The Basic Works of Aristotle (Modern Library Classics) (146 page)

10
     The infinite is either that which is incapable of being traversed because it is not its nature to be traversed (this corresponds to the sense in which the voice is ‘invisible’),
(35)
or that which admits only of incomplete traverse or scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited; further, a thing may be infinite in respect of addition or of subtraction, or both. The infinite cannot be a separate, independent thing.
[1066b]
For if it is neither a spatial magnitude nor a plurality, but infinity itself is its substance and not an accident of it, it will be indivisible; for the divisible is either magnitude or plurality. But if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this,
(5)
nor are we examining this sort of infinite, but the infinite as untraversable.
⁶³
Further, how can an infinite exist by itself, unless number and magnitude also exist by themselves—since infinity is an attribute of these?
⁶⁴
Further, if the infinite is an accident of something else,
(10)
it cannot be
qua
infinite an element in things, as the invisible is not an element in speech, though the voice is invisible.
⁶⁵
And evidently the infinite cannot exist actually. For then any part of it that might be taken would be infinite (for ‘to be infinite’ and ‘the infinite’ are the same, if the infinite is substance and not predicated of a subject). Therefore it is either indivisible, or if it is partible,
(15)
it is divisible into infinites; but the same thing cannot be many infinites (as a part of air is air, so a part of the infinite would be infinite, if the infinite is a substance and a principle). Therefore it must be impartible and indivisible. But the actually infinite cannot be indivisible; for it must be of a certain quantity. Therefore infinity belongs to its subject incidentally.
(20)
But if so, then (as we have said
⁶⁶
) it cannot be it that is a principle, but that of which it is an accident—the air or the even number.
⁶⁷

This inquiry is universal; but that the infinite is not
among sensible things
, is evident from the following argument. If the definition of a body is ‘that which is bounded by planes’, there cannot be an infinite body either sensible or intelligible; nor a separate and infinite number,
(25)
for number or that which has a number is numerable.
⁶⁸
Concretely, the truth is evident from the following argument. The infinite can neither be composite nor simple. For (
a
) it cannot be a composite body, since the elements are limited in multitude. For the contraries must be equal and no
one
of them must be infinite; for if one of the two bodies falls at all short of the other in potency,
(30)
the finite will be destroyed by the infinite. And that
each
should be infinite is impossible. For body is that which has extension in all directions, and the infinite is the boundlessly extended, so that if the infinite is a body it will be infinite in every direction. Nor (
b
) can the infinite body be one and simple—neither,
(35)
as some say,
⁶⁹
something apart from the elements, from which they generate these
⁷⁰
(for there is no such body apart from the elements; for everything can be resolved into that of which it consists, but no such product of analysis is observed except the simple bodies), nor fire nor any other of the elements.
[1067a]
For apart from the question how any of them could be infinite, the All, even if
it is finite, cannot either be or become any one of them, as Heraclitus says all things sometimes become fire. The same argument applies to this as to the One which the natural philosophers posit
besides
the elements.
(5)
For everything changes from contrary to contrary, e. g. from hot to cold.
⁷¹

Further, a sensible body is somewhere, and whole and part have the same proper place, e. g. the whole earth and part of the earth. Therefore if (
a
) the infinite body is homogeneous, it will be unmovable or it will be always moving. But this is impossible; for why should it rather rest,
(10)
or move, down, up, or anywhere, rather than anywhere else? e. g. if there were a clod which were part of an infinite body, where will this move or rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole place, then? And how? [This is impossible.] What then is its rest or its movement? It will either rest everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still. But (
b
) if the All has unlike parts,
(15)
the proper places of the parts are unlike also, and, firstly, the body of the All is not one except by contact, and, secondly, the parts will be either finite or infinite in variety of kind.
Finite
they cannot be; for then those of one kind will be infinite in quantity and those of another will not (if the All is infinite), e. g. fire or water would be infinite, but such an infinite element would be destruction to the contrary elements. But if the parts are
infinite
and simple,
(20)
their places also are infinite and there will be an infinite number of elements; and if this is impossible, and the places are finite, the All also must be limited.
⁷²

