Aristotle: Time is the Measure of Change
From Aristotle’s Physics (Book IV, part 10-13) For full text,
Next for discussion after the subjects mentioned is Time. The best plan will
be to begin by working out the difficulties connected with it, making use of
the current arguments. First, does it belong to the class of things that
exist or to that of things that do not exist? Then secondly, what is its
nature? To start, then: the following considerations would make one suspect
that it either does not exist at all or barely, and in an obscure way. One
part of it has been and is not, while the other is going to be and is not
yet. Yet time-both infinite time and any time you like to take-is made up of
these. One would naturally suppose that what is made up of things which do
not exist could have no share in reality.
Further, if a divisible thing is to exist, it is necessary that, when it
exists, all or some of its parts must exist. But of time some parts have
been, while others have to be, and no part of it is though it is divisible.
For what is 'now' is not a part: a part is a measure of the whole, which must
be made up of parts. Time, on the other hand, is not held to be made up of 'nows'.
Again, the 'now' which seems to bound the past and the future-does it always
remain one and the same or is it always other and other? It is hard to say.
(1) If it is always different and different, and if none of the parts in time
which are other and other are simultaneous (unless the one contains and the
other is contained, as the shorter time is by the longer), and if the 'now'
which is not, but formerly was, must have ceased-to-be at some time, the 'nows' too cannot be simultaneous with one another, but
the prior 'now' must always have ceased-to-be. But the prior 'now' cannot
have ceased-to-be in itself (since it then existed);
yet it cannot have ceased-to-be in another 'now'. For we may lay it down that
one 'now' cannot be next to another, any more than point to point. If then it
did not cease-to-be in the next 'now' but in another, it would exist
simultaneously with the innumerable 'nows' between
the two-which is impossible.
Yes, but (2) neither is it possible for the 'now' to remain always the same.
No determinate divisible thing has a single termination, whether it is
continuously extended in one or in more than one dimension: but the 'now' is
a termination, and it is possible to cut off a determinate time. Further, if
coincidence in time (i.e. being neither prior nor posterior) means to be 'in
one and the same "now"', then, if both what is before and what is
after are in this same 'now', things which happened ten thousand years ago
would be simultaneous with what has happened to-day, and nothing would be
before or after anything else.
This may serve as a statement of the difficulties about the attributes of
As to what time is or what is its nature, the traditional accounts give us as
little light as the preliminary problems which we have worked through.
Some assert that it is (1) the movement of the whole, others that it is (2)
the sphere itself.
(1) Yet part, too, of the revolution is a time, but it certainly is not a
revolution: for what is taken is part of a revolution, not a revolution.
Besides, if there were more heavens than one, the movement of any of them
equally would be time, so that there would be many times at the same time.
(2) Those who said that time is the sphere of the whole thought so, no doubt,
on the ground that all things are in time and all things are in the sphere of
the whole. The view is too naive for it to be worth while to consider the
impossibilities implied in it.
But as time is most usually supposed to be (3) motion and a kind of change,
we must consider this view.
Now (a) the change or movement of each thing is only in the thing which
changes or where the thing itself which moves or changes may chance to be.
But time is present equally everywhere and with all things.
Again, (b) change is always faster or slower, whereas time is not: for 'fast'
and 'slow' are defined by time-'fast' is what moves much in a short time,
'slow' what moves little in a long time; but time is not defined by time, by
being either a certain amount or a certain kind of it.
Clearly then it is not movement. (We need not distinguish at present between
'movement' and 'change'.)
But neither does time exist without change; for when the state of our own
minds does not change at all, or we have not noticed its changing, we do not
realize that time has elapsed, any more than those who are fabled to sleep
among the heroes in Sardinia do when they are awakened; for they connect the
earlier 'now' with the later and make them one, cutting out the interval
because of their failure to notice it. So, just as, if the 'now' were not
different but one and the same, there would not have been time, so too when
its difference escapes our notice the interval does not seem to be time. If,
then, the non-realization of the existence of time happens to us when we do
not distinguish any change, but the soul seems to stay in one indivisible
state, and when we perceive and distinguish we say time has elapsed, evidently
time is not independent of movement and change. It is evident, then, that
time is neither movement nor independent of movement.
We must take this as our starting-point and try to discover-since we wish to
know what time is-what exactly it has to do with movement.
