linguistic competence/performance
distinction, there are performance details (such as prototype effects
and introspections about features) that are not central to the basic
problem of modeling the competence. (When I say "categorization
performance capacity" I mean category competence, not performance.)
--
Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu
srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp
BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net
(609)-921-7771michael@roberta.UUCP (Michael A. Moran ) (01/15/89)
In article <687@cogsci.ucsd.EDU>, zhang@cogsci.ucsd.EDU (Jiajie Zhang) writes: > (2) Internal representations of categories. There are two parts: > structure and process. Classical view, prototypical view, and > examplar view are among many of the traditional approaches which tried > to give a theory of how categories are represented in the mind. > Lakoff's ICM is one of several recent approaches. Connectionism, in my > opinion, might be the best tool (so far) to study categorization, though > there hasn't been a connectionist theory of categorization yet. A > theory of categorization should not only answer the question of what > are the structures of internal representation of categories but also > the question of HOW human beings actually DO the categorization. It > should also be able to explain empirical data, such as prototypical > effect. Actually there has been a connectionist theory of categorization proposed. Like me it has fallen into obscurity, but it can be found in: Moran, Michael A., A Perceptual Model of Episodic Memory and its Explanation of Recognition and Categorization. Dissertation Abstacts International, 1983. Sorry I don't have the DAI volume and number. It is also available at the U.C. Davis main library. I proposed a structure and process for categorization and related this to both categorization effects and to word frequency effects, drawing a parallel between the results found in these two generally separate lines of research. A mechanism was proposed that would explain a large number of results in both lines of work. -- Michael A. Moran { ...}!comix!roberta!michael {uunet, pyramid, ...}!vdx!roberta!michael
throopw@xyzzy.UUCP (Wayne A. Throop) (01/18/89)
> harnad@elbereth.rutgers.edu (Stevan Harnad) > Some categories are indeed arbitrary (such as "things bigger than a > breadbox," [...] but not the interesting and important > ones, such as [...] (edible) mushroom vs. (poisonous) > toadstool, The mushroom/toadstool distinction is no less arbitrary than is the bigger/smaller-than-a-breadbox distinction. After all, the consequences of not being bigger than a breadbox can be that one can hide inside it from a predator, every bit as important to somebody who *is* smaller than a breadbox as the distinction among fungi is to *you*. A visitor from a planet of silicon-based life would have a hard time saying that the mushroom/toadstool classification was anything other than completely arbitrary. After all, who cares about it's toxicity to some irrelevant biped? So, other than the motives and goals of the categorizer, there is nothing to make one categorization more "natural" or "less arbitrary" than another. Hence, categorization is inherrently subjective, not objective. -- "When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean -- neither more nor less." --- Lewis Carol -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
throopw@xyzzy.UUCP (Wayne A. Throop) (01/18/89)
> harnad@elbereth.rutgers.edu (Stevan Harnad) > Two different senses of arbitrary seem to be at issue here, but only > one is relevant to the problem of the internal representation of > categories: The reason we single out a given feature and sort objects in > the world according to it may be arbitrary: No, it *must* be (not may be) arbitrary. The choice of categorization (as outlined in a previous posting) involves the motives and goals of the categorizer, and is thus subjective (and objectively arbitrary). > A dictator may have decreed > that we must worship all creatures that exceed his own weight; [...] > With nonarbitrary categories, nature is the dictator. I fail to see why nature is any less arbitrary than a human dictator. In each case, categorization happens relative to features "important" to some categorizer. Hence, in this sense, *all* categories are arbitrary. > The second sense of arbitrary would be one in which there really were > no objective features subserving an all-or-none distinction -- no > objective consequences whatsoever arising from miscategorization: Humpty > Dumpty's dictum that words mean what I want them to mean. Or an "X" is > whatever I say is an X. But even these categories have an objective feature which makes them what Steve has been calling "classical" categories. That is, one can use Humpty Dumpty's word as a category marker. "It doesn't say Haynes until *Dumpty* says it says Haynes." is just as objectively based a category as any other. So: the first sense of arbitrary is moot: all categorizations are arbitrary in this sense. The second sense of arbitrary is also moot: no categorizations are arbitrary in this sense. As somebody else already said (I think) all this is based on the notion that in/out distinctions are binary and certain. > I believe that the incoherent sort of category representation recommended > to us by those who think categories are represented nonclassically > would be arbitrary in this second sense. I think Steve is misinterpreting the position of the other posters here. I don't see them as saying that categories (as Steve defines categories) can be fuzzy. I see them as saying that it may well be that people in practice don't categorize in order to derive "X-is-like-Y" measures, but rather pseudocategorize according to these measures. (Note that I've put the mark on the non-Objectivist term here rather than placing a "$" mark on the Objectivist term. Uh... at least that's what I've done as near as I can tell.) -- "When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean -- neither more nor less." --- Lewis Carol -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/20/89)
throopw@xyzzy.UUCP (Wayne A. Throop) of Data General, RTP NC. wrote:
" the consequences of not being bigger than a breadbox can be...
" every bit as important... as the distinction among fungi is to *you*...
" So, other than the motives and goals of the categorizer, there is
" nothing to make one categorization more "natural" or "less arbitrary"
" than another. Hence, categorization is inherently subjective,
" not objective.
In my posting I distinguished two senses in which a category might be
arbitrary; the first was because it did not pick out a "natural kind"
[note that this is also a nonstandard sense of "natural kind"]
and the second was because it was merely subjective. I suggested that the
first sense of "arbitrary" was not relevant to the problem of how
categories were internally represented, because a category might be
arbitrary in the first sense, yet still be based on classical
features; the features would then simply be picked out because of
socially imposed consequences rather than nature-imposed ones.
Bigger-than-a-breadbox may be an arbitrary socially imposed distinction
for us and a biological imperative to another organism. The difference
between these two cases does not much matter for the kind of internal
representation you may need to perform this categorization successfully
(except inasmuch as differences in size and sensorimotor equipment may
entail differences in detectability and means of detection).
Subjective categories, on the other hand ("looks pretty to me,"
"reminds me of his sister") are arbitrary in the second sense, in that
there may indeed exist no objective invariant features "out there" whose
presence or absence is guiding the judgment. Under those conditions
there can be no MIScategorization, no feedback, no consequences.
The relevant distinction for modeling category representation, I
suggested, was "imposed" vs "ad lib" categorization. For no matter what the
source of the imposition, the imposed categories that we can successfully
sort must be classical; the ad lib ones need not be. But a model for
ad lib categories is no model for imposed ones.
[Philosophers, by the way, use "natural kind" in a different way; they
would say a natural kind is not merely a category that is picked out
by our sense organs because of its biological consequences for us;
they would say it's something picked out by empirical scientific
inquiry because of its role in a causal theory of the physical world;
this would make only things like matter, energy, electrons, galaxies
proteins, and perhaps species, etc., the candidates for being natural
kinds. Not aspiring to be an ontologist, I am not concerned with this
distinction, but only with the cognitive question of how the
categories that ARE imposed on us, by nature or nurture, are internally
represented so as to allow us to pick them out correctly as we do.]
