Heavens E-book
Author: Aristotle
Genre: Biology / Medicine, Philosophy, Science
350 BC
ON THE HEAVENS
by Aristotle
translated by J. L. Stocks
Electronically Enhanced Text (c) Copyright 1996, World Library(R)
Book I
1
-
THE science which has to do with nature clearly concerns itself
for the most part with bodies and magnitudes and their properties
and movements, but also with the principles of this sort of substance,
as many as they may be. For of things constituted by nature some are
bodies and magnitudes, some possess body and magnitude, and some are
principles of things which possess these. Now a continuum is that
which is divisible into parts always capable of subdivision, and a
body is that which is every way divisible. A magnitude if divisible
one way is a line, if two ways a surface, and if three a body.
Beyond these there is no other magnitude, because the three dimensions
are all that there are, and that which is divisible in three
directions is divisible in all. For, as the Pythagoreans say, the
world and all that is in it is determined by the number three, since
beginning and middle and end give the number of an 'all', and the
number they give is the triad. And so, having taken these three from
nature as (so to speak) laws of it, we make further use of the
number three in the worship of the Gods. Further, we use the terms
in practice in this way. Of two things, or men, we say 'both', but not
'all': three is the first number to which the term 'all' has been
appropriated. And in this, as we have said, we do but follow the
lead which nature gives. Therefore, since 'every' and 'all' and
'complete' do not differ from one another in respect of form, but
only, if at all, in their matter and in that to which they are
applied, body alone among magnitudes can be complete. For it alone
is determined by the three dimensions, that is, is an 'all'. But if it
is divisible in three dimensions it is every way divisible, while
the other magnitudes are divisible in one dimension or in two alone:
for the divisibility and continuity of magnitudes depend upon the
number of the dimensions, one sort being continuous in one
direction, another in two, another in all. All magnitudes, then, which
are divisible are also continuous. Whether we can also say that
whatever is continuous is divisible does not yet, on our present
grounds, appear. One thing, however, is clear. We cannot pass beyond
body to a further kind, as we passed from length to surface, and
from surface to body. For if we could, it would cease to be true
that body is complete magnitude. We could pass beyond it only in
virtue of a defect in it; and that which is complete cannot be
defective, since it has being in every respect. Now bodies which are
classed as parts of the whole are each complete according to our
formula, since each possesses every dimension. But each is
determined relatively to that part which is next to it by contact, for
which reason each of them is in a sense many bodies. But the whole
of which they are parts must necessarily be complete, and thus, in
accordance with the meaning of the word, have being, not in some
respect only, but in every respect.
2
-
The question as to the nature of the whole, whether it is infinite
in size or limited in its total mass, is a matter for subsequent
inquiry. We will now speak of those parts of the whole which are
specifically distinct. Let us take this as our starting-point. All
natural bodies and magnitudes we hold to be, as such, capable of
locomotion; for nature, we say, is their principle of movement. But
all movement that is in place, all locomotion, as we term it, is
either straight or circular or a combination of these two, which are
the only simple movements. And the reason of this is that these two,
the straight and the circular line, are the only simple magnitudes.
Now revolution about the centre is circular motion, while the upward
and downward movements are in a straight line, 'upward' meaning motion
away from the centre, and 'downward' motion towards it. All simple
motion, then, must be motion either away from or towards or about
the centre. This seems to be in exact accord with what we said
above: as body found its completion in three dimensions, so its
movement completes itself in three forms.
Bodies are either simple or compounded of such; and by simple bodies
I mean those which possess a principle of movement in their own
nature, such as fire and earth with their kinds, and whatever is
akin to them. Necessarily, then, movements also will be either
simple or in some sort compound-simple in the case of the simple
bodies, compound in that of the composite-and in the latter case the
motion will be that of the simple body which prevails in the
composition. Supposing, then, that there is such a thing as simple
movement, and that circular movement is an instance of it, and that
both movement of a simple body is simple and simple movement is of a
simple body (for if it is movement of a compound it will be in
virtue of a prevailing simple element), then there must necessarily be
some simple body which revolves naturally and in virtue of its own
nature with a circular movement. By constraint, of course, it may be
brought to move with the motion of something else different from
itself, but it cannot so move naturally, since there is one sort of
movement natural to each of the simple bodies. Again, if the unnatural
movement is the contrary of the natural and a thing can have no more
than one contrary, it will follow that circular movement, being a
simple motion, must be unnatural, if it is not natural, to the body
moved. If then (1) the body, whose movement is circular, is fire or
some other element, its natural motion must be the contrary of the
circular motion. But a single thing has a single contrary; and
upward and downward motion are the contraries of one another. If, on
the other hand, (2) the body moving with this circular motion which is
unnatural to it is something different from the elements, there will
be some other motion which is natural to it. But this cannot be. For
if the natural motion is upward, it will be fire or air, and if
downward, water or earth. Further, this circular motion is necessarily
primary. For the perfect is naturally prior to the imperfect, and
the circle is a perfect thing. This cannot be said of any straight
line:-not of an infinite line; for, if it were perfect, it would
have a limit and an end: nor of any finite line; for in every case
there is something beyond it, since any finite line can be extended.
And so, since the prior movement belongs to the body which naturally
prior, and circular movement is prior to straight, and movement in a
straight line belongs to simple bodies-fire moving straight upward and
earthy bodies straight downward towards the centre-since this is so,
it follows that circular movement also must be the movement of some
simple body. For the movement of composite bodies is, as we said,
determined by that simple body which preponderates in the composition.
These premises clearly give the conclusion that there is in nature
some bodily substance other than the formations we know, prior to them
all and more divine than they. But it may also be proved as follows.
We may take it that all movement is either natural or unnatural, and
that the movement which is unnatural to one body is natural to
another-as, for instance, is the case with the upward and downward
movements, which are natural and unnatural to fire and earth
respectively. It necessarily follows that circular movement, being
unnatural to these bodies, is the natural movement of some other.
Further, if, on the one hand, circular movement is natural to
something, it must surely be some simple and primary body which is
ordained to move with a natural circular motion, as fire is ordained
to fly up and earth down. If, on the other hand, the movement of the
rotating bodies about the centre is unnatural, it would be
remarkable and indeed quite inconceivable that this movement alone
should be continuous and eternal, being nevertheless contrary to
nature. At any rate the evidence of all other cases goes to show
that it is the unnatural which quickest passes away. And so, if, as
some say, the body so moved is fire, this movement is just as
unnatural to it as downward movement; for any one can see that fire
moves in a straight line away from the centre. On all these grounds,
therefore, we may infer with confidence that there is something beyond
the bodies that are about us on this earth, different and separate
from them; and that the superior glory of its nature is
proportionate to its distance from this world of ours.
3
-
In consequence of what has been said, in part by way of assumption
and in part by way of proof, it is clear that not every body either
possesses lightness or heaviness. As a preliminary we must explain
in what sense we are using the words 'heavy' and 'light',
sufficiently, at least, for our present purpose: we can examine the
terms more closely later, when we come to consider their essential
nature. Let us then apply the term 'heavy' to that which naturally
moves towards the centre, and 'light' to that which moves naturally
away from the centre. The heaviest thing will be that which sinks to
the bottom of all things that move downward, and the lightest that
which rises to the surface of everything that moves upward. Now,
necessarily, everything which moves either up or down possesses
lightness or heaviness or both-but not both relatively to the same
thing: for things are heavy and light relatively to one another;
air, for instance, is light relatively to water, and water light
relatively to earth. The body, then, which moves in a circle cannot
possibly possess either heaviness or lightness. For neither
naturally nor unnaturally can it move either towards or away from
the centre. Movement in a straight line certainly does not belong to
it naturally, since one sort of movement is, as we saw, appropriate to
each simple body, and so we should be compelled to identify it with
one of the bodies which move in this way. Suppose, then, that the
movement is unnatural. In that case, if it is the downward movement
which is unnatural, the upward movement will be natural; and if it
is the upward which is unnatural, the downward will be natural. For we
decided that of contrary movements, if the one is unnatural to
anything, the other will be natural to it. But since the natural
movement of the whole and of its part of earth, for instance, as a
whole and of a small clod-have one and the same direction, it results,
in the first place, that this body can possess no lightness or
heaviness at all (for that would mean that it could move by its own
nature either from or towards the centre, which, as we know, is
impossible); and, secondly, that it cannot possibly move in the way of
locomotion by being forced violently aside in an upward or downward
direction. For neither naturally nor unnaturally can it move with
any other motion but its own, either itself or any part of it, since
the reasoning which applies to the whole applies also to the part.
It is equally reasonable to assume that this body will be
ungenerated and indestructible and exempt from increase and
alteration, since everything that comes to be comes into being from
its contrary and in some substrate, and passes away likewise in a
substrate by the action of the contrary into the contrary, as we
explained in our opening discussions. Now the motions of contraries
are contrary. If then this body can have no contrary, because there
can be no contrary motion to the circular, nature seems justly to have
exempted from contraries the body which was to be ungenerated and
indestructible. For it is in contraries that generation and decay
subsist. Again, that which is subject to increase increases upon
contact with a kindred body, which is resolved into its matter. But
there is nothing out of which this body can have been generated. And
if it is exempt from increase and diminution, the same reasoning leads
us to suppose that it is also unalterable. For alteration is
movement in respect of quality; and qualitative states and
dispositions, such as health and disease, do not come into being
without changes of properties. But all natural bodies which change
their properties we see to be subject without exception to increase
and diminution. This is the case, for instance, with the bodies of
animals and their parts and with vegetable bodies, and similarly
also with those of the elements. And so, if the body which moves
with a circular motion cannot admit of increase or diminution, it is
reasonable to suppose that it is also unalterable.
The reasons why the primary body is eternal and not subject to
increase or diminution, but unaging and unalterable and unmodified,
will be clear from what has been said to any one who believes in our
assumptions. Our theory seems to confirm experience and to be
confirmed by it. For all men have some conception of the nature of the
gods, and all who believe in the existence of gods at all, whether
barbarian or Greek, agree in allotting the highest place to the deity,
surely because they suppose that immortal is linked with immortal
and regard any other supposition as inconceivable. If then there is,
as there certainly is, anything divine, what we have just said about
the primary bodily substance was well said. The mere evidence of the
senses is enough to convince us of this, at least with human
certainty. For in the whole range of time past, so far as our
inherited records reach, no change appears to have taken place
either in the whole scheme of the outermost heaven or in any of its
proper parts. The common name, too, which has been handed down from
our distant ancestors even to our own day, seems to show that they
conceived of it in the fashion which we have been expressing. The same
ideas, one must believe, recur in men's minds not once or twice but
again and again. And so, implying that the primary body is something
else beyond earth, fire, air, and water, they gave the highest place a
name of its own, aither, derived from the fact that it 'runs always'
for an eternity of time. Anaxagoras, however, scandalously misuses
this name, taking aither as equivalent to fire.
