) The serial-order among moments of the same time-system has the Cantor-Dedekind type of continuity.
Nothing has yet been said about the measurement of the lapse of time. This topic will be considered as part of the general theory of congruence.
[35. Levels, Rects, and Puncts]. 35.1 The electromagnetic theory of relativity is obviously the more general of the two. It has also the merit of providing definitions of flatness, of straightness, of punctual position, of parallelism, of time-order and spatial order as interconnected phenomena, and (with the help of cogredience) of perpendicularity and of congruence. The theory of extension has also provided the definition of a duration. It is a remarkable fact that the characteristic concepts of time and of geometry should thus be exhibited as arising out of the nature of things as expressed by the two fundamental relations of extension and cogredience. It has already been explained that a moment is the route of approximation towards an instantaneous three-dimensional whole of nature. The set of abstractive elements and abstractive classes covered by both of two non-parallel moments is the locus which is their common intersection. Such a locus will be called a 'level' in either moment. A level is in fact an instantaneous plane in the instantaneous space of any moment in which it lies. But we reserve the conventional spatial terms, such as 'plane,' for the time-less spaces to be defined later. Accordingly the word 'level' is used here.
35.2 An indefinite number of non-parallel moments will intersect each other in the same level, forming their complete intersection; and one level will never be merely a (logical) part of another level. Let three mutually intersecting moments (
, say) intersect in the levels
. Then three cases can arise: either (i) the levels are all identical [this will happen if any two are identical], or (ii) no pair of the levels intersect, or (iii) a pair of the levels, say
and