Page:Philosophical Review Volume 30.djvu/519

No. 5.] with proper defining characteristics, which class he calls a moment, the locus of intersection of moments of two families is a 'level', which is the analogue, in the moment, of a plane in the timeless space of the classical tradition. Levels intersect in 'rects', the analogues of straight lines; and rects intersect in 'puncts' or 'event- particles', the analogues of points.

Every event occurs in every family of durations; but in each different family it has different simultaneous associates, taken as a whole. However, there is a sub-class of simultaneous associates which it has in either of two families of durations. Such families of associates have relations to each other which furnish the basis for our conception of a plane in timeless space. By following out this line of thought, we arrive at the conclusion that 'space' is a conceptual derivative from the fact of the passage of nature. It corresponds to an aspect of the passage of nature, but there is no such thing as a merely timeless space.

The metrical relations between the different families of durations, when we have derived ' time ' and ' space ' from them in their interrelations, are substantially expressed by the now famous transformation equations of the special theory of relativity. The whole discussion of this subject presupposes a four-dimensional geometry.

The very brief statement of what I take to be Whitehead's view is necessarily unintelligible, except on the supposition that the reader is fairly familiar with the text of the work under review. Whether it is a correct statement I do not dare to say; it is at least a brief statement that expresses my understanding of the text. If this understanding be correct, I am now in a position to bring forward one query the answer to which may be decisive as to the satisfactoriness of the whole view.

Does not Professor Whitehead's definition of 'position' (pp. 92 and ff.) expose him to exactly the same sort of criticism that he has himself urged with such telling force against certain views of temporal congruence (pp. 137 ff.)? There he says that the prevalent view is that if we take time-measurements "so that certain familiar velocities which seem to us to be uniform are uniform, then the laws of motion are true. ... Suppose that with some expositors we cut out the reference to familiar velocities such as the rate of rotation of the earth. We are then driven to admit that there is no meaning in temporal congruence except that certain assumptions make the laws of motion true. Such a statement is historically false. King Alfred the