Movement, Change and Number: Aristotle’s View of Time
Number, Potentiality and Actuality as they Relate to Time
In Physics book 4, chapter 11, it seems that Aristotle has yet to commit to any exact theory of time. Nonetheless, Aristotle asserts that time does not exist without change. Edward Hussey in his translation and commentary to Aristotle’s Physics points out that “Aristotle uses two claims about the perception of change and time: (a) when we do not perceive any change to have taken place, we do not think any time has elapsed; (b) when we do perceive change to have taken place, we do think some time has elapsed.”[1] Using an illustration of sleep (‘those who are fabled to sleep among the heroes in Sardinia’) Aristotle points out that the interval between the time ‘before’ sleep and the time ‘after’ is a type of connection between the prior ‘now’ and the posterior ‘now’ and the two are made one. The two are ‘made one’ in the sense that those who slept failed to consciously notice the interval between the two ‘nows.’
W. Von Leyden comments on this difficult passage by concluding, “The argument [of Aristotle’s that time is closely related to change] is significant in that the sufficient as well as necessary condition of any time-lapse is found to lie in the distinction of two ‘nows’ and a ‘before’ and ‘after’ in motion.”[2] Adding to Von Leyden’s comments, it seems this passage (218b 21-28) is at best an attempt by Aristotle to make sense of how time cannot exist without change and some perceiver of change. To illustrate this point, if a person were by a railroad track sitting on a bench and a very long train proceeded to pass by, the perceiver would be conscious of time’s passing via the movement of the train and the counting of the cars which pass. However, let us assume this is a very long train, and as it passes the perceiver falls asleep. Now let us assume that the train has completely passed the person who is asleep. Knowing the train was there ‘before’ the perceiver fell asleep, the perceiver would realize time had elapsed upon waking up from slumber since the train is no longer there ‘after’ the perceiver awakes. This is the connection Aristotle makes between the now of the ‘before’ and the now of the ‘after’ which is essentially perceived and counted by the perceiver upon awakening. And this is accomplished in that the perceiver understands change has occurred due to the train’s absence. In all this a perceiver is needed in order for the realization of motion and change to have occurred. Thus, time, in terms of ‘before’ and ‘after’ and Aristotle’s concept of the now needs a perceiver to be real.
Aristotle’s notion of the ‘now’ is quite intricate and complicated. Paul F. Conen describes Aristotle’s now as “The plurality of before and after in motion which time is, is a plurality of ‘nows.’ As a line is pluralized by the points actually numbered or numerable on it, so motion is pluralized by the ‘nows’ counted or countable in it.”[3] Thus, Conen understands Aristotle’s ‘now’ in time and motion as that which is numbered. This is in fact how Aristotle defines the ‘now.’[4] However, in relation to Aristotle’s puzzle of the parts of time, he concludes that time “is not held to be made up of ‘nows.’”[5] Therefore, if time is a kind of number, in respect of ‘before’ and ‘after,’ and motion is a perpetual succession (as Aristotle declares of both motion and time, 219b 5-13), and time is not independent of motion but is apart of motion in that it admits of enumeration, and the ‘now’ is a given present moment, then how is it that time is not held to be made up of ‘nows?’ Prima Facie this seems to be a strong discrepancy in Aristotle’s philosophy of time, albeit the possible aporetic nature of the assertions. However, even if this section is aporetic discrepancies are still evident and need to be accounted for in one way or another. Moreover, giving Aristotle the benefit of the doubt regarding these discrepancies, a more focused examination of the ‘now’ is needed.
In discussing the ‘now’ Aristotle claims that since motion is always different, time too is always different. The ‘before’ (prior) and ‘after’ (posterior) in time comes about because the same occurs in motion. There is a ‘before’ and ‘after’ in motion, and thus time follows suit. John Callahan helps elaborate on the concept of Aristotle’s ‘now’ by declaring, “Motion, which is the actualization of the potential, takes place in various stages that correspond to the magnitude which is traversed by the motion.” Callahan continues by declaring, “The motion does not exist with all its parts together; there is an order in the parts, and this order, insofar as it is made numerable by the now, is time.”[6] These comments are helpful in understanding the ‘now’ in several ways.
