We have arrived at the conclusion that an electron at an instant is a grouping of events; the question is: what sort of group is it? Obviously it includes all the events that[Pg 321] happen where the electron is. If we may regard the electron as a material point, the events constituting an electron will have the two characteristic properties of points, viz. any five are co-punctual, and not all sub-classes of four events are co-punctual with any event outside the group. I do not know whether there is any valid ground for supposing that an electron is of finite size; none of the usual arguments seem at all conclusive, since they only show the forces developed in the neighbourhood of an electron. However, it is usual to assume a finite size, and for us the matter is one of indifference. If we assume a finite size, the events belonging to the electron can be grouped into many points, not only into one; in this case, the electron is a group of points, i.e. a class of classes of events. It will save circumlocution to speak of the electron as a point, and leave it to the reader to make the necessary verbal alterations for adaptation to the hypothesis of finite size. But it should be remembered that in Heisenberg's theory the electron is neither a point nor of finite size, since ordinary spatial conceptions are inapplicable to it. For the moment, we will, however, confine ourselves to the older theory of the electron. If the electron is a point, it is a material point, and thus differs from points in empty space. This difference, I believe, does not consist in anything characteristic of the electron at an instant, but in its causal laws. What distinguishes a material point from a point of empty space-time is that we can recognize a series of earlier and later material points as all parts of the history of one electron. In the Newtonian theory, one could say the same of a point of absolute space; but with the abandonment of absolute space we have become unable to regard a point at one time as in any sense the same as a point at another time, except in the case of a material point. The existence of this connection may be taken as the definition of "matter"; and obviously the connection is causal. [Pg 322]