Xref: utzoo comp.ai:3367 sci.lang:4098 Path: utzoo!dciem!client1!mmt From: mmt@client1.dciem.dnd.ca (Martin Taylor) Newsgroups: comp.ai,sci.lang Subject: Re: Categorization Message-ID: <1435@client1.dciem.dnd.ca> Date: 10 Feb 89 22:35:35 GMT Article-I.D.: client1.1435 References: <15585@cisunx.UUCP> <3200@uhccux.uhcc.hawaii.edu> Reply-To: mmt@client1.dciem.dnd.ca (Martin Taylor) Organization: D.C.I.E.M., Toronto, Canada Lines: 44 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).