Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!rutgers!princeton!mind!harnad From: harnad@mind.UUCP (Stevan Harnad) Newsgroups: comp.ai,comp.cog-eng Subject: Re: The symbol grounding problem: "Fuzzy" categories? Message-ID: <967@mind.UUCP> Date: Fri, 3-Jul-87 15:26:40 EDT Article-I.D.: mind.967 Posted: Fri Jul 3 15:26:40 1987 Date-Received: Sat, 4-Jul-87 13:59:22 EDT References: <764@mind.UUCP> <768@mind.UUCP> <770@mind.UUCP> <6174@diamond.BBN.COM> <2238@mmintl.UUCP> Organization: Cognitive Science, Princeton University Lines: 123 Summary: On thresholds, continua, and graded vs. all-or-none categories Xref: mnetor comp.ai:610 comp.cog-eng:179 In Article 176-8 of comp.cog-eng: franka@mmintl.UUCP (Frank Adams) of Multimate International, E. Hartford, CT.writes: > I don't believe there are any truly "all-or-none" categories. There are > always, at least potentially, ambiguous cases... no "100% accuracy > every time"... how do you know that "graded" categories are less > fundamental than the other kind? On the face of it, this sounds self-contradictory, since you state that you don't believe "the other kind" exists. But let's talk common sense. Most of our object categories are indeed all-or-none, not graded. A penguin is not a bird as a matter of degree. It's a bird, period. And if we're capable of making that judgment reliably and categorically, then there must be something about our transactions with penguins that allows us to do so. In the case of sensory categories, I'm claiming that a sufficient set of sensory features is what allows as to make reliable all-or-none judgments; and in the case of higher-order categories, I claim they are grounded in the sensory ones (and their features). I don't deny that graded categories exist too (e.g., "big," "smart"), but those are not the ones under consideration here. And, yes, I hypothesize that all-or-none categories are more fundamental in the problem of categorization and its underlying mechanisms than graded categories. I also do not deny that regions of uncertainty (and even arbitrariness) -- natural and contrived -- exist, but I do not think that those regions are representative of the mechanisms underlying successful categorization. The book under discussion ("Categorical Perception: The Groundwork of Cognition") is concerned with the problem of how graded sensory continua become segmented into bounded all-or-none categories (e.g., colors, semitones). This is accomplished by establishing upper and lower thresholds for regions of the continuum. These thresholds, I must point out, are FEATURES, and they are detected by feature-detectors. The rest is a matter of grain: If you are speaking at the level of resolution of our sensory acuity (the "jnd" or just-noticeable-difference), then there is always a region of uncertainty at the border of a category, dependent on the accuracy and sensitivity of the threshold-detector. But discrimination grain is not the right level of analysis for questions about higher-order sensory categories, and all-or-none categorization in general. The case for the putative "gradedness" of "penguin"'s membership in the category "bird" is surely not being based on the limits of sensory acuity. If it is, I'll concede at once, and add that that sort of gradedness is trivial; the categorization problem is concerned with identification grain, not discrimination grain. All categories will of course be fuzzy at the limits of our sensory resolution capacity. My own grounding hypothesis BEGINS with bounded sensory categories (modulo threshold uncertainty) and attempts to ground the rest of our category hierarchy bottom-up on those. Finally, as I've stressed in responses to others, there's one other form of category uncertainty I'm quite prepared to concede, but that likewise fails to imply that category membership is a matter of degree: All categories -- true graded ones as well as all-or-none ones -- are provisional and approximate, relative to the context of interconfusable members and nonmembers that have been sampled to date. If the sample ever turns out to have been nonrepresentative, the feature-set that was sufficient to generate successful sorting in the old context must be revised and updated to handle the new, wider context. Anomalies and ambiguities that had never occurred before must now be handled. But what happens next (if all-or-none sorting performance can be successfully re-attained at all) is just the same as with the initial category learning in the old context: A set of features must be found that is sufficient to subserve correct performance in the extended context. The approximation must be tightened. This open-endedness of all of our categories, however, is really just a symptom of inductive risk rather than of graded representations. > "Analog" means "invertible". The invertible properties of a > representation are those properties which it preserves...[This > sounds] tautologically true of *all* representations. For the reply to this, see my response to Cugini, whose criticism you cite. Sensory icons need only be invertible with the discriminable properties of the sensory projection. There is no circularity in this. And in a dedicated system invertibility at various stages may well be a matter of degree, but this has nothing to do with the issue of graded/nongraded category membership, which is much more concerned with selective NONinvertibility. > It is quite possible to make all-or-none judgements based on graded > features [e.g., thermostats] Apart from (1) thresholds (which are features, and which I discussed earlier), (2) probabilistic features so robust as to be effectively all-or-none, and (3) gerrymandered examples (usually playing on the finiteness of the cases sampled, and the underdetermination of the winning feature set), can you give examples? > "chair"... with no back... [is a] "stool"... Now vary the size > of the back The linguist Labov, with examples such as cup/bowl, specialized in finding graded regions for seemingly all-or-none categories. Categorization is always a context-dependent, "compared-to-what" task . Features must reliably sort the members from the nonmembers they can be confused with. Sometimes nature cooperates and gives us natural discontinuities (horses could have graded continuously into zebras). Where she does not, we have only one recourse left: an all-or-none sensory threshold at some point in the continuum. One can always generate a real or hypothetical continuum that would foil our current feature-detectors and necessitate a threshold-detector. Such cases are only interesting if they are representative of the actual context of confusable alternatives that our category representation must resolve. Otherwise they are not informative about our actual current (provisional) feature-set. > I see nothing about "all-or-none" categories which is not explainable > by arbitrary cutoffs of graded sensory data... [and] avoid[ing] > borderline situations. Neither do I. (Most feature-detection problems, by the way, do not arise from the need to place thresholds along true continua, but from the problem of underdetermination: there are so many features that it is hard to find a set that will reliably sort the confusable alternatives into their proper all-or-none categories.) -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU