Infomotions, Inc.On The Heavens / Aristotle



Author: Aristotle
Title: On The Heavens
Publisher: Eris Etext Project
Tag(s): finite; movement; infinite; centre; motion; downward; weight; earth; contrary; circular movement; circular motion; western philosophy
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Identifier: aristotle-on-271
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                                     350 BC

                                 ON THE HEAVENS

                                  by Aristotle

                           translated by J. L. Stocks

                              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 fixed stars it is
quivering because of the distance and its excessive extension; and its
tremor produces an appearance of movement in the star: for it makes no
difference whether movement is set up in the ray or in the object of
vision.

  (2) On the other hand, it is also clear that the stars do not
roll. For rolling involves rotation: but the 'face', as it is
called, of the moon is always seen. Therefore, since any movement of
their own which the stars possessed would presumably be one proper
to themselves, and no such movement is observed in them, clearly
they have no movement of their own.

  There is, further, the absurdity that nature has bestowed upon
them no organ appropriate to such movement. For nature leaves
nothing to chance, and would not, while caring for animals, overlook
things so precious. Indeed, nature seems deliberately to have stripped
them of everything which makes selforiginated progression possible,
and to have removed them as far as possible from things which have
organs of movement. This is just why it seems proper that the whole
heaven and every star should be spherical. For while of all shapes the
sphere is the most convenient for movement in one place, making
possible, as it does, the swiftest and most selfcontained motion,
for forward movement it is the most unsuitable, least of all
resembling shapes which are self-moved, in that it has no dependent or
projecting part, as a rectilinear figure has, and is in fact as far as
possible removed in shape from ambulatory bodies. Since, therefore,
the heavens have to move in one lace, and the stars are not required
to move themselves forward, it is natural that both should be
spherical-a shape which best suits the movement of the one and the
immobility of the other.

                                 9

  From all this it is clear that the theory that the movement of the
stars produces a harmony, i.e. that the sounds they make are
concordant, in spite of the grace and originality with which it has
been stated, is nevertheless untrue. Some thinkers suppose that the
motion of bodies of that size must produce a noise, since on our earth
the motion of bodies far inferior in size and in speed of movement has
that effect. Also, when the sun and the moon, they say, and all the
stars, so great in number and in size, are moving with so rapid a
motion, how should they not produce a sound immensely great?
Starting from this argument and from the observation that their
speeds, as measured by their distances, are in the same ratios as
musical concordances, they assert that the sound given forth by the
circular movement of the stars is a harmony. Since, however, it
appears unaccountable that we should not hear this music, they explain
this by saying that the sound is in our ears from the very moment of
birth and is thus indistinguishable from its contrary silence, since
sound and silence are discriminated by mutual contrast. What happens
to men, then, is just what happens to coppersmiths, who are so
accustomed to the noise of the smithy that it makes no difference to
them. But, as we said before, melodious and poetical as the theory is,
it cannot be a true account of the facts. There is not only the
absurdity of our hearing nothing, the ground of which they try to
remove, but also the fact that no effect other than sensitive is
produced upon us. Excessive noises, we know, shatter the solid
bodies even of inanimate things: the noise of thunder, for instance,
splits rocks and the strongest of bodies. But if the moving bodies are
so great, and the sound which penetrates to us is proportionate to
their size, that sound must needs reach us in an intensity many
times that of thunder, and the force of its action must be immense.
Indeed the reason why we do not hear, and show in our bodies none of
the effects of violent force, is easily given: it is that there is
no noise. But not only is the explanation evident; it is also a
corroboration of the truth of the views we have advanced. For the very
difficulty which made the Pythagoreans say that the motion of the
stars produces a concord corroborates our view. Bodies which are
themselves in motion, produce noise and friction: but those which
are attached or fixed to a moving body, as the parts to a ship, can no
more create noise, than a ship on a river moving with the stream.
Yet by the same argument one might say it was absurd that on a large
vessel the motion of mast and poop should not make a great noise,
and the like might be said of the movement of the vessel itself. But
sound is caused when a moving body is enclosed in an unmoved body, and
cannot be caused by one enclosed in, and continuous with, a moving
body which creates no friction. We may say, then, in this matter
that if the heavenly bodies moved in a generally diffused mass of
air or fire, as every one supposes, their motion would necessarily
cause a noise of tremendous strength and such a noise would
necessarily reach and shatter us. Since, therefore, this effect is
evidently not produced, it follows that none of them can move with the
motion either of animate nature or of constraint. It is as though
nature had foreseen the result, that if their movement were other than
it is, nothing on this earth could maintain its character.

