Aristotle
to it; and each thing has but one opposite. Moreover the oppositions
between one motion (or one current--[Greek: phora/]) and another are
founded upon oppositions of place, which are three in number: (1)
Above and Below; (2) Before and Behind; (3) Right and Left. Now the
motion in circular rotation **from A to B is not opposite to that
from B to A: the opposition of motion is along the straight line
which joins the two; for an infinite number of different circles may
be drawn, not interfering with each other but all passing through the
same two points A and B. In the same circle, the opposition between
the current from A to B and that from B to A, is along the line of
diameter--not along the line of circumference. If one circular
current were really opposed to any other circular current, one or
other of the two would have existed to no purpose; for both have the
same object. That is to say: what is carried round in a circle, let
it begin from any point whatever, must necessarily come round equally
to all the opposite places, above, below, before, behind, right,
left. If the two (presumed) opposite circular currents were equal,
they would neutralize each other, and there would be no motion at all
of either of them. If one of the two were the more powerful, it would
extinguish the other; so that to suppose the existence of both is to
suppose that one or both exists in vain (_i.e._, can never be
realized). We say that a sandal exists in vain ([Greek: ma/tên]),
when it cannot be fastened on. But God and nature do nothing in vain
(ss. 1-8).
CH. 5.--Most of the ancient philosophers admitted an infinite body;
but this may be shown to be impossible. The question is very
important; for the consequences which follow from admitting the
Infinite as principium, affect our speculations concerning the whole
of Nature (s. 1).
Every body is of necessity either simple or compound. The infinite
body therefore, if it exists, must of necessity be either one or the
other. But there can be no infinite compound composed of simple
bodies finite in magnitude and in number: so that, if an infinite
body exist, it must be simple. We shall first enquire whether the
First Body, whose nature it is to move in a circle, can be infinite
in magnitude. Now, if it were infinite, the radii thrown out from the
centre would be infinite, and the distance between them would also be
infinite; that is, no finite peripheral line can be found touching
all the extremities of the radii without: if any such line be
assumed, you may always assume a greater. We call Number infinite,
because the greatest number cannot be given; and the like may be said
about this distance. Now, as an infinite distance cannot be passed
over, no circular motion passing over it is possible, so as to come
round to the point of departure. But we see plainly that the First
Body or the Heaven does come round in a circle; and it has been shown
by reasoning _à priori_ that there _is_ a variety of body whose
nature it is to move in a circle. Such a body therefore as the First
(revolving) Body cannot be infinite (ss. 2, 3).
Four other arguments are added, proving the same conclusion (s. 4,
seq.). One of them is: That an infinite square, circle, or sphere, is
an impossibility; each of these figures being defined or determined.
As there can be no infinite circle, so neither can an infinite body
be moved round in a circle (s. 7).
CH. 6.--As the First Body cannot be infinite, so neither can those
bodies be infinite whose nature it is to move to the centre and from
the centre--neither the centripetal nor the centrifugal body. For
these two currents are opposite in nature; opposite currents being
characterized by the opposite places to which they tend. But of two
opposites, if the one be fixed and determinate, the other must be
fixed and determinate also. Now the centre is determined; for the
centripetal body, let it fall from what height it will, can never
fall lower than the centre; and, since the centre is determined, the
upper region or extremity must also be determined. The places at each
extreme being thus determined, the intermediate space must be
determined also; otherwise there would exist motion undetermined or
infinite, which has been shown in a former treatise to be impossible
(Physica, VIII. viii.); and therefore that body which either is
therein, or may possibly be therein, must be determined. But it is a
fact that the centripetal body and the centrifugal body can be
therein; for centripetality and centrifugality are of the nature of
each respectively (ss. 1, 2).
Hence we see that there can be no infinite body. There are other
reasons also. As the centripetal body is heavy, if it be infinite,
its gravity must also be infinite; and, if gravity cannot be
infinite, neither can any heavy body be infinite. The like about any
light body, such as the centrifugal (s. 3).
He then shows (by a long process of reasoning, not easy to follow)
first, that there cannot be an infinite body with finite gravity;
next, that there can be no infinite gravity. Accordingly there can be
no infinite body at all, having gravity. At the end, he considers
that this is established, (1) by the partial arguments ([Greek: dia\
tô=n kata\ me/ros]) immediately preceding; (2) by the general
reasonings in his other treatises respecting first principles, in
which he explained the Infinite--in what sense it existed and did not
exist; (3) by an argument about the Infinite, upon which he touches
in the next chapter (ss. 4-13).
CH. 7.--Every body is of necessity either infinite or finite. If
infinite, it is as a whole either of like constituents or of unlike.
