Laws@STRIPE.SRI.COM.UUCP (06/29/87)
From: mind!harnad@princeton.edu (Stevan Harnad) Finally, and perhaps most important: In bypassing the problem of categorization capacity itself -- i.e., the problem of how devices manage to categorize as correctly and successfully as they do, given the inputs they have encountered -- in favor of its fine tuning, this line of research has unhelpfully blurred the distinction between the following: (a) the many all-or-none categories that are the real burden for an explanatory theory of categorization (a penguin, after all, be it ever so atypical a bird, and be it ever so time-consuming for us to judge that it is indeed a bird, is, after all, indeed a bird, and we know it, and can say so, with 100% accuracy every time, irrespective of whether we can successfully introspect what features we are using to say so) and (b) true "graded" categories such as "big," "intelligent," etc. Let's face the all-or-none problem before we get fancy... Is a mechanical rubber penguin a penguin? Is a dead or dismembered penguin a penguin? How about a genetically damaged or altered penguin? When does an penguin embryo become a penguin? When does it become a bird? I think your example depends on circularities inherent in our use of natural language. I can't unambiguously define the class of penguins, so how can I be 100% certain that every penguin is a bird? If, on the other hand, we are dealing only in abstractions, and the only "penguin" involved is a idealized living adult penguin bird, then the question is a tautology. We would then be saying that we are 100% certain that our abstraction satisfies its own sufficient conditions -- and even that could change if scientists someday discover incontrovertible evidence that penguins are really fish. In short, every category is a graded one except for those that we postulate to be exact as part of their defining characteristics. After writing the above, I saw the following reply: I am not, of course, claiming that noise does not exist and that errors may not occur under certain conditions. Perhaps I should have put it this way: Categorization preformance (with all-or-none categories) is highly reliable (close to 100%) and MEMBERSHIP is 100%. Only speed/ease of categorization and typicality ratings are a matter of degree. The underlying representation must hence account for all-or-none categorization capacity itself first, then worry about its fine-tuning. This is not to deny that even all-or-none categorization may encounter regions of uncertainty. Since ALL category representations in my model are provisional and approximate (relative to the context of confusable alternatives that have been sampled to date), it is always possible that the categorizer will encounter an anomalous instance that he cannot classify according to his current representation. The representation must hence be revised and updated under these conditions, if ~100% accuracy is to be re-attained. This still does not imply that membership is fuzzy or a matter of degree, however, only that the (provisional "defining") features that will successfully sort the members must be revised or extended. The approximation must be tightened. You are entitled to such an opinion, of course, but I do not accept the position as proven. We do, of course, sort and categorize objects when forced to do so. At the point of observable behavior, then, some kind of noninvertible or symbolic categorization has taken place. Such behavior, however, is distinct from any of the internal representations that produce it. I can carry fuzzy and even conflicting representations until -- and often long after -- the behavior is initiated. Even at the instant of commitment, my representations need be unambiguous only in the implicit sense that one interpretation is momentarily stronger than the other -- if, indeed, the choice is not made at random. It may also be true that I do reduce some representations to a single neural firing or to some other unambiguous event -- e.g., when storing a memory. I find this unlikely as a general model. Coarse coding, graded or frequency encodings, and widespread activation seem better models of what's going on. Symbolic reasoning exists in pure form only on the printed page; our mental manipulation even of abstract symbols is carried out with fuzzy reasoning apparatus. -- Ken Laws