Now we perceive movement and time together: for even when it is dark and we
are not being affected through the body, if any movement takes place in the
mind we at once suppose that some time also has elapsed; and not only that
but also, when some time is thought to have passed, some movement also along
with it seems to have taken place. Hence time is either movement or something
that belongs to movement. Since then it is not movement, it must be the
But what is moved is moved from something to something, and all magnitude is
continuous. Therefore the movement goes with the magnitude. Because the
magnitude is continuous, the movement too must be continuous, and if the
movement, then the time; for the time that has passed is always thought to be
in proportion to the movement.
The distinction of 'before' and 'after' holds primarily, then, in place; and
there in virtue of relative position. Since then 'before' and 'after' hold in
magnitude, they must hold also in movement, these corresponding to those. But
also in time the distinction of 'before' and 'after' must hold, for time and
movement always correspond with each other. The 'before' and 'after' in
motion is identical in substratum with motion yet differs from it in
definition, and is not identical with motion.
But we apprehend time only when we have marked motion, marking it by 'before'
and 'after'; and it is only when we have perceived 'before' and 'after' in
motion that we say that time has elapsed. Now we mark them by judging that A
and B are different, and that some third thing is intermediate to them. When
we think of the extremes as different from the middle and the mind pronounces
that the 'nows' are two, one before and one after,
it is then that we say that there is time, and this that we say is time. For
what is bounded by the 'now' is thought to be time-we may assume this.
When, therefore, we perceive the 'now' one, and neither as before and after
in a motion nor as an identity but in relation to a 'before' and an 'after',
no time is thought to have elapsed, because there has been no motion either.
On the other hand, when we do perceive a 'before' and an 'after', then we say
that there is time. For time is just this-number of motion in respect of
'before' and 'after'.
Hence time is not movement, but only movement in so far as it admits of
enumeration. A proof of this: we discriminate the more or the less by number,
but more or less movement by time. Time then is a kind of number. (Number, we
must note, is used in two senses-both of what is counted or the countable and
also of that with which we count. Time obviously is what is counted, not that
with which we count: there are different kinds of thing.) Just as motion is a
perpetual succession, so also is time. But every simultaneous time is
self-identical; for the 'now' as a subject is an identity, but it accepts
different attributes. The 'now' measures time, in so far as time involves the
'before and after'.
The 'now' in one sense is the same, in another it is not the same. In so far
as it is in succession, it is different (which is just what its being was
supposed to mean), but its substratum is an identity: for motion, as was
said, goes with magnitude, and time, as we maintain, with motion. Similarly,
then, there corresponds to the point the body which is carried along, and by
which we are aware of the motion and of the 'before and after' involved in
it. This is an identical substratum (whether a point or a stone or something
else of the kind), but it has different attributes as the sophists assume
that Coriscus' being in the Lyceum is a different
thing from Coriscus' being in the market-place. And
the body which is carried along is different, in so far as it is at one time
here and at another there. But the 'now' corresponds to the body that is
carried along, as time corresponds to the motion. For it is by means of the
body that is carried along that we become aware of the 'before and after' the
motion, and if we regard these as countable we get the 'now'. Hence in these
also the 'now' as substratum remains the same (for it is what is before and
after in movement), but what is predicated of it is different; for it is in
so far as the 'before and after' is numerable that we get the 'now'. This is
what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is
carried. What is carried is a real thing, the movement is not. Thus what is
called 'now' in one sense is always the same; in another it is not the same:
for this is true also of what is carried.
Clearly, too, if there were no time, there would be no 'now', and vice versa.
just as the moving body and its locomotion involve
each other mutually, so too do the number of the moving body and the number
of its locomotion. For the number of the locomotion is time, while the 'now'
corresponds to the moving body, and is like the unit of number.
Time, then, also is both made continuous by the 'now' and divided at it. For
here too there is a correspondence with the locomotion and the moving body.
For the motion or locomotion is made one by the thing which is moved, because
it is one-not because it is one in its own nature (for there might be pauses
in the movement of such a thing)-but because it is one in definition: for
this determines the movement as 'before' and 'after'. Here, too there is a
correspondence with the point; for the point also both connects and
terminates the length-it is the beginning of one and the end of another. But
when you take it in this way, using the one point as two, a pause is
necessary, if the same point is to be the beginning and the end. The 'now' on
the other hand, since the body carried is moving, is always different.
