SOWA@IBM.COM.UUCP (08/28/87)
Wittgenstein's basic point is that the most important concepts of ordinary language cannot be defined by a set of necessary and sufficient conditions. No matter whether you try to give structural definitions or functional definitions, you cannot state a precise set of conditions that will admit all relevant instances while ruling out all irrelevant ones. In my book, Conceptual Structures (Addison-Wesley, 1984), I made the distinction between natural types (or kinds) and role types. Something can be recognized as belonging to a natural type by its own properties. Examples include MAN, WOMAN, CAT, DOG, NUMBER, or NAIL. A role type can be recognized only by relationships to something outside of itself: FATHER, LAWYER, PET, WATCHDOG, QUOTIENT, or FASTENER. The number 4, for example, can be recognized as a number in isolation, but as a sum, divisor, quotient, product, etc., only in relation to something else. A tee shirt had the slogan "Food is the only edible thing in the universe." That is true by definition, since FOOD is a role type, defined by its role of being considered edible. Yet that distinction does not solve Wittgenstein's problem. Every culture has its own standards of what is considered edible. In Scandinavia, there is a rotten fish delicacy that requires a mound of raw onions and garlic to prepare the taste buds and liberal quantities of aquavit to wash it down. Even for a particular individual, degree of hunger shifts the boundary line between the roles of FOOD and GARBAGE. Even mathematical concepts have shifting definitions. Consider what happened to the concept of number as rational number, irrational number, complex number, transfinite number, etc., were introduced. If you try to give a precise definition today, somebody tomorrow is sure to invent some kind of hyper-quaternary-irresolute number that will violate your definition, yet be so similar to what mathematicians like to call a number that they would not want to exclude it. To handle Wittgenstein's notion of meaning as use, I introduced schematic clusters (in Section 4.1 of Conceptual Structures) as an open-ended collection of schemata (or frames) associated with a concept type. Each schema would represent one pattern of use (or perspective) for a type, but it would not exhaust the complete meaning of that type. There would always be the possibility of some new experience that would add new schemata to the cluster. Consider the concept ADD: one schema would show its use in arithmetic. But if someone wants to talk about adding a line to a file, another schema could be added to the cluster for that use. And then one should add a new schema for adding schemata to clusters. Every schema in a cluster represents one valid use of the concept type. The meaning is determined not by any definition, but by the collection of all the permissible uses, which can grow and change with time. Does that solve the problem? Maybe, but we still need criteria for determining what kinds of uses can legitimately be added to a cluster. Could I say "To add something means to eat it with garlic and onions"? What are the criteria for accepting or rejecting a proposed extension to a concept's meaning? John Sowa