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Aristotle’s account of time in Physics, Book 4, chapters 10–14 (translated in Hussey 1993), is at once fascinating and frustratingly obscure. In it, he discusses time’s relation to the present, to change, and to the mind. The view that emerges is one on which temporal order depends on a more basic order: an order of the stages within changes.

On this view, for there to be time, there must be changes. Moreover, Aristotle holds that if there is to be time, changes must be marked out, or “counted” in a certain way.

Because of this, time also depends on the mind: for there to be time, there must be beings capable of counting. These are intriguing claims, but what exactly do they mean?

This essay suggests one way in which we might make sense of them.

Time and the now Is time something that “is”?

Aristotle starts out with a puzzle about whether there can be such a thing as time. Time seems to be divided into two parts, neither of which exists. The past is something that was, but is no longer; the future is something that will be, but is not yet. How can time be something that exists, if none of its parts exists? (Physics, Bk 4, ch. 10, 217b29–218a3).

You might think that there is a third part of time – the present – and that the present is something that exists. But Aristotle argues that the present (or “now” as he calls it) is not really a part of time (218a6). The now (he claims) is a mere boundary between the past and the future; it itself has no duration. If the now is a mere boundary, its existence cannot be what grounds the existence of time. For how can there be a boundary between two things, neither of which exist? No one would think it possible for the coast to exist in a world in which there was neither sea nor land: the coast just is the boundary between the sea and the land. How, then, can the now be all there is to time, if the now is simply a boundary between two parts of time (the past and the future)?

Aristotle himself never explains how to answer this puzzle. After presenting it, he goes on to give his own positive account of time. As we shall see, he says that time is something that depends for its existence on change. Perhaps he thinks that he can

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establish that there are such things as changes and can use this fact to solve the puzzle about time. However, it is not immediately clear how such a solution would work. At least on the face of it, the puzzles about time’s existence would seem to apply also to the existence of change. Any change that is going on will have a part that is past and a part that is future. So we can ask: is the present part of the change anything more than an instantaneous boundary between the past and the future?

A moving now?

Aristotle also raises another puzzle about the now. Is the now always the same or is it always different? The best way to understand his question is to perform the following thought experiment. Consider the present now … wait a bit … consider the present now. What is the relation between the two times you have identifi ed? On the one hand, they seem to be two different times: one of them is earlier than the other. On the other hand, each of them was present (or now) when you identifi ed it. What is this feature presentness that the two times have in common?

Aristotle explains the relation between earlier and later “nows,” using an analogy. He compares the now to a moving thing. Imagine a man, Coriscos, moving from the marketplace to the Lyceum. In some respects Coriscos remains the same throughout this movement, but in other respects he is always different: he is fi rst at one place and then at another. Similarly, earlier and later nows are in some respect the same, but in another respect different (Physics, Bk 4, ch. 11, 219b9ff.).

What exactly is Aristotle trying to establish when he makes this comparison? Many philosophers have thought that he is endorsing a “moving-now” view of time (see, for instance, Hussey 1993: xliii–xliv). On such a view, one and the same thing, the now, moves through time, being fi rst earlier and then later. So if, on two different occasions, you refer to the present, you are each time picking out one and the same thing, the present, but you are picking it out at different stages of its movement. On this view, time itself is the movement of the present (or now), as it progresses further and further into the future.

But there is reason to doubt whether this is really Aristotle’s view. For he argues that time itself is not a kind of movement. His argument is that movement is the sort of thing that can be quicker or slower, but time cannot be quicker or slower (Physics, Bk 4, ch. 10, 218b13–18). A very similar argument would show that the now does not move. The now is not the sort of thing that can move more or less quickly. This suggests that on Aristotle’s own view the now is not the kind of thing that can move.

What, then are we to make of his comparison between the now and a moving thing?

One clue is that Aristotle here invokes what the sophists say about Coriscos in the Lyceum and Coriscos in the marketplace: the moving thing is different in defi nition “in the way in which the sophists assume that being Coriscos-in-the-Lyceum is different from being Coricos-in-the-marketplace” (my italics; Physics, Bk 4, ch. 11, 219b20–21; here, and in what follows, translations are from Hussey [1993]). The sophists were notorious for raising puzzles about how a thing could retain its identity though changing in some respect. For instance, at Metaphysics Book 4, chapter 2, 1026b15–18, Aristotle presents

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a sophistical worry about whether musical-Coriscos and Coriscos are one and the same.

Perhaps, then, Aristotle’s point is that the now is analogous to a moving thing, as a moving thing would be conceived by the sophists.