First, it helps us understand and consider time in terms of number through the ‘prior’ and ‘posterior.’ For example, going back to the train illustration. Considering the train itself, the cars are linked together as parts which make up a whole. The train is in motion and is thus countable when there is a perceiver to count the cars as they pass. Thus numbering is occurring in that the cars can be counted as they pass and in all this motion there is a ‘prior’ car which passes and becomes ‘posterior.’ The different events occurring in the train’s motion are the series of cars which pass at given points in the count.
Time may be “defined differently by the different events that are taking place in it.”[7] This is true even though Aristotle declares time, more specifically all of time that is simultaneous, is the same (219b 10-12). Second, when we consider the ‘now’ in the flow of time we discover that Aristotle thinks that in one sense it is the same, and in another sense it is different (219b 10-12). Here we see motion as the actualization of the potential, as Callahan described above.
Moreover, for Aristotle the number (or count) in motion is, in reality, fluid. Unlike Zeno’s paradox where a given two points, A to B, has a series of divisions which are infinite (i.e. A1, A2, A3 . . . ad infinitum), Aristotle denies that this can be the case. Thus, time is not composed of a series of ‘nows’ between the motion of something from point A to B. The motion would be fluid unless interrupted, but there would never be an infinite amount (or even a series) of ‘nows’ between point A and B. In other words, if an individual were to walk from one point to another (regardless of the distance), the act of the walker would be fluid and could not, in reality, be broken into divisible points from A to B. As a logical construct there are an infinite amount of points from A to B, but not in reality. In relation to time, Aristotle believes that the motion between time T1 and T2 is fluid, unless interrupted, and can never be divided into an infinite amount of points, or ‘nows.’ In Physics IV (219a 4-14) Aristotle argues the fluidity of magnitude, movement, and thus time in this way:
1) All Magnitude is continuous.
2) Movement goes with magnitude (thus movement is continuous).
3) Time is a part of movement.
4) Therefore, time is continuous.[8]
In making sense of the above complications regarding Aristotle’s ‘now,’ Conen uses Simplicius’ explanation to sort out the difficulties and provide a fair answer. Describing Simplicius’ solutions, Conen states,
There are three elements to Simplicius’ explanation: (1) He decides in precisely what sense the “now” is a unit of number. The “now” is a unit of number, he says, because a unit is that which makes an indivisible thing correspond to another indivisible, and the “now” is that which makes the indivisible subject of motion correspond to the indivisible phase of motion. (2) He decides in just what sense there is a similarity between the generation of number from a unit, and the generation of motion from the subject of motion and time from the “now.” The similarity lies in this, that just as a unit, taken again and again, results in number, so the subject of motion and the “now” taken again and again, result in motion and time. But (3) he immediately qualifies the last statement—and here is the heart of the explanation. He says that the “being taken again and again” as applied to the subject of change and to the “now”: the former is a discrete again and again, the latter is a continuous succession; the former results in a discrete number, the later in a continuum.[9]
Thus, we can see once again, how the ‘now’ in one sense is the same and in another sense it is different.
[1] Aristotle, Physics, trans. with commentary Edward Hussey (Oxford: Clarendon Press, 1983), 141.
[2] W. Von Leyden, “Time, Number, and Eternity in Plato and Aristotle,” The Philosophical Quarterly, 14 (January 1964), 48-49.
[3] Paul F. Conen, “Aristotle’s Definition of Time,” The New Scholasticism, XXVI (October 1952), 445.
[4] 219b 1-17, 372.
[5] 218a 7-8, 370.
[6] John F. Callahan, Four Views of Time in Ancient Philosophy (Cambridge: Harvard University Press, 1948), 53.
[7] Ibid.
[8] The original text is not in syllogistic form. I put this argument in syllogistic form to highlight Aristotle’s contention that time is fluid and not broken up into ‘nows.’. See also 220a 1- 24.
