Distributed attention to similarity and difference is critical to maintaining relations among categories in a semantic field. And this distribution determines the lower and upper number of such categories, although numbers will differ in accord with selected properties on which the categories are based. The determining constraint is the total amount of attention that a person will normally devote to similarity and difference, which is proposed to be universal. Vantage theory provides the explanatory framework, by which the distribution is actively (...) managed by a person who, as with any system so managed, will perform effectively or dysfunctionally. Occasional aberration suggests that people indeed are involved in their cognitive systems. Vantage theory, too, then models how distributed attention may go amiss. (shrink)