" [The reason we single out a given feature and sort objects in the world
" according to it] *must* be (not may be) arbitrary. The choice of
" categorization... involves the motives and goals of the categorizer,
" and is thus subjective (and objectively arbitrary).
I really don't know what you mean by "arbitrary." If a hungry rat
that has learned to turn right for food in a maze is behaving
arbitrarily, then everything we do is arbitrary and the word loses its
meaning. Nor is the rat behaving "subjectively": It may be behaving
automatically, just like a machine (though I doubt it). But even if it
makes its decision consciously, and hence subjectively, the decision,
because it is based on objective consequences, is not MERELY
subjective, hence not arbitrary in my second sense. (It's not
arbitrary in my first sense either, if nature imposes the maze.)
[One can always substitute such an operant-responding situation for a
categorization problem by the way, because many operants ARE
categorical responses.]
" I fail to see why nature is any less arbitrary than a human dictator.
" In each case, categorization happens relative to features "important"
" to some categorizer. Hence, in this sense, *all* categories are
" arbitrary.
Then what is NOT arbitrary, and why? And what does "arbitrary" mean?
I think that its complement, "nonarbitrary," always has an implicit
user- or task-relativity built into it (just as, in a prior posting,
I noted that "feature" does, namely, it is a detectable state of affairs
-- one that is either directly dectectable by some organism or
instrument, or symbolically describable in terms that are themselves
the names of categories with features that are detectable by some organism or
instrument or ... etc.; this is my "symbol grounding" theory).
When a category-name, such as "arbitrary," is applied to "everything,"
it fails to be informative, for reasons that are deeply related to the
internal representation of categories. (I have discussed this in a
paper called "Uncomplemented Categories." I think it would be equally
uninformative to say that all categories are "metaphorical," for this
simply throws out the literal/figurative distinction and the
(classical) features underlying it, hence it throws out the meaning of
the category "metaphorical.")
" one can use Humpty Dumpty's word as a category marker. "It doesn't
" say Haynes until *Dumpty* says it says Haynes." is just as objectively
" based a category as any other...
For ME it becomes objective then, but not for Humpty Dumpty! I can
pick it out, using the unfailing cue that Dumpty says so. But
Dumpty could be doing it just because of a whim, as the spirit moves
him. But before you hasten to inform me that that makes all categories
"observer relative," hence arbitrary after all, note that Dumpty and I
are not picking out the same categories, even though we're picking out
the same objects! I'm picking out the category "things Dumpty calls X."
Apart from Dumpty's say-so, there may be NOTHING these things have in
common, yet his say-so is enough to make it a classical category for
me. But not for Dumpty! He has no external cue. He's not picking out
the things so-and-so says are X, based reliably and validly on the cue
of so-and-so's say-so. God knows HOW he's picking them out. He's using
some subjective, internal cue; perhaps just a momentary, spontaneous
impulse. That makes it a different category, even though it has the
same members as mine; and a subjective, arbitrary one at that. (I trust
there's no problem with the idea that different categories can have the
same members, as with Frege's morning-star/evening-star/Venus,
or sets in mathematics that differ in their intensions but not
their extensions, etc.)
" no categorizations are arbitrary in [the second] sense.
Humpty Dumpty's, for example, is; or perhaps it's better to say that,
being arbitrary in the second sense, it's not really a category at all.
" it may well be that people in practice don't categorize in order to
" derive "X-is-like-Y" measures, but rather pseudocategorize according to
" these measures.
I can't understand this point. To me, to categorize is to sort
instances in a reliable, correct, objective, all-or-none fashion. If
it's not reliable, correct or all-or-none, it's not categorization (or
not categorical to the degree that it's not reliable, correct or
all-or-none). If it's not objective, it's subjective; then you can call
it what you like, because I have no idea what's being sorted, and on
what basis.
--
Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu
srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp
BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net
(609)-921-7771arm@ihlpb.ATT.COM (Macalalad) (01/21/89)
In the ongoing discussion of categorization, there seems to be two
different types of categorization:
1. An "arbitrary" type of categorization, arbitrary in the sense
that the same object may be categorized one way in one situation
but in another situation may be categorized some other way. For
example, a kid may describe his bike as "big" in comparison to
his little sister's tricycle, but "small" compared to his big
brother's ten speed. His bike's size is arbitrarily categorized.
2. The "classical" type of categorization, where an object is
categorized one way, 100% all-or-none.
Now no one, not even Stevan Harnad, denies the existence of (1).
But there has been much debate, and much confusion about (2).
My claim is that the existence of (2) would just add unnecessary
complexity to any theory of categorization, and unless Harnad has
some compelling evidence to the contrary, which he has not yet
brought forth, I further claim that (1) is sufficient.
Remember that even though (1) is labeled "arbitrary" categories, it
does not follow that these categories are meaningless. When that
kid is telling his little sister's friends that his bike is "big,"
he's telling them that his bike is bigger than any of their little
tricycles. And when he tells his dad that his bike is "small,"
he's implying that he needs a bigger bike, like his brother's ten
speed.
The categories then are not so much arbitrary as they are dependent
on the situation and the information that they convey. Thus, you
can still apply a rule for categorization, such as "x is big if x
is bigger than a tricycle." The rules vary with the situation.
(Note that I'm not suggesting a cognitive theory where we actually
apply rules for categorization. I'm merely saying that if we attempted
to come up with a rule for our internal categories, these rules would
vary with the situation.)
Now consider the category "bird" which has been proposed as a classical
category. A boy may point to a flying object and say to his friend,
"Look at that bird." Later on, when the object flies closer, he may
say, "Oh,that's no bird. That's a bat." Under classical categorization,
as I understand it, the boy committed a miscategorization, which he
later corrected. However, the boy didn't learn anything new about
the category. He was just as capable of distinguishing between a bird
and a bat before and after.
I would argue that instead, the boy was applying two different rules.
The first was something like, "If there's a distant flying object that
has wings flapping up and down and a head and a body, then it's a bird."
And presumably the categorization was appropriate enough for his friend
to recognize what object he was talking about. Once the object was
closer and provided his senses with more detail, he could apply
a different rule which yielded more information about the object.
Actually, (2) could be a special case of (1), where only one rule
is applied in every situation. So even if (2) did exist, (1) would
still be sufficient.
Comments?
