What Is Time?: On Aristotle’s Definition of Time in Physics Book IV

Time, for Aristotle, is fundamentally linked to change and movement.  Where there is alteration or movement, there is time, for everything that comes to be and ceases to be are in time.  Another way of putting it is that there is change because there is time. Of things that come to be and pass away are things that belong to the world of nature (phusis).  For this reason we say about the concept of God that it is a being that cannot be said to be “in” time because it is a being without temporal finitude: an unchanging absolute being, summum ens, as when Augustine writes in Book I of Confessions,  “For you, God, are infinite and never change…you yourself are eternally the same.”  By contrast, natural beings are finite in virtue of their being in time.  This is why Aristotle’s analysis of time belongs not to his Metaphysics but to Physics, to his natural philosophy, for  “every alteration and all that changes is in time” (222b31).   Thus, in Book IV Chapters 10-14, Aristotle lays out his treatise on time to establish an account of time as essentially part of nature.  The question, “What is time?”, will be expounded in terms of what it is for time to exist; by virtue of what can we say that time “is”; and whether time can be said to be among things that are or things that are not, that is to say, whether time is in the order of being or in the order of nonbeing.
Time appears prima facie to be identical to change and movement.  When we pause to think what time “is,” we often think of this “is” of time as the now.  Indeed, as we shall see and say more below, Aristotle argues that the essence of time is the now, to nun.  Because the now is the temporal instant that is our most immediate experience of time, it is what seems immediately graspable by theoretical apprehension.  (Consider for instance, when someone asks what time it is, we normally take it to mean what time it is at the present moment, i.e., time as now.)  But, time is also a movement of some kind, namely, the movement from time-not-yet to time-no-longer.  Insofar as time implies a sense of a before and after, we can say that time is the coming-to-be and passing-away of nows moving in an irreversible, linear fashion.  Time, hence, is essentially successive.  However, we can grasp this succession of nows if and only if we have some conceptual means of distinguishing one now from another now, and this we have if and only if we perceive that a change has in fact taken place between the passage of one now to another now.  In other words, time cannot elapse unless there is change, and change cannot occur unless there is time.  Indeed, the very movement of time from one now to another now, its passage from a before and an after, presupposes that some change is taking place.  As Aristotle writes, “not only do we measure change by time, but time by change, because they are defined by one another” (220b14-15).
But it is not entirely accurate to say that time is identical to change and movement.  First, as Aristotle points out, time is not identical to change because change presupposes movement in space, and time has no location.  We cannot point to time as an actual thing, whose form is extended in space: time is not, to use a Kantian term, a sensible object (see my post on Kant on time).  We can only point to time, so to speak, as a “now”: as when we say “this presenttime that is the now.”  We point to the now-ness of time by means of a spatial analogy by abstracting a now from a postulated series of nows proceeding in an infinite line.  Such an analogical operation is, I believe, always at work when we speak of time in this way.  Secondly, time is not identical to change because change involves differentiations in speed and velocity, properties which time neither possesses nor obeys as laws that condition it.  So although time, for instance, appears to inhere in our physical concept of speed, s = d/t, time itself, strictly speaking, is not motion (“hoti men toinun ouk estin kinesis,”  218b18).  Yet it is nevertheless not without movement for the experience of time necessarily implies something in motion and in a state of change.  As Heidegger would later say regarding the transitionary character of time, “The now also is never the same and never a single one, but another, a not-the-same and not-one, a manifold”  (The Basic Problems of Phenomenology, 233).  The task for us is to clarify where exactly to attribute this movement of time: (1) does it belong to things in motion or (2) does it, more generally, belong to how humans experience time or (3) does it, in fact, inhere in time itself?  If Aristotle holds that time is not change yet also that time and change necessarily imply one another, then how precisely to think the interrelation of time and change?
It is at this point Aristotle offers his definition of time.
Aristotle defines time as “a number of change in respect of the before and after” (“arithmos kineseos kata to proteron kai husteron,” 219b1).  Time is not change; it is a number, more exactly, a number of change.  Time is not movement, but that by which movement can be numerically estimated.  It is important to note here that by defining time as a number of change, Aristotle does not mean that time is a number with which we count, time is not a number as such.  Rather, time is a number of change, that by which we can quantitatively express the qualitative modification of something undergoing change.  More succinctly, time is not a number, but of the number that is numbered.
Earlier in Physics, Aristotle conceptualizes change as “the actuality of that which potentially is, qua such” (201a9-11), as for instance in the coming-into-being (energeia)of that which is capable of coming-to-be (dunamis).  With this definition of change in mind, Aristotle argues that time is that by which we measure the progressive realization of a potentiality qua potentiality.  Of this we can illustrate with the concept of motion (kinesis).  When an object moves from point A to point B, the movement from point A to point B indicates an alteration in location, a change in place (topos).  Obviously we can measure the change in location in terms of spatial distance, say one yard.  But Aristotle’s point is that we can also measure it in terms of the amount of time it takes for the object to move from point A to point B, say five seconds.  Five seconds would hence be the quantitative measurement of the qualitative change of the object’s movement from point A to point B.  This is what Aristotle means by time being a number of change.  But by defining time as a number of change (arithmos kineseos), does Aristotle suggest that change is something that is prior to time?  It seems impossible, however, to discuss change without making reference to time, since change is dependent on time and vice versa.  What, then, is meant by defining time as a number of change?  In what sense is time a kind of number?