It is also clear from what has been said why the number of what we
call simple bodies cannot be greater than it is. The motion of a
simple body must itself be simple, and we assert that there are only
these two simple motions, the circular and the straight, the latter
being subdivided into motion away from and motion towards the centre.
4
-
That there is no other form of motion opposed as contrary to the
circular may be proved in various ways. In the first place, there is
an obvious tendency to oppose the straight line to the circular. For
concave and convex are a not only regarded as opposed to one
another, but they are also coupled together and treated as a unity
in opposition to the straight. And so, if there is a contrary to
circular motion, motion in a straight line must be recognized as
having the best claim to that name. But the two forms of rectilinear
motion are opposed to one another by reason of their places; for up
and down is a difference and a contrary opposition in place. Secondly,
it may be thought that the same reasoning which holds good of the
rectilinear path applies also the circular, movement from A to B being
opposed as contrary to movement from B to A. But what is meant is
still rectilinear motion. For that is limited to a single path,
while the circular paths which pass through the same two points are
infinite in number. Even if we are confined to the single semicircle
and the opposition is between movement from C to D and from D to C
along that semicircle, the case is no better. For the motion is the
same as that along the diameter, since we invariably regard the
distance between two points as the length of the straight line which
joins them. It is no more satisfactory to construct a circle and treat
motion 'along one semicircle as contrary to motion along the other.
For example, taking a complete circle, motion from E to F on the
semicircle G may be opposed to motion from F to E on the semicircle H.
But even supposing these are contraries, it in no way follows that the
reverse motions on the complete circumference contraries. Nor again
can motion along the circle from A to B be regarded as the contrary of
motion from A to C: for the motion goes from the same point towards
the same point, and contrary motion was distinguished as motion from a
contrary to its contrary. And even if the motion round a circle is the
contrary of the reverse motion, one of the two would be ineffective:
for both move to the same point, because that which moves in a circle,
at whatever point it begins, must necessarily pass through all the
contrary places alike. (By contrarieties of place I mean up and
down, back and front, and right and left; and the contrary oppositions
of movements are determined by those of places.) One of the motions,
then, would be ineffective, for if the two motions were of equal
strength, there would be no movement either way, and if one of the two
were preponderant, the other would be inoperative. So that if both
bodies were there, one of them, inasmuch as it would not be moving
with its own movement, would be useless, in the sense in which a
shoe is useless when it is not worn. But God and nature create nothing
that has not its use.
5
-
This being clear, we must go on to consider the questions which
remain. First, is there an infinite body, as the majority of the
ancient philosophers thought, or is this an impossibility? The
decision of this question, either way, is not unimportant, but
rather all-important, to our search for the truth. It is this
problem which has practically always been the source of the
differences of those who have written about nature as a whole. So it
has been and so it must be; since the least initial deviation from the
truth is multiplied later a thousandfold. Admit, for instance, the
existence of a minimum magnitude, and you will find that the minimum
which you have introduced, small as it is, causes the greatest
truths of mathematics to totter. The reason is that a principle is
great rather in power than in extent; hence that which was small at
the start turns out a giant at the end. Now the conception of the
infinite possesses this power of principles, and indeed in the
sphere of quantity possesses it in a higher degree than any other
conception; so that it is in no way absurd or unreasonable that the
assumption that an infinite body exists should be of peculiar moment
to our inquiry. The infinite, then, we must now discuss, opening the
whole matter from the beginning.
Every body is necessarily to be classed either as simple or as
composite; the infinite body, therefore, will be either simple or
composite.
But it is clear, further, that if the simple bodies are finite,
the composite must also be finite, since that which is composed of
bodies finite both in number and in magnitude is itself finite in
respect of number and magnitude: its quantity is in fact the same as
that of the bodies which compose it. What remains for us to
consider, then, is whether any of the simple bodies can be infinite in
magnitude, or whether this is impossible. Let us try the primary
body first, and then go on to consider the others.
The body which moves in a circle must necessarily be finite in every
respect, for the following reasons. (1) If the body so moving is
infinite, the radii drawn from the centre will be infinite. But the
space between infinite radii is infinite: and by the space between the
radii I mean the area outside which no magnitude which is in contact
with the two lines can be conceived as falling. This, I say, will be
infinite: first, because in the case of finite radii it is always
finite; and secondly, because in it one can always go on to a width
greater than any given width; thus the reasoning which forces us to
believe in infinite number, because there is no maximum, applies
also to the space between the radii. Now the infinite cannot be
traversed, and if the body is infinite the interval between the
radii is necessarily infinite: circular motion therefore is an
impossibility. Yet our eyes tell us that the heavens revolve in a
circle, and by argument also we have determined that there is
something to which circular movement belongs.
(2) Again, if from a finite time a finite time be subtracted, what
remains must be finite and have a beginning. And if the time of a
journey has a beginning, there must be a beginning also of the
movement, and consequently also of the distance traversed. This
applies universally. Take a line, ACE, infinite in one direction, E,
and another line, BB, infinite in both directions. Let ACE describe
a circle, revolving upon C as centre. In its movement it will cut BB
continuously for a certain time. This will be a finite time, since the
total time is finite in which the heavens complete their circular
orbit, and consequently the time subtracted from it, during which
the one line in its motion cuts the other, is also finite. Therefore
there will be a point at which ACE began for the first time to cut BB.
This, however, is impossible. The infinite, then, cannot revolve in
a circle; nor could the world, if it were infinite.
(3) That the infinite cannot move may also be shown as follows.
Let A be a finite line moving past the finite line, B. Of necessity
A will pass clear of B and B of A at the same moment; for each
overlaps the other to precisely the same extent. Now if the two were
both moving, and moving in contrary directions, they would pass
clear of one another more rapidly; if one were still and the other
moving past it, less rapidly; provided that the speed of the latter
were the same in both cases. This, however, is clear: that it is
impossible to traverse an infinite line in a finite time. Infinite
time, then, would be required. (This we demonstrated above in the
discussion of movement.) And it makes no difference whether a finite
is passing by an infinite or an infinite by a finite. For when A is
passing B, then B overlaps A and it makes no difference whether B is
moved or unmoved, except that, if both move, they pass clear of one
another more quickly. It is, however, quite possible that a moving
line should in certain cases pass one which is stationary quicker than
it passes one moving in an opposite direction. One has only to imagine
the movement to be slow where both move and much faster where one is
stationary. To suppose one line stationary, then, makes no
difficulty for our argument, since it is quite possible for A to
pass B at a slower rate when both are moving than when only one is.
If, therefore, the time which the finite moving line takes to pass the
other is infinite, then necessarily the time occupied by the motion of
the infinite past the finite is also infinite. For the infinite to
move at all is thus absolutely impossible; since the very smallest
movement conceivable must take an infinity of time. Moreover the
heavens certainly revolve, and they complete their circular orbit in a
finite time; so that they pass round the whole extent of any line
within their orbit, such as the finite line AB. The revolving body,
therefore, cannot be infinite.
(4) Again, as a line which has a limit cannot be infinite, or, if it
is infinite, is so only in length, so a surface cannot be infinite
in that respect in which it has a limit; or, indeed, if it is
completely determinate, in any respect whatever. Whether it be a
square or a circle or a sphere, it cannot be infinite, any more than a
foot-rule can. There is then no such thing as an infinite sphere or
square or circle, and where there is no circle there can be no
circular movement, and similarly where there is no infinite at all
there can be no infinite movement; and from this it follows that, an
infinite circle being itself an impossibility, there can be no
circular motion of an infinite body.
(5) Again, take a centre C, an infinite line, AB, another infinite
line at right angles to it, E, and a moving radius, CD. CD will
never cease contact with E, but the position will always be
something like CE, CD cutting E at F. The infinite line, therefore,
refuses to complete the circle.
(6) Again, if the heaven is infinite and moves in a circle, we shall
have to admit that in a finite time it has traversed the infinite. For
suppose the fixed heaven infinite, and that which moves within it
equal to it. It results that when the infinite body has completed
its revolution, it has traversed an infinite equal to itself in a
finite time. But that we know to be impossible.
(7) It can also be shown, conversely, that if the time of revolution
is finite, the area traversed must also be finite; but the area
traversed was equal to itself; therefore, it is itself finite.
We have now shown that the body which moves in a circle is not
endless or infinite, but has its limit.
6
-
Further, neither that which moves towards nor that which moves
away from the centre can be infinite. For the upward and downward
motions are contraries and are therefore motions towards contrary
places. But if one of a pair of contraries is determinate, the other
must be determinate also. Now the centre is determined; for, from
whatever point the body which sinks to the bottom starts its
downward motion, it cannot go farther than the centre. The centre,
therefore, being determinate, the upper place must also be
determinate. But if these two places are determined and finite, the
corresponding bodies must also be finite. Further, if up and down
are determinate, the intermediate place is also necessarily
determinate. For, if it is indeterminate, the movement within it
will be infinite; and that we have already shown to be an
impossibility. The middle region then is determinate, and consequently
any body which either is in it, or might be in it, is determinate. But
the bodies which move up and down may be in it, since the one moves
naturally away from the centre and the other towards it.
From this alone it is clear that an infinite body is an
impossibility; but there is a further point. If there is no such thing
as infinite weight, then it follows that none of these bodies can be
infinite. For the supposed infinite body would have to be infinite
in weight. (The same argument applies to lightness: for as the one
supposition involves infinite weight, so the infinity of the body
which rises to the surface involves infinite lightness.) This is
proved as follows. Assume the weight to be finite, and take an
infinite body, AB, of the weight C. Subtract from the infinite body
a finite mass, BD, the weight of which shall be E. E then is less than
C, since it is the weight of a lesser mass. Suppose then that the
smaller goes into the greater a certain number of times, and take BF
bearing the same proportion to BD which the greater weight bears to
the smaller. For you may subtract as much as you please from an
infinite. If now the masses are proportionate to the weights, and
the lesser weight is that of the lesser mass, the greater must be that
of the greater. The weights, therefore, of the finite and of the
infinite body are equal. Again, if the weight of a greater body is
greater than that of a less, the weight of GB will be greater than
that of FB; and thus the weight of the finite body is greater than
that of the infinite. And, further, the weight of unequal masses
will be the same, since the infinite and the finite cannot be equal.