-Alexbwk@mbunix.mitre.org (Barry W. Kort) (01/22/89)
In article <Jan.19.12.50.59.1989.2589@elbereth.rutgers.edu> harnad@elbereth.rutgers.edu (Stevan Harnad) writes: > To me, to categorize is to sort instances in a reliable, > correct, objective, all-or-none fashion. If it's not reliable, > correct or all-or-none, it's not categorization (or not > categorical to the degree that it's not reliable, correct or > all-or-none). If it's not objective, it's subjective; then you > can call it what you like, because I have no idea what's being > sorted, and on what basis. This discussion reminds me of the notion of Fuzzy Sets, as introduced by Berkeley's Lofti Zadeh some twenty years ago. By way of contrast, Stanford's Tom Cover coined the phrase Crisp Sets to emphasize Stevan's concept of reliable all-or-none categorization. I like the notion of Fuzzy Sets, because they better capture our human nature of disagreeing on the boundaries of set membership. But I also like Fuzzy Sets because they map into Fuzzy Logic much the way Crisp Sets map into Boolean Logic. Fuzzy Logic models the mental state associated with such vague and confusing ideas. When we have no clear idea, but we have something more than "no idea", we have a fuzzy idea. --Barry Kort
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/23/89)
arm@ihlpb.ATT.COM (Macalalad) of AT&T Bell Laboratories - Naperville, Illinois, wrote: " there seem to be [claims of] two different types of categorization: " (1) An "arbitrary" type... in that the same object may be categorized " one way in one situation [and another way in another,... e.g.,] a kid " may describe his bike as "big" in comparison to his little sister's " tricycle, but "small" compared to his big brother's ten speed. " [And] (2) The "classical" type of categorization, where an object is " categorized one way, 100% all-or-none... " (2) would just add unnecessary complexity to any theory of " categorization,... unless Harnad has some compelling evidence to the " contrary... (1) is sufficient. None of the distinctions discussed so far has corresponded to this "arbitrary"/"classical" distinction, which does not seem to me to be coherent. Two things seem to be conflated in the above example: First, it's true for virtually ALL categories that the very same object can belong to MANY different categories: All birds are vertebrates, animals, concrete objects, etc. This bird is a pet, Tweety, etc. Nor is it just a vertical hierarchy that governs all these different names for the same object. There's what's called in my book "the `context' of interconfusable alternatives": The purpose of a category name is to resolve uncertainty among alternatives, i.e., to INFORM; the uncertainty must be objective, namely, MIScategorizing must have detectable consequences. So a horizontal context might be that my life depended on singling out THAT BIRD for someone (without pointing to it), and the alternatives were: (a) a bird, a stick and a stone (solution: "the bird"); (b) a robin, a parakeet and a canary (solution: "the canary"); (c) three canaries (solution: "Tweety" or "the middle one") etc. There is nothing arbitrary about this context-dependence of categorization: It's intrinsic to the informative function of categorization itself. Nor is it involved only in the USE of existing categories; even more important, according to my theory, is the fact that the LEARNING of the categories in the first place is always context-dependent too. (Q: "What's that? A: "Compared to what?") In my model, it is the context of confusable alternatives which one samples and must sort into categories, guided by the consequences of miscategorizing, that makes it possible to focus the search for the invariant features that reliably distinguish the inputs one is sorting. Categorization would never converge if the context were infinite, and "everything" were potentially confusable with "everything else." (This is related to what philosophers have called "category errors" or "type crossings," as well as to the phenomenon of "underdetermination" and the problem of negative instances.) The second conflation in the above example concerns what psychophysicists carefully distinguish as "relative" versus "absolute" (categorical) judgment. For the context-dependence of categorization does not make it a mere relative judgment, such as a similarity judgment, because relative judgments depend on explicit (usually pairwise) comparisons, with the pair usually jointly present. "Bigger" vs. "smaller" is a relative judgment. Nobody would say that there was a category of things called "bigger" things. This kind of "situation-dependence" is very different from the context-dependence I described above, for it always depends on two things in particular. If there is an absolute category here, it is one defined on PAIRS of objects: the relational property invariantly present in the larger of the two in any pair (within the same context: I don't have to worry about whether the smell of mint is "bigger" than the smell of juniper, or whether goodness is bigger than truth). "Big," on the other hand, as opposed to "bigger," is indeed a graded rather than an all-or-none "category," as I indicated in my very first contribution to this discussion. But I am focusing on all-or-none categories like "bird" here, which are not to be confused or conflated with graded ones like "big." Macalalad asks for compelling evidence of all-or-none categories: I offer "bird" and the myriad other categories like it that we are perfectly capable of sorting and labeling correctly and reliably with virtually 100% success. These categories, too, are context-dependent, in that the features picked out by their representations are only good enough to tell apart birds from among the alternatives encountered so far. But this approximation seems pretty secure for most of the cases most nonbiologists are ever likely to encounter. As to whether all-or-none categories "add unnecessary complexity to any theory of categorization," they no doubt do, but only in the sense that plants add unnecessary complexity to a theory of botany. What I've called the "Roschian" tradition -- fueled, perhaps, by a misreading or misapplication of Wittgenstein -- has simply managed to forget or ignore what it is that categories, categorization, and modeling their underlying substrates is all about. [Here's some food for thought for would-be Wittgensteinians: I categorically deny that Wittgenstein's paradigmatic example of a "family resemblance" category, namely, "games," is nonclassical, in the sense that it lacks underlying invariant features that pick out the category "games." The features may well include disjunctions, conditionals, etc., but they will all add up to necessary and sufficient conditions for what counts as a "game." The fact that Wittgenstein and others have failed to come up with these necessary and sufficient conditions by introspection does not impress me; what impresses me is the vast quantity of candidates that we can all reliably sort as "games" or "nongames." Underlying these there must be a classical basis for the sorting, both in the candidates and in their representations in our heads. There are of course also ambiguous or uncertain cases that no one can sort, or not everyone agrees on. But these certainly can't be counted in favor of a nonclassical internal representation of the category "games," because they're precisely the cases we CAN'T categorize!] " categories... are not so much arbitrary as... dependent on the " situation and the information that they convey... The rules vary with the " situation. (Note that I'm not suggesting a cognitive theory where we " actually apply rules for categorization. I'm merely saying that if we " attempted to come up with a rule for our internal categories, these " rules would vary with the situation.) Rules are largely logical operations on strings of features, or on symbols grounded in features. "Satisfying a rule" thus counts as "being describable by a predicate," which in turn (as I've argued in earlier installments) amounts to "having a `feature' (in the general sense of `a detectable state of affairs')." I think that the reluctance to come out and say that the features/rules are actually USED (hence internally represented somehow), even though it is admitted that they exist, may arise from giving far too much weight to arguments based on the fact that we do not know what the features are introspectively. Nor (as I suggested above) does their context-dependence, both in acquisition and use, make these features/rules any less real. Context-dependence may be one of the most important properties of categories and category formation. [Macalalad seems somewhat ambivalent about whether or not rules are "actually applied." See below.] " A boy may point to a flying object and say... "Look at that bird." " Later on, when the object flies closer, he may say, "Oh, that's no " bird. That's a bat." Under classical categorization, as I understand " it, the boy committed a miscategorization, which he later corrected. " However, the boy didn't learn