  That the stars are spherical and are not selfmoved, has now been
explained.

                                10

  With their order-I mean the position of each, as involving the
priority of some and the posteriority of others, and their
respective distances from the extremity-with this astronomy may be
left to deal, since the astronomical discussion is adequate. This
discussion shows that the movements of the several stars depend, as
regards the varieties of speed which they exhibit, on the distance
of each from the extremity. It is established that the outermost
revolution of the heavens is a simple movement and the swiftest of
all, and that the movement of all other bodies is composite and
relatively slow, for the reason that each is moving on its own
circle with the reverse motion to that of the heavens. This at once
leads us to expect that the body which is nearest to that first simple
revolution should take the longest time to complete its circle, and
that which is farthest from it the shortest, the others taking a
longer time the nearer they are and a shorter time the farther away
they are. For it is the nearest body which is most strongly
influenced, and the most remote, by reason of its distance, which is
least affected, the influence on the intermediate bodies varying, as
the mathematicians show, with their distance.

                                11

  With regard to the shape of each star, the most reasonable view is
that they are spherical. It has been shown that it is not in their
nature to move themselves, and, since nature is no wanton or random
creator, clearly she will have given things which possess no
movement a shape particularly unadapted to movement. Such a shape is
the sphere, since it possesses no instrument of movement. Clearly then
their mass will have the form of a sphere. Again, what holds of one
holds of all, and the evidence of our eyes shows us that the moon is
spherical. For how else should the moon as it waxes and wanes show for
the most part a crescent-shaped or gibbous figure, and only at one
moment a half-moon? And astronomical arguments give further
confirmation; for no other hypothesis accounts for the crescent
shape of the sun's eclipses. One, then, of the heavenly bodies being
spherical, clearly the rest will be spherical also.

                                12

  There are two difficulties, which may very reasonably here be
raised, of which we must now attempt to state the probable solution:
for we regard the zeal of one whose thirst after philosophy leads
him to accept even slight indications where it is very difficult to
see one's way, as a proof rather of modesty than of overconfidence.

  Of many such problems one of the strangest is the problem why we
find the greatest number of movements in the intermediate bodies,
and not, rather, in each successive body a variety of movement
proportionate to its distance from the primary motion. For we should
expect, since the primary body shows one motion only, that the body
which is nearest to it should move with the fewest movements, say two,
and the one next after that with three, or some similar arrangement.
But the opposite is the case. The movements of the sun and moon are
fewer than those of some of the planets. Yet these planets are farther
from the centre and thus nearer to the primary body than they, as
observation has itself revealed. For we have seen the moon, half-full,
pass beneath the planet Mars, which vanished on its shadow side and
came forth by the bright and shining part. Similar accounts of other
stars are given by the Egyptians and Babylonians, whose observations
have been kept for very many years past, and from whom much of our
evidence about particular stars is derived. A second difficulty
which may with equal justice be raised is this. Why is it that the
primary motion includes such a multitude of stars that their whole
array seems to defy counting, while of the other stars each one is
separated off, and in no case do we find two or more attached to the
same motion?