[9] Conen, 448.
In Physics book 4, chapter 11, it seems that Aristotle has yet to commit to any exact theory of time. Nonetheless, Aristotle asserts that time does not exist without change. Edward Hussey in his translation and commentary to Aristotle’s Physics points out that “Aristotle uses two claims about the perception of change and time: (a) when we do not perceive any change to have taken place, we do not think any time has elapsed; (b) when we do perceive change to have taken place, we do think some time has elapsed.”[1] Using an illustration of sleep (‘those who are fabled to sleep among the heroes in Sardinia’) Aristotle points out that the interval between the time ‘before’ sleep and the time ‘after’ is a type of connection between the prior ‘now’ and the posterior ‘now’ and the two are made one. The two are ‘made one’ in the sense that those who slept failed to consciously notice the interval between the two ‘nows.’
W. Von Leyden comments on this difficult passage by concluding, “The argument [of Aristotle’s that time is closely related to change] is significant in that the sufficient as well as necessary condition of any time-lapse is found to lie in the distinction of two ‘nows’ and a ‘before’ and ‘after’ in motion.”[2] Adding to Von Leyden’s comments, it seems this passage (218b 21-28) is at best an attempt by Aristotle to make sense of how time cannot exist without change and some perceiver of change. To illustrate this point, if a person were by a railroad track sitting on a bench and a very long train proceeded to pass by, the perceiver would be conscious of time’s passing via the movement of the train and the counting of the cars which pass. However, let us assume this is a very long train, and as it passes the perceiver falls asleep. Now let us assume that the train has completely passed the person who is asleep. Knowing the train was there ‘before’ the perceiver fell asleep, the perceiver would realize time had elapsed upon waking up from slumber since the train is no longer there ‘after’ the perceiver awakes. This is the connection Aristotle makes between the now of the ‘before’ and the now of the ‘after’ which is essentially perceived and counted by the perceiver upon awakening. And this is accomplished in that the perceiver understands change has occurred due to the train’s absence. In all this a perceiver is needed in order for the realization of motion and change to have occurred. Thus, time, in terms of ‘before’ and ‘after’ and Aristotle’s concept of the now needs a perceiver to be real.
Aristotle’s notion of the ‘now’ is quite intricate and complicated. Paul F. Conen describes Aristotle’s now as “The plurality of before and after in motion which time is, is a plurality of ‘nows.’ As a line is pluralized by the points actually numbered or numerable on it, so motion is pluralized by the ‘nows’ counted or countable in it.”[3] Thus, Conen understands Aristotle’s ‘now’ in time and motion as that which is numbered. This is in fact how Aristotle defines the ‘now.’[4] However, in relation to Aristotle’s puzzle of the parts of time, he concludes that time “is not held to be made up of ‘nows.’”[5] Therefore, if time is a kind of number, in respect of ‘before’ and ‘after,’ and motion is a perpetual succession (as Aristotle declares of both motion and time, 219b 5-13), and time is not independent of motion but is apart of motion in that it admits of enumeration, and the ‘now’ is a given present moment, then how is it that time is not held to be made up of ‘nows?’ Prima Facie this seems to be a strong discrepancy in Aristotle’s philosophy of time, albeit the possible aporetic nature of the assertions. However, even if this section is aporetic discrepancies are still evident and need to be accounted for in one way or another. Moreover, giving Aristotle the benefit of the doubt regarding these discrepancies, a more focused examination of the ‘now’ is needed.
In discussing the ‘now’ Aristotle claims that since motion is always different, time too is always different. The ‘before’ (prior) and ‘after’ (posterior) in time comes about because the same occurs in motion. There is a ‘before’ and ‘after’ in motion, and thus time follows suit. John Callahan helps elaborate on the concept of Aristotle’s ‘now’ by declaring, “Motion, which is the actualization of the potential, takes place in various stages that correspond to the magnitude which is traversed by the motion.” Callahan continues by declaring, “The motion does not exist with all its parts together; there is an order in the parts, and this order, insofar as it is made numerable by the now, is time.”[6] These comments are helpful in understanding the ‘now’ in several ways.
