we shall call elementary parts, or briefly elements of the given entity. Thus, for instance, the entity “the family of Mr. X,” consists of entities: “the parents X,” “the children X,” etc.; and of the elements: Mr. AX., Mrs. MX., their son FX, their daughter BX, etc.; the entity “colour” will have parts which in their turn are entities, for instance the colour of sodium light, but also parts which have no extension with respect to the general characteristic which makes colour an extended entity—therefore elementary parts—e.g., the colour Na1.
It is therefore possible to consider every entity as an aggregate of entities, which are its parts, or an aggregate of elements, which, although its parts, are no longer entities with respect to its extensional characteristic.
12.1. A given entity can have a limited or an unlimited number of elements, and will thus be either a finite or an infinite collection. In the first case it is easy to find all of its elements by means of the relation of inclusiveness (applied repeatedly as a relation of part of a part until a part is reached which does not admit of a further application of this relation); in the case of infinite aggregates the task is a more complicated one, and we shall later—in a concrete perceptual case—attempt to find a different method.
Co-intersection, dissection and complementary parts.— 13. In what follows we shall find it useful to have at our disposal a few concepts based on the relation of extension. In the first place we shall use the term co-intersection of n mutually intersecting entities to denote the entity which is the aggregate of all parts which all the n entities in question have in common. Again, if in a given entity R we can find two non-intersecting entities A and B such that no part of R can be found which is not either a part of A or a part of B, or wholly composed of two parts, one of which is a part of A and one a part of B, we say that we have dissected R into A and B; A and B are called complementary parts of R, and each is called the other’s complement in R (written: B is co-A, and A is co-B).
Order.—14. The second relation which we shall place in the foundations of our logical analysis, is the relation of order. The concept of order is based upon the properties of a relation expressed by the words “before and after” or “between”. Between these two relations there is a close logical connection: If A is before (or after) B, and B is before (or after) C, then B is between A and C. From this, and the transitiveness of the relation “before and after,” and from the other properties of the relation “between,” as they are usually given