  On these questions, I say, it is well that we should seek to
increase our understanding, though we have but little to go upon,
and are placed at so great a distance from the facts in question.
Nevertheless there are certain principles on which if we base our
consideration we shall not find this difficulty by any means
insoluble. We may object that we have been thinking of the stars as
mere bodies, and as units with a serial order indeed but entirely
inanimate; but should rather conceive them as enjoying life and
action. On this view the facts cease to appear surprising. For it is
natural that the best-conditioned of all things should have its good
without action, that which is nearest to it should achieve it by
little and simple action, and that which is farther removed by a
complexity of actions, just as with men's bodies one is in good
condition without exercise at all, another after a short walk, while
another requires running and wrestling and hard training, and there
are yet others who however hard they worked themselves could never
secure this good, but only some substitute for it. To succeed often or
in many things is difficult. For instance, to throw ten thousand
Coan throws with the dice would be impossible, but to throw one or two
is comparatively easy. In action, again, when A has to be done to
get B, B to get C, and C to get D, one step or two present little
difficulty, but as the series extends the difficulty grows. We must,
then, think of the action of the lower stars as similar to that of
animals and plants. For on our earth it is man that has the greatest
variety of actions-for there are many goods that man can secure; hence
his actions are various and directed to ends beyond them-while the
perfectly conditioned has no need of action, since it is itself the
end, and action always requires two terms, end and means. The lower
animals have less variety of action than man; and plants perhaps
have little action and of one kind only. For either they have but
one attainable good (as indeed man has), or, if several, each
contributes directly to their ultimate good. One thing then has and
enjoys the ultimate good, other things attain to it, one immediately
by few steps, another by many, while yet another does not even attempt
to secure it but is satisfied to reach a point not far removed from
that consummation. Thus, taking health as the end, there will be one
thing that always possesses health, others that attain it, one by
reducing flesh, another by running and thus reducing flesh, another by
taking steps to enable himself to run, thus further increasing the
number of movements, while another cannot attain health itself, but
only running or reduction of flesh, so that one or other of these is
for such a being the end. For while it is clearly best for any being
to attain the real end, yet, if that cannot be, the nearer it is to
the best the better will be its state. It is for this reason that
the earth moves not at all and the bodies near to it with few
movements. For they do not attain the final end, but only come as near
to it as their share in the divine principle permits. But the first
heaven finds it immediately with a single movement, and the bodies
intermediate between the first and last heavens attain it indeed,
but at the cost of a multiplicity of movement.

  As to the difficulty that into the one primary motion is crowded a
vast multitude of stars, while of the other stars each has been
separately given special movements of its own, there is in the first
place this reason for regarding the arrangement as a natural one. In
thinking of the life and moving principle of the several heavens one
must regard the first as far superior to the others. Such a
superiority would be reasonable. For this single first motion has to
move many of the divine bodies, while the numerous other motions
move only one each, since each single planet moves with a variety of
motions. Thus, then, nature makes matters equal and establishes a
certain order, giving to the single motion many bodies and to the
single body many motions. And there is a second reason why the other
motions have each only one body, in that each of them except the last,
i.e. that which contains the one star, is really moving many bodies.
For this last sphere moves with many others, to which it is fixed,
each sphere being actually a body; so that its movement will be a
joint product. Each sphere, in fact, has its particular natural
motion, to which the general movement is, as it were, added. But the
force of any limited body is only adequate to moving a limited body.

  The characteristics of the stars which move with a circular
motion, in respect of substance and shape, movement and order, have
now been sufficiently explained.

                                13

  It remains to speak of the earth, of its position, of the question
whether it is at rest or in motion, and of its shape.