We begin by clarifying what the activity of numbering entails.  To number something involves the activity of counting, and counting implies the positing of differences.  For example, when one counts, “1, 2, 3, 4, 5,” one counts by designating a numerical series in which the number 1 is differentiated from the number 2, which in turn is differentiated from the number 3 and so on.  Counting thus presupposes an order of difference.  It entails the differentiation of entities as discrete from one another according to an implied standard of measurement (“This is 1, that is 2,” etc.).  Thus the meaning of a series like “1, 2, 3, 4, 5″ derives from the differences presupposed between each numerical term.  It is in this sense that we can read the Aristotelian concept of time not as a number but a number of change, where we take change to be the expression of a difference.  Thus, time is “a number of change” (arithmos kineseos) in that time is what informs and presides over the production of differences that is itself the condition for us to postulate and count the series “1, 2, 3, 4, 5.”  Without time, there is no counting, or the converse.  Time is what is counted, which means: the essentiality of time is its numerability.
If time is “a number of change,” this also means that time is productive of difference.  Time is productive of difference by virtue of its movement from one now to another now.  To put it another way, the movement of time in terms of the before and after necessarily always implies a change, the interval between one now and another now denoting difference as such.  Time shores up this order of difference, which is also the condition of possibility of counting, because the positing of numbers depends on this prior order of difference.  In other words, to posit “1” and “2” requires there to be time, in order for us to posit the identity of “1” as “1,” but also to posit the difference of “1” from “2” and so on.  This is why time is necessary for us to evaluate change. But the more profound point to make here is that this also means that the difference expressed by “1” and “2” is itself temporal.  To use our previous example of an object moving from point A to point B, the alteration that the object undergoes from its movement from point A to point B is expressible as a number precisely because the change in location takes place in time and therefore implies duration: five seconds.  The determination of temporal difference (e.g., five seconds), however, means that even though the moments of change are by definition different and stand apart, the time in which change takes place must always remain the same throughout.  If time were not the same everywhere, time cannot be used as a general measurement of change.  For Aristotle, time is a universal order within which change can be related and measured, hence the Aristotelian definition of time as a number of change.
Let us now consider the second part of Aristotle’s definition of time: time is “a number of change in respect of the before and after.”  What does Aristotle mean by the “before” and the “after” (the proteron and husteron) and by virtue of what distinguishes beforeness and afterness?  According to Aristotle, it is “the now that measures time” (219b12).  The now (nun) is that which allows us to divide time between earlier and later times, such that the interval or space between two nows is what defines the temporal-difference between a before and after.  That the now is that by which we measure time implies two things about the nature of time: time is continuous and time is divisible.  For we in fact divide time by marking a now, whose punctuation within the continuum of time allows us to differentiate between past, present, and future phases along a sequential and successive order.  Aristotle writes, “the now is a link [sunecheia] of time…for it links together past and future time, and is a limit of time, since it is a beginning of one and an end of another” (222a10-12).  We will need to stay close with the problems that arise in Aristotle’s formulation here: in what sense do we read now as that which links different phases of time but also that which is the boundary-limit the peras between past and future, between a before and after?  In what sense do we understand the now as the limit for the now-that-is-no-longer, the now-that-is, and the not-yet-now?  That is, in what sense do we understand the now as that which simultaneously links and divides?  This question points us to the problem of just how to regard the ontological status of the now.  If the now simultaneously links and divides, can the now be said to be something that “is,” something that is actual and present?  For when we point to a now, as when we say “this moment” or “this now,” do we not already in some sense miss it?  The now eludes our capture, for it disappears at the very moment we apprehend it.
How, then, do we regard the now?  To be sure, the now is an element of time insofar as it is something by which we mark and differentiate the passage/passing of time.  For Aristotle, the now is what constitutes time:  it is the essence of time, that which holds time together, its continuity rooted in the now.  It is in this sense we can provisionally understand the now to be itself “in” time.  But because the now is always in transience, or better still, because the now is the linking and the de-limiting of the succession of nows, the now in its becoming-now must contain within it something that negates itself in order for another now to come to be.  The now must therefore be thought simultaneously as a boundary-limit and as transition in connection with motion, peras and kinesis.  The now is therefore not an indivisible unit, but is radically divided within itself.  Because the principle of temporal succession requires that each now is superseded by another now, the now effaces itself in its very becoming.  This originary division or split of the now means not only that it is negated by what it is not in order to be, but also that the now is infinitely divided within itself, such that it can never be fully present as such This is why it is impossible to grasp the now as a fixed point, for the now, as that which links and as that which functions as a boundary-limit, is always both the beginning and the end of another now.  If time is determined on the basis of the now, such that the movement of time is the incessant tearing of nows, Aristotle needs to clarify, whether or not the now is in fact part of time, and whether or not the now remains always one and the same or is different in the supersession of nows.  Aristotle writes,
