shares the error of Kant: empty space cannot be imagined, much less examined physically. But it is necessary to distinguish here clearly between the space (point-space) which in accordance with our nomenclature can be called momentary, (therefore an aggregate of points in a given moment), and the space, which in accordance with the conventional terminology we have called permanent space (therefore the aggregate of permanent points, i.e., routes, consisting of points of the various momentary spaces). As far as the latter is concerned, the objection of its “undistinguishableness” from matter and therefore superfluousness comes into play in its full weight; if this space has different properties in its various parts, it will be possible to ascertain these properties only when something enters these parts (a particle of matter, energy, like a ray of light)—but how is it possible to distinguish a space which has an influence on what enters it from a material medium? If we reply that such a distinction is not necessary, and still adhere to the point-aggregate conception of space, we shall get another space in which this medium is placed, and in a similar way a whole hierarchy of spaces in an infinite regress.
46. In the case of a momentary space the conception of empty space loses its sense altogether: into an empty momentary space, i.e., into a momentary space (point-aggregate) in which there is nothing, nothing will ever come, and it is therefore superfluous to maintain that the space is there, and that it has such and such (unascertainable) properties. The postulate of the existence of points of empty space has meaning in the pre-Einsteinian space of classical mechanics, where every eternal point is a possible recipient of a particle of matter; the moment, however, we amalgamate space and time into one continuum, as it is amalgamated in Einstein’s theory, empty space becomes a superfluous multiplication of entities, a useless fiction, satisfying perhaps the requirements of æesthetics (not even transcendental) but not of logics and physics. Empty space, as empty time, is an empty word, with no meaning save that of a possibility of ordering relations: if we say that between the particle A and the particle B there is an empty space, it means that there exists the possibility of placing a particle X between them; evidently it has a meaning only in the case of permanent space.
47. Convincing ourselves that the concept of space as an aggregate of points is untenable, we are reduced to the solution, developed in the preceding paragraphs: space and time is a relation between things, i.e., between parts of the contents