anything new about the category. He was " just as capable of distinguishing between a bird and a bat before and " after... [T]he boy was applying two different rules... "If there's a " " distant flying object that has wings flapping up and down and a head " and a body, then it's a bird." And presumably the categorization was " appropriate enough for his friend to recognize what object he was " talking about. Once the object was closer and provided his senses with " more detail, he could apply a different rule which yielded more " information about the object. This case simply illustrates that, along with being context-dependent, categories are also always approximate: They are based only on the features that reliably pick out the category in question from among the confusable alternatives. Categories and approximations have the virtue of (in principle) always being amenable to tightening whenever the context of alternatives (and its corresponding uncertainties) is widened. The only thing I would add is that the above example happened to be an example of context widening and category tightening in the USE of existing categories. Similar effects can also occur in the acquisition of new categories, as well as in their revision. (Cognitive theorists, as I've suggested in other postings, must be careful not to fall into an ontological stance -- concerned with what things "really" are: Their mission can only be to determine how we reliably sort and label the actual alternatives we sample.) Macalalad seems to share with much of the field an ambivalence about attributing to the internal representation of a category the rules the subject "applies" in order to accomplish the categorization. I don't know whether this again arises from a misreading of Wittgenstein (this time "On Rules") or whether it is just another spin-off of the Roschian denial of classical features. I for one have no hesitation in concluding that if an all-or-none categorization of inputs is reliable and correct, then there must be a classical featural basis for it in the input, and that whatever that classical featural basis is, it is actually used and actually internally represented (though not necessarily as an explicit rule; perhaps as an implicit feature detector). " Actually, (2) [all-or-none categories] could be a special case of (1) " ["situation-dependent" categories], where only one rule is applied in " every situation. So even if (2) did exist, (1) would still be sufficient. I trust that this is all straightened out now by the discussion above. All categories are context-dependent, both in acquisition and use. There is no contradiction between being context-dependent and being all-or-none. "Conformity to a rule" is a classical feature, and categories picked out on that basis are perfectly classical. -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
throopw@xyzzy.UUCP (Wayne A. Throop) (01/24/89)
> harnad@elbereth.rutgers.edu (Stevan Harnad) > In my posting I distinguished two senses in which a category might be > arbitrary; the first was because it did not pick out a "natural kind" Yes... what I was calling arbitrary categorization (as opposed to an arbitrary category). > and the second was because it was merely subjective. Yes... what I was calling an arbitrary category. By "categorization", I meant the feature(s) that pick(s) out a category. By "arbitrary categorization" I meant that the features chosen from some set of possibilities might seem, to some observers at least, to be chosen without motive or "at random". The point I was trying to make here is that there are no non-arbitrary categorizations. This is because it is simply a mistake to suppose that one categorization (choice of distinguishing feature) is any more "natural" than another. All useable distinguishing features have effects of some sort. If they did not, they could not be observed. The "importance" or "naturalness" of these features is based purely on the goals and motives of the categorizer, and thus can appear motiveless to an observer with goals and motives that make the effect irrelevant. By "arbitrary category" I meant that the basis for inclusion could not be objectively determined, and thus seemed "random". The point I was trying to make here is that there are no arbitrary categories. This is because it is always possible to "objectify" a category based on subjective grounds, by the "inspector 12" method. "It don't say (it's in category X) until *I* say it says (it's in category X)." Two potential objections arise: First, this is only objective to other people, not to inspector 12. I disagree. Inspector 12 can objectively determine what inspector 12 utters. Second, others cannot, in the absense of inspector 12, make the categorization. But then, people cannot make the categorization "colored ultraviolet" on objects without bees, or artificial instruments, or whatnot. I don't see that it makes a fundamental difference whether a particular "category detector" such as "this scene is good/bad looking", or this "flower smells good/bad" needs a particular person or instrument to act as oracle. In other words, the claim that such categories are "really baseless" is insupportable, because the person involved may very well be making the judgement objectively by criteria that other observers cannot perceive, as a person who has had the cornea removed might make the judgement "ultraviolet colored" and appear to be choosing totally at random to all "normal" persons. On to other points. > I suggested that the > first sense of "arbitrary" was not relevant to the problem of how > categories were internally represented, because a category might be > arbitrary in the first sense, yet still be based on classical > features I agree, but for a much stronger reason, as one can see from my argument above. > Subjective categories, on the other hand ("looks pretty to me," > "reminds me of his sister") are arbitrary in the second sense, in that > there may indeed exist no objective invariant features "out there" whose > presence or absence is guiding the judgment. I disagree, unless the categorizer is lying or confused. Either the object really bears some resemblance (or has some other property which evokes memory of the categorizers female sibling) or it does not. Just because every Tom, Dick and Harry can't pick out these objective features is as irrelevant as whether Tom, Dick or Harry can see gamma rays. > When a category-name, such as "arbitrary," is applied to "everything," > it fails to be informative Agreed, but then I didn't apply it to "everything". I applied it to what I called "categorizations". Dealing with various "Dumpty" issues, I point out that a categorizer oracle for "Dumpty finds X pretty" is not arbitrary as I outlined above... counterpoints raised to this position tend to involve Dumpty lying, or involve the fact that Dumpty's tastes can change over time. I don't see that either of these are relevant, since by analogy, a geiger counter can be improperly calibrated and "lie", and it's calibration can change over time and drift. This doesn't matter in categorizing radioactive materials in the abstract, and it shouldn't matter in categorizing things-Dumpty-finds-pretty in the abstract. ( Now, there is one way of arriving at a category which is truely arbitrary in the second sense, but it doesn't involve "subjectivity" or "Dumptyness". It involves categorizing photons on where they strike a screen after passing through slits which cause interference (or some other quantum-mechanical-determined outcome). Current understanding says that these events really are arbitrary and causeless in the strongest sense. But I'm not really prepared to deal with this case, and it doesn't seem to belong to the domain of discussion anyway, which is how folks categorize in the everyday world. ) >> it may well be that people in practice don't categorize in order to >> derive "X-is-like-Y" measures, but rather pseudocategorize according to >> these measures. > I can't understand this point. To me, to categorize is to sort > instances in a reliable, correct, objective, all-or-none fashion. What I'm saying is that other people may not mean the same thing that you do when they use the world "categorize". This does not necessarily mean that they are "wrong". -- I mean, where do you even FIND a Jewish hard-line conservative Republican pot-smoker? --- A. Whitney Brown -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
rwojcik@bcsaic.UUCP (Rick Wojcik) (01/24/89)