Just as the change is always other and other, so the time is too, though the whole time in sum is the same.  For the now is the same X, whatever X it may be which makes it what it is; but its being is not the same.  It is the now that measures time, considered as before and after.  The now is in a way the same, and in a way not the same: considered as being at different stages, it is different—that is what it is for it to be a now—but whatever it is that makes it a now is the same.” (219 b9-14)
Aristotle distinguishes time from space in that time is not an order of coexistence, but an order of succession.  The essence of the now is such that it cannot coexist with another now.  The coexistence of nows (simultaneity) is impossible because, as mentioned above, the internal division of the now requires not only that the now cannot coexist with another now, but also that the now cannot inhabit itself, so to speak, precisely because it annuls itself in its coming to be.  But the order of succession requires that although the now is not the same (the nows in succession differ from each other in terms of a before and after), there is something that persists as the same, or as Aristotle writes, “whatever it is that makes it a now is the same.”  For example, under the rule of temporal succession, the movement from now-A to now-B means that now-A is before now-B, and therefore now-A and now-B are different.  Simply put, the now we count is in each instant a different now.  Aristotle, however, will argue that although they are different with respect to their placement or punctuation within temporal succession, now-A and now-B are in their essence the same.  Thus the peculiarity regarding the nature of the now is that its movement from a now-not-yet to a now-no-longer means that the ever different nows are different but are nevertheless always exactly the same, namely, a now, in their coming-to-be.  What gives now-A and now-B their sameness or identity is precisely that which constitutes their now-ness.  Because now-A and now-B derive their difference from a sequential order of time, there is something in the order of time that persists as the same over and beyond the interval between now-A and now-B.  The now-ness, so to speak, that binds now-A and now-B together within the sequential order of temporal succession, is the same.  It is the being-held-together-within-itself, or the suneches, of time as a succession of nows.  Thus in our reading we see that Aristotle holds that there is an identity of the same for each and every now that comes-to-be and passes away, an essential element of now-ness on the basis of which the serial consecution of nows progresses in an infinite line.  Heidegger’s interpretation of this moment in the Physics is particularly striking and worth quoting in some length:
“The now is the same with respect to what it always already was—that is, in each now it is now; its essentia, its what, is always the same (tauto)—and nevertheless every now is, by its nature, different in each now, to d’einai auto heteron; nowness, being-now, is always othernessbeing-other (being how or howness—existentiaheteron … the now is in a certain way always the same and in a certain way never the same” (The Basic Problems of Phenomenology, 247-248).
In a word, Aristotle’s concept of time in terms of the now means that time’s being-now is also its otherhood.
The paradox of time as now, which can be restated from the foregoing interpretation as   “the now is never the same, it is always the same”  alights to us a fundamental problem of ontology, namely, how to think the relation between time and presence, that is, time and being.  For if time is determined on the basis of the now, and if the now is radically divided within itself in its very constitution such that it can never fully be present, it follows then that time does not belong to presence, it does not belong in the order of being.  Yet, there can be no presence, no being, without time.  This is the aporia of time and presence in Aristotle’s account of time.  In Book Theta of Metaphysics, Aristotle sets out a theory of causal powers by distinguishing two ways of being: being-in-dunamis and being-in-energeia.  For Aristotle, being-in-dunamis designates merely what is potential, whereas being-in-energeia is the being of what is actually present.  Hence, in Aristotle’s ontology, “to be” means “to be actual,” being-in-energeia.  Beings are what is.  Aristotle’s prioritization of being as being-in-energeia poses the problem of the ontology of time, the beingness or nonbeingness of time, which is the first question of Aristotle (poteron ton onton estin e ton me onton,217 b31).  If the now gives itself as the boundary-limit between a before and after, such that it can never be fully present as such, the now is not, that is to say, a nonbeing.  Derrida’s formulation of this Aristotelian aporia is “Time is not (among beings).”  There can be no presence or being without time, but insofar as time is the now, time is composed of nonbeings.  Derrida writes,
“The nun is the form from which time cannot ever depart, the form in which it cannot not be given; and yet the nun, in a certain sense, is not.  If one things time on the basis of the now, one must conclude that it is not.  The now is given simultaneously as that which is no longer and as that which is not yet.  It is what it is not, and is not what it is” (“Ousia and Gramme,” 39).
The now becomes a figure of the impossible in the sense that it is constituted as the impossibility of coexisting with another now; but because the now is the form (morphe) from which time actualizes itself, “the form in which it cannot not be given,” it is also what makes time possible.  Hence, the synthesis of two nows that is both the experience of temporality and the movement of temporalization means that time, as Derrida suggests, is the name for the “possibility of the impossible.”  Insofar as Aristotle’s account of time is a necessary component to a philosophy and science of nature, what, then, does it mean that the condition of possibility of all organic forms of nature (phusis), which are by definition entities in time and in the order of being, contains within it a nonbeing, an impossible presence, that is to say, time as the now?
Paul Nadal
Image: Wassily Kandinsky, Circles in a Circle, oil on canvas, 1923.
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This entry was published on February 17, 2011 at 4:05 PM. It’s filed under Critical Theory, Philosophy, Reading Notes, Time and Temporality and tagged , , , , , , , , , , , , , , , , , , . Bookmark the permalink. Follow any comments here with the RSS feed for this post.

