  The Stranger mentions two kinds in addition to the not-beautiful, since he marks off the not-beautiful from some one kind among beings, and then sets it in opposition to the nature of the beautiful. The not-beautiful is not just anything other than beautiful, but something other than beautiful within a kind that covers both (call it “the aesthetic”). On this view a part of difference gets its categorial content in two ways from the item whose name is negated. First, the part falls within a wider kind (such as size, temperature, the aesthetic) determined by the positive attribute F-ness, and that wider kind is divided into subkinds which exclude one another and jointly exhaust the genus; and second, the part has an attribute different from F-ness within that genus. All individuals located under the genus occupy one and only one subkind. The subkinds can form an incompatibility range—an ordered continuum under a covering kind, such as degrees of coldness and heat under temperature or degrees of smallness and largeness under size—but they need not constitute an ordered series. They can instead constitute an incompatibility set, such as circle, square, triangle, and other species under shape; or man, ox, horse, and other species under animal. The earlier mistake about negation was the assumption that “the not-F” specifies the opposite of F-ness. According to the new proposal “the not-F” specifies the complement of F-ness under a wider kind—that is, all the disjoint subkinds under the wider kind other than F-ness. Any individual characterized as “not-F” falls under the complement of F-ness and has some feature other than F-ness within the wider kind. Thus, for example, when you say “Simmias is not large,” you indicate that Simmias has some definite size other than largeness, either the polar contrary smallness or some intermediate size. (Brown, 2008, calls this treatment of negation the “incompatibility range” interpretation; see also Ferejohn 1989, Szaif 1996, and M. L. Gill, 2012, ch. 5.)