spatiality which appears in such representation, is not an attribute of extension, but of the symbols employed.
10. The term entity we have so far employed to denote any existens which is not contrary to the laws of thought, but without any further limitation; it can be of a physical as well as only an abstract, purely conceptual nature. In what follows we shall be concerned mainly with entities which admit of division into parts; and the term entity we shall henceforward use to denote any existens, whether physical or purely conceptual, possessing extension. This means that, of classes of pure concepts, only those will be termed entities, which it is possible to define as collections, and not solely by intension.
11. If we exclude the case where an entity A can be its own part (“part” therefore meaning “proper part”) there exist, as is shown in every text-book of logic, four possibilities of extensional relation of entity A to entity B:
(a) a part of A is B (B is a part of A); or
(b) vice versa; or
(c) a part of A is also a part of B, in which case the reverse is also true; or
(d) there exists no part of A which is also a part of B, and vice versa.
The first case is only the reverse of the second, but the relation is the same, and we have already applied to it the name inclusiveness; the relation described by the third case we shall call intersection, and that indicated by the fourth we shall denote as exclusiveness. Inclusiveness, exclusiveness, and intersection, are three different aspects of the purely formal relation of extension, and are therefore equally free of all spatial and temporal content.
12. Every entity is defined by a number of attributes, by the totality of which it is distinguished from all entities not identical with it. These attributes can be divided into two classes: those attributes which are common to all parts of a given entity, and by virtue of which (with respect to which) this entity has extension; and attributes, which are not common to all parts of a given entity and which, in so far as the extension of the entity is concerned, can be neglected. The totality of the attributes of the first class in a given entity we shall call its extensional characteristic. It follows from our definition that in every entity it will be possible to find either parts which still are entities (have extension) with respect to the extensional characteristic of the original entity, and also parts which are without extension with respect to this characteristic, or only the latter; these latter