It does not matter whether the weights are commensurable or not. If
(a) they are incommensurable the same reasoning holds. For instance,
suppose E multiplied by three is rather more than C: the weight of
three masses of the full size of BD will be greater than C. We thus
arrive at the same impossibility as before. Again (b) we may assume
weights which are commensurate; for it makes no difference whether
we begin with the weight or with the mass. For example, assume the
weight E to be commensurate with C, and take from the infinite mass
a part BD of weight E. Then let a mass BF be taken having the same
proportion to BD which the two weights have to one another. (For the
mass being infinite you may subtract from it as much as you please.)
These assumed bodies will be commensurate in mass and in weight alike.
Nor again does it make any difference to our demonstration whether the
total mass has its weight equally or unequally distributed. For it
must always be Possible to take from the infinite mass a body of equal
weight to BD by diminishing or increasing the size of the section to
the necessary extent.
From what we have said, then, it is clear that the weight of the
infinite body cannot be finite. It must then be infinite. We have
therefore only to show this to be impossible in order to prove an
infinite body impossible. But the impossibility of infinite weight can
be shown in the following way. A given weight moves a given distance
in a given time; a weight which is as great and more moves the same
distance in a less time, the times being in inverse proportion to
the weights. For instance, if one weight is twice another, it will
take half as long over a given movement. Further, a finite weight
traverses any finite distance in a finite time. It necessarily follows
from this that infinite weight, if there is such a thing, being, on
the one hand, as great and more than as great as the finite, will move
accordingly, but being, on the other hand, compelled to move in a time
inversely proportionate to its greatness, cannot move at all. The time
should be less in proportion as the weight is greater. But there is no
proportion between the infinite and the finite: proportion can only
hold between a less and a greater finite time. And though you may
say that the time of the movement can be continually diminished, yet
there is no minimum. Nor, if there were, would it help us. For some
finite body could have been found greater than the given finite in the
same proportion which is supposed to hold between the infinite and the
given finite; so that an infinite and a finite weight must have
traversed an equal distance in equal time. But that is impossible.
Again, whatever the time, so long as it is finite, in which the
infinite performs the motion, a finite weight must necessarily move
a certain finite distance in that same time. Infinite weight is
therefore impossible, and the same reasoning applies also to
infinite lightness. Bodies then of infinite weight and of infinite
lightness are equally impossible.
That there is no infinite body may be shown, as we have shown it, by
a detailed consideration of the various cases. But it may also be
shown universally, not only by such reasoning as we advanced in our
discussion of principles (though in that passage we have already
determined universally the sense in which the existence of an infinite
is to be asserted or denied), but also suitably to our present purpose
in the following way. That will lead us to a further question. Even if
the total mass is not infinite, it may yet be great enough to admit
a plurality of universes. The question might possibly be raised
whether there is any obstacle to our believing that there are other
universes composed on the pattern of our own, more than one, though
stopping short of infinity. First, however, let us treat of the
infinite universally.
7
-
Every body must necessarily be either finite or infinite, and if
infinite, either of similar or of dissimilar parts. If its parts are
dissimilar, they must represent either a finite or an infinite
number of kinds. That the kinds cannot be infinite is evident, if
our original presuppositions remain unchallenged. For the primary
movements being finite in number, the kinds of simple body are
necessarily also finite, since the movement of a simple body is
simple, and the simple movements are finite, and every natural body
must always have its proper motion. Now if the infinite body is to
be composed of a finite number of kinds, then each of its parts must
necessarily be infinite in quantity, that is to say, the water,
fire, &c., which compose it. But this is impossible, because, as we
have already shown, infinite weight and lightness do not exist.
Moreover it would be necessary also that their places should be
infinite in extent, so that the movements too of all these bodies
would be infinite. But this is not possible, if we are to hold to
the truth of our original presuppositions and to the view that neither
that which moves downward, nor, by the same reasoning, that which
moves upward, can prolong its movement to infinity. For it is true
in regard to quality, quantity, and place alike that any process of
change is impossible which can have no end. I mean that if it is
impossible for a thing to have come to be white, or a cubit long, or
in Egypt, it is also impossible for it to be in process of coming to
be any of these. It is thus impossible for a thing to be moving to a
place at which in its motion it can never by any possibility arrive.
Again, suppose the body to exist in dispersion, it may be maintained
none the less that the total of all these scattered particles, say, of
fire, is infinite. But body we saw to be that which has extension
every way. How can there be several dissimilar elements, each
infinite? Each would have to be infinitely extended every way.
It is no more conceivable, again, that the infinite should exist
as a whole of similar parts. For, in the first place, there is no
other (straight) movement beyond those mentioned: we must therefore
give it one of them. And if so, we shall have to admit either infinite
weight or infinite lightness. Nor, secondly, could the body whose
movement is circular be infinite, since it is impossible for the
infinite to move in a circle. This, indeed, would be as good as saying
that the heavens are infinite, which we have shown to be impossible.
Moreover, in general, it is impossible that the infinite should move
at all. If it did, it would move either naturally or by constraint:
and if by constraint, it possesses also a natural motion, that is to
say, there is another place, infinite like itself, to which it will
move. But that is impossible.
That in general it is impossible for the infinite to be acted upon
by the finite or to act upon it may be shown as follows.
(1. The infinite cannot be acted upon by the finite.) Let A be an
infinite, B a finite, C the time of a given movement produced by one
in the other. Suppose, then, that A was heated, or impelled, or
modified in any way, or caused to undergo any sort of movement
whatever, by in the time C. Let D be less than B; and, assuming that a
lesser agent moves a lesser patient in an equal time, call the
quantity thus modified by D, E. Then, as D is to B, so is E to some
finite quantum. We assume that the alteration of equal by equal
takes equal time, and the alteration of less by less or of greater
by greater takes the same time, if the quantity of the patient is such
as to keep the proportion which obtains between the agents, greater
and less. If so, no movement can be caused in the infinite by any
finite agent in any time whatever. For a less agent will produce
that movement in a less patient in an equal time, and the
proportionate equivalent of that patient will be a finite quantity,
since no proportion holds between finite and infinite.
(2. The infinite cannot act upon the finite.) Nor, again, can
the infinite produce a movement in the finite in any time whatever.
Let A be an infinite, B a finite, C the time of action. In the time C,
D will produce that motion in a patient less than B, say F. Then
take E, bearing the same proportion to D as the whole BF bears to F. E
will produce the motion in BF in the time C. Thus the finite and
infinite effect the same alteration in equal times. But this is
impossible; for the assumption is that the greater effects it in a
shorter time. It will be the same with any time that can be taken,
so that there will no time in which the infinite can effect this
movement. And, as to infinite time, in that nothing can move another
or be moved by it. For such time has no limit, while the action and
reaction have.
(3. There is no interaction between infinites.) Nor can infinite
be acted upon in any way by infinite. Let A and B be infinites, CD
being the time of the action A of upon B. Now the whole B was modified
in a certain time, and the part of this infinite, E, cannot be so
modified in the same time, since we assume that a less quantity
makes the movement in a less time. Let E then, when acted upon by A,
complete the movement in the time D. Then, as D is to CD, so is E to
some finite part of B. This part will necessarily be moved by A in the
time CD. For we suppose that the same agent produces a given effect on
a greater and a smaller mass in longer and shorter times, the times
and masses varying proportionately. There is thus no finite time in
which infinites can move one another. Is their time then infinite? No,
for infinite time has no end, but the movement communicated has.
If therefore every perceptible body possesses the power of acting or
of being acted upon, or both of these, it is impossible that an
infinite body should be perceptible. All bodies, however, that
occupy place are perceptible. There is therefore no infinite body
beyond the heaven. Nor again is there anything of limited extent
beyond it. And so beyond the heaven there is no body at all. For if
you suppose it an object of intelligence, it will be in a
place-since place is what 'within' and 'beyond' denote-and therefore
an object of perception. But nothing that is not in a place is
perceptible.
The question may also be examined in the light of more general
considerations as follows. The infinite, considered as a whole of
similar parts, cannot, on the one hand, move in a circle. For there is
no centre of the infinite, and that which moves in a circle moves
about the centre. Nor again can the infinite move in a straight
line. For there would have to be another place infinite like itself to
be the goal of its natural movement and another, equally great, for
the goal of its unnatural movement. Moreover, whether its
rectilinear movement is natural or constrained, in either case the
force which causes its motion will have to be infinite. For infinite
force is force of an infinite body, and of an infinite body the
force is infinite. So the motive body also will be infinite. (The
proof of this is given in our discussion of movement, where it is
shown that no finite thing possesses infinite power, and no infinite
thing finite power.) If then that which moves naturally can also
move unnaturally, there will be two infinites, one which causes, and
another which exhibits the latter motion. Again, what is it that moves
the infinite? If it moves itself, it must be animate. But how can it
possibly be conceived as an infinite animal? And if there is something
else that moves it, there will be two infinites, that which moves
and that which is moved, differing in their form and power.
If the whole is not continuous, but exists, as Democritus and
Leucippus think, in the form of parts separated by void, there must
necessarily be one movement of all the multitude. They are
distinguished, we are told, from one another by their figures; but
their nature is one, like many pieces of gold separated from one
another. But each piece must, as we assert, have the same motion.
For a single clod moves to the same place as the whole mass of
earth, and a spark to the same place as the whole mass of fire. So
that if it be weight that all possess, no body is, strictly
speaking, light: and if lightness be universal, none is heavy.
Moreover, whatever possesses weight or lightness will have its place
either at one of the extremes or in the middle region. But this is
impossible while the world is conceived as infinite. And, generally,
that which has no centre or extreme limit, no up or down, gives the
bodies no place for their motion; and without that movement is
impossible. A thing must move either naturally or unnaturally, and the
two movements are determined by the proper and alien places. Again,
a place in which a thing rests or to which it moves unnaturally,
must be the natural place for some other body, as experience shows.
Necessarily, therefore, not everything possesses weight or
lightness, but some things do and some do not. From these arguments
then it is clear that the body of the universe is not infinite.
8
-
We must now proceed to explain why there cannot be more than one
heaven-the further question mentioned above. For it may be thought
that we have not proved universal of bodies that none whatever can
exist outside our universe, and that our argument applied only to
those of indeterminate extent.
