Note 132 — Introductory material

The next step, in defining a form of externality, is obtained from the idea of dimensions. Positions, we have seen, are defined solely by their relations to other positions. But in order that such definition may be possible, a finite number of relations must suffice, since infinite numbers are philosophically inadmissible. A position must be definable, therefore, if knowledge of our form is to be possible at all, by some finite integral number of relations to other positions. Every relation thus necessary for definition we call a dimension. Hence we obtain the proposition: Any form of externality must have a finite integral number of dimensions.