Page:Mind-a quarterly review of psychology and philosophy, vol33, no129 (1924).djvu/20

 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.

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