5 thoughts on “What Is Time?: On Aristotle’s Definition of Time in Physics Book IV

  1. Pingback: Critical Times and the Time of Critique « Be Late.

  2. Hi Paul,

    I’ve just stumbled on your site, and think it is great. I just wanted to make on point here. You say towards the beginning that time is not a sensible thing for Aristotle. In one sense that is correct; it isn’t what he calls a proper sensible. However, in the beginning of “De Anima” III he includes time among the common sensibles, though things sensed through or by means of the proper sensibles.

    He’s weird on time because in “Physics” he has it as a measure, but in “Categories” he has it as its own category. The tricky part seems to be that as a measure it requires a soul to exist (what would measure it if there were souls?), but as a category it seems to be mind-independent. Perhaps he gets around the problem through recourse to potentiality. Certainly motion is mind-independent, and anything in motion is potentially measurable, and thus time exists apart from souls as potentially measurable motion.

    Either way, I’m just musing on your blog, which is probably kind of rude. It’s a great site. Keep it up!

  3. Pingback: Winter 2013: PHL 2500, Contemporary Issues « Course Materials

  4. Louis Brassard on said:

    You said: ” It seems impossible, however, to discuss change without making reference to time”. You probably have seen many computer graphic simulations where a form is modified with a parameter. Here we a form that is changing in function of a geometrical parameter and there is no time involved. The world is changing and these changes can be expressed relatively to each other without any reference to something called time. IN a commercial systems where we exchange merchandises it was usefull to invent a standard mechandise called a money unit. It is very practical for the market but we can make the market work without it. Time is a standard of change like money. It is usefull but it is not fundamental to reality.

  5. Thanks Paul.
    Of immense help to me for a lecture I am giving on the illusion of time.

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