The Basic Works of Aristotle (Modern Library Classics) (52 page)

12
     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.
(30)
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
¹⁶
and as long or short.
[220b]
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,
(5)
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,
(10)
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,
(15)
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,
(20)
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,
(25)
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,
(30)
if the road is long—the time, too, if the movement, and the movement, if the time.

[221a]
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,
(5)
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,
(10)
(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 number.

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,
(15)
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 coexist with time, any more than to be in motion or in place means to coexist with motion or place.
(20)
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,
(25)
and that which is in motion that there is motion when
it
is.

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,
(30)
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.
[221b]

Hence, plainly, things which are always are not, as such, in time, for they are not contained by 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.
(5)

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.
(10)
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.
¹⁷

‘To be in number’ means that there is a number of the thing,
(15)
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,
(20)
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,
(25)
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,
(30)
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.
[222a]
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 non-existents whose opposites always are,
(5)
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.

13
      The ‘now’ is the link of time,
(10)
as has been said
¹⁸
(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,
(15)
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 same.

So one kind of ‘now’ is described in this way: another is when the time is
near
this kind of ‘now’.
(20)
‘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,
(25)
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,
(30)
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.
[222b]
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,
(5)
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’,
(10)
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.

‘Suddenly’ refers to what has departed from its former condition in
a time imperceptible because of its smallness; but it is the nature of
all
change to alter things from their former condition.
(15)
In time all things come into being and pass away; for which reason some called it the wisest of all things, but the Pythagorean Paron called it the most stupid, because in it we also forget; and his was the truer view. It is clear then that it must be in itself, as we said before
¹⁹
the condition of destruction rather than of coming into being (for change,
(20)
in itself, makes things depart from their former condition), and only incidentally of coming into being, and of being. A sufficient evidence of this is that nothing comes into being without itself moving somehow and acting, but a thing can be destroyed even if it does not move at all. And this is what, as a rule, we chiefly mean by a thing’s being destroyed by time.
(25)
Still, time does not work even this change; even this sort of change takes place
incidentally
in time.

We have stated, then, that time exists and what it is, and in how many senses we speak of the ‘now’, and what ‘at some time’, ‘lately’, ‘presently’ or ‘just’, ‘long ago’, and ‘suddenly’ mean.

14
      These distinctions having been drawn,
(30)
it is evident that every change and everything that moves is in time; for the distinction of faster and slower exists in reference to all change, since it is found in every instance. In the phrase ‘moving faster’ I refer to that which changes before another into the condition in question, when it moves over the same interval and with a regular movement; e. g. in the case of locomotion, if both things move along the circumference of a circle, or both along a straight line; and similarly in all other cases.
[223a]
(5)
But what is
before
is in time; for we say ‘before’ and ‘after’ with reference to the distance from the ‘now’, and the ‘now’ is the boundary of the past and the future; so that since ‘nows’ are in time, the before and the after will be in time too; for in that in which the ‘now’ is, the distance from the ‘now’ will also be. But ‘before’ is used contrariwise with reference to past and to future time; for in the past we call ‘before’ what is farther from the ‘now’,
(10)
and ‘after’ what is nearer, but in the future we call the nearer ‘before’ and the farther ‘after’. So that since the ‘before’ is in time, and every movement involves a ‘before’,
(15)
evidently every change and every movement is in time.

It is also worth considering how time can be related to the soul; and why time is thought to be in everything, both in earth and in sea and in heaven. Is it because it is an attribute, or state, of movement (since it is the number of movement) and all these things are
movable (for they are all in place), and time and movement are together,
(20)
both in respect of potentiality and in respect of actuality?

Whether if soul did not exist time would exist or not, is a question that may fairly be asked; for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can be, counted. But if nothing but soul, or in soul reason, is qualified to count,
(25)
there would not be time unless there were soul, but only that of which time is an attribute, i. e. if
movement
can exist without soul, and the before and after are attributes of movement, and time is these
qua
numerable.

One might also raise the question what sort of movement time is the number of. Must we not say ‘of
any
kind’? For things both come into being in time and pass away,
(30)
and grow, and are altered in time, and are moved locally; thus it is of each movement
qua
movement that time is the number. And so it is simply the number of continuous movement, not of any particular kind of it.

But other things as well may have been moved now, and there would be a number of each of the two movements.
[223b]
Is there another time, then, and will there be two equal times at once? Surely not. For a time that is both equal and simultaneous is one and the same time, and even those that are not simultaneous are one in kind; for if there were dogs, and horses, and seven of each, it would be the same number.
(5)
So, too, movements that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration; still the time of the two changes is the same if their number also is equal and simultaneous; and for this reason, while the movements are different and separate,
(10)
the time is everywhere the same, because the number of equal and simultaneous movements is everywhere one and the same.

Now there is such a thing as locomotion, and in locomotion there is included circular movement, and everything is measured by some one thing homogeneous with it, units by a unit, horses by a horse, and similarly times by some definite time, and, as we said,
²⁰
time is measured by motion as well as motion by time (this being so because by a motion definite in time the quantity both of the motion and of the time is measured): if,
(15)
then, what is first is the measure of everything homogeneous with it, regular circular motion is above all else the measure, because the number of this is the best known.
(20)
Now neither alteration nor increase nor coming into being can be regular, but locomotion can be. This also is why time is thought to be the
movement of the sphere, viz. because the other movements are measured by this, and time by this movement.

This also explains the common saying that human affairs form a circle,
(25)
and that there is a circle in all other things that have a natural movement and coming into being and passing away. This is because all other things are discriminated by time, and end and begin as though conforming to a cycle; for even time itself is thought to be a circle.
(30)
And this opinion again is held because time is the measure of this kind of locomotion and is itself measured by such. So that to say that the things that come into being form a circle is to say that there is a circle of time; and this is to say that it is measured by the circular movement; for apart from the measure nothing else to be measured is observed; the whole is just a plurality of measures.
[224a]

It is said rightly, too, that the number of the sheep and of the dogs is the same
number
if the two numbers are equal, but not the same
decad
or the same
ten;
just as the equilateral and the scalene are not the same
triangle,
(5)
yet they are the same
figure,
because they are both triangles. For things are called the same so-and-so if they do not differ by a differentia of that thing, but not if they do; e. g. triangle differs from triangle by a differentia of triangle, therefore they are different triangles; but they do not differ by a differentia of figure, but are in one and the same division of it. For a figure of one kind is a circle and a figure of another kind a triangle,
(10)
and a triangle of one kind is equilateral and a triangle of another kind scalene. They are the same figure, then, and that, triangle, but not the same triangle. Therefore the number of two groups also is the same number (for their number does not differ by a differentia of number), but it is not the same decad; for the things of which it is asserted differ; one group are dogs, and the other horses.

We have now discussed time—both time itself and the matters appropriate to the consideration of it.
(15)