Movement, Change and Number: Aristotle’s View of Time

Number, Potentiality and Actuality as they Relate to Time (Part 2)


For Aristotle motions (or change) have countability in that they can actually be counted as they occur and they have the potential to be counted. Aristotle declares that we “apprehend time only when we have marked motion, marking it by before and after, and it is only when we perceive before and after in motion that we say that time has elapsed. Now we mark them by judging that one thing is different from another, and that some third thing is intermediate to them.” [1] This third thing which is intermediate to before and after is the now. Thus, there is an asymmetry of potentiality and actuality in enumerable motion.

If the two ‘nows’ were perceived, which occurred before and after the unnoticed interval, then according to Aristotle the two ‘nows’ have been marked and a connection has been made between the ‘before’ and ‘after’ of the unnoticed interval. This is best illustrated by the train once again. The perceiver marked a connection between the ‘before’ and ‘after’ of the unnoticed interval (the train passing while the perceiver was asleep) in that the train was no longer there when the perceiver awoke. The perceiver would surmise that time had passed (based on change between moments of ‘before’ sleep with the train in motion and ‘after’ sleep with the realization that the train had passed—changed had occurred) because of the absence of the train which was there when the perceiver fell asleep. Hussey elaborates on this by declaring, “We think that some time has elapsed, between the two ‘nows’, if and only if we have some means of distinguishing the two ‘nows’, and this we have if and only if we perceive that a change has taken place between them. To perceive this is to mark off the change by means of the ‘nows’ which bound it (elaborated at 219 a 22-30).” [2] All this complication of enumeration of motion, the nonexistence of the past, and the now seems to raise several problems for which Aristotle has been criticized in the past.

First, time is viewed as a continuum and Aristotle’s view of the ‘now’ seems to be discrete. [3] Von Leyden hints that in terms of number Aristotle’s view is discrete. Von Leyden points out that “Aristotle himself was aware [due to a passage from De Anima I. 3, 407 a 6-10] of the fact that thoughts, being like integers, do not correspond to the organization of undivided continua such as time or motion.” Von Leyden continues by declaring, “The reason why he [Aristotle] nevertheless defined time as a number was that, if the before and after in movement are counted by successive nows, sections of a continuum are counted, of which time is the number counted, not that by which it is counted.” [4]

Secondly, if Aristotle in fact affirms that the parts of time (past and future) are non-existent, [5] then he must account for the tensed predication which is used in languages (including his own—Greek) which indicate past and future. In other words, there must be some sense in which the past and future are existent, if by no other means than logical abstraction through tensed predication. This criticism is not too weighty due to the aporetic nature of Aristotle’s views on the parts of time. Moreover, Richard Sorabji suggests that this apparent problem is easily solved. Sorabji declares,

I want to suggest two ways of solving this paradox, although only the first, I believe, gets to the heart of the matter. It does so by asking what is meant when we say that there is a past and a future, or that they exist. The author of the paradox may not have thought out what is meant, but the truth behind his paradox depends on the fact that ‘exist’ sometimes means ‘be present’, and that neither past nor future exists in this sense. Of course, when the point is spelt out in this way, the non-existence, the non-existence of past and future appears quite unremarkable, but, until it is spelt, the author of the paradox may well feel that his claim of non-existence is more significant. He is in any case still entitled to ask whether there is some other sense in which the past and future do exist, and this question puts an onus on us.


. . . Instead of merely saying ‘there was no universe in the past’, or ‘there will be no universe in the future’, he could ‘there is no past’, or ‘there is no future’. It is in contrast to this denial that we can see a sense for the claim that there is a future and a past; and not only does this claim turn out to have a sense, but it is, furthermore, a claim that any rational person ought to endorse. I believe, therefore, that this constitutes a solution to the paradox: it is only in the irrelevant sense being present that the past and future do not exist. In the sense that matters, there is a past and there is a future, and so there is time. [6]

Sorabji points out that since there is no one English equivalent of Aristotle’s ‘to be’ verb, it is more natural to say there is no past in English. Moreover, Sorabji points out that Aristotle moves in the right direction in Physics 3. 6, 206a 21-3, by recognizing “that a different sense of the verb ‘exist’ applies to temporal entities.” [7]

[1] 219a 22-26.
[2] Aristotle, Physics, trans. with commentary Edward Hussey, 142.
[3] This is a criticism pointed out in Von Leyden’s article “Time, Number, and Eternity, in Plato and Aristotle.” This criticism seems to be valid only if there is an absence of a perceiver between the two apparently disconnected ‘nows.’ Von Leyden is not forthcoming in his article about how Aristotle’s view is discrete.
[4] Von Leyden, 50.
[5] This criticism is conditional since Aristotle seems to be aporetic (a point which was brought to my attention by Dr. Owen Goldin via correspondence on November 9th, 2001) regarding the issue of the parts of time.
[6] Sorabji, 12.
[7] Ibid., 13.