A specialization of mathematical concept. Something is an instance of intensional or extensional set just in case it is a collection (i.e. an instance of type of thing) or a mathematical set (i.e. an instance of set). Instances of set and instances of type of thing (and thus instances of intensional or extensional set) share some basic common features. All instances of type of thing and all instances of set (and thus all instances of intensional or extensional set) are abstract entities, lacking spatial and temporal properties. Nearly all instances of type of thing (except empty collections) and nearly all instances of set (except the empty set; see the empty set) have elements (i.e. instances or members; see Element Of); hence set-or-collections may stand to one another in generalized set-theoretic relations such as subset and Disjoint With (qq.v.). (It is this shared feature of having elements that provides the basic rationale for reifying the collection intensional or extensional set.) Nevertheless, sets and collections differ in two important ways. First, each collection is intrinsically associated with an intensional criterion for membership -- a more or less natural property (or group of properties) possessed by all of (and only) its elements. Collections are thus akin to kinds. In contrast, the elements of a set are not required to be homogeneous in any respect: any things whatsoever may together constitute the elements of a set. The second major difference between sets and collections is that no two distinct sets can be coextensional (i.e. have exactly the same elements; see Co Extensional). Sets can thus be identified purely on the basis of their extensions (see Extent). Collections, on the other hand, are individuated by their intensional criteria for membership. So collections that have exactly the same elements might nevertheless be distinct, differing in their respective membership criteria. (Note that the general relationship between collections and their intensional criteria for membership in the above sense is not something that is currently represented explicitly in the Knowledge Base (though this seems a worthwhile area for future work); still the Comment and other definitional assertions on a given collection should ideally convey a reasonably clear and precise idea of its associated membership criterion.)