In general, there cannot be an infinite body and also a proper place for bodies, if every sensible body has either weight or lightness. For it must move either towards the middle or upwards,
(25)
and the infinite—either the whole or the half of it—cannot do either; for how will you divide it? Or how will part of the infinite be down and part up, or part extreme and part middle? Further, every sensible body is in a place, and there are six kinds of place,
⁷³
but these cannot exist in an infinite body. In general, if there cannot be an infinite place,
(30)
there cannot be an infinite body; [and there cannot be an infinite place,] for that which is in a place is somewhere, and this means either up or down or in one of the other directions, and each of these is a limit.
⁷⁴

The infinite is not the same in the sense that it is a single thing whether exhibited in distance or in movement or in time, but the
posterior among these is called infinite in virtue of its relation to the prior; i. e. a movement is called infinite in virtue of the distance covered by the spatial movement or alteration or growth,
(35)
and a time is called infinite because of the movement which occupies it.
⁷⁵

11
     
[1067b]
Of things which change, some change in an accidental sense, like that in which ‘the musical’ may be said to walk, and others are said, without qualification, to change, because something in them changes, i. e. the things that change in parts; the body becomes healthy, because the eye does. But there is something which is by its own nature moved directly,
(5)
and this is the essentially movable. The same distinction is found in the case of the mover; for it causes movement either in an accidental sense or in respect of a part of itself or essentially. There is something that directly causes movement; and there is something that is moved, also the time in which it is moved, and that from which and that into which it is moved.
⁷⁶
But the forms and the affections and the place, which are the terminals of the movement of moving things,
(10)
are unmovable, e. g. knowledge or heat; it is not heat that is a movement, but heating.
⁷⁷
Change which is not accidental is found not in all things, but between contraries, and their intermediates, and between contradictories. We may convince ourselves of this by induction.
⁷⁸

That which changes changes either from positive into positive,
(15)
or from negative into negative, or from positive into negative, or from negative into positive. (By positive I mean that which is expressed by an affirmative term.) Therefore there must be three changes; for that from negative into negative is not change,
(20)
because (since the terms are neither contraries nor contradictories) there is no opposition. The change from the negative into the positive which is its contradictory is generation—absolute change absolute generation, and partial change partial generation; and the change from positive to negative is destruction—absolute change absolute destruction, and partial change partial destruction.
(25)
If, then, ‘that which is not’ has several senses,
⁷⁹
and movement can attach neither to that which implies putting together or separating,
⁸⁰
nor to that which implies potency and is opposed to that which is in the full sense
⁸¹
(true, the not-white or not-good
can
be moved
incidentally
, for the not-white might be a man; but that which is not a particular thing at all can in no wise be moved), that which is not cannot be moved (and if this is so,
(30)
generation cannot be movement; for that which is not
is
generated; for even if we admit to the full that its generation is accidental, yet it is true to say that ‘not-being’ is predicable of that which is generated absolutely).
⁸²
Similarly
rest
cannot belong to that which is not. These consequences, then, turn out to be awkward, and also this, that everything that is moved is in a place,
(35)
but that which is not is not in a place; for then it would be somewhere. Nor is destruction movement; for the contrary of movement is movement or rest, but the contrary of destruction is generation. Since every movement is a change, and the kinds of change are the three named above,
⁸³
and of these those in the way of generation and destruction are not movements, and these are the changes from a thing to its contradictory, it follows that only the change from positive into positive is movement.
[1068a]
And the positives are either contrary or intermediate (for even privation must be regarded as contrary),
(5)
and are expressed by an affirmative term, e. g. ‘naked’ or ‘toothless’ or ‘black’.