In article <Jan.19.12.50.59.1989.2589@elbereth.rutgers.edu> harnad@elbereth.rutgers.edu (Stevan Harnad) writes: >" it may well be that people in practice don't categorize in order to >" derive "X-is-like-Y" measures, but rather pseudocategorize according to >" these measures. >I can't understand this point. To me, to categorize is to sort >instances in a reliable, correct, objective, all-or-none fashion. If >it's not reliable, correct or all-or-none, it's not categorization (or >not categorical to the degree that it's not reliable, correct or >all-or-none). If it's not objective, it's subjective; then you can call >it what you like, because I have no idea what's being sorted, and on >what basis. We seem to be going around in circles on this. I think that the original posting that started all this was correct in bringing Lakoff's book into it. Human categorization simply is not of the all-or-none variety. Analogy is a fundamental property of human cognition. I hope that those who are interested in this discussion, which can only be carried on at a superficial level in a newsgroup like this, will take the time to read "Women, Fire, and Dangerous Things." I particularly call people's attention to 118 ff., which discuss the question of biological taxonomy--the cladists vs. the pheneticists. Stevan Harnad, at one point, said that we should leave biological classification up to the experts, that the discussion on that point wasn't relevant. Lakoff gives a very nice discussion of why expert taxonomies of that sort are relevant to everyday categorization. Biologists, like most of us, labor under the illusion of what Lakoff calls a "folk theory of categorization"--the view that "things come in well-defined kinds, that the kinds are characterized by shared properties, and that there is one right taxonomy of kinds." (p. 121) When different taxonomies for reality fail to converge, our common sense tells us that one or the other must give. Lakoff suggests that 'common sense' may be leading us astray in this case. -- Rick Wojcik csnet: rwojcik@atc.boeing.com uucp: uw-beaver!ssc-vax!bcsaic!rwojcik
throopw@xyzzy.UUCP (Wayne A. Throop) (01/25/89)
> arm@ihlpb.ATT.COM (Macalalad) > In the ongoing discussion of categorization, there seems to be two > different types of categorization: > 1. [... arbitrary, meaning situational or context sensitive ...] > 2. [... "classical", meaning context free ...] Hmmmmm.... Seems to me everybody is using a different definition of "arbitrary", including me. Which opens the possibility of superficially conflicting claims all being correct. Sigh. > I would argue that instead, the boy was applying two different rules. > The first was something like, "If there's a distant flying object that > has wings flapping up and down and a head and a body, then it's a bird." > Once the object was > closer and provided his senses with more detail, he could apply > a different rule which yielded more information about the object. I see it slightly differently. It isn't so much that two rules are applied, but that a large set of rules are applied and the appropriate categorization changes when the sense impressions relevant to "the bird" change. That is, by claiming "there is a bird" in the first statement, the observer is really saying that there exists a set of sense impressions the accounting for which a bird is a sufficent hypothesis. In the correction to "nope, it's a bat", the observer "really means" that the current sense impressions contradict the former sufficent hypothesis, and a new sufficent hypothesis is advanced. Note that a bat was also, even at first, a sufficent hypothesis, but it wasn't the *least* sufficent hypothesis (presumably because seeing a bird there/then was more likely than seeing a bat... IE, it was daytime, or outside any bat species' normal range or whatnot). In fact, I think that all statements of "fact" (about the real world) are best understood to be claims about the least sufficent hypothesis which explains our sense impressions. -- The optimist says "This is the best of all possible worlds." The pessimist answers "That's right." --- Joseph Weizenbaum -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
arm@ihlpb.ATT.COM (Macalalad) (01/25/89)
I wrote (among other things) (paraphrased) >The distinction between graded and all-or-none categories is that >graded categories are dependent on context, whereas all-or-none >categories are not. [various arguments that all-or-none categories >are also dependent on context follow] Stevan Harnad replies (among other things) (paraphrased) >Oh no, that is not the distinction at all. Of course all-or-none >categories are dependent on context. Please forgive me if that was not a sufficiently correct or complete paraphrase, but I didn't want to repost pages and pages of commentary. I'm rather confused now about what the distinction between a graded and an all-or-none category. What does it mean to call "big" a graded category? Does it mean that sometimes I categorize something as big and sometimes as small, depending on the situation? Apparently not, from the above. Does it mean that I categorize something as 65% big and 35% small? Does it mean that 65% of the people categorize something as big, and 35% categorize the same thing as small? As a side note, I am not sure whether to classify Harnad's comments about my misreading of Wittgenstein as a compliment or an insult. Compliment: That I write as if I had a working knowledge of such philosophical tomes as Wittgenstein's. Insult: That I misread Wittgenstein. Compliment: That I anticipated (in the sense of coming up with independently) ideas like Wittgenstein's. Insult: That I anticipated a misreading of Wittgenstein. I wonder what the consequences of MIScategorization would be. (:-)
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/25/89)
throopw@xyzzy.UUCP (Wayne A. Throop) of Data General, RTP NC wrote: " [T]here are no non-arbitrary categorizations... By "categorization", I " meant the features that pick out a category. By "arbitrary " categorization" I meant that the features chosen from some set of " possibilities might seem, to some observers at least, to be chosen " without motive or "at random"... " [T]there are no arbitrary categories... By "arbitrary category" I " meant that the basis for inclusion could not be objectively determined, " and thus seemed "random". " [I]t is always possible to "objectify" a category based on subjective " grounds, by the "inspector 12" method: "It don't say (it's in category " X) until *I* say it says (it's in category X)." " I don't see that it makes a fundamental difference whether a particular " "category detector" such as "this scene is good/bad looking", or this " "flower smells good/bad" needs a particular person or instrument to act " as oracle... the person involved may very well be making the judgement " objectively by criteria that other observers cannot perceive The first passage is getting too complicated for me. Sounds like it's saying no category is arbitrary but all features on the basis of which you pick them out are arbitrary. Seems like a strained form of realism. Fine. But the trouble is that features are categories too, which makes the whole thing sound like it's either incoherent or an arbitrary semantic quibble. Yes, things are what they are irrespective of my 'druthers, but my sorting still either does or does not depend on something objective and invariant "out there." My *motives* for picking features are not what's at issue in the debate about whether or not the "classical" view is correct, but the objective *existence* and *use* of those (classical) features. The second point has to do with using another person as your feature-detecting instrument. Fine. But there's still the question of whether HIS sorting is based on features he's detecting "out there" or he's merely listening to some inner voice, which in turn has no objective external basis. If the latter, then for HIM no objective miscategorization is possible -- no OBJECTIVE consequences follow from sorting "incorrectly." Hence the category he is picking out is purely subjective, and hence arbitrary in the second sense we were discussing. (This would NOT be like, say, ultraviolet light detection, where your human oracle/instrument would indeed be using classical features.) -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
rwojcik@bcsaic.UUCP (Rick Wojcik) (01/26/89)
In article <43780@linus.UUCP> bwk@mbunix.mitre.org (Barry Kort) writes: >This discussion reminds me of the notion of Fuzzy Sets, as >introduced by Berkeley's Lofti Zadeh some twenty years ago. >By way of contrast, Stanford's Tom Cover coined the phrase >Crisp Sets to emphasize Stevan's concept of reliable all-or-none >categorization. The discussion ought to remind you of Zadeh. The discussion started as a reaction to Lakoff's work, which has very strong historical ties to Zadeh. (Read Lakoff's book. Stevan doesn't want to take the time, but it is worth the effort.) Linguists have long been aware of the problems with all-or-none categorization. What Stevan does is he simply defines the word 'categorization' to suit his all-or-none criterion, without any regard for the way in which humans actually assign categories. But consider the classic examples of 'semantic vagueness'. We have the mental illusion that mountains and waves are discrete objects. Questions like 'How many mountains are there in the Cascades?' or 'How many waves are there in the ocean?' are semantically well-formed, but impossible to answer from a conceptual point of view. There are no natural discrete boundaries to these categories, such that you can always tell where one mountain or wave leaves off and another begins. It is also relevant to the discussion to consider how we categorize objects in the earliest stages of language. The child's earliest uses involve complexive organization, overextensions, and underextensions (the last being very difficult to detect). 'Complexive' organization, a term coined by Melissa Bowerman, seems to involve some kind of shifting categorization. A child might use the word 'doggie' on different occasions to refer to four-legged things, furry things (e.g. a blanket), things that move, etc. It is quite easy to relate such gross 'miscategorizations' to the many legitimate examples of complex adult categoriztion cited in Lakoff's book. Such behavior is very reminiscent of what Lakoff calls 'radially structured' categories. Overextensions and underextensions seem to involve a fine-tuning of categorization that looks more like the so-called 'classical' type. -- Rick Wojcik csnet: rwojcik@atc.boeing.com uucp: uw-beaver!ssc-vax!bcsaic!rwojcik
