occur in time. It is, then, nothing but an affirmation of the fact that all percepts are in space and in time; no new truth certainly, but one strangely overlooked in most attempts to define space and time, which omit to notice the fact that space (or spatial relations) exists only in perception (or in objects which this perception represents, if our philosophy requires such reservations), and in ideas which are ideas of perceptions, and that “physical time” likewise exists only in perceptions. The essence of our definition lies in the fact that it defines space and time as relations between percepts; and it permits of the distinction between time and space by making time also a relation between the non-perceptual parts of the mind.
34. We know empirically that elements of experience forming a given moment can be ordered by the spatial relation in one-, two-, or at most three-dimensional continuous aggregates; every element of experience contained in a given moment can be uniquely determined by the correlation of three co-ordinates or by correlation with a three-dimensional continuum of real numbers; a moment of experience is thus a three-dimensional continuum of elements of experience.
A one-dimensional continuum of co-momentary elements, or instantaneous co-momentary “points,” we will call an instantaneous line, a two-dimensional an instantaneous surface, a three-dimensional an instantaneous body.
35. Since the temporal ordering of a given experience is independent of the spatial ordering of events in different moments of this experience, and vice versa, and since we have found that the temporal ordering of experience is one-dimensional and the spatial ordering three-dimensional, it is evident that the continuum of elements of experience which forms the totality of our perceptions is four-dimensional.
Elements of experience can thus be ordered in from one up to four-dimensional aggregates, of which three, mentioned in the foregoing paragraph, will be instantaneous, being composed of instantaneous co-momentary elements, and four enduring, or persistent, forming a one-dimensional continuum of which the elements are instantaneous points, instantaneous surfaces and instantaneous bodies; we call them progressive figures of the first, second, third and fourth order. Specially important for the construction of a geometry of Experience is the first figure of the second group, which is a progressive continuous aggregate of elements of experience (or instantaneous points), that is, the progressive figure of the first order, which we call a route.
The spatial relations of which, on the thesis here advanced,