  I. As to its position there is some difference of opinion. Most
people-all, in fact, who regard the whole heaven as finite-say it lies
at the centre. But the Italian philosophers known as Pythagoreans take
the contrary view. At the centre, they say, is fire, and the earth
is one of the stars, creating night and day by its circular motion
about the centre. They further construct another earth in opposition
to ours to which they give the name counterearth. In all this they are
not seeking for theories and causes to account for observed facts, but
rather forcing their observations and trying to accommodate them to
certain theories and opinions of their own. But there are many
others who would agree that it is wrong to give the earth the
central position, looking for confirmation rather to theory than to
the facts of observation. Their view is that the most precious place
befits the most precious thing: but fire, they say, is more precious
than earth, and the limit than the intermediate, and the circumference
and the centre are limits. Reasoning on this basis they take the
view that it is not earth that lies at the centre of the sphere, but
rather fire. The Pythagoreans have a further reason. They hold that
the most important part of the world, which is the centre, should be
most strictly guarded, and name it, or rather the fire which
occupies that place, the 'Guardhouse of Zeus', as if the word 'centre'
were quite unequivocal, and the centre of the mathematical figure were
always the same with that of the thing or the natural centre. But it
is better to conceive of the case of the whole heaven as analogous
to that of animals, in which the centre of the animal and that of
the body are different. For this reason they have no need to be so
disturbed about the world, or to call in a guard for its centre:
rather let them look for the centre in the other sense and tell us
what it is like and where nature has set it. That centre will be
something primary and precious; but to the mere position we should
give the last place rather than the first. For the middle is what is
defined, and what defines it is the limit, and that which contains
or limits is more precious than that which is limited, see ing that
the latter is the matter and the former the essence of the system.

  II. As to the position of the earth, then, this is the view which
some advance, and the views advanced concerning its rest or motion are
similar. For here too there is no general agreement. All who deny that
the earth lies at the centre think that it revolves about the
centre, and not the earth only but, as we said before, the
counter-earth as well. Some of them even consider it possible that
there are several bodies so moving, which are invisible to us owing to
the interposition of the earth. This, they say, accounts for the
fact that eclipses of the moon are more frequent than eclipses of
the sun: for in addition to the earth each of these moving bodies
can obstruct it. Indeed, as in any case the surface of the earth is
not actually a centre but distant from it a full hemisphere, there
is no more difficulty, they think, in accounting for the observed
facts on their view that we do not dwell at the centre, than on the
common view that the earth is in the middle. Even as it is, there is
nothing in the observations to suggest that we are removed from the
centre by half the diameter of the earth. Others, again, say that
the earth, which lies at the centre, is 'rolled', and thus in
motion, about the axis of the whole heaven, So it stands written in
the Timaeus.

  III. There are similar disputes about the shape of the earth. Some
think it is spherical, others that it is flat and drum-shaped. For
evidence they bring the fact that, as the sun rises and sets, the part
concealed by the earth shows a straight and not a curved edge, whereas
if the earth were spherical the line of section would have to be
circular. In this they leave out of account the great distance of
the sun from the earth and the great size of the circumference, which,
seen from a distance on these apparently small circles appears
straight. Such an appearance ought not to make them doubt the circular
shape of the earth. But they have another argument. They say that
because it is at rest, the earth must necessarily have this shape. For
there are many different ways in which the movement or rest of the
earth has been conceived.

  The difficulty must have occurred to every one. It would indeed be a
complacent mind that felt no surprise that, while a little bit of
earth, let loose in mid-air moves and will not stay still, and more
there is of it the faster it moves, the whole earth, free in midair,
should show no movement at all. Yet here is this great weight of
earth, and it is at rest. And again, from beneath one of these
moving fragments of earth, before it falls, take away the earth, and
it will continue its downward movement with nothing to stop it. The
difficulty then, has naturally passed into a common place of
philosophy; and one may well wonder that the solutions offered are not
seen to involve greater absurdities than the problem itself.