12
     If the categories are classified as substance, quality, place, acting or being acted on, relation, quantity, there must be three kinds of movement—of quality, of quantity, of place. There is no movement in respect of substance (because there is nothing contrary to substance),
(10)
nor of relation (for it is possible that if one of two things in relation changes, the relative term which was true of the other thing ceases to be true, though this other does not change at all—so that their movement is accidental), nor of agent and patient, or mover and moved, because there is no movement of movement nor generation of generation,
(15)
nor, in general, change of change. For there
might
be movement of movement in two senses; (1) movement might be the subject moved, as a man is moved because he changes from pale to dark—so that on this showing movement, too, may be either heated or cooled or change its place or increase. But this is impossible; for change is not a subject. Or (2) some other subject might change from change into some other form of existence (e. g. a man from disease into health).
(20)
But this also is not possible except incidentally. For every movement is change from
something into something.
(25)
(And so are generation and destruction; only, these are changes into things opposed in certain ways while the other, movement, is into things opposed in another way.
⁸⁴
) A thing changes, then, at the same time from health into illness, and from this changes itself into another. Clearly, then, if it has become ill, it will have changed into whatever may be the other change concerned (though it
may
be at rest
⁸⁵
), and, further, into a determinate change each time; and that new change will be from something definite into some other definite thing; therefore it will be the opposite change,
(30)
that of growing well. We answer that this happens only incidentally; e. g. there is a change from the process of recollection to that of forgetting, only because
that to which the process attaches
is changing, now into a state of knowledge, now into one of ignorance.

Further, the process will go on to infinity, if there is to be change of change and coming to be of coming to be. What is true of the later,
(35)
then, must be true of the earlier; e. g.
[1068b]
if the simple coming to be was once coming to be, that which comes to be something was also once coming to be; therefore that which simply comes to be something was not yet in existence, but something which was coming to be coming to be something was already in existence. And this was once coming to be, so that at that time it was not yet coming to be something else. Now since of an infinite number of terms there is not a first, the first in this series will not exist, and therefore no following term will exist.
(5)
Nothing, then, can either come to be or move or change. Further, that which is capable of a movement is also capable of the contrary movement and rest, and that which comes to be also ceases to be. Therefore that which is coming to be is ceasing to be when it has come to be coming to be; for it cannot cease to be as soon as it is coming to be coming to be, nor after it has come to be; for that which is ceasing to be must
be
.
(10)
Further, there must be a matter underlying that which comes to be and changes. What will this be, then—what is it that becomes movement or becoming, as body or soul is that which suffers alteration? And, again, what is it that they move into? For it must be the movement or becoming of something from something into something. How, then, can this condition be fulfilled? There can be no learning of learning, and therefore no becoming of becoming.
⁸⁶

Since there is not movement either of substance or of relation or of activity and passivity,
(15)
it remains that movement is in respect of
quality and quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the substance (for even the differentia is a quality), but the passive quality, in virtue of which a thing is said to be acted on or to be incapable of being acted on.
⁸⁷
The immobile is either that which is wholly incapable of being moved,
(20)
or that which is moved with difficulty in a long time or begins slowly, or that which is of a nature to be moved and can be moved but is not moved when and where and as it would naturally be moved. This alone among immobiles I describe as being at rest; for rest is contrary to movement, so that it must be a privation, in that which is
receptive of movement.
⁸⁸

Things which are in one proximate place are
together in place
,
(25)
and things which are in different places are
apart
: things whose extremes are together
touch
: that at which a changing thing, if it changes continuously according to its nature, naturally arrives before it arrives at the extreme into which it is changing, is
between
.
⁸⁹
That which is most distant in a straight line is
contrary in place.
(30)
That is
successive
which is after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between it and that which it succeeds, e. g. lines in the case of a line, units in that of a unit, or a house in that of a house. (There is nothing to prevent a thing of some
other
class from being between.) For the successive succeeds something and is something later; ‘one’ does not succeed ‘two’,
(35)
nor the first day of the month the second.
[1069a]
That which, being successive, touches, is
contiguous
. (Since all change is between opposites, and these are either contraries or contradictories, and there is no middle term for contradictories, clearly that which is
between
is between contraries.) The
continuous
is a species of the contiguous.
(5)
I call two things continuous when the limits of each, with which they touch and by which they are kept together, become one and the same, so that plainly the continuous is found in the things out of which a unity naturally arises in virtue of their contact. And plainly the successive is the first of these concepts (for the successive does not necessarily touch, but that which touches is successive; and if a thing is continuous,
(10)
it touches, but if it touches, it is not necessarily continuous; and in things in which there is no touching, there is no organic unity); therefore a point is not the same as a unit; for contact belongs to points, but not to units, which have only succession; and there is something between two of the former, but not between two of the latter.
⁹⁰