The following explains the concept of time in Aristotle. It is a section from a larger work in progress on the subject of time.
Aristotle begins his inquiry into time by saying:
To attack the subject of time is connected with the things that have been said. And first, it is a good idea to come to an impasse about it by way of popular arguments about whether it is something that is or something that is not, and then about what its nature is.
This section proceeds according to the method Aristotle lays out in Book I. This method begins with “what is more familiar and clearer to us” and then moves from here to “what is clearer and better known by nature.” To know something by nature, for Aristotle, is to know its sources or causes.
The reason we are starting with the familiar things said about time seems to be that, before we can discuss time at all, we need to have some initial idea of what it is we are talking about. This initial idea, however, is a jumbled mess- a nest of contemporary opinions on the subject. The movement from this jumbled mess to what is simple, clear by nature, and defined involves separating those things which are indeed related to time (but are mistakenly equivocated with time) from time itself and its parts. Aristotle uses the following example to illustrate this point: “Children too at first address all men and women as mother, but later distinguish each of them.” In this example, the children are confusing relation and equivocation.
Aristotle gives us an argument (which I assume is a contemporary argument) that states that time cannot exist because it is composed of past and future. The past no longer exists and the future does not yet exist. If time is a composite of past and future, none of its parts exist; therefore, time does not exist. What this argument shows is that we cannot give an account of what time is by giving an account of what time is composed of. Rather, we must give an account of the source or cause of time.
The next point Aristotle makes is that the now is not a part of time, although it is related to time. By “the now” Aristotle means the thing which divides past from future, or more generally, into before and after. In the same way that a point on a line is not part of the line (rather, the two segments created in the division are the parts of the line), the now is not a part of time. Admitting the now exists, if we assume it to be a part of time, it would seem to be the only part of time that exists. It is also infinitely small. The now, by itself, does not do justice to what we include when we speak of time. Also the now is infinitely small and we cannot put our finger on it. The now is confusing, and the past and future seem to not exist. People contemporary to Aristotle say that time is the motion of the whole in a circular pattern, but Aristotle rejects this. This is because we can take from this “circular whole” a certain portion of time. The section under our consideration is not in itself circular (that is, it does not work its way back to the beginning of the segment). Even though it might ultimately be part of a circuit, it seems that we are able to consider this segment of time as time without reference to the whole. We have no way of accessing time as a circular whole. Rather, we only have access to time in segments.
People also say that time is the orbit of the celestial sphere. Aristotle rejects this because, if there were more than one heavenly sphere, the motion of eachwould be time. This would mean that there would be two separate times, each relative to a specific heavenly sphere. But we would not conceive these as being separate time, as it seems that we can correctly say that the motions of each heavenly sphere can coincide (that is, we can abstract a time in which both motions exist). Each sphere cannot be a separate time because this would mean there would be many times at the same time, which would be absurd.
It is as if we said that time is the setting and rising of the sun. But why is it not the orbit of the moon? If time is defined in such a way, we could take both to be time. But, of course, they cannot both be separate times; rather, they share a certain temporal relationship.
While we can measure time by either days or months, these celestial orbits are not what time is. Rather, they are what we measure time by. Time is something separate from what measures it.
Aristotle also says that time is not change. If time were to be change, change is only in the changing thing itself, or in the place where it happens to be changing. Since we can say that two different changes happen at the same time, it is clear that time is universal among objects and that time is not change.
Also, change can be faster or slower, but time cannot be faster or slower. In fact, slow and fast are defined according to time- and time cannot be defined by means of itself.
We might get time and change confused, however, because it seems that there is never time without change. For example, if I fell slept for a long time and did not realize how long I had been unconscious, I would join together the earlier and later now. This is because I was not aware of the changes occurring while I was sleeping.
Time seems to be relative to our perceiving motion. Whenever time seems to happen, there is a perception of motion. Even if it were dark and I experienced nothing through our sense, I am still having a kind of internal experience of time passing (which Aristotle says is the motion of the soul).
When we observe a motion, we notice a before and after; or rather, all perception of motion necessarily has a before and an after. This before and after observed in motion belongs to time. From this, Aristotle derives what I am calling the ‘phenomenological account of time.’
And that is when we say that time has happened, whenever we take cognizance of the before and after in a motion.
Although “the now” is not a part of time, it is a condition for the possibility of us having an experience of time. This is because it is the now which divides a motion into a before and after (thus making our experience of the motion a temporal experience). If there were no now, there would be no time. This is because the now is necessary for having a before and after in a motion. The now is not part of time (in the way that we speak of a line having parts), but an attribute of time. As soon as we talk about before and after, we evoke a “now.” The before and after we talk about, however, are in the motion.
“Universal time” is derived from the “universal now” among object. The “now”, abstracted in a universal sense, is the same among objects. So if the kettle boils at the same time I wake up, we speak of these motions as being coincident.
Our way of access to motion- and therefore to time- is the thing in motion. The clock, for example, is a thing in motion. Putting the motion of the clock into terms of before and after gives us access to time. When we say something happened at a certain time, we are speaking of that motion as being coincidental to the motion of the clock.
Time is not fast or slow, but rather long or short. Motions can be fast or slow, in respect to time. In the same way as the number by which we measure speed is neither fast nor slow (as it is the speed itself that is fast or slow, not the numbers used to represent it), time- as measurement- is neither fast nor slow. So when we speak of time as passing slowly, we are speaking of a motion’s speed, not of its time.
Rest is also measured by time because rest is a deprivation or absence of motion. The same unit of measurement is applied to both rest and motion. So let us say that the book has been at rest on my desk for an hour. By this, we mean that the book has been without motion for the duration of an hour’s worth of motion of the clock.
When we consider that time is a kind of “number” applied to motion, we conclude that for there to be time there must be someone to measure the change in motion. Time, for Aristotle, is the act of a human being measuring something. It is dependent on the existence of a soul who- by means of intelligence- is able to apply measurement to motion. “The before and after are in motion, and insofar as they are counted, they are time.”
 One of Aristotle’s teachers said something quite similar, didn’t he? Cf.Meno.
 “But since the meaning of number is twofold (for we call that which is counted or countable a number, but also that by which we count), time is the counted and not the number by which we count. The two senses of number are different.” 219b