  By these considerations some have been led to assert that the
earth below us is infinite, saying, with Xenophanes of Colophon,
that it has 'pushed its roots to infinity',-in order to save the
trouble of seeking for the cause. Hence the sharp rebuke of
Empedocles, in the words 'if the deeps of the earth are endless and
endless the ample ether-such is the vain tale told by many a tongue,
poured from the mouths of those who have seen but little of the whole.
Others say the earth rests upon water. This, indeed, is the oldest
theory that has been preserved, and is attributed to Thales of
Miletus. It was supposed to stay still because it floated like wood
and other similar substances, which are so constituted as to rest upon
but not upon air. As if the same account had not to be given of the
water which carries the earth as of the earth itself! It is not the
nature of water, any more than of earth, to stay in mid-air: it must
have something to rest upon. Again, as air is lighter than water, so
is water than earth: how then can they think that the naturally
lighter substance lies below the heavier? Again, if the earth as a
whole is capable of floating upon water, that must obviously be the
case with any part of it. But observation shows that this is not the
case. Any piece of earth goes to the bottom, the quicker the larger it
is. These thinkers seem to push their inquiries some way into the
problem, but not so far as they might. It is what we are all
inclined to do, to direct our inquiry not by the matter itself, but by
the views of our opponents: and even when interrogating oneself one
pushes the inquiry only to the point at which one can no longer
offer any opposition. Hence a good inquirer will be one who is ready
in bringing forward the objections proper to the genus, and that he
will be when he has gained an understanding of all the differences.

  Anaximenes and Anaxagoras and Democritus give the flatness of the
earth as the cause of its staying still. Thus, they say, it does not
cut, but covers like a lid, the air beneath it. This seems to be the
way of flat-shaped bodies: for even the wind can scarcely move them
because of their power of resistance. The same immobility, they say,
is produced by the flatness of the surface which the earth presents to
the air which underlies it; while the air, not having room enough to
change its place because it is underneath the earth, stays there in
a mass, like the water in the case of the water-clock. And they adduce
an amount of evidence to prove that air, when cut off and at rest, can
bear a considerable weight.

  Now, first, if the shape of the earth is not flat, its flatness
cannot be the cause of its immobility. But in their own account it
is rather the size of the earth than its flatness that causes it to
remain at rest. For the reason why the air is so closely confined that
it cannot find a passage, and therefore stays where it is, is its
great amount: and this amount great because the body which isolates
it, the earth, is very large. This result, then, will follow, even
if the earth is spherical, so long as it retains its size. So far as
their arguments go, the earth will still be at rest.

  In general, our quarrel with those who speak of movement in this way
cannot be confined to the parts; it concerns the whole universe. One
must decide at the outset whether bodies have a natural movement or
not, whether there is no natural but only constrained movement.
Seeing, however, that we have already decided this matter to the
best of our ability, we are entitled to treat our results as
representing fact. Bodies, we say, which have no natural movement,
have no constrained movement; and where there is no natural and no
constrained movement there will be no movement at all. This is a
conclusion, the necessity of which we have already decided, and we
have seen further that rest also will be inconceivable, since rest,
like movement, is either natural or constrained. But if there is any
natural movement, constraint will not be the sole principle of
motion or of rest. If, then, it is by constraint that the earth now
keeps its place, the so-called 'whirling' movement by which its
parts came together at the centre was also constrained. (The form of
causation supposed they all borrow from observations of liquids and of
air, in which the larger and heavier bodies always move to the
centre of the whirl. This is thought by all those who try to
generate the heavens to explain why the earth came together at the
centre. They then seek a reason for its staying there; and some say,
in the manner explained, that the reason is its size and flatness,
others, with Empedocles, that the motion of the heavens, moving
about it at a higher speed, prevents movement of the earth, as the
water in a cup, when the cup is given a circular motion, though it
is often underneath the bronze, is for this same reason prevented from
moving with the downward movement which is natural to it.) But suppose
both the 'whirl' and its flatness (the air beneath being withdrawn)
cease to prevent the earth's motion, where will the earth move to
then? Its movement to the centre was constrained, and its rest at
the centre is due to constraint; but there must be some motion which
is natural to it. Will this be upward motion or downward or what? It
must have some motion; and if upward and downward motion are alike
to it, and the air above the earth does not prevent upward movement,
then no more could air below it prevent downward movement. For the
same cause must necessarily have the same effect on the same thing.

