1. 國立清華大學哲學研究所 專任助理教授 陳斐婷
西方思想經典：亞里斯多德《物理學》
國立清華大學哲學研究所 專任助理教授 陳斐婷

2. Aristotle on Time
Introduction

3. The number of motion and the flowing now
Theme #1: the physical analysis of time
“This, then, is [a] time: the number of motion with respect to the earlier [or ‘prior’] and the latter [or ‘posterior’].” (Physics 4.11, 219b1-2)
Theme #2: the transitory, evanescent, or “flowing” character that attaches to our experience of time.
“A thing, then, is affected by time, as we are wont to say that time wastes things away and that all things grow old because of time and people forget on account of time—but not that one has learned or become young or beautiful [on account of the passage of time]. Rather, time is essentially the cause of corruption. For it is the number of process [or ‘motion’] and process does away with what exists [or what is present]. (Physics 4.12, 221a30-b3)

4. Theme#1 the physical analysis of time

5. The geometrical and metrical components
The distinction between a geometrical or topological component and metrical component of Aristotle’s account of time.
Geometrical component refers to Aristotle’s conception of time as a continuous, linear dimension of κίνησις (process, motion, or change that is incremental and development).
Metrical component refers to the idea of “a time” in the sense of a unit of temporal measure (defined in terms of some continuous and unitary but repeating or repeatable motion), or some definite multiple of such a unit.

6. Geometrical component
Time is one of the species of continuous quantity (along with lines, surfaces, bodies, solids, and place).
Aristotle does not conceive of time as some substantive principle or entity within which occur processes and events that are metaphysically separable from that time.
In Physics 4.14, Aristotle describes time as an affect or state of motion (223a18-19).
Aristotle thinks of time as analogous to one-dimensional or linear magnitude (“a line”). Finite stretches or intervals of time are bounded, in both the prior and the posterior temporal directions, by temporal points or instances (literally, “nows”), which do not themselves have “positive measure” or duration but which serve as the limits of stretches of time.

7. The now
Just as a line is not composed of points according to Aristotle, so time is not composed of nows or instants. “Insofar as the now is a boundary/limit, it is not time but belongs to it as a property” (Physics 4.11, 220a21-22). And, “because time is a number of motion with respect to the prior and the posterior it is clear that it is continuous (for motion is continuous)” (220a24-6).
“The now is not a part [of time], for the part measures [that of which it is a part], and it is necessary that a whole [time] is constituted of parts. So time seems not to be constituted of nows” (Physics 4.10, 218a6-8)
“Let it be [understood to be] impossible that nows are in immediate succession to one another, just as it is impossible for point immediately to succeed point” (218a18-19).

8. The now
Any interval or stretch of time is continuous and “infinitely divisible” (in Aristotle’s sense) into smaller sub-intervals. Temporal points or instants can be demarcated or constructed (as, for example, the boundaries of processes and, perhaps, as instantaneous events).

9. Metrical component
Time has neither beginning nor end. But there is a fundamental cyclical character to Aristotle’s conception of time: celestial motions provide the principal numbers that constitute time in the metrical sense.
“A time” as the number of motion with respect to prior or posterior is not properly said to be fast or slow. Rather, it is “many or few and long or short: long or short qua continuous, and many or few qua a number” (220a32-b3).
The idea is that time is a number insofar as its duration can be measured by a multiple of some unit, the unit being defined by a certain (repeatable) motion.
Thus, there is a certain reciprocity of measurement between a time and a motion since “they are delimited by one another” (220b16).

10. The horse analogy
“We speak of ‘much time’ and ‘little time,’ measuring it by change, just as we measure the number by what is countable: e.g., by the one horse we measure the number of the horses, for it is by number that we become acquainted with the multiply of the horses and, conversely, by the one horse that we become acquainted with the number of horse itself.” (Physics 4.12, 220b18-23)

11. Response to Strato’s challenge
According to Simplicius, Strato of Lampsacus (the successor of Theorphastus as Peripatetic scholarch, who succeeded Aristotle) “does not agree that time is a number of motion, because number is discrete quantity, but motion and time are continuous, and what is continuous is not numerable” (Simplicius, Physics, CAG, 9, 789).
From the geometrical perspective, Strato is correct: as a continuous quantity, time does not possess an intrinsic metric.
Time as a species of continuous quantity does not exhibit a single, intrinsic and obvious unit by which it can be measured—in the way that a discrete multiplicity, such as a herd of horses, exhibits the intrinsic and natural unit of one horse.

12. Response to Strato’s challenge
But from the metrical perspective, the assignment of a discrete but repeatable/repeating motion (e.g., a complete transit of sun around the ecliptic) introduces the notion of discrete “number” by which time may be measured.
Once an extrinsic unit of measure has been selected for a continuous quantity such as time, one can speak of time in metrical terms as a “number of motion with respect to earlier and later” (220a24-25).

13. Theme#2 the flowing now

14. The nunc fluens (“flowing now”)
There is an aspect of Aristotle’s conception of time that does not fit well into either metrical or geometrical categories.
In modern scholarship, the picture of the flowing now is sometimes presented in terms of McTaggart’s A-series tense concepts (past, present, future) and his B-series concepts of temporal ordering (before, simultaneous with, after).
A-series tense concepts: past, present, future.
B-series concepts of temporal ordering: before, simultaneous with, after.

15. B-series concepts of temporal ordering
Aristotle makes use of one notion of nows—that of temporal points, limits, or instants—in order to define stretches of time to which the B-series concepts can be applied.
But it is not obvious whether Aristotle conceives of each temporal instant as representing “the present” from its own perspective and possessing its own particular determinate past and partially indeterminate future.

16. A-series tense concepts
A-series: The now also appears as the notion of “the present,” as in the A-series concepts: “the now is the link of time, as has been said, for it links what has happened and what will happen” (Physics 13, 222a10-11).
But it is not obvious whether Aristotle sees this, token-reflexive now as unique temporal instant that, as it were, “moves through time,” generating a unique past out of a partially indeterminate future.

17. Time is anisotropic.
What is more certain is that Aristotle holds that time is anisotropic: that is, the future is quite different from the past.
In De Caelo 1.12, capacities or potentialities pertain not to the past but only to the present-or-future. (283b13-14)
In De Interpretation 9, a sort of indeterminacy or openness pertains to the future, while the past is regarded as determinate or fixed.
It does seem that he accepts a commonsensical picture of the future as “containing” various possibilities in a way that the past does not.