jay@ROCHESTER.ARPA (Jay Weber) (07/09/86)
In repsonse to my claim that particular analogies are transitive, Uttam Mukhopadhyay writes: >However, the SPACE of analogies does not partition the space of >categories because the world can concurrently be modeled by multiple >abstraction lattices (not necessarily hierarchies) in which the >transitivity property may not hold. Consider the following: > > a) "A battery is like a reservoir" (storage capability) > AND b) "A reservoir is like a pond" (body of water) > >DO NOT IMPLY: > c) "A battery is like a pond" But I orginally wrote: >> 3) transitive. "A battery is like a reservoir" and >> "A reservoir is like a ketchup bottle" imply >> "A battery is like a ketchup bottle" WHEN THE SAME >> ANALOGY HOLDS BETWEEN THEM (same R). Note the use of "SAME ANALOGY" which is not the same as "any analogy" as is the basis of Uttam's example above. Of course, any two categories are analogous with respect to some mapping function, so the relation "is analogous to" is vacuous. This distinction tends to be obscured by the fact that most linguistic examples of analogy (like those above) leave the mapping function implicit. Furthermore, I did not claim that the SPACE of analogies partitions the space of categories, but that a particular analogy does: >> Then any analogy R is an equivalence relation, partitioning the space >> of categories. I also questioned the value of asking whether "creativity" is equivalent to "making interesting analogies" to which Uttam replied: > I am glad that scientists, by and large, have not let "slipperiness" in >some linguistic sense (as you define it) discourage them from carrying on >their research. Proper scientists (by definition) do not construct theories about things that cannot be empirically examined, e.g. using structure mapping functions to model the communal descriptive definition of the English word "creativity". Scientists pick testable domains such as problem solving where you can test predictions of a particular theory with respect to correct problem solving. In the past, scientists have left debate over such concepts as "truth" and "beauty" to philosophers, and I think we should do the same with "creativity" and "intelligence". In Cognitive Science, researchers have too often exaggerated the impact of their work through the careless and unscientific use of such terms. Jay Weber Computer Science Department University of Rochester Rochester, NY 14627 jay@rochester