  Further, against Empedocles there is another point which might be
made. When the elements were separated off by Hate, what caused the
earth to keep its place? Surely the 'whirl' cannot have been then also
the cause. It is absurd too not to perceive that, while the whirling
movement may have been responsible for the original coming together of
the art of earth at the centre, the question remains, why now do all
heavy bodies move to the earth. For the whirl surely does not come
near us. Why, again, does fire move upward? Not, surely, because of
the whirl. But if fire is naturally such as to move in a certain
direction, clearly the same may be supposed to hold of earth. Again,
it cannot be the whirl which determines the heavy and the light.
Rather that movement caused the pre-existent heavy and light things to
go to the middle and stay on the surface respectively. Thus, before
ever the whirl began, heavy and light existed; and what can have
been the ground of their distinction, or the manner and direction of
their natural movements? In the infinite chaos there can have been
neither above nor below, and it is by these that heavy and light are
determined.

  It is to these causes that most writers pay attention: but there are
some, Anaximander, for instance, among the ancients, who say that
the earth keeps its place because of its indifference. Motion upward
and downward and sideways were all, they thought, equally
inappropriate to that which is set at the centre and indifferently
related to every extreme point; and to move in contrary directions
at the same time was impossible: so it must needs remain still. This
view is ingenious but not true. The argument would prove that
everything, whatever it be, which is put at the centre, must stay
there. Fire, then, will rest at the centre: for the proof turns on
no peculiar property of earth. But this does not follow. The
observed facts about earth are not only that it remains at the centre,
but also that it moves to the centre. The place to which any
fragment of earth moves must necessarily be the place to which the
whole moves; and in the place to which a thing naturally moves, it
will naturally rest. The reason then is not in the fact that the earth
is indifferently related to every extreme point: for this would
apply to any body, whereas movement to the centre is peculiar to
earth. Again it is absurd to look for a reason why the earth remains
at the centre and not for a reason why fire remains at the
extremity. If the extremity is the natural place of fire, clearly
earth must also have a natural place. But suppose that the centre is
not its place, and that the reason of its remaining there is this
necessity of indifference-on the analogy of the hair which, it is
said, however great the tension, will not break under it, if it be
evenly distributed, or of the men who, though exceedingly hungry and
thirsty, and both equally, yet being equidistant from food and
drink, is therefore bound to stay where he is-even so, it still
remains to explain why fire stays at the extremities. It is strange,
too, to ask about things staying still but not about their
motion,-why, I mean, one thing, if nothing stops it, moves up, and
another thing to the centre. Again, their statements are not true.
It happens, indeed, to be the case that a thing to which movement this
way and that is equally inappropriate is obliged to remain at the
centre. But so far as their argument goes, instead of remaining there,
it will move, only not as a mass but in fragments. For the argument
applies equally to fire. Fire, if set at the centre, should stay
there, like earth, since it will be indifferently related to every
point on the extremity. Nevertheless it will move, as in fact it
always does move when nothing stops it, away from the centre to the
extremity. It will not, however, move in a mass to a single point on
the circumference-the only possible result on the lines of the
indifference theory-but rather each corresponding portion of fire to
the corresponding part of the extremity, each fourth part, for
instance, to a fourth part of the circumference. For since no body
is a point, it will have parts. The expansion, when the body increased
the place occupied, would be on the same principle as the contraction,
in which the place was diminished. Thus, for all the indifference
theory shows to the contrary, earth also would have moved in this
manner away from the centre, unless the centre had been its natural
place.

  We have now outlined the views held as to the shape, position, and
rest or movement of the earth.

                                14

  Let us first decide the question whether the earth moves or is at
rest. For, as we said, there are some who make it one of the stars,
and others who, setting it at the centre, suppose it to be 'rolled'
and in motion about the pole as axis. That both views are untenable
will be clear if we take as our starting-point the fact that the
earth's motion, whether the earth be at the centre or away from it,
must needs be a constrained motion. It cannot be the movement of the
earth itself. If it were, any portion of it would have this
movement; but in fact every part moves in a straight line to the
centre. Being, then, constrained and unnatural, the movement could not
be eternal. But the order of the universe is eternal. Again,
everything that moves with the circular movement, except the first
sphere, is observed to be passed, and to move with more than one
motion. The earth, then, also, whether it move about the centre or
as stationary at it, must necessarily move with two motions. But if
this were so, there would have to be passings and turnings of the
fixed stars. Yet no such thing is observed. The same stars always rise
and set in the same parts of the earth.