throopw@xyzzy.UUCP (Wayne A. Throop) (01/28/89)
> harnad@elbereth.rutgers.edu (Stevan Harnad) > Sounds like it's > saying no category is arbitrary but all features on the basis of which > you pick them out are arbitrary. Righto. > But the trouble is that features are categories too, which makes > the whole thing sound like it's either incoherent or an arbitrary > semantic quibble. Yes, it is a semantic quibble, but no semantic quibbles are arbitrary. After all "semantics" in this case is refering to the meaning of the utterances I am making. My meanings are not arbitrary, nor can they be, for much the same reason that my categories can't be (always assuming the framework we started out with, of course... it is clearly possible to redefine "category" and "meaning" so that these things are not true, but this contradicts the original context Stevan himself set up). (And by the way, only half a smiley on that last paragraph, in case anybody was wondering. Or maybe a full smiley about the "no semantic quibbles", but I do think *this* one is not arbitrary.) As to features being categories, I disagree. Features *belong* to a category, but that doesn't stop them from being arbitrary... *they* are arbitrary, but whether or not they belong in the category "feature" is *not* arbitrary. > Yes, things are what they are irrespective of my > 'druthers, but my sorting still either does or does not depend on > something objective and invariant "out there." The point I was making was that, according to your own previous assertions about what a category *is*, a sorting that does NOT depend on something objective is not a category at all. > Hence the category he is picking out is purely > subjective, and hence arbitrary in the second sense we were discussing. > (This would NOT be like, say, ultraviolet light detection, where your > human oracle/instrument would indeed be using classical features.) No, I still think this is not possible (in the sense that it implies a self-contradiction). If the person is sorting based upon truely random criteria, then what is picked out is not a category, and if the person picking it out insists that it is, the person is either lying or mistaken. (I realize that "random" does not completely cover the "subjective" classification Stevan put forward, but the "non-random-but- subjective" portion of the classification must, as pointed out before, be reducible to classical features. -- Life is a foreign language: all men mispronounce it. --- Christopher Morley -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
harnad@elbereth.rutgers.edu (Stevan Harnad) (01/29/89)
rwojcik@bcsaic.UUCP (Rick Wojcik) of Boeing Computer Services AI Center, Seattle wrote: " Linguists have long been aware of the problems with all-or-none " categories. Stevan... simply defines the word 'categorization' to suit " his all-or-none criterion, without any regard for the way humans " actually assign categories. But consider the classic examples of " 'semantic vagueness'. We have the mental illusion that mountains and " waves are discrete objects. Questions like 'How many mountains are " there in the Cascades?' or 'How many waves are there in the ocean?' are " semantically well-formed, but impossible to answer from a conceptual " point of view. There are no natural discrete boundaries to these " categories, such that you can always tell where one mountain or wave " leaves off and another begins. The problem of how we categorize (i.e., sort and label objects and states of affairs) is basically not a linguistic one, though it of course makes contact with linguistics at some level (because the category labels form our lexicon, and language allows us not only to label categories, but to describe them). For example, how we manage to sort and label mountains and waves is basically a perceptual problem: What are the internal representations that allow us to categorize members and nonmembers of these categories successfully, in those many cases in which we are able to do so? It is those who ignore (or take for granted) this enormous core of reliable, correct, all-or-none categorization performance who are not showing due "regard for the way humans actually assign categories." The solution to the problem of HOW people manage to sort and label things as they actually do will not come from linguistics, it will come from a theory of perceptual and cognitive representation. Nor will how we categorize in most cases be determined from our introspective discourse about how we categorize, any more than how we perceive will be determined from our introspections about our perception. The explanation will come from theoretical inference and the building and testing of causal models for the underlying mechanism. I also remind the reader that the question to which these discussions were addresses was whether or not the representation that allows us to categorize is "classical," i.e., consists of features that are necessary and sufficient to sort members from nonmembers, NOT whether or not we can sort EVERY instance of ANYTHING we ever encounter in an all-or-none fashion. The question under discussion is simply moot for cases in which we CANNOT sort members from nonmembers (e.g., "vague" cases). Note that this point is a logical, not an empirical one; its only empirical aspect is the evidence (and it's all over the map -- unless you're in the grip of an introspective theory) that there do indeed exist myriad categories that we can and do sort and label in a reliable, correct, all-or-none fashion. " A child might use the word 'doggie' on different occasions to refer to " four-legged things, furry things (e.g. a blanket), things that move, " etc. Overextensions and underextensions seem to involve a fine-tuning " of categorization that looks more like the so-called 'classical' type. Indeed it does -- and the process leads ultimately to our asymptotic core of perfectly "classical" categories. My only quarrel with this terminology has been that to call this "overextension" and "underextension" is to adopt too omniscient or ontological a view. According to my theory, ALL categories are provisional and approximate, including our adult ones. Their context of interconfusable alternatives could always in principle be widened so as to show up our former representations as having been over- or underextended (based on hindsight). At a given point in its experience a child's category may accordingly NOT be over- or underextended relative to the actual sample of alternatives he has so far encountered and the feedback he has so far received from the consequences of miscategorization; the over/underextension may only be relative to OUR categories and their larger and more representative contexts. Subsequent experience may force the child to revise his categories and eventually converge on ours, but that does not necessarily mean they are over- underextended at THIS point. Sometimes we expect too much from children and other category learners on the basis of the data available to them; for similar reasons we sometimes also attribute too much to them (as in the chimpanzee "language" studies). It is only by taking account of the categorizer's actual sorting performance in its actual context of confusable alternatives that one can infer a category's actual extension and intension, and hence its underlying representation. (On the other hand, over- and underextension CAN be be defined during this actual learning phase WITHIN the child's actual local context of alternatives, while miscategorization with feedback is going on; this, however, is probably more perspicuously described as the formation or revision of the child's own provisional categories, guided by the consequences of miscategorization, rather than as the "fine-tuning" of OUR categories.) -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
throopw@xyzzy.UUCP (Wayne A. Throop) (01/31/89)
