[8]. Max Müller’s translation.
“I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it.[[9]] I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all the portions of time, and their addition, a definite quantity of time.”
[9]. Italics mine, and also in the second passage.
The second passage runs thus:
“This peculiar property of quantities that no part of them is the smallest possible part (no part indivisible) is called continuity. Time and space are quanta continua, because there is no part of them that is not enclosed between limits (points and moments), no part that is not itself again a space or a time. Space consists of spaces only, time of times. Points and moments are only limits, mere places of limitation, and as places presupposing always those intuitions which they are meant to limit or to determine. Mere places or parts that might be given before space or time, could never be compounded into space or time.”
I am in complete agreement with the second extract if ‘time and space’ is the extensive continuum; but it is inconsistent with its predecessor. For Zeno would object that a vicious infinite regress is involved. Every part of time involves some smaller part of itself, and so on. Also this series regresses backwards ultimately to nothing; since the initial moment is without duration and merely marks the relation of contiguity to an earlier time. Thus time is impossible, if the two extracts are both adhered to. I accept the later, and reject the earlier, passage. Realisation is the becoming of time in the field of extension. Extension is the complex of events, quâ their potentialities. In realisation the potentiality becomes actuality. But the potential pattern requires a duration; and the duration must be exhibited as an epochal whole, by the realisation of the pattern. Thus time is the succession of elements in themselves divisible and contiguous. A duration, in becoming temporal, thereby incurs realisation in respect to some enduring object. Temporalisation is realisation. Temporalisation is not another continuous process. It is an atomic succession. Thus time is atomic (i.e., epochal), though what is temporalised is divisible. This doctrine follows from the doctrine of events, and of the nature of enduring objects. In the next chapter we must consider its relevance to the quantum theory of recent science.
It is to be noted that this doctrine of the epochal character of time does not depend on the modern doctrine of relativity, and holds equally—and indeed, more simply—if this doctrine be abandoned. It does depend on the analysis of the intrinsic character of an event, considered as the most concrete finite entity.
In reviewing this argument, note first that the second quotation from Kant, on which it is based, does not depend on any peculiar Kantian doctrine. The latter of the two is in agreement with Plato as against Aristotle.[[10]] In the second place, the argument assumes that Zeno understated his argument. He should have urged it against the current notion of time in itself, and not against motion, which involves relations between time and space. For, what becomes has duration. But no duration can become until a smaller duration (part of the former) has antecedently come into being [Kant’s earlier statement]. The same argument applies to this smaller duration, and so on. Also the infinite regress of these durations converges to nothing—and even on the Aristotelian view there is no first moment. Accordingly time would be an irrational notion. Thirdly, in the epochal theory Zeno’s difficulty is met by conceiving temporalisation as the realisation of a complete organism. This organism is an event holding in its essence its spatio-temporal relationships (both within itself, and beyond itself) throughout the spatio-temporal continuum.
[10]. Cf. ‘Euclid in Greek,’ by Sir T. L. Heath, Camb. Univ. Press, in a note on Points.