  Further, the natural movement of the earth, part and whole alike, is
the centre of the whole-whence the fact that it is now actually
situated at the centre-but it might be questioned since both centres
are the same, which centre it is that portions of earth and other
heavy things move to. Is this their goal because it is the centre of
the earth or because it is the centre of the whole? The goal,
surely, must be the centre of the whole. For fire and other light
things move to the extremity of the area which contains the centre. It
happens, however, that the centre of the earth and of the whole is the
same. Thus they do move to the centre of the earth, but
accidentally, in virtue of the fact that the earth's centre lies at
the centre of the whole. That the centre of the earth is the goal of
their movement is indicated by the fact that heavy bodies moving
towards the earth do not parallel but so as to make equal angles,
and thus to a single centre, that of the earth. It is clear, then,
that the earth must be at the centre and immovable, not only for the
reasons already given, but also because heavy bodies forcibly thrown
quite straight upward return to the point from which they started,
even if they are thrown to an infinite distance. From these
considerations then it is clear that the earth does not move and
does not lie elsewhere than at the centre.

  From what we have said the explanation of the earth's immobility
is also apparent. If it is the nature of earth, as observation
shows, to move from any point to the centre, as of fire contrariwise
to move from the centre to the extremity, it is impossible that any
portion of earth should move away from the centre except by
constraint. For a single thing has a single movement, and a simple
thing a simple: contrary movements cannot belong to the same thing,
and movement away from the centre is the contrary of movement to it.
If then no portion of earth can move away from the centre, obviously
still less can the earth as a whole so move. For it is the nature of
the whole to move to the point to which the part naturally moves.
Since, then, it would require a force greater than itself to move
it, it must needs stay at the centre. This view is further supported
by the contributions of mathematicians to astronomy, since the
observations made as the shapes change by which the order of the stars
is determined, are fully accounted for on the hypothesis that the
earth lies at the centre. Of the position of the earth and of the
manner of its rest or movement, our discussion may here end.

  Its shape must necessarily be spherical. For every portion of
earth has weight until it reaches the centre, and the jostling of
parts greater and smaller would bring about not a waved surface, but
rather compression and convergence of part and part until the centre
is reached. The process should be conceived by supposing the earth
to come into being in the way that some of the natural philosophers
describe. Only they attribute the downward movement to constraint, and
it is better to keep to the truth and say that the reason of this
motion is that a thing which possesses weight is naturally endowed
with a centripetal movement. When the mixture, then, was merely
potential, the things that were separated off moved similarly from
every side towards the centre. Whether the parts which came together
at the centre were distributed at the extremities evenly, or in some
other way, makes no difference. If, on the one hand, there were a
similar movement from each quarter of the extremity to the single
centre, it is obvious that the resulting mass would be similar on
every side. For if an equal amount is added on every side the
extremity of the mass will be everywhere equidistant from its
centre, i.e. the figure will be spherical. But neither will it in
any way affect the argument if there is not a similar accession of
concurrent fragments from every side. For the greater quantity,
finding a lesser in front of it, must necessarily drive it on, both
having an impulse whose goal is the centre, and the greater weight
driving the lesser forward till this goal is reached. In this we
have also the solution of a possible difficulty. The earth, it might
be argued, is at the centre and spherical in shape: if, then, a weight
many times that of the earth were added to one hemisphere, the
centre of the earth and of the whole will no longer be coincident.
So that either the earth will not stay still at the centre, or if it
does, it will be at rest without having its centre at the place to
which it is still its nature to move. Such is the difficulty. A
short consideration will give us an easy answer, if we first give
precision to our postulate that any body endowed with weight, of
whatever size, moves towards the centre. Clearly it will not stop when
its edge touches the centre. The greater quantity must prevail until
the body's centre occupies the centre. For that is the goal of its
impulse. Now it makes no difference whether we apply