categories. That is, since cue validity is the probability of being in some category given some property, this probability will increase (or at worst not decrease) as the size of the category increases (e.g. the probability of being an animal given the property of flying is greater than the probability of bird given flying, since there must be more animals that fly than birds that fly).6 The idea that cohesive categories maximize the probability of particular properties given the category fares no better. In this case, the most specific categories will always be picked out. Medin (1982) has analyzed a variety of formal measures of category cohe­ siveness and pointed out problems with all of them. For example, one possible principle is to have concepts such that they minimize the similarity between contrasting categories; but minimizing between-category similarity will always lead one to sort a set of n objects into exactly two categories. Similarly, functions based on maximizing within-category similarity while minimizing between-category similarity lead to a variety of problems and counterintuitive expectations about when to accept new members into existent categories versus when to set up new categories. At a less formal but still abstract level, Sternberg (1982) has tried to translate some of Goodman's (e.g. 1983) ideas about induction into possible constraints on natural concepts. Sternberg suggests that the apparent naturalness of a concept increases with the familiarity of the concept (where familiarity is related to Goodman's notion of entrenchment), and decreases with the number of transformations specified in the concept (e.g. aging specifies certain trans­