What would this sophistic view be? A sophist might hold that, as Coriscos moves from the Lyceum to the market, there are a series of different entities: Coriscos-in-the-Lyceum, Coriscos-at-a-point-partway-to-the-market, Coriscos-at-another-point-partway-to-the-market, and so on, to Coriscos-at-the-market. These different entities all have something in common (they are all part of the series that makes up Coriscos-in-motion-from-the-Lyceum-to-the-market), but they are nevertheless distinct things.

If Aristotle is comparing the now to the moving thing as conceived of by the sophists, then we do not have to saddle him with the view that the now is a thing that moves. His view is that just as (on the sophistic view) what we call Coriscos is, in fact, a series of different entities, so also what we call now is on each occasion something different. Similarly, just as the series Coriscos-in-the-Lyceum, and so on, to Coriscos-in-the-market all have something in common (they are members of the series that makes up Coriscos-in-movement-from-the Lyceum-to-the-market), so also different nows all share membership in a series: they are all members of a single temporal before-and-after ordering.

Change as more basic than time

Aristotle defi nes time as a “number of change in respect of the before and after” (Physics, Bk 4, ch. 11, 219b1–2). There are at least two things that are puzzling about this defi nition: the claim that time is a kind of number, and addition of the qualifi cation “in respect of the before and after.”

Time as a kind of number

It is odd to describe time as a kind of number. After all, time is something continuous:

it is not a collection of things that can be counted. For this reason, some interpreters have suggested that Aristotle really means to say that time is that by which we measure change (see, for instance, Annas 1975). In support of this, they point out that Aristotle himself says (later in his account) that time is that by which we measure change (though he adds that we also measure time by change) (Physics, Bk 4, ch. 12, 220b14–16).

However, it is unlikely that this is the point he is making when he defi nes time as a kind of number. Aristotle presents this defi nition as if it follows uncontroversially from claims he makes about how we are aware of time by being aware of the occurrence of change, but nowhere in these claims does he mention the need to be aware of any regularly repeated change, of the sort that could be used as a kind of measure.

We shall get closer to understanding Aristotle’s defi nition if we look at his immedi-ately preceding remarks about our awareness of change. He says that we are aware that time has passed when we mark off earlier and later stages in a change, recognising that these stages are different from one another. When we do this, we identify two different nows. Time is what is between these two nows: “what is marked off by the now is thought to be time” (Physics, Bk 4, ch. 12, 219a29–30).

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This emphasis on marking off different nows suggests a solution to our problem about the sense in which time is “counted.” We count nows, but by so doing, we also (in a derivative sense) count the time that is between them. Suppose that I identify a now at an early stage of Coriscos’ movement to the market and a now at a later stage of Coriscos’

movement to the market. Since the nows are each at different stages of one and the same change, they must be two different nows. I can, then, count them as two and recognise that there is a period of time between them.

If this is Aristotle’s view, then the counting that goes on here is of a very special type.

Normally, when we count things, the point of doing so is to fi nd out how many of them there are. Aristotle thinks that whenever we mark out two nows, we could always have marked out another now between them. So the point of counting nows cannot be to fi nd out how many there are. Counting must, then, have a different purpose. We can fi nd a hint as to what this purpose might be if we look back at the defi nition: time is a number of change in respect of the before and after. In counting nows, we are putting them in a certain order. If this is right, then to say that time is a number of change is to say that it is a kind of order within which changes occur. Time is what is marked out by the nows that we count, and to count these nows is to arrange them in a single order within which every change has a position.

To understand this claim more fully, we need to look at the other puzzling aspect of Aristotle’s defi nition. What exactly does it mean to say that time is a number of change in respect of the before and after?

The before and after

To defi ne time as a number of change “in respect of the before and after” might seem self-defeating. Before and after are themselves naturally understood as temporal notions.

How, then, can a defi nition of time that uses them in this way be explanatory?

The answer to this question lies in Aristotle’s earlier remarks about the relations between time and change. (For the sake of simplicity, I pass over his diffi cult remarks about the relation between change and magnitude. For discussion of these, see Coope [2005].) Aristotle says that time follows change (Physics, Bk 4, ch. 11, 219a16–18). By this he seems to mean that certain features of time depend upon corresponding features of change. One such feature is the before and after. There is a before-and-after relation in change and because of this there is a before-and-after relation in time. What does this mean?

Aristotle’s view seems to be that within any one change there is a pre-temporal before-and-after series. Consider, for instance, the growth of a particular acorn into an oak tree. There is a series of stages in this change: acorn, shoot, small sapling, oak.

Aristotle’s claim is that these stages have a pre-temporal before-and-after order. That is, they have an order that is not itself derived from their order in time. It is an order that is defi ned only on the stages of one and the same change: the acorn-stage is before the shoot-stage in this change. There is no one change that has as stages, say, the acorn-stage and the Coriscos-in-the-market stage, so there is no relation of before-in-change or after-in-change that holds between the acorn-stage and the Coriscos-in-the-market stage.