Now all things rest and move naturally and by constraint. A thing
moves naturally to a place in which it rests without constraint, and
rests naturally in a place to which it moves without constraint. On
the other hand, a thing moves by constraint to a place in which it
rests by constraint, and rests by constraint in a place to which it
moves by constraint. Further, if a given movement is due to
constraint, its contrary is natural. If, then, it is by constraint
that earth moves from a certain place to the centre here, its movement
from here to there will be natural, and if earth from there rests here
without constraint, its movement hither will be natural. And the
natural movement in each case is one. Further, these worlds, being
similar in nature to ours, must all be composed of the same bodies
as it. Moreover each of the bodies, fire, I mean, and earth and
their intermediates, must have the same power as in our world. For
if these names are used equivocally, if the identity of name does
not rest upon an identity of form in these elements and ours, then the
whole to which they belong can only be called a world by equivocation.
Clearly, then, one of the bodies will move naturally away from the
centre and another towards the centre, since fire must be identical
with fire, earth with earth, and so on, as the fragments of each are
identical in this world. That this must be the case is evident from
the principles laid down in our discussion of the movements, for these
are limited in number, and the distinction of the elements depends
upon the distinction of the movements. Therefore, since the
movements are the same, the elements must also be the same everywhere.
The particles of earth, then, in another world move naturally also
to our centre and its fire to our circumference. This, however, is
impossible, since, if it were true, earth must, in its own world, move
upwards, and fire to the centre; in the same way the earth of our
world must move naturally away from the centre when it moves towards
the centre of another universe. This follows from the supposed
juxtaposition of the worlds. For either we must refuse to admit the
identical nature of the simple bodies in the various universes, or,
admitting this, we must make the centre and the extremity one as
suggested. This being so, it follows that there cannot be more
worlds than one.
To postulate a difference of nature in the simple bodies according
as they are more or less distant from their proper places is
unreasonable. For what difference can it make whether we say that a
thing is this distance away or that? One would have to suppose a
difference proportionate to the distance and increasing with it, but
the form is in fact the same. Moreover, the bodies must have some
movement, since the fact that they move is quite evident. Are we to
say then that all their movements, even those which are mutually
contrary, are due to constraint? No, for a body which has no natural
movement at all cannot be moved by constraint. If then the bodies have
a natural movement, the movement of the particular instances of each
form must necessarily have for goal a place numerically one, i.e. a
particular centre or a particular extremity. If it be suggested that
the goal in each case is one in form but numerically more than one, on
the analogy of particulars which are many though each undifferentiated
in form, we reply that the variety of goal cannot be limited to this
portion or that but must extend to all alike. For all are equally
undifferentiated in form, but any one is different numerically from
any other. What I mean is this: if the portions in this world behave
similarly both to one another and to those in another world, then
the portion which is taken hence will not behave differently either
from the portions in another world or from those in the same world,
but similarly to them, since in form no portion differs from
another. The result is that we must either abandon our present
assumption or assert that the centre and the extremity are each
numerically one. But this being so, the heaven, by the same evidence
and the same necessary inferences, must be one only and no more.
A consideration of the other kinds of movement also makes it plain
that there is some point to which earth and fire move naturally. For
in general that which is moved changes from something into
something, the starting-point and the goal being different in form,
and always it is a finite change. For instance, to recover health is
to change from disease to health, to increase is to change from
smallness to greatness. Locomotion must be similar: for it also has
its goal and starting-point--and therefore the starting-point and
the goal of the natural movement must differ in form-just as the
movement of coming to health does not take any direction which
chance or the wishes of the mover may select. Thus, too, fire and
earth move not to infinity but to opposite points; and since the
opposition in place is between above and below, these will be the
limits of their movement. (Even in circular movement there is a sort
of opposition between the ends of the diameter, though the movement as
a whole has no contrary: so that here too the movement has in a
sense an opposed and finite goal.) There must therefore be some end to
locomotion: it cannot continue to infinity.
This conclusion that local movement is not continued to infinity
is corroborated by the fact that earth moves more quickly the nearer
it is to the centre, and fire the nearer it is to the upper place. But
if movement were infinite speed would be infinite also; and if speed
then weight and lightness. For as superior speed in downward
movement implies superior weight, so infinite increase of weight
necessitates infinite increase of speed.
Further, it is not the action of another body that makes one of
these bodies move up and the other down; nor is it constraint, like
the 'extrusion' of some writers. For in that case the larger the
mass of fire or earth the slower would be the upward or downward
movement; but the fact is the reverse: the greater the mass of fire or
earth the quicker always is its movement towards its own place. Again,
the speed of the movement would not increase towards the end if it
were due to constraint or extrusion; for a constrained movement always
diminishes in speed as the source of constraint becomes more
distant, and a body moves without constraint to the place whence it
was moved by constraint.
A consideration of these points, then, gives adequate assurance of
the truth of our contentions. The same could also be shown with the
aid of the discussions which fall under First Philosophy, as well as
from the nature of the circular movement, which must be eternal both
here and in the other worlds. It is plain, too, from the following
considerations that the universe must be one.
The bodily elements are three, and therefore the places of the
elements will be three also; the place, first, of the body which sinks
to the bottom, namely the region about the centre; the place,
secondly, of the revolving body, namely the outermost place, and
thirdly, the intermediate place, belonging to the intermediate body.
Here in this third place will be the body which rises to the
surface; since, if not here, it will be elsewhere, and it cannot be
elsewhere: for we have two bodies, one weightless, one endowed with
weight, and below is place of the body endowed with weight, since
the region about the centre has been given to the heavy body. And
its position cannot be unnatural to it, for it would have to be
natural to something else, and there is nothing else. It must then
occupy the intermediate place. What distinctions there are within
the intermediate itself we will explain later on.
We have now said enough to make plain the character and number of
the bodily elements, the place of each, and further, in general, how
many in number the various places are.
9
-
We must show not only that the heaven is one, but also that more
than one heaven is and, further, that, as exempt from decay and
generation, the heaven is eternal. We may begin by raising a
difficulty. From one point of view it might seem impossible that the
heaven should be one and unique, since in all formations and
products whether of nature or of art we can distinguish the shape in
itself and the shape in combination with matter. For instance the form
of the sphere is one thing and the gold or bronze sphere another;
the shape of the circle again is one thing, the bronze or wooden
circle another. For when we state the essential nature of the sphere
or circle we do not include in the formula gold or bronze, because
they do not belong to the essence, but if we are speaking of the
copper or gold sphere we do include them. We still make the
distinction even if we cannot conceive or apprehend any other
example beside the particular thing. This may, of course, sometimes be
the case: it might be, for instance, that only one circle could be
found; yet none the less the difference will remain between the
being of circle and of this particular circle, the one being form, the
other form in matter, i.e. a particular thing. Now since the
universe is perceptible it must be regarded as a particular; for
everything that is perceptible subsists, as we know, in matter. But if
it is a particular, there will be a distinction between the being of
'this universe' and of 'universe' unqualified. There is a
difference, then, between 'this universe' and simple 'universe'; the
second is form and shape, the first form in combination with matter;
and any shape or form has, or may have, more than one particular
instance.
On the supposition of Forms such as some assert, this must be the
case, and equally on the view that no such entity has a separate
existence. For in every case in which the essence is in matter it is a
fact of observation that the particulars of like form are several or
infinite in number. Hence there either are, or may be, more heavens
than one. On these grounds, then, it might be inferred either that
there are or that there might be several heavens. We must, however,
return and ask how much of this argument is correct and how much not.
Now it is quite right to say that the formula of the shape apart
from the matter must be different from that of the shape in the
matter, and we may allow this to be true. We are not, however,
therefore compelled to assert a plurality of worlds. Such a
plurality is in fact impossible if this world contains the entirety of
matter, as in fact it does. But perhaps our contention can be made
clearer in this way. Suppose 'aquilinity' to be curvature in the
nose or flesh, and flesh to be the matter of aquilinity. Suppose
further, that all flesh came together into a single whole of flesh
endowed with this aquiline quality. Then neither would there be, nor
could there arise, any other thing that was aquiline. Similarly,
suppose flesh and bones to be the matter of man, and suppose a man
to be created of all flesh and all bones in indissoluble union. The
possibility of another man would be removed. Whatever case you took it
would be the same. The general rule is this: a thing whose essence
resides in a substratum of matter can never come into being in the
absence of all matter. Now the universe is certainly a particular
and a material thing: if however, it is composed not of a part but
of the whole of matter, then though the being of 'universe' and of
'this universe' are still distinct, yet there is no other universe,
and no possibility of others being made, because all the matter is
already included in this. It remains, then, only to prove that it is
composed of all natural perceptible body.
First, however, we must explain what we mean by 'heaven' and in
how many senses we use the word, in order to make clearer the object
of our inquiry. (a) In one sense, then, we call 'heaven' the substance
of the extreme circumference of the whole, or that natural body
whose place is at the extreme circumference. We recognize habitually a
special right to the name 'heaven' in the extremity or upper region,
which we take to be the seat of all that is divine. (b) In another
sense, we use this name for the body continuous with the extreme
circumference which contains the moon, the sun, and some of the stars;
these we say are 'in the heaven'. (c) In yet another sense we give the
name to all body included within extreme circumference, since we
habitually call the whole or totality 'the heaven'. The word, then, is
used in three senses.
Now the whole included within the extreme circumference must be
composed of all physical and sensible body, because there neither
is, nor can come into being, any body outside the heaven. For if there
is a natural body outside the extreme circumference it must be
either a simple or a composite body, and its position must be either
natural or unnatural. But it cannot be any of the simple bodies.
For, first, it has been shown that that which moves in a circle cannot
change its place. And, secondly, it cannot be that which moves from
the centre or that which lies lowest. Naturally they could not be
there, since their proper places are elsewhere; and if these are there
unnaturally, the exterior place will be natural to some other body,
since a place which is unnatural to one body must be natural to
another: but we saw that there is no other body besides these. Then it
is not possible that any simple body should be outside the heaven.
But, if no simple body, neither can any mixed body be there: for the
presence of the simple body is involved in the presence of the
mixture. Further neither can any body come into that place: for it
will do so either naturally or unnaturally, and will be either
simple or composite; so that the same argument will apply, since it
makes no difference whether the question is 'does A exist?' or
'could A come to exist?' From our arguments then it is evident not
only that there is not, but also that there could never come to be,
any bodily mass whatever outside the circumference. The world as a
whole, therefore, includes all its appropriate matter, which is, as we
saw, natural perceptible body. So that neither are there now, nor have
there ever been, nor can there ever be formed more heavens than one,
but this heaven of ours is one and unique and complete.