First, it helps us understand and consider time in terms of number through the ‘prior’ and ‘posterior.’ For example, going back to the train illustration. Considering the train itself, the cars are linked together as parts which make up a whole. The train is in motion and is thus countable when there is a perceiver to count the cars as they pass. Thus numbering is occurring in that the cars can be counted as they pass and in all this motion there is a ‘prior’ car which passes and becomes ‘posterior.’ The different events occurring in the train’s motion are the series of cars which pass at given points in the count.
Time may be “defined differently by the different events that are taking place in it.”[7] This is true even though Aristotle declares time, more specifically all of time that is simultaneous, is the same (219b 10-12). Second, when we consider the ‘now’ in the flow of time we discover that Aristotle thinks that in one sense it is the same, and in another sense it is different (219b 10-12). Here we see motion as the actualization of the potential, as Callahan described above.
Moreover, for Aristotle the number (or count) in motion is, in reality, fluid. Unlike Zeno’s paradox where a given two points, A to B, has a series of divisions which are infinite (i.e. A1, A2, A3 . . . ad infinitum), Aristotle denies that this can be the case. Thus, time is not composed of a series of ‘nows’ between the motion of something from point A to B. The motion would be fluid unless interrupted, but there would never be an infinite amount (or even a series) of ‘nows’ between point A and B. In other words, if an individual were to walk from one point to another (regardless of the distance), the act of the walker would be fluid and could not, in reality, be broken into divisible points from A to B. As a logical construct there are an infinite amount of points from A to B, but not in reality. In relation to time, Aristotle believes that the motion between time T1 and T2 is fluid, unless interrupted, and can never be divided into an infinite amount of points, or ‘nows.’ In Physics IV (219a 4-14) Aristotle argues the fluidity of magnitude, movement, and thus time in this way:
1) All Magnitude is continuous.
2) Movement goes with magnitude (thus movement is continuous).
3) Time is a part of movement.
4) Therefore, time is continuous.[8]
In making sense of the above complications regarding Aristotle’s ‘now,’ Conen uses Simplicius’ explanation to sort out the difficulties and provide a fair answer. Describing Simplicius’ solutions, Conen states,
There are three elements to Simplicius’ explanation: (1) He decides in precisely what sense the “now” is a unit of number. The “now” is a unit of number, he says, because a unit is that which makes an indivisible thing correspond to another indivisible, and the “now” is that which makes the indivisible subject of motion correspond to the indivisible phase of motion. (2) He decides in just what sense there is a similarity between the generation of number from a unit, and the generation of motion from the subject of motion and time from the “now.” The similarity lies in this, that just as a unit, taken again and again, results in number, so the subject of motion and the “now” taken again and again, result in motion and time. But (3) he immediately qualifies the last statement—and here is the heart of the explanation. He says that the “being taken again and again” as applied to the subject of change and to the “now”: the former is a discrete again and again, the latter is a continuous succession; the former results in a discrete number, the later in a continuum.[9]
Thus, we can see once again, how the ‘now’ in one sense is the same and in another sense it is different.
[1] Aristotle, Physics, trans. with commentary Edward Hussey (Oxford: Clarendon Press, 1983), 141.
[2] W. Von Leyden, “Time, Number, and Eternity in Plato and Aristotle,” The Philosophical Quarterly, 14 (January 1964), 48-49.
[3] Paul F. Conen, “Aristotle’s Definition of Time,” The New Scholasticism, XXVI (October 1952), 445.
[4] 219b 1-17, 372.
[5] 218a 7-8, 370.
[6] John F. Callahan, Four Views of Time in Ancient Philosophy (Cambridge: Harvard University Press, 1948), 53.
[7] Ibid.
[8] The original text is not in syllogistic form. I put this argument in syllogistic form to highlight Aristotle’s contention that time is fluid and not broken up into ‘nows.’. See also 220a 1- 24.
[9] Conen, 448.
Labels: Aristotle, philosophy, Time
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