at the same time we have laid broad foundations for the construction of a “natural geometry,” or “geometry of experience,” as we can now call physics. For its complete construction it would be necessary to supplement our inquiry by determining the properties of the relation of “interval”—the proper metrical relation—a task which, as we have already stated, will not be attempted in this essay. At this point it may, however, be useful to pause and enquire as to the relation of our definition to the views prevailing in contemporary physics, and as to the manner in which it solves the differences which arise out of the divergency of these views. I am purposely using the word views, and not definitions, because, as we noted at the beginning, we should vainly search for a satisfactory (useful) definition of space and time in text-books of physics; only with the greatest difficulty shall we find it in some text-books of logic and mathematics. Text-books of physics usually assume that definitions of these fundamental concepts belong to, and are given by, philosophy; philosophy, however, has given several answers, the majority of which, besides being of no use for physics, to the latter’s great misfortune also contradict one another: and physics only inherits the controversies arising out of these philosophical—or better, metaphysical—divergencies, as we can easily see in the controversy raging around the Einstein theory of relativity, or the Planck theory of quanta. The basis of these controversies, and the motive of the passionate opposition which they encounter in certain circles, does not lie in the disagreement of these theories with physical facts, but in their disagreement with the metaphysical preconceptions of their opponents; it is only a repetition of history, for from the same motives there arose the opposition to the Newton theory of gravitation, to the principle of conservation of energy, and to other principles now generally recognised. Besides the fact that the controversy is to a considerable extent a controversy about the aim and nature of physical theory in general—a point which we can only mention here in passing—its source in my opinion is a noetical, and not a physical, disagreement of the disputing parties as to the nature of space and time, a disagreement rendered considerably more acute by some of the philosophical expositors of the new theories.
42. In rough outline, the current conceptions of space and time, in so far as they are at all important for physics, may be placed in two classes, parallel with whose lines of division runs also the line distinguishing the followers of the new theories from their opponents. A good, though not an