It is therefore evident that there is also no place or void or
time outside the heaven. For in every place body can be present; and
void is said to be that in which the presence of body, though not
actual, is possible; and time is the number of movement. But in the
absence of natural body there is no movement, and outside the
heaven, as we have shown, body neither exists nor can come to exist.
It is clear then that there is neither place, nor void, nor time,
outside the heaven. Hence whatever is there, is of such a nature as
not to occupy any place, nor does time age it; nor is there any change
in any of the things which lie beyond the outermost motion; they
continue through their entire duration unalterable and unmodified,
living the best and most selfsufficient of lives. As a matter of fact,
this word 'duration' possessed a divine significance for the ancients,
for the fulfilment which includes the period of life of any
creature, outside of which no natural development can fall, has been
called its duration. On the same principle the fulfilment of the whole
heaven, the fulfilment which includes all time and infinity, is
'duration'-a name based upon the fact that it is always-duration
immortal and divine. From it derive the being and life which other
things, some more or less articulately but others feebly, enjoy. So,
too, in its discussions concerning the divine, popular philosophy
often propounds the view that whatever is divine, whatever is
primary and supreme, is necessarily unchangeable. This fact confirms
what we have said. For there is nothing else stronger than it to
move it-since that would mean more divine-and it has no defect and
lacks none of its proper excellences. Its unceasing movement, then, is
also reasonable, since everything ceases to move when it comes to
its proper place, but the body whose path is the circle has one and
the same place for starting-point and goal.
10
-
Having established these distinctions, we may now proceed to the
question whether the heaven is ungenerated or generated,
indestructible or destructible. Let us start with a review of the
theories of other thinkers; for the proofs of a theory are
difficulties for the contrary theory. Besides, those who have first
heard the pleas of our adversaries will be more likely to credit the
assertions which we are going to make. We shall be less open to the
charge of procuring judgement by default. To give a satisfactory
decision as to the truth it is necessary to be rather an arbitrator
than a party to the dispute.
That the world was generated all are agreed, but, generation over,
some say that it is eternal, others say that it is destructible like
any other natural formation. Others again, with Empedliocles of
Acragas and Heraclitus of Ephesus, believe that there is alternation
in the destructive process, which takes now this direction, now
that, and continues without end.
Now to assert that it was generated and yet is eternal is to
assert the impossible; for we cannot reasonably attribute to
anything any characteristics but those which observation detects in
many or all instances. But in this case the facts point the other way:
generated things are seen always to be destroyed. Further, a thing
whose present state had no beginning and which could not have been
other than it was at any previous moment throughout its entire
duration, cannot possibly be changed. For there will have to be some
cause of change, and if this had been present earlier it would have
made possible another condition of that to which any other condition
was impossible. Suppose that the world was formed out of elements
which were formerly otherwise conditioned than as they are now. Then
(1) if their condition was always so and could not have been
otherwise, the world could never have come into being. And (2) if
the world did come into being, then, clearly, their condition must
have been capable of change and not eternal: after combination
therefore they will be dispersed, just as in the past after dispersion
they came into combination, and this process either has been, or could
have been, indefinitely repeated. But if this is so, the world
cannot be indestructible, and it does not matter whether the change of
condition has actually occurred or remains a possibility.
Some of those who hold that the world, though indestructible, was
yet generated, try to support their case by a parallel which is
illusory. They say that in their statements about its generation
they are doing what geometricians do when they construct their
figures, not implying that the universe really had a beginning, but
for didactic reasons facilitating understanding by exhibiting the
object, like the figure, as in course of formation. The two cases,
as we said, are not parallel; for, in the construction of the
figure, when the various steps are completed the required figure
forthwith results; but in these other demonstrations what results is
not that which was required. Indeed it cannot be so; for antecedent
and consequent, as assumed, are in contradiction. The ordered, it is
said, arose out of the unordered; and the same thing cannot be at
the same time both ordered and unordered; there must be a process
and a lapse of time separating the two states. In the figure, on the
other hand, there is no temporal separation. It is clear then that the
universe cannot be at once eternal and generated.
To say that the universe alternately combines and dissolves is no
more paradoxical than to make it eternal but varying in shape. It is
as if one were to think that there was now destruction and now
existence when from a child a man is generated, and from a man a
child. For it is clear that when the elements come together the result
is not a chance system and combination, but the very same as
before-especially on the view of those who hold this theory, since
they say that the contrary is the cause of each state. So that if
the totality of body, which is a continuum, is now in this order or
disposition and now in that, and if the combination of the whole is
a world or heaven, then it will not be the world that comes into being
and is destroyed, but only its dispositions.
If the world is believed to be one, it is impossible to suppose that
it should be, as a whole, first generated and then destroyed, never to
reappear; since before it came into being there was always present the
combination prior to it, and that, we hold, could never change if it
was never generated. If, on the other hand, the worlds are infinite in
number the view is more plausible. But whether this is, or is not,
impossible will be clear from what follows. For there are some who
think it possible both for the ungenerated to be destroyed and for the
generated to persist undestroyed. (This is held in the Timaeus,
where Plato says that the heaven, though it was generated, will none
the less exist to eternity.) So far as the heaven is concerned we have
answered this view with arguments appropriate to the nature of the
heaven: on the general question we shall attain clearness when we
examine the matter universally.
11
-
We must first distinguish the senses in which we use the words
'ungenerated' and 'generated', 'destructible' and 'indestructible'.
These have many meanings, and though it may make no difference to
the argument, yet some confusion of mind must result from treating
as uniform in its use a word which has several distinct
applications. The character which is the ground of the predication
will always remain obscure.
The word 'ungenerated' then is used (a) in one sense whenever
something now is which formerly was not, no process of becoming or
change being involved. Such is the case, according to some, with
contact and motion, since there is no process of coming to be in
contact or in motion. (b) It is used in another sense, when
something which is capable of coming to be, with or without process,
does not exist; such a thing is ungenerated in the sense that its
generation is not a fact but a possibility. (c) It is also applied
where there is general impossibility of any generation such that the
thing now is which then was not. And 'impossibility' has two uses:
first, where it is untrue to say that the thing can ever come into
being, and secondly, where it cannot do so easily, quickly, or well.
In the same way the word 'generated' is used, (a) first, where what
formerly was not afterwards is, whether a process of becoming was or
was not involved, so long as that which then was not, now is; (b)
secondly, of anything capable of existing, 'capable' being defined
with reference either to truth or to facility; (c) thirdly, of
anything to which the passage from not being to being belongs, whether
already actual, if its existence is due to a past process of becoming,
or not yet actual but only possible. The uses of the words
'destructible' and 'indestructible' are similar. 'Destructible' is
applied (a) to that which formerly was and afterwards either is not or
might not be, whether a period of being destroyed and changed
intervenes or not; and (b) sometimes we apply the word to that which a
process of destruction may cause not to be; and also (c) in a third
sense, to that which is easily destructible, to the 'easily
destroyed', so to speak. Of the indestructible the same account
holds good. It is either (a) that which now is and now is not, without
any process of destruction, like contact, which without being
destroyed afterwards is not, though formerly it was; or (b) that which
is but might not be, or which will at some time not be, though it
now is. For you exist now and so does the contact; yet both are
destructible, because a time will come when it will not be true of you
that you exist, nor of these things that they are in contact.
Thirdly (c) in its most proper use, it is that which is, but is
incapable of any destruction such that the thing which now is later
ceases to be or might cease to be; or again, that which has not yet
been destroyed, but in the future may cease to be. For
indestructible is also used of that which is destroyed with
difficulty.
This being so, we must ask what we mean by 'possible' and
'impossible'. For in its most proper use the predicate
'indestructible' is given because it is impossible that the thing
should be destroyed, i.e. exist at one time and not at another. And
'ungenerated' also involves impossibility when used for that which
cannot be generated, in such fashion that, while formerly it was
not, later it is. An instance is a commensurable diagonal. Now when we
speak of a power to move or to lift weights, we refer always to the
maximum. We speak, for instance, of a power to lift a hundred
talents or walk a hundred stades-though a power to effect the
maximum is also a power to effect any part of the maximum-since we
feel obliged in defining the power to give the limit or maximum. A
thing, then, which is within it. If, for example, a man can lift a
hundred talents, he can also lift two, and if he can walk a hundred
stades, he can also walk two. But the power is of the maximum, and a
thing said, with reference to its maximum, to be incapable of so
much is also incapable of any greater amount. It is, for instance,
clear that a person who cannot walk a thousand stades will also be
unable to walk a thousand and one. This point need not trouble us, for
we may take it as settled that what is, in the strict sense,
possible is determined by a limiting maximum. Now perhaps the
objection might be raised that there is no necessity in this, since he
who sees a stade need not see the smaller measures contained in it,
while, on the contrary, he who can see a dot or hear a small sound
will perceive what is greater. This, however, does not touch our
argument. The maximum may be determined either in the power or in
its object. The application of this is plain. Superior sight is
sight of the smaller body, but superior speed is that of the greater
body.
12
-
Having established these distinctions we car now proceed to the
sequel. If there are thing! capable both of being and of not being,
there must be some definite maximum time of their being and not being;
a time, I mean, during which continued existence is possible to them
and a time during which continued nonexistence is possible. And this
is true in every category, whether the thing is, for example, 'man',
or 'white', or 'three cubits long', or whatever it may be. For if
the time is not definite in quantity, but longer than any that can
be suggested and shorter than none, then it will be possible for one
and the same thing to exist for infinite time and not to exist for
another infinity. This, however, is impossible.