Hence time is not number in the sense in which there is 'number' of the same
point because it is beginning and end, but rather as the extremities of a
line form a number, and not as the parts of the line do so, both for the
reason given (for we can use the middle point as two, so that on that analogy
time might stand still), and further because obviously the 'now' is no part
of time nor the section any part of the movement, any more than the points
are parts of the line-for it is two lines that are parts of one line.
In so far then as the 'now' is a boundary, it is not time, but an attribute
of it; in so far as it numbers, it is number; for boundaries belong only to
that which they bound, but number (e.g. ten) is the number of these horses,
and belongs also elsewhere.
It is clear, then, that time is 'number of movement in respect of the before
and after', and is continuous since it is an attribute of what is continuous.
The smallest number, in the strict sense of the word 'number', is two. But of
number as concrete, sometimes there is a minimum, sometimes not: e.g. of a 'line',
the smallest in respect of multiplicity is two (or, if you like, one), but in
respect of size there is no minimum; for every line is divided ad infinitum.
Hence it is so with time. In respect of number the minimum is one (or two);
in point of extent there is no minimum.
It is clear, too, that time is not described as fast or slow, but as many or
few and as long or short. For as continuous it is long or short and as a
number many or few, but it is not fast or slow-any more than any number with
which we number is fast or slow.
Further, there is the same time everywhere at once, but not the same time
before and after, for while the present change is one, the change which has
happened and that which will happen are different. Time is not number with which
we count, but the number of things which are counted, and this according as
it occurs before or after is always different, for the 'nows'
are different. And the number of a hundred horses and a hundred men is the
same, but the things numbered are different-the horses from the men. Further,
as a movement can be one and the same again and again, so too can time, e.g.
a year or a spring or an autumn.
Not only do we measure the movement by the time, but also the time by the
movement, because they define each other. The time marks the movement, since
it is its number, and the movement the time. We describe the time as much or
little, measuring it by the movement, just as we know the number by what is
numbered, e.g. the number of the horses by one horse as the unit. For we know
how many horses there are by the use of the number; and again by using the
one horse as unit we know the number of the horses itself. So it is with the
time and the movement; for we measure the movement by the time and vice
versa. It is natural that this should happen; for the movement goes with the
distance and the time with the movement, because they are quanta and
continuous and divisible. The movement has these attributes because the
distance is of this nature, and the time has them because of the movement.
And we measure both the distance by the movement and the movement by the
distance; for we say that the road is long, if the journey is long, and that
this is long, if the road is long-the time, too, if the movement, and the movement,
if the time.
Time is a measure of motion and of being moved, and it measures the motion by
determining a motion which will measure exactly the whole motion, as the
cubit does the length by determining an amount which will measure out the
whole. Further 'to be in time' means for movement, that both it and its
essence are measured by time (for simultaneously it measures both the
movement and its essence, and this is what being in time means for it, that
its essence should be measured).
Clearly then 'to be in time' has the same meaning for other things also,
namely, that their being should be measured by time. 'To be in time' is one
of two things: (1) to exist when time exists, (2) as we say of some things
that they are 'in number'. The latter means either what is a part or mode of
number-in general, something which belongs to number-or that things have a
Now, since time is number, the 'now' and the 'before' and the like are in
time, just as 'unit' and 'odd' and 'even' are in number, i.e. in the sense
that the one set belongs to number, the other to time. But things are in time
as they are in number. If this is so, they are contained by time as things in
place are contained by place.
Plainly, too, to be in time does not mean to co-exist with time, any more
than to be in motion or in place means to co-exist with motion or place. For
if 'to be in something' is to mean this, then all things will be in anything,
and the heaven will be in a grain; for when the grain is, then also is the
heaven. But this is a merely incidental conjunction, whereas the other is
necessarily involved: that which is in time necessarily involves that there
is time when it is, and that which is in motion that there is motion when it
Since what is 'in time' is so in the same sense as what is in number is so, a
time greater than everything in time can be found. So it is necessary that
all the things in time should be contained by time, just like other things
also which are 'in anything', e.g. the things 'in place' by place.
A thing, then, will be affected by time, just as we are accustomed to say
that time wastes things away, and that all things grow old through time, and
that there is oblivion owing to the lapse of time, but we do not say the same
of getting to know or of becoming young or fair. For time is by its nature
the cause rather of decay, since it is the number of change, and change
removes what is.
