When we wish to describe a structure, we have to do so by means of terms and relations. It may turn out that the terms themselves have a structure, as, e.g., in arithmetic, when cardinal integers are defined as classes of similar classes. In the technique of mathematical physics, there is a considerable apparatus which belongs to the formal method, and would not be regarded by most physicists as having any physical reality. Such is the manifold of space-time points. Space-time is held to represent a system of physical facts, but its mathematical points are generally conceded to be fictions. Such a state of affairs is unsatisfactory until we can say just what non-fictional assertion is implicit in a true proposition of physics which technically uses "points." I propose to deal with this problem in the next chapter. But what shall we say of electrons? Are they physical realities, or are they mathematical conveniences, like points? Or are they something intermediate between these two extremes? We think of a light-ray as a series of events; is an electron perhaps something similar? But the light-ray also raises problems: it has a certain assigned mathematical structure, but it is difficult to say what we axe to think of the mathematical terms of this structure. Formerly, the conception of a transverse wave in the æther seemed fairly clear:[Pg 277] the æther was composed of particles, each of which could move in the required manner. But nowadays the æther is grown insubstantial and incapable of "motion" in any straightforward sense; certainly few people would venture to regard it as composed of point-particles, like the homogeneous fluid of a hydrodynamical text-book. Thus the light-wave has become a structure in the air, like a genealogical tree whose members are all imaginary. This illustrates a necessity in describing a structure: the terms are as important as the relations, and we cannot rest content with terms which we believe to be fictitious. It is the terms of the physical structure that will concern us in the present chapter.