class term sometimes used as a synonym for ‘set’. When the two are distinguished, a class is understood as a collection in the logical sense, i.e., as the extension of a concept (e.g. the class of red objects). By contrast, sets, i.e., collections in the mathematical sense, are understood as occurring in stages, where each stage consists of the sets that can be formed from the non-sets and the sets already formed at previous stages. When a set is formed at a given stage, only the non-sets and the previously formed sets are even candidates for membership, but absolutely anything can gain membership in a class simply by falling under the appropriate concept. Thus, it is classes, not sets, that figure in the inconsistent principle of unlimited comprehension. In set theory, proper classes are collections of sets that are never formed at any stage, e.g., the class of all sets (since new sets are formed at each stage, there is no stage at which all sets are available to be collected into a set). See also SET THEORY. P.Mad.