Note 17 — LECTURE IV THE WORLD OF PHYSICS AND THE WORLD OF SENSE

The assumptions made concerning time-relations in the above are as follows:—

I. In order to secure that instants form a series, we assume:

(a) No event wholly precedes itself. (An “event” is defined as whatever is simultaneous with something or other.)

(b) If one event wholly precedes another, and the other wholly precedes a third, then the first wholly precedes the third.

(c) If one event wholly precedes another, it is not simultaneous with it.

(d) Of two events which are not simultaneous, one must wholly precede the other.

II. In order to secure that the initial contemporaries of a given event should form an instant, we assume:

(e) An event wholly after some contemporary of a given event is wholly after some initial contemporary of the given event.

III. In order to secure that the series of instants shall be compact, we assume:

(f) If one event wholly precedes another, there is an event wholly after the one and simultaneous with something wholly before the other.

This assumption entails the consequence that if one event covers the whole of a stretch of time immediately preceding another event, then it must have at least one instant in common with the other event; i.e. it is impossible for one event to cease just before another begins. I do not know whether this should be regarded as inadmissible. For a mathematico-logical treatment of the above topics, cf. N. Wilner, “A Contribution to the Theory of Relative Position,” Proc. Camb. Phil. Soc., xvii. 5, pp. 441–449.