Let us take our start from this point. The impossible and the
false have not the same significance. One use of 'impossible' and
'possible', and 'false' and 'true', is hypothetical. It is impossible,
for instance, on a certain hypothesis that the triangle should have
its angles equal to two right angles, and on another the diagonal is
commensurable. But there are also things possible and impossible,
false and true, absolutely. Now it is one thing to be absolutely
false, and another thing to be absolutely impossible. To say that
you are standing when you are not standing is to assert a falsehood,
but not an impossibility. Similarly to say that a man who is playing
the harp, but not singing, is singing, is to say what is false but not
impossible. To say, however, that you are at once standing and
sitting, or that the diagonal is commensurable, is to say what is
not only false but also impossible. Thus it is not the same thing to
make a false and to make an impossible hypothesis, and from the
impossible hypothesis impossible results follow. A man has, it is
true, the capacity at once of sitting and of standing, because when he
possesses the one he also possesses the other; but it does not
follow that he can at once sit and stand, only that at another time he
can do the other also. But if a thing has for infinite time more
than one capacity, another time is impossible and the times must
coincide. Thus if a thing which exists for infinite time is
destructible, it will have the capacity of not being. Now if it exists
for infinite time let this capacity be actualized; and it will be in
actuality at once existent and non-existent. Thus a false conclusion
would follow because a false assumption was made, but if what was
assumed had not been impossible its consequence would not have been
impossible.
Anything then which always exists is absolutely imperishable. It
is also ungenerated, since if it was generated it will have the
power for some time of not being. For as that which formerly was,
but now is not, or is capable at some future time of not being, is
destructible, so that which is capable of formerly not having been
is generated. But in the case of that which always is, there is no
time for such a capacity of not being, whether the supposed time is
finite or infinite; for its capacity of being must include the
finite time since it covers infinite time.
It is therefore impossible that one and the same thing should be
capable of always existing and of always not-existing. And 'not always
existing', the contradictory, is also excluded. Thus it is
impossible for a thing always to exist and yet to be destructible.
Nor, similarly, can it be generated. For of two attributes if B cannot
be present without A, the impossibility A of proves the
impossibility of B. What always is, then, since it is incapable of
ever not being, cannot possibly be generated. But since the
contradictory of 'that which is always capable of being' 'that which
is not always capable of being'; while 'that which is always capable
of not being' is the contrary, whose contradictory in turn is 'that
which is not always capable of not being', it is necessary that the
contradictories of both terms should be predicable of one and the same
thing, and thus that, intermediate between what always is and what
always is not, there should be that to which being and not-being are
both possible; for the contradictory of each will at times be true
of it unless it always exists. Hence that which not always is not will
sometimes be and sometimes not be; and it is clear that this is true
also of that which cannot always be but sometimes is and therefore
sometimes is not. One thing, then, will have the power of being, and
will thus be intermediate between the other two.
Expresed universally our argument is as follows. Let there be two
attributes, A and B, not capable of being present in any one thing
together, while either A or C and either B or D are capable of being
present in everything. Then C and D must be predicated of everything
of which neither A nor B is predicated. Let E lie between A and B; for
that which is neither of two contraries is a mean between them. In E
both C and D must be present, for either A or C is present
everywhere and therefore in E. Since then A is impossible, C must be
present, and the same argument holds of D.
Neither that which always is, therefore, nor that which always is
not is either generated or destructible. And clearly whatever is
generated or destructible is not eternal. If it were, it would be at
once capable of always being and capable of not always being, but it
has already been shown that this is impossible. Surely then whatever
is ungenerated and in being must be eternal, and whatever is
indestructible and in being must equally be so. (I use the words
'ungenerated' and 'indestructible' in their proper sense,
'ungenerated' for that which now is and could not at any previous time
have been truly said not to be; 'indestructible' for that which now is
and cannot at any future time be truly said not to be.) If, again, the
two terms are coincident, if the ungenerated is indestructible, and
the indestructible ungenearted, then each of them is coincident with
'eternal'; anything ungenerated is eternal and anything indestructible
is eternal. This is clear too from the definition of the terms,
Whatever is destructible must be generated; for it is either
ungenerated, or generated, but, if ungenerated, it is by hypothesis
indestructible. Whatever, further, is generated must be
destructible. For it is either destructible or indestructible, but, if
indestructible, it is by hypothesis ungenerated.
If, however, 'indestructible' and 'ungenerated' are not
coincident, there is no necessity that either the ungenerated or the
indestructible should be eternal. But they must be coincident, for the
following reasons. The terms 'generated' and 'destructible' are
coincident; this is obvious from our former remarks, since between
what always is and what always is not there is an intermediate which
is neither, and that intermediate is the generated and destructible.
For whatever is either of these is capable both of being and of not
being for a definite time: in either case, I mean, there is a
certain period of time during which the thing is and another during
which it is not. Anything therefore which is generated or destructible
must be intermediate. Now let A be that which always is and B that
which always is not, C the generated, and D the destructible. Then C
must be intermediate between A and B. For in their case there is no
time in the direction of either limit, in which either A is not or B
is. But for the generated there must be such a time either actually or
potentially, though not for A and B in either way. C then will be, and
also not be, for a limited length of time, and this is true also of D,
the destructible. Therefore each is both generated and destructible.
Therefore 'generated' and 'destructible' are coincident. Now let E
stand for the ungenerated, F for the generated, G for the
indestructible, and H for the destructible. As for F and H, it has
been shown that they are coincident. But when terms stand to one
another as these do, F and H coincident, E and F never predicated of
the same thing but one or other of everything, and G and H likewise,
then E and G must needs be coincident. For suppose that E is not
coincident with G, then F will be, since either E or F is
predictable of everything. But of that of which F is predicated H will
be predicable also. H will then be coincident with G, but this we
saw to be impossible. And the same argument shows that G is coincident
with E.
Now the relation of the ungenerated (E) to the generated (F) is
the same as that of the indestructible (G) to the destructible (H). To
say then that there is no reason why anything should not be
generated and yet indestructible or ungenerated and yet destroyed,
to imagine that in the one case generation and in the other case
destruction occurs once for all, is to destroy part of the data. For
(1) everything is capable of acting or being acted upon, of being or
not being, either for an infinite, or for a definitely limited space
of time; and the infinite time is only a possible alternative
because it is after a fashion defined, as a length of time which
cannot be exceeded. But infinity in one direction is neither
infinite or finite. (2) Further, why, after always existing, was the
thing destroyed, why, after an infinity of not being, was it
generated, at one moment rather than another? If every moment is alike
and the moments are infinite in number, it is clear that a generated
or destructible thing existed for an infinite time. It has therefore
for an infinite time the capacity of not being (since the capacity
of being and the capacity of not being will be present together), if
destructible, in the time before destruction, if generated, in the
time after generation. If then we assume the two capacities to be
actualized, opposites will be present together. (3) Further, this
second capacity will be present like the first at every moment, so
that the thing will have for an infinite time the capacity both of
being and of not being; but this has been shown to be impossible.
(4) Again, if the capacity is present prior to the activity, it will
be present for all time, even while the thing was as yet ungenerated
and non-existent, throughout the infinite time in which it was capable
of being generated. At that time, then, when it was not, at that
same time it had the capacity of being, both of being then and of
being thereafter, and therefore for an infinity of time.
It is clear also on other grounds that it is impossible that the
destructible should not at some time be destroyed. For otherwise it
will always be at once destructible and in actuality indestructible,
so that it will be at the same time capable of always existing and
of not always existing. Thus the destructible is at some time actually
destroyed. The generable, similarly, has been generated, for it is
capable of having been generated and thus also of not always existing.
We may also see in the following way how impossible it is either for
a thing which is generated to be thenceforward indestructible, or
for a thing which is ungenerated and has always hitherto existed to be
destroyed. Nothing that is by chance can be indestructible or
ungenerated, since the products of chance and fortune are opposed to
what is, or comes to be, always or usually, while anything which
exists for a time infinite either absolutely or in one direction, is
in existence either always or usually. That which is by chance,
then, is by nature such as to exist at one time and not at another.
But in things of that character the contradictory states proceed
from one and the same capacity, the matter of the thing being the
cause equally of its existence and of its non-existence. Hence
contradictories would be present together in actuality.
Further, it cannot truly be said of a thing now that it exists
last year, nor could it be said last year that it exists now. It is
therefore impossible for what once did not exist later to be
eternal. For in its later state it will possess the capacity of not
existing, only not of not existing at a time when it exists-since then
it exists in actuality-but of not existing last year or in the past.
Now suppose it to be in actuality what it is capable of being. It will
then be true to say now that it does not exist last year. But this
is impossible. No capacity relates to being in the past, but always to
being in the present or future. It is the same with the notion of an
eternity of existence followed later by non-existence. In the later
state the capacity will be present for that which is not there in
actuality. Actualize, then, the capacity. It will be true to say now
that this exists last year or in the past generally.
Considerations also not general like these but proper to the subject
show it to be impossible that what was formerly eternal should later
be destroyed or that what formerly was not should later be eternal.
Whatever is destructible or generated is always alterable. Now
alteration is due to contraries, and the things which compose the
natural body are the very same that destroy it.
Book II
1
-
THAT the heaven as a whole neither came into being nor admits of
destruction, as some assert, but is one and eternal, with no end or
beginning of its total duration, containing and embracing in itself
the infinity of time, we may convince ourselves not only by the
arguments already set forth but also by a consideration of the views
of those who differ from us in providing for its generation. If our
view is a possible one, and the manner of generation which they assert
is impossible, this fact will have great weight in convincing us of
the immortality and eternity of the world. Hence it is well to
persuade oneself of the truth of the ancient and truly traditional
theories, that there is some immortal and divine thing which possesses
movement, but movement such as has no limit and is rather itself the
limit of all other movement. A limit is a thing which contains; and
this motion, being perfect, contains those imperfect motions which
have a limit and a goal, having itself no beginning or end, but
unceasing through the infinity of time, and of other movements, to
some the cause of their beginning, to others offering the goal. The
ancients gave to the Gods the heaven or upper place, as being alone
immortal; and our present argument testifies that it is indestructible
and ungenerated. Further, it is unaffected by any mortal discomfort,
and, in addition, effortless; for it needs no constraining necessity
to keep it to its path, and prevent it from moving with some other
movement more natural to itself. Such a constrained movement would
necessarily involve effort the more so, the more eternal it were-and
would be inconsistent with perfection. Hence we must not believe the
old tale which says that the world needs some Atlas to keep it
safe-a tale composed, it would seem, by men who, like later
thinkers, conceived of all the upper bodies as earthy and endowed with
weight, and therefore supported it in their fabulous way upon
animate necessity. We must no more believe that than follow Empedocles
when he says that the world, by being whirled round, received a
movement quick enough to overpower its own downward tendency, and thus
has been kept from destruction all this time. Nor, again, is it
conceivable that it should persist eternally by the necessitation of a
soul. For a soul could not live in such conditions painlessly or
happily, since the movement involves constraint, being imposed on
the first body, whose natural motion is different, and imposed
continuously. It must therefore be uneasy and devoid of all rational
satisfaction; for it could not even, like the soul of mortal
animals, take recreation in the bodily relaxation of sleep. An Ixion's
lot must needs possess it, without end or respite. If then, as we
said, the view already stated of the first motion is a possible one,
it is not only more appropriate so to conceive of its eternity, but
also on this hypothesis alone are we able to advance a theory
consistent with popular divinations of the divine nature. But of
this enough for the present.