> harnad@elbereth.rutgers.edu (Stevan Harnad) > Nor will how we categorize in most cases be determined from our > introspective discourse about how we categorize, [...] > The explanation will come from theoretical inference and > the building and testing of causal models for the underlying > mechanism. I quite agree, mod a few nits about "THE explanation" as opposed to "well founded explanations" or "scientific explanations". > What are the internal representations that allow us to categorize > members and nonmembers of these categories successfully, in those many > cases in which we are able to do so? It is those who ignore (or take > for granted) this enormous core of reliable, correct, all-or-none > categorization performance who are not showing due "regard for the way > humans actually assign categories." Here, however, I'm not so sure I agree fully. To be specific, while it is indeed the case that "those who ignore" sharp-seeming categorizations are not "showing due 'regard'" (etc), it is NOT the case that all those who propose fuzzy internal representations of categories ignore this evidence. It is, after all, a plausible hypothesis that the "all-or-none" nature of some human categorization is due to there being no actual objects occupying fuzzy ground around fuzzy internal categories, instead of because the internal categories are non-fuzzy but the sensory evidence is ambiguous or insufficent to resolve the non-fuzzy question. In fact, I personally suspect that there is a mix of strategies and internal representations, at various "levels" and degrees of "automaticness". However that may be, I see no particular evidence upon which to base the "theoretical inference" that human internal category representation is non-fuzzy. The point is that while fuzzness is far from established confidently, the same is true of crispness. -- When asked how to pronounce his name, Nicklaus Wirth replied, "You can call me by name, 'virt', or call me by value, 'worth'.". -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
harnad@elbereth.rutgers.edu (Stevan Harnad) (02/05/89)
anwst@cisunx.UUCP (Anders N. Weinstein) of Univ. of Pittsburgh, Comp & Info Sys wrote: " [We must distinguish] the normative question of which things are " *correctly* classified as birds or even numbers, and the descriptive " question of how in fact our neural machinery functions to enable us to " so classify things. I agree also with Harnad that psychology ought to " keep its focus on the latter and not the former of these questions. A kind of "correctness" factor does figure in the second question too: To model how people categorize things we have to have data on what inputs they categorize as members of what categories, according to what constraints on MIScategorization. However, it's certainly not an ontological correctness that's at issue, i.e., we're not concerned with what the things people categorize really ARE "sub specie aeternitatis": We're just concerned with what people get provisionally right and wrong, under the constraints of the sample they've encountered so far and the feedback they've so far received from the consequences of miscategorization. " I think Harnad errs... that reliable categorization *must* be " interestingly describable as application of some (perhaps complex) rule " in "featurese" (for some appropriate set of detectable features)... " Limiting ourselves (as I think we must) to quick and automatic " observational classification... If... the effects of context on such tasks " are minimal... there must be within us some isolable module which can " take sensory input and produce a one bit yes-or-no output for category " membership... But how does it follow that such a device must be " describable as applying some *rule*? Any physical object in the world " could be treated as a recognition device for something by interpreting " some of its states as "inputs" and some as "yes-or-no responses." But " intuitively, it looks like not every such machine is usefully described " as applying a rule in this way. In particular, this certainly doesn't " seem a natural way of describing connectionist pattern recognizers. So " why couldn't it turn out that there is just no simpler description of " the "rule" for certain category membership than: whatever a machine of " a certain type recognizes? I don't care whether or not the internal basis for a machine's feature-detecting and categorizing success is described by us as a "rule" (though I suspect it can always be described that way). I don't even care whether or not the internal basis consists of an explicit representation of a symbolic rule that is actually "applied" (in fact, according to my theory, such symbolic representations of categories would first have to be grounded in prior nonsymbolic representations). A connectionist feature-detector would be perfectly fine with me; I even suggest in my book that that would be a natural (and circumscribed) role for a connectionist module to play in a category representation system (if it can actually deliver the goods). To rehabilitate the "classical" view I've been trying to rescue from well over a decade of red herrings and incoherent criticism all I need to re-establish is that where there is reliable, correct, all-or-none categorization performance, there must surely exist detectable features in the input that are actually detected by the categorizing device as a basis for its successful categorization performance. I think this should be self-evident to anyone who is mindful of the obvious facts about our categorization performance capacity and is not in the grip of a California theory (and does not believe in magic). The so-called "classical" view is only that features must EXIST in the inputs that we are manifestly able to sort and label, and that these features are actually DETECTED and USED to generate our successful performance. The classical view is not committed to internal representations of rules symbolically describing the features in "featurese" or operating on symbolic descriptions of features. That's another issue. (According to my own theory, symbolic "featurese" itself, like all abstract category labels in the "language of thought," must first be grounded in nonsymbolic, sensory categories and their nonsymbolic, sensory features.) [By the way, I don't think there's really a problem with sorting out which devices are actually categorizing and which ones aren't. Do you, really? That sounds like a philosopher's problem only. (If what you're worried about is whether the categorizer really has a mind, then apply my Total Turing Test -- require it to have all of our robotic and linguistic capacities.) Nor does "whatever a machine of a certain type recognizes" sound like a satisfactory answer to the "question of how in fact our neural machinery functions to enable us to so classify things." You have to say what features it detects, and HOW.] [Related to the last point, Greg Lee (lee@uhccux.uhcc.hawaii.edu), University of Hawaii, had added, concerning connectionist feature-detectors: "If you don't understand how the machine works, how can you give a rule?" I agree that the actual workings of connectionist black boxes need more analysis, but to a first approximation the answer to the question of how they work (if and when they work) is: "they learn features by sampling inputs, with feedback about miscategorization, `using' back-prop and the delta rule." And that's certainly a lot better than nothing. A fuller analysis would require specifying what features they're detecting, and how they arrived at them on the available data, as constrained by back-prop and the delta rule. There's no need whatsoever for any rules to be explicitly "represented" in order to account fully for their success, however. -- In any case, connectionist black boxes apparently do not settle the classical/nonclassical matter one way or the other, as evidenced by the fact that there seems to be ample room for them in both nonclassical approaches (e.g., Lakoff's) and classical ones (e.g., mine).] I also see no reason to limit our discussion to "quick, automatic, observational" categorization; it applies just as much to slow perceptual pattern learning and, with proper grounding, to abstract, nonperceptual categorization too (although here is where explicitly represented symbolic rules [in "featurese"?] do play more of a role, according to my grounding theory). And I think context effects are rarely "minimal": All categorization is provisional and approximate, dependent on the context of confusable alternatives so far sampled, and the consequences (so far) of miscategorizing them. -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771
mmt@client1.dciem.dnd.ca (Martin Taylor) (02/11/89)
I am surprised that in this long debate no-one has referenced Watanabe's
"Theorem of the Ugly Duckling" (Watanabe, 1965, 1969). To quote from
"Knowing and Guessing" (Watanabe, 1969, p376):
... from the formal point of view there exists no such thing as a class of
similar objects in the world, insofar as all predicates (of the same
dimension) have the same importance. Conversely, if we acknowledge the
empirical existence of classes of similar objects, it means that we are
attaching nonumiform importance to various predicates, and that this
weighting has an extralogical origin.