If the latter, either of a finite number of species, or of an
infinite number. The last is impossible, if our fundamental
assumptions are allowed to stand. For since the simple modes of
motion are limited in number, the simple bodies must be alike
limited; each simple mode of notion belonging to its own special
simple body, and each natural body having always its own natural
motion. But, if the Infinite be composed of a finite number of
species, each of these constituent parts must be infinite; that is,
water and fire must be infinite. Yet this too, is impossible; for we
have seen that there cannot be either infinite levity or infinite
gravity (the attributes of fire and water). Moreover, if these bodies
be infinite, the places which they occupy, and the motions which they
make, must also be infinite; but this also we have shown to be
inadmissible, if our fundamental assumptions are admitted. The
centripetal body cannot be carried to an infinite distance downward,
nor the centrifugal body to an infinite distance upward. That which
cannot come to pass, cannot be in course of coming to pass; thus, if
a thing cannot come to be white, or a cubit long, or domiciled in
Egypt, it cannot be in course of becoming white, or a cubit long, &c.
It cannot be in course of being carried to a terminus which cannot be
reached. It might be argued that fire, though discontinuous and
dispersed, might still be infinite, in the sum total of its different
masses. But body is that which is extended in every direction: how
can there be many bodies unlike to each other, yet each of them
infinite? Each of them, if infinite at all, ought to be infinite in
every direction (ss. 1-5).
We thus see that the Infinite cannot consist of unlike constituents.
But neither can it consist of constituents all similar. For, first,
there are only three simple motions, and one of the three it must
have; but we have shown that it cannot have either centripetal or
centrifugal motion (_i.e._, that it cannot have either infinite
gravity or infinite levity); nor can it again have circular motion,
for the Infinite cannot be carried in a circle: this would amount to
saying that the Heaven is infinite, which we have shown to be
impossible. The Infinite indeed cannot be moved in any way at all;
for, if moved, it must be moved either according to nature, or
contrary to nature (violently), and, if its present motion be
violent, it must have some other mode of motion which is natural to
it. But, if it have any such, this assumes that there exists some
other place belonging to it, into which it may be conveyed--an
obvious impossibility (ss. 6, 7).
Farthermore, the Infinite cannot act in any way upon the Finite, nor
be acted upon thereby (ss. 8-10). Nor can the Infinite be acted upon
in any way by the Infinite (ss. 11-12).
If then every perceptible body possesses powers, as agent or patient
or both, there can be no perceptible body which is infinite. But all
bodies which are in any place are perceptible; therefore no body
which is in any place can be infinite. There is no infinite body,
indeed there can be no body at all, outside of the Heaven; for that
which is outside of the Heaven is in a place. Even if perceivable
only up to a certain point ([Greek: me/chri tino/s]), even if merely
intelligible, it would still be in a place, and would therefore come
under the foregoing argument--that there is no body outside of the
Heaven (ss. 13, 14).
The foregoing reasoning may be summed up, in more general language
([Greek: logikô/teron]), as follows:--The Infinite assumed as
homogeneous cannot be moved in a circle, since the Infinite has no
centre; nor in a straight line, since this would imply a second
infinite place into which it must be moved according to nature, and a
third infinite place into which it must be moved against nature, and
since in either case the force which causes it to be moved must be
infinite. But we have already argued, in treating of Motion (Phys.
VIII. x.) that nothing finite can have infinite power, nothing
infinite can have finite power; and, if that which is moved according
to nature can also be moved contrary to nature, there must of
necessity be two Infinites--Movens and Motum. Yet what can that be
which causes the Infinite to move? If it cause itself to move, it
must be animated ([Greek: e)/mpsuchon]): but how can an infinite
animated being ([Greek: zô=|on]) exist? And, if there be anything
else which causes it to move, there must exist two Infinites, each
distinguished from the other in form and power (ss. 15-17).
Again, even if we admit the doctrine of Leukippus and
Demokritus--That the whole is not continuous, but discontinuous,
atoms divided by intervening spaces--still the Infinite is
inadmissible. For the nature and essence of these atoms is all the
same, though they are different from each other in figure and
arrangement; accordingly the motion of all must be the same: if one
is heavy or centripetal, all must be so alike; if one is light or
centrifugal, all must be so alike. But either of these motions would
imply the existence of centre and periphery; which does not consist
with an infinite whole. In the Infinite, there is neither centre nor
periphery; no terminus prefixed either for upward or downward motion;
no _own place_ either for centripetal or centrifugal matter.
Therefore in an infinite universe, there can be no motion at all
(ss. 18, 19).
CH. 8.--There cannot be more than one Kosmos. All things both rest
and are moved, either by violence, or according to nature. In that
place to which it is carried by nature, it also rests by nature: in
that place to which it is carried by violence, it rests by violence.
If the current which we see towards the centre is by violence, the
opposite current must be natural; if earth is carried by violence
from thence hitherward, its natural current must be from hence
thitherward; and, if being here it rests without violence, its
current towards here must be a natural one. For there is one only
which is natural. Now, if there be many Kosmi, they must be alike in