have both properties; they are not merely different properties, they are exclusively different. It is impossible for any object that has the one property to have the other. So thinking about things from the extensionalist direction, beginning with mere differences of objects and identifying merely different properties in effect with sets of them, does yield a version of the principle of Exclusivity of Objects. If object is red and object differs from it a b by not having that property, then appeal to the notion of formal or abstract negation yields the result that has the property that is the contradictory of red. It has the property not-red. That b property is exclusively different from red, in that it is a property of formal negation that it is impossible for any object to have both properties simultaneously. The fact that the logically principle of the Exclusivity of Objects, that merely different objects will have not only compatibly different properties but also incompatibly different ones, arises early in the Hegelian order of explanation and late in the extensionalist one is a consequence and reflection of the two orders of explanation regarding the relations between material contrariety and formal contradictoriness that they adopt. For distinguishing at the outset compatibly from incompatibly different properties, as Hegel does, commits one to a picture of properties as coming in compatible families of incompatible properties, as in the paradigmatic case of shapes and colors of monochromatic Euclidean plane figures. If objects and differ merely in compatible properties, they differ in properties drawn a b from different families of incompatibles. For example, is red and is square. But for them to a b be distinguished from each other thereby, must not also be square and must not also be red. a b But if is not square, it will exhibit some other shape, incompatible with being square, and if is a b not red it will exhibit some other color, incompatible with being red. But then and will have a b properties that are not merely different from one another, but incompatible with one another. That is just what the Exclusivity of Objects claims. According to this picture, kinds of things are characterized by which compatible families of incompatible properties they must exhibit. Sounds can be shapeless and colorless—though they must have some pitch and volume. But any monochromatic Euclidean plane figure must have both shape and color on pain of not qualifying as a determinate particular of that kind.
have both properties; they are not merely different properties, they are exclusively different. It is impossible for any object that has the one property to have the other. So thinking about things from the extensionalist direction, beginning with mere differences of objects and identifying merely different properties in effect with sets of them, does yield a version of the principle of Exclusivity of Objects. If object a is red and object b differs from it by not having that property, then appeal to the notion of formal or abstract negation yields the result that b has the property that is the contradictory of red. It has the property not-red. That property is exclusively different from red, in that it is a property of formal negation that it is logically impossible for any object to have both properties simultaneously. The fact that the principle of the Exclusivity of Objects, that merely different objects will have not only compatibly different properties but also incompatibly different ones, arises early in the Hegelian order of explanation and late in the extensionalist one is a consequence and reflection of the two orders of explanation regarding the relations between material contrariety and formal contradictoriness that they adopt. For distinguishing at the outset compatibly from incompatibly different properties, as Hegel does, commits one to a picture of properties as coming in compatible families of incompatible properties, as in the paradigmatic case of shapes and colors of monochromatic Euclidean plane figures. If objects a and b differ merely in compatible properties, they differ in properties drawn from different families of incompatibles. For example, a is red and b is square. But for them to be distinguished from each other thereby, a must not also be square and b must not also be red. But if a is not square, it will exhibit some other shape, incompatible with being square, and if b is not red it will exhibit some other color, incompatible with being red. But then a and b will have properties that are not merely different from one another, but incompatible with one another. That is just what the Exclusivity of Objects claims. According to this picture, kinds of things are characterized by which compatible families of incompatible properties they must exhibit. Sounds can be shapeless and colorless—though they must have some pitch and volume. But any monochromatic Euclidean plane figure must have both shape and color on pain of not qualifying as a determinate particular of that kind.