of mutual co-intersections; and these, by our definition of spherical event, will themselves be spherical events. If we take a co-intersection of any number of mutually intersecting spherical events, we can always find a spherical event, the co-intersection of which with these original events will be a part of the original co-intersection; and by increasing the number of such spherical events we can obtain as small a co-intersection as we please of a finite aggregate of spherical events. If we include in this aggregate every spherical event which has a common co-intersection with all the members of the aggregate, we tend to an ultimate element which is the co-intersection of the infinite class, an element which will not be further divisible into parts and which will not intersect any element other than itself; in other words, an element of experience.[1]
23.2. That an element of experience has not parts can be proved as follows: Let us suppose that an element of experience R has parts A and B; then it is possible to find a spherical event X which does not contain the whole of R, but only one of its parts. Since a co-intersection of n spherical events is, by definition, contained in each one of these events, the event X is not a member of the class of events, the co-intersection of which is the element of experience R; but since an element is a co-intersection common to all spherical events which mutually intersect, such an event X cannot exist; therefore the element R cannot have parts.
24. As the number of events comprising a given element of experience is infinite, an infinite number of determinations would be required to identify a given element. Now that is
- ↑ Prof. Whitehead, who very kindly discussed with me a considerable part of the present work, on the basis of this definition proposed an alternative definition of an element of experience which, while accepting mine, made room for his view that there can be classes of events which, though they stand to one another in the relation of inclusiveness and so of intersection have no co-intersection common to all; his proposal is as follows: “An element of experience is a class of spherical events such that(1) each of its finite sub-classes has a co-intersection;(2) every spherical event, which has a co-intersection with each finite sub-class of a given class, itself belongs to this class.”As will be seen, this definition agrees with mine except that Prof. Whitehead calls an element of experience a class of events which have a given co-intersection, whereas I call an element this co-intersection itself. Both definitions have their advantages and disadvantages; I prefer my original definition, because it agrees with our current view of a point, and because it has its justification in perception, in that it leads us direct to the perceptual limit of the compass which we usually understand by the conception of point.