2
-
Since there are some who say that there is a right and a left in the
heaven, with those who are known as Pythagoreans-to whom indeed the
view really belongs-we must consider whether, if we are to apply these
principles to the body of the universe, we should follow their
statement of the matter or find a better way. At the start we may
say that, if right and left are applicable, there are prior principles
which must first be applied. These principles have been analysed in
the discussion of the movements of animals, for the reason that they
are proper to animal nature. For in some animals we find all such
distinctions of parts as this of right and left clearly present, and
in others some; but in plants we find only above and below. Now if
we are to apply to the heaven such a distinction of parts, we must
exect, as we have said, to find in it also the distinction which in
animals is found first of them all. The distinctions are three,
namely, above and below, front and its opposite, right and left-all
these three oppositions we expect to find in the perfect body-and each
may be called a principle. Above is the principle of length, right
of breadth, front of depth. Or again we may connect them with the
various movements, taking principle to mean that part, in a thing
capable of movement, from which movement first begins. Growth starts
from above, locomotion from the right, sensemovement from in front
(for front is simply the part to which the senses are directed). Hence
we must not look for above and below, right and left, front and
back, in every kind of body, but only in those which, being animate,
have a principle of movement within themselves. For in no inanimate
thing do we observe a part from which movement originates. Some do not
move at all, some move, but not indifferently in any direction;
fire, for example, only upward, and earth only to the centre. It is
true that we speak of above and below, right and left, in these bodies
relatively to ourselves. The reference may be to our own right
hands, as with the diviner, or to some similarity to our own
members, such as the parts of a statue possess; or we may take the
contrary spatial order, calling right that which is to our left, and
left that which is to our right. We observe, however, in the things
themselves none of these distinctions; indeed if they are turned round
we proceed to speak of the opposite parts as right and left, a boy
land below, front and back. Hence it is remarkable that the
Pythagoreans should have spoken of these two principles, right and
left, only, to the exclusion of the other four, which have as good a
title as they. There is no less difference between above and below
or front and back in animals generally than between right and left.
The difference is sometimes only one of function, sometimes also one
of shape; and while the distinction of above and below is
characteristic of all animate things, whether plants or animals,
that of right and left is not found in plants. Further, inasmuch as
length is prior to breadth, if above is the principle of length, right
of breadth, and if the principle of that which is prior is itself
prior, then above will be prior to right, or let us say, since 'prior'
is ambiguous, prior in order of generation. If, in addition, above
is the region from which movement originates, right the region in
which it starts, front the region to which it is directed, then on
this ground too above has a certain original character as compared
with the other forms of position. On these two grounds, then, they may
fairly be criticized, first, for omitting the more fundamental
principles, and secondly, for thinking that the two they mentioned
were attributable equally to everything.
Since we have already determined that functions of this kind
belong to things which possess, a principle of movement, and that
the heaven is animate and possesses a principle of movement, clearly
the heaven must also exhibit above and below, right and left. We
need not be troubled by the question, arising from the spherical shape
of the world, how there can be a distinction of right and left
within it, all parts being alike and all for ever in motion. We must
think of the world as of something in which right differs from left in
shape as well as in other respects, which subsequently is included
in a sphere. The difference of function will persist, but will
appear not to by reason of the regularity of shape. In the same
fashion must we conceive of the beginning of its movement. For even if
it never began to move, yet it must possess a principle from which
it would have begun to move if it had begun, and from which it would
begin again if it came to a stand. Now by its length I mean the
interval between its poles, one pole being above and the other
below; for two hemispheres are specially distinguished from all others
by the immobility of the poles. Further, by 'transverse' in the
universe we commonly mean, not above and below, but a direction
crossing the line of the poles, which, by implication, is length:
for transverse motion is motion crossing motion up and down. Of the
poles, that which we see above us is the lower region, and that
which we do not see is the upper. For right in anything is, as we say,
the region in which locomotion originates, and the rotation of the
heaven originates in the region from which the stars rise. So this
will be the right, and the region where they set the left. If then
they begin from the right and move round to the right, the upper
must be the unseen pole. For if it is the pole we see, the movement
will be leftward, which we deny to be the fact. Clearly then the
invisible pole is above. And those who live in the other hemisphere
are above and to the right, while we are below and to the left. This
is just the opposite of the view of the Pythagoreans, who make us
above and on the right side and those in the other hemisphere below
and on the left side; the fact being the exact opposite. Relatively,
however, to the secondary revolution, I mean that of the planets, we
are above and on the right and they are below and on the left. For the
principle of their movement has the reverse position, since the
movement itself is the contrary of the other: hence it follows that we
are at its beginning and they at its end. Here we may end our
discussion of the distinctions of parts created by the three
dimensions and of the consequent differences of position.
3
-
Since circular motion is not the contrary of the reverse circular
motion, we must consider why there is more than one motion, though
we have to pursue our inquiries at a distance-a distance created not
so much by our spatial position as by the fact that our senses
enable us to perceive very few of the attributes of the heavenly
bodies. But let not that deter us. The reason must be sought in the
following facts. Everything which has a function exists for its
function. The activity of God is immortality, i.e. eternal life.
Therefore the movement of that which is divine must be eternal. But
such is the heaven, viz. a divine body, and for that reason to it is
given the circular body whose nature it is to move always in a circle.
Why, then, is not the whole body of the heaven of the same character
as that part? Because there must be something at rest at the centre of
the revolving body; and of that body no part can be at rest, either
elsewhere or at the centre. It could do so only if the body's
natural movement were towards the centre. But the circular movement is
natural, since otherwise it could not be eternal: for nothing
unnatural is eternal. The unnatural is subsequent to the natural,
being a derangement of the natural which occurs in the course of its
generation. Earth then has to exist; for it is earth which is at
rest at the centre. (At present we may take this for granted: it shall
be explained later.) But if earth must exist, so must fire. For, if
one of a pair of contraries naturally exists, the other, if it is
really contrary, exists also naturally. In some form it must be
present, since the matter of contraries is the same. Also, the
positive is prior to its privation (warm, for instance, to cold),
and rest and heaviness stand for the privation of lightness and
movement. But further, if fire and earth exist, the intermediate
bodies must exist also: each element stands in a contrary relation
to every other. (This, again, we will here take for granted and try
later to explain.) these four elements generation clearly is involved,
since none of them can be eternal: for contraries interact with one
another and destroy one another. Further, it is inconceivable that a
movable body should be eternal, if its movement cannot be regarded
as naturally eternal: and these bodies we know to possess movement.
Thus we see that generation is necessarily involved. But if so,
there must be at least one other circular motion: for a single
movement of the whole heaven would necessitate an identical relation
of the elements of bodies to one another. This matter also shall be
cleared up in what follows: but for the present so much is clear, that
the reason why there is more than one circular body is the necessity
of generation, which follows on the presence of fire, which, with that
of the other bodies, follows on that of earth; and earth is required
because eternal movement in one body necessitates eternal rest in
another.
4
-
The shape of the heaven is of necessity spherical; for that is the
shape most appropriate to its substance and also by nature primary.
First, let us consider generally which shape is primary among planes
and solids alike. Every plane figure must be either rectilinear or
curvilinear. Now the rectilinear is bounded by more than one line, the
curvilinear by one only. But since in any kind the one is naturally
prior to the many and the simple to the complex, the circle will be
the first of plane figures. Again, if by complete, as previously
defined, we mean a thing outside which no part of itself can be found,
and if addition is always possible to the straight line but never to
the circular, clearly the line which embraces the circle is
complete. If then the complete is prior to the incomplete, it
follows on this ground also that the circle is primary among
figures. And the sphere holds the same position among solids. For it
alone is embraced by a single surface, while rectilinear solids have
several. The sphere is among solids what the circle is among plane
figures. Further, those who divide bodies into planes and generate
them out of planes seem to bear witness to the truth of this. Alone
among solids they leave the sphere undivided, as not possessing more
than one surface: for the division into surfaces is not just
dividing a whole by cutting it into its parts, but division of another
fashion into parts different in form. It is clear, then, that the
sphere is first of solid figures.
If, again, one orders figures according to their numbers, it is most
natural to arrange them in this way. The circle corresponds to the
number one, the triangle, being the sum of two right angles, to the
number two. But if one is assigned to the triangle, the circle will
not be a figure at all.
Now the first figure belongs to the first body, and the first body
is that at the farthest circumference. It follows that the body
which revolves with a circular movement must be spherical. The same
then will be true of the body continuous with it: for that which is
continuous with the spherical is spherical. The same again holds of
the bodies between these and the centre. Bodies which are bounded by
the spherical and in contact with it must be, as wholes, spherical;
and the bodies below the sphere of the planets are contiguous with the
sphere above them. The sphere then will be spherical throughout; for
every body within it is contiguous and continuous with spheres.
Again, since the whole revolves, palpably and by assumption, in a
circle, and since it has been shown that outside the farthest
circumference there is neither void nor place, from these grounds also
it will follow necessarily that the heaven is spherical. For if it
is to be rectilinear in shape, it will follow that there is place
and body and void without it. For a rectilinear figure as it
revolves never continues in the same room, but where formerly was
body, is now none, and where now is none, body will be in a moment
because of the projection at the corners. Similarly, if the world
had some other figure with unequal radii, if, for instance, it were
lentiform, or oviform, in every case we should have to admit space and
void outside the moving body, because the whole body would not
always occupy the same room.
Again, if the motion of the heaven is the measure of all movements
whatever in virtue of being alone continuous and regular and
eternal, and if, in each kind, the measure is the minimum, and the
minimum movement is the swiftest, then, clearly, the movement of the
heaven must be the swiftest of all movements. Now of lines which
return upon themselves the line which bounds the circle is the
shortest; and that movement is the swiftest which follows the shortest
line. Therefore, if the heaven moves in a circle and moves more
swiftly than anything else, it must necessarily be spherical.
