Xref: utzoo comp.ai:3162 talk.philosophy.misc:1874 sci.lang:3995 Path: utzoo!attcan!uunet!husc6!rutgers!elbereth.rutgers.edu!harnad From: harnad@elbereth.rutgers.edu (Stevan Harnad) Newsgroups: comp.ai,talk.philosophy.misc,sci.lang Subject: Re: Categorization Summary: ALL categories are provisional and approximate and depend on features that reliably pick them out from the context of confusable alternatives Message-ID: Date: 23 Jan 89 02:31:57 GMT References: <681@cogsci.ucsd.EDU> <2959@uhccux.uhcc.hawaii.edu> <2899@xyzzy.UUCP> <9450@ihlpb.ATT.COM> Organization: Rutgers Univ., New Brunswick, N.J. Lines: 186 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