Hence, plainly, things which are always are not, as such, in time, for they
are not contained time, nor is their being measured
by time. A proof of this is that none of them is affected by time, which
indicates that they are not in time.
Since time is the measure of motion, it will be the measure of rest
too-indirectly. For all rest is in time. For it does not follow that what is
in time is moved, though what is in motion is necessarily moved. For time is
not motion, but 'number of motion': and what is at rest, also, can be in the
number of motion. Not everything that is not in motion can be said to be 'at
rest'-but only that which can be moved, though it actually is not moved, as
was said above.
'To be in number' means that there is a number of the thing, and that its
being is measured by the number in which it is. Hence if a thing is 'in time'
it will be measured by time. But time will measure what is moved and what is
at rest, the one qua moved, the other qua at rest; for it will measure their
motion and rest respectively.
Hence what is moved will not be measurable by the time simply in so far as it
has quantity, but in so far as its motion has quantity. Thus none of the
things which are neither moved nor at rest are in
time: for 'to be in time' is 'to be measured by time', while time is the
measure of motion and rest.
Plainly, then, neither will everything that does not exist be in time, i.e.
those non-existent things that cannot exist, as the diagonal cannot be
commensurate with the side.
Generally, if time is directly the measure of motion and indirectly of other
things, it is clear that a thing whose existence is measured by it will have
its existence in rest or motion. Those things therefore which are subject to
perishing and becoming-generally, those which at one time exist, at another
do not-are necessarily in time: for there is a greater time which will extend
both beyond their existence and beyond the time which measures their
existence. Of things which do not exist but are contained by time some were,
e.g. Homer once was, some will be, e.g. a future event; this depends on the
direction in which time contains them; if on both, they have both modes of
existence. As to such things as it does not contain in any way, they neither
were nor are nor will be. These are those nonexistents
whose opposites always are, as the incommensurability of the diagonal always
is-and this will not be in time. Nor will the commensurability, therefore;
hence this eternally is not, because it is contrary to what eternally is. A
thing whose contrary is not eternal can be and not be, and it is of such
things that there is coming to be and passing away.
The 'now' is the link of time, as has been said (for it connects past and
future time), and it is a limit of time (for it is the beginning of the one
and the end of the other). But this is not obvious as it is with the point,
which is fixed. It divides potentially, and in so far as it is dividing the
'now' is always different, but in so far as it connects it is always the
same, as it is with mathematical lines. For the intellect it is not always
one and the same point, since it is other and other when one divides the
line; but in so far as it is one, it is the same in every respect.
So the 'now' also is in one way a potential dividing of time, in another the
termination of both parts, and their unity. And the dividing and the uniting
are the same thing and in the same reference, but in essence they are not the
So one kind of 'now' is described in this way: another is when the time is
near this kind of 'now'. 'He will come now' because he will come to-day; 'he
has come now' because he came to-day. But the things in the Iliad have not
happened 'now', nor is the flood 'now'-not that the time from now to them is
not continuous, but because they are not near.
'At some time' means a time determined in relation to the first of the two
types of 'now', e.g. 'at some time' Troy was taken, and 'at some time' there
will be a flood; for it must be determined with reference to the 'now'. There
will thus be a determinate time from this 'now' to that, and there was such
in reference to the past event. But if there be no time which is not
'sometime', every time will be determined.
Will time then fail? Surely not, if motion always exists. Is time then always
different or does the same time recur? Clearly time
is, in the same way as motion is. For if one and the same motion sometimes
recurs, it will be one and the same time, and if not, not.
Since the 'now' is an end and a beginning of time, not of the same time
however, but the end of that which is past and the beginning of that which is
to come, it follows that, as the circle has its convexity and its concavity,
in a sense, in the same thing, so time is always at a beginning and at an
end. And for this reason it seems to be always different; for the 'now' is
not the beginning and the end of the same thing; if it were, it would be at
the same time and in the same respect two opposites. And time will not fail;
for it is always at a beginning.
'Presently' or 'just' refers to the part of future time which is near the
indivisible present 'now' ('When do you walk? 'Presently', because the time
in which he is going to do so is near), and to the part of past time which is
not far from the 'now' ('When do you walk?' 'I have just been walking'). But
to say that Troy
has just been taken-we do not say that, because it is too far from the 'now'.
'Lately', too, refers to the part of past time which is near the present
'now'. 'When did you go?' 'Lately', if the time is near the existing now.
'Long ago' refers to the distant past.