When we employ a concept, we usually understand that there is a group
of objects corresponding to this concept that any two members of the group
resemble each other more than a member and a nonmember. Two sparrows are
very much alike, while a sparrow and a rose are not alike. It is natural
to translate the term "to resemble" as "to share many predicates in common."
But this interpretation can be shown to lead to a denial of the existence
of a class of similar objects by the following theorem [not quoted. MMT],
which I have dubbed the theorem of the ugly duckling. The reader
will soon understand the reason for referring to the story of Hans
Christian Anderson, because this theorem, combined with the foregoing
interpretation, would lead to the conclusion that an ugly duckling and
a swan are just as similar to each other as are two swans.
The point is that categories cannot be logically derived as groups of objects
sharing features, but (as I interpret Harnad) as groups of objects toward
which actions have common consequences, and have been found to have
common consequences in past experience. The problem with this is that
it is very limited. We have far more classes than those composed of objects
with which we have interacted. Most categories are determined linguistically,
by mutual agreement (or the apparent occurrence of agreement). Harnad
insists on the right to declare that someone has "MIScategorized" something,
as if the category existed outside the linguistic agreement or the feedback
from experience. Earlier, he also used the term "natural kinds". I believe
that both these usages assert a kind of Newtonian universe, in which a
God has prescribed some knowable structure; but we could not know such a
universe, and an Einsteinian mode seems more appropriate. We can know
(and categorize) only what we can sense, derive, and discuss. And in those
categories there can only be grades of usefulness, never error.
--
Martin Taylor (mmt@zorac.arpa ...!uunet!dciem!mmt) (416) 635-2048
If the universe transcends formal methods, it might be interesting.
(Steven Ryan).harnad@elbereth.rutgers.edu (Stevan Harnad) (02/19/89)
mmt@client1.dciem.dnd.ca (Martin Taylor) of D.C.I.E.M., Toronto, Canada writes about Watanabe's "Ugly Duckling Theorem," quoting: " "When we employ a concept, we usually understand that there is a " group of objects corresponding to this concept that any two " members of the group resemble each other more than a member and " a nonmember [but]... from the formal point of view there exists " no such thing as a class of similar objects in the world, " insofar as all predicates (of the same dimension) have the same " importance" (Watanabe 1969). " " [C]ategories cannot be logically derived as groups of objects sharing " features, but (as I interpret Harnad) as groups of objects toward which " actions have common consequences, and have been found to have common " consequences in past experience... [But] We have far more classes than " those composed of objects with which we have interacted. Most " categories are determined linguistically, by mutual agreement... Harnad " insists... someone [can have] "MIScategorized" something, as if the " category existed outside the linguistic agreement or the feedback from " experience. Earlier, he also used the term "natural kinds"... [B]oth " these usages assert a kind of... universe, in which a God has " prescribed some knowable structure; but we could not know such a " universe... We can know (and categorize) only what we can sense, " derive, and discuss. And in those categories there can only be grades " of usefulness, never error. Let me clarify some misunderstandings: (1) I have been writing AGAINST, not FOR the ontological (or "God's Eye") view of categories. Our internal representations are our provisional bases for sorting and labeling inputs based on what we've encountered so far, as guided by feedback from the consequences of mis-sorting and mis-labeling. Although this categorization mechanism may be converging on what things "really are," we have no way of knowing this. At best, our sorting and labeling is an approximation to reality. I AM a realist, though: There are things out there. I prefer to avoid ontological questions, however, because they are simply irrelevant to modeling human categorization. Our "errors" are determined relative to their pragmatic consequences, not an omniscient or ontological criterion. Forget about ontology; this discussion is only about whether or not our internal representations of categories are "classical," i.e., whether they are based on detectable features that provide conditions that are necessary and sufficient to guide our correct, all-or-none sorting/labeling performance. I'm claiming that they are indeed "classical," and that there's absolutely nothing wrong with the "classical" view that Rosch and Lakoff [and perhaps Wittgenstein] are widely interpreted as having invalidated in favor of "prototypes," family-resemblances, exemplars, or any other form of graded, hence "nonclassical" representation. (2) It doesn't matter what the source of the feedback about MIScategorization is, just as long as it comes from "out there." (Purely subjective "categories" would be susceptible, for example, to Wittgenstein's argument against "private language.") Feedback from a teacher or a parent or from the "linguistic community" to the effect that you have mis-labeled something as a "mushroom" is just as good as feedback from stomach cramps. In the end, unless everyone miraculously shares a purely subjective delusion, the "linguistic community's" own labeling of mushrooms will have to be guided by detectable features of mushrooms. (3) Watanabe's theorem is relevant to what I've called "ad lib" similarity judgments, where one sorts as one pleases, guided only by how similar things "look." He was right that in this case we are being guided by "weights" on a subset of an infinity of inherent similarities and dissimilarities (the weight being either arbitrary or governed by existing NON-ad-lib categories we already have). But I have stressed that models for categorization should not focus on ad lib similarity judgments but on IMPOSED categorization tasks, the ones with feedback from the consequences of miscategorizing. Apart from our arbitrary subjective "categories," all of our categories are of the imposed kind, and certainly most of the linguistic ones -- the ones that are labeled by the words in our vocabulary -- are imposed categories. It's precisely their imposed (i.e., constrained) as opposed to ad lib nature that makes these categories immune to Watanabe's theorem: For a "classical" basis for the correct sorting and labeling of the inputs must be SELECTED out of the Watanabean confusion matrix whenever the categorization successfully converges. Otherwise there's no way to explain our success! Watanabe's theorem is also related to (mostly irrelevant red herrings) associated with Hempel's Raven paradoxes (of theory confirmation: does a white swan confirm that all ravens are black?) as well as problems variously labeled as the "frame" problem (how to specify in general what remains invariant in a change of circumstances under a symbolic description?) and the "credit assignment" problem (when a set of formerly reliable features fails, i.e., miscategorizes, how is one to determine which features are to blame, or which features deserve the credit for restoring successful categorization?). These in turn are related to what I've called the "symbol grounding problem" (how are the meanings of symbols to be grounded in something other than just more meaningless symbols?), and ultimately to the problem of underdetermination: How do you pick out the "right" features to solve a categorization problem when there are so many confusable candidates? Which brings us right back to the problem of category learning and representation, guided by feedback from "error." So the take-home message is this: The ad lib similarity structure of a huge Laplacean feature matrix will not give you categorization, but a "classical" subset selected on the basis of feedback from miscategorization will. -- Stevan Harnad INTERNET: harnad@confidence.princeton.edu harnad@princeton.edu srh@flash.bellcore.com harnad@elbereth.rutgers.edu harnad@princeton.uucp BITNET: harnad@pucc.bitnet CSNET: harnad%princeton.edu@relay.cs.net (609)-921-7771