Corroborative evidence may be drawn from the bodies whose position
is about the centre. If earth is enclosed by water, water by air,
air by fire, and these similarly by the upper bodies-which while not
continuous are yet contiguous with them-and if the surface of water is
spherical, and that which is continuous with or embraces the spherical
must itself be spherical, then on these grounds also it is clear
that the heavens are spherical. But the surface of water is seen to be
spherical if we take as our starting-point the fact that water
naturally tends to collect in a hollow place-'hollow' meaning
'nearer the centre'. Draw from the centre the lines AB, AC, and let
their extremities be joined by the straight line BC. The line AD,
drawn to the base of the triangle, will be shorter than either of
the radii. Therefore the place in which it terminates will be a hollow
place. The water then will collect there until equality is
established, that is until the line AE is equal to the two radii. Thus
water forces its way to the ends of the radii, and there only will
it rest: but the line which connects the extremities of the radii is
circular: therefore the surface of the water BEC is spherical.
It is plain from the foregoing that the universe is spherical. It is
plain, further, that it is turned (so to speak) with a finish which no
manufactured thing nor anything else within the range of our
observation can even approach. For the matter of which these are
composed does not admit of anything like the same regularity and
finish as the substance of the enveloping body; since with each step
away from earth the matter manifestly becomes finer in the same
proportion as water is finer than earth.
5
-
Now there are two ways of moving along a circle, from A to B or from
A to C, and we have already explained that these movements are not
contrary to one another. But nothing which concerns the eternal can be
a matter of chance or spontaneity, and the heaven and its circular
motion are eternal. We must therefore ask why this motion takes one
direction and not the other. Either this is itself an ultimate fact or
there is an ultimate fact behind it. It may seem evidence of excessive
folly or excessive zeal to try to provide an explanation of some
things, or of everything, admitting no exception. The criticism,
however, is not always just: one should first consider what reason
there is for speaking, and also what kind of certainty is looked
for, whether human merely or of a more cogent kind. When any one shall
succeed in finding proofs of greater precision, gratitude will be
due to him for the discovery, but at present we must be content with a
probable solution. If nature always follows the best course
possible, and, just as upward movement is the superior form of
rectilinear movement, since the upper region is more divine than the
lower, so forward movement is superior to backward, then front and
back exhibits, like right and left, as we said before and as the
difficulty just stated itself suggests, the distinction of prior and
posterior, which provides a reason and so solves our difficulty.
Supposing that nature is ordered in the best way possible, this may
stand as the reason of the fact mentioned. For it is best to move with
a movement simple and unceasing, and, further, in the superior of
two possible directions.
6
-
We have next to show that the movement of the heaven is regular
and not irregular. This applies only to the first heaven and the first
movement; for the lower spheres exhibit a composition of several
movements into one. If the movement is uneven, clearly there will be
acceleration, maximum speed, and retardation, since these appear in
all irregular motions. The maximum may occur either at the
starting-point or at the goal or between the two; and we expect
natural motion to reach its maximum at the goal, unnatural motion at
the starting-point, and missiles midway between the two. But
circular movement, having no beginning or limit or middle in the
direct sense of the words, has neither whence nor whither nor
middle: for in time it is eternal, and in length it returns upon
itself without a break. If then its movement has no maximum, it can
have no irregularity, since irregularity is produced by retardation
and acceleration. Further, since everything that is moved is moved
by something, the cause of the irregularity of movement must lie
either in the mover or in the moved or both. For if the mover moved
not always with the same force, or if the moved were altered and did
not remain the same, or if both were to change, the result might
well be an irregular movement in the moved. But none of these
possibilities can be conceived as actual in the case of the heavens.
As to that which is moved, we have shown that it is primary and simple
and ungenerated and indestructible and generally unchanging; and the
mover has an even better right to these attributes. It is the
primary that moves the primary, the simple the simple, the
indestructible and ungenerated that which is indestructible and
ungenerated. Since then that which is moved, being a body, is
nevertheless unchanging, how should the mover, which is incorporeal,
be changed?
It follows then, further, that the motion cannot be irregular. For
if irregularity occurs, there must be change either in the movement as
a whole, from fast to slow and slow to fast, or in its parts. That
there is no irregularity in the parts is obvious, since, if there
were, some divergence of the stars would have taken place before now
in the infinity of time, as one moved slower and another faster: but
no alteration of their intervals is ever observed. Nor again is a
change in the movement as a whole admissible. Retardation is always
due to incapacity, and incapacity is unnatural. The incapacities of
animals, age, decay, and the like, are all unnatural, due, it seems,
to the fact that the whole animal complex is made up of materials
which differ in respect of their proper places, and no single part
occupies its own place. If therefore that which is primary contains
nothing unnatural, being simple and unmixed and in its proper place
and having no contrary, then it has no place for incapacity, nor,
consequently, for retardation or (since acceleration involves
retardation) for acceleration. Again, it is inconceivable that the
mover should first show incapacity for an infinite time, and
capacity afterwards for another infinity. For clearly nothing which,
like incapacity, unnatural ever continues for an infinity of time; nor
does the unnatural endure as long as the natural, or any form of
incapacity as long as the capacity. But if the movement is retarded it
must necessarily be retarded for an infinite time. Equally
impossible is perpetual acceleration or perpetual retardation. For
such movement would be infinite and indefinite, but every movement, in
our view, proceeds from one point to another and is definite in
character. Again, suppose one assumes a minimum time in less than
which the heaven could not complete its movement. For, as a given walk
or a given exercise on the harp cannot take any and every time, but
every performance has its definite minimum time which is
unsurpassable, so, one might suppose, the movement of the heaven could
not be completed in any and every time. But in that case perpetual
acceleration is impossible (and, equally, perpetual retardation: for
the argument holds of both and each), if we may take acceleration to
proceed by identical or increasing additions of speed and for an
infinite time. The remaining alternative is to say that the movement
exhibits an alternation of slower and faster: but this is a mere
fiction and quite inconceivable. Further, irregularity of this kind
would be particularly unlikely to pass unobserved, since contrast
makes observation easy.
That there is one heaven, then, only, and that it is ungenerated and
eternal, and further that its movement is regular, has now been
sufficiently explained.
7
-
We have next to speak of the stars, as they are called, of their
composition, shape, and movements. It would be most natural and
consequent upon what has been said that each of the stars should be
composed of that substance in which their path lies, since, as we
said, there is an element whose natural movement is circular. In so
saying we are only following the same line of thought as those who say
that the stars are fiery because they believe the upper body to be
fire, the presumption being that a thing is composed of the same stuff
as that in which it is situated. The warmth and light which proceed
from them are caused by the friction set up in the air by their
motion. Movement tends to create fire in wood, stone, and iron; and
with even more reason should it have that effect on air, a substance
which is closer to fire than these. An example is that of missiles,
which as they move are themselves fired so strongly that leaden
balls are melted; and if they are fired the surrounding air must be
similarly affected. Now while the missiles are heated by reason of
their motion in air, which is turned into fire by the agitation
produced by their movement, the upper bodies are carried on a moving
sphere, so that, though they are not themselves fired, yet the air
underneath the sphere of the revolving body is necessarily heated by
its motion, and particularly in that part where the sun is attached to
it. Hence warmth increases as the sun gets nearer or higher or
overhead. Of the fact, then, that the stars are neither fiery nor move
in fire, enough has been said.
8
-
Since changes evidently occur not only in the position of the
stars but also in that of the whole heaven, there are three
possibilities. Either (1) both are at rest, or (2) both are in motion,
or (3) the one is at rest and the other in motion.
(1) That both should be at rest is impossible; for, if the earth
is at rest, the hypothesis does not account for the observations;
and we take it as granted that the earth is at rest. It remains either
that both are moved, or that the one is moved and the other at rest.
(2) On the view, first, that both are in motion, we have the
absurdity that the stars and the circles move with the same speed,
i.e. that the ace of every star is that of the circle in it moves. For
star and circle are seen to come back to the same place at the same
moment; from which it follows that the star has traversed the circle
and the circle has completed its own movement, i.e. traversed its
own circumference, at one and the same moment. But it is difficult
to conceive that the pace of each star should be exactly
proportioned to the size of its circle. That the pace of each circle
should be proportionate to its size is not absurd but inevitable:
but that the same should be true of the movement of the stars
contained in the circles is quite incredible. For if, on the one
and, we suppose that the star which moves on the greater circle is
necessarily swifter, clearly we also admit that if stars shifted their
position so as to exchange circles, the slower would become swifter
and the swifter slower. But this would show that their movement was
not their own, but due to the circles. If, on the other hand, the
arrangement was a chance combination, the coincidence in every case of
a greater circle with a swifter movement of the star contained in it
is too much to believe. In one or two cases it might not inconceivably
fall out so, but to imagine it in every case alike is a mere
fiction. Besides, chance has no place in that which is natural, and
what happens everywhere and in every case is no matter of chance.
(3) The same absurdity is equally plain if it is supposed that the
circles stand still and that it is the stars themselves which move.
For it will follow that the outer stars are the swifter, and that
the pace of the stars corresponds to the size of their circles.
Since, then, we cannot reasonably suppose either that both are in
motion or that the star alone moves, the remaining alternative is that
the circles should move, while the stars are at rest and move with the
circles to which they are attached. Only on this supposition are we
involved in no absurd consequence. For, in the first place, the
quicker movement of the larger circle is natural when all the
circles are attached to the same centre. Whenever bodies are moving
with their proper motion, the larger moves quicker. It is the same
here with the revolving bodies: for the are intercepted by two radii
will be larger in the larger circle, and hence it is not surprising
that the revolution of the larger circle should take the same time
as that of the smaller. And secondly, the fact that the heavens do not
break in pieces follows not only from this but also from the proof
already given of the continuity of the whole.
Again, since the stars are spherical, as our opponents assert and we
may consistently admit, inasmuch as we construct them out of the
spherical body, and since the spherical body has two movements
proper to itself, namely rolling and spinning, it follows that if
the stars have a movement of their own, it will be one of these. But
neither is observed. (1) Suppose them to spin. They would then stay
where they were, and not change their place, as, by observation and
general consent, they do. Further, one would expect them all to
exhibit the same movement: but the only star which appears to
possess this movement is the sun, at sunrise or sunset, and this
appearance is due not to the sun itself but to the distance from which
we observe it. The visual ray being excessively prolonged becomes weak
and wavering. The same reason probably accounts for the apparent
twinkling of the fixed stars and the absence of twinkling in the
planets. The planets are near, so that the visual ray reaches them
in its full vigour, but when it comes to the fi |
|