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When Aristotle says that the before and after in time follows the before and after in change, his point is that temporal order (the order of nows) depends on the pre-temporal orders of before-and-after series within changes. For example, suppose that the acorn-stage is before the shoot-acorn-stage in the change that is the acorn’s growth into an oak.

Aristotle thinks that because of this, the time of the acorn-stage will be temporally before the time of the shoot-stage. If we mark out a now when the acorn appears and another now when the shoot appears, the now of the acorn-stage will be temporally before the now of the shoot-stage.

But this just raises the question: what is the basis for thinking that the order of the stages in a change is pre-temporal? Isn’t it more natural to think that this order itself depends upon time: that the acorn-stage is before the shoot-stage in the change just because it is temporally before the shoot stage? To see how Aristotle might answer this, we need to look at his account of change.

Aristotle’s view of change

Modern philosophers have sometimes defi ned changing as being in incompatible states at different times. Bertrand Russell, for instance, says that motion “consists merely in the fact that bodies are sometimes in one place and sometimes in another, and that they are at intermediate places at intermediate times” (Russell 1953 [1918]: 83). Aristotle must reject any account that appeals to time in this way. Since he thinks that temporal order depends upon a prior order that holds between stages of a change, he needs some independent account of what it is for something to change.

In Physics, Book 3, chapters 1–2, he seems to be providing just such an account. He gives a defi nition of change in terms of two other notions: potentiality and actuality.

Change, he says, is “the actuality of that which potentially is, qua such” (Physics, Bk 3, ch.1, 201a10–11). What does he mean by this?

The notions of potentiality and actuality that Aristotle employs in this defi nition fi gure centrally in much of his thinking about metaphysics. Unfortunately, they are notoriously diffi cult to understand. His thought here seems to be this. For there to be a change, there must be something that exists before the change and that has the potential to be in the end state of the change. Consider, for example, the change that is the coming-to-be of a statue. For this change to occur, there must be some stuff (some bronze, perhaps) that is not (yet) a statue but has the potential to be a statue. When Aristotle writes of “that which potentially is,” he is referring to that which is potentially in the end state of the change. For instance, in our example, “that which potentially is”

is the bronze and the potential that the bronze has is the potential to be a statue.

The change into a statue is the actuality (or fulfi lment) of the bronze, insofar as the bronze is potentially a statue. In other words, becoming a statue is the fulfi lment of the bronze’s potential to be a statue. This leaves one obvious diffi culty. It might seem that the bronze’s potential to be a statue is most fulfi lled when the statue exists in its fi nished state. But at that point the change we are trying to defi ne is already over: the bronze is no longer becoming a statue. Given that he wants to defi ne change as the actuality of a potential to be in some end state, how can Aristotle distinguish between changing into

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that state and statically being in that state? How, in our example, can he distinguish between becoming a statue and simply being a statue?

To answer this, it is necessary to think about the signifi cance of the “qua” clause in the defi nition. The change in question is the actuality of the bronze qua potentially (but not actually) a statue. Aristotle explains that, as he is using the notion of “potential”

here, something only counts as potentially F, when it is not in fact F. When the statue has been made, the bronze is no longer something that is (in this sense) “potentially a statue.” Or, as he puts it (using a different example), “when the house is, the buildable [i.e. what is potentially but not actually a house] no longer is” (Physics, Bk 3, ch.1, 201b11). Change is the actuality of something that is, in this way, merely potential.

When something is becoming F, its potential to be F is as actual in a way compatible with merely being a potential. Though being a statue is a kind of actuality of the bronze, it is not the actuality of the bronze’s potential to be a statue, considered as a mere potential.

Becoming a statue is the actuality of the bronze insofar as it is potentially, but only poten-tially, a statue. That is to say, it is “the actuality of that which potentially is, qua such”

(201a10–11). Another way to put this (suggested by Aristotle’s remarks at Physics, Bk 3, ch. 2, 201b31–3) is to say that the changing thing is fulfi lling a certain potential, but fulfi lling it incompletely. When the bronze is becoming a statue, it is fulfi lling its potential to be a statue, but it is fulfi lling this potential incompletely.

There are, of course, several objections one might make to this account of change.

What about the kind of change that is not a progression towards some defi nite end state? What account can Aristotle give of infi nitely long changes, which have no end at all? Can we really make sense of the notions of potentiality and actuality without

What about the kind of change that is not a progression towards some defi nite end state? What account can Aristotle give of infi nitely long changes, which have no end at all? Can we really make sense of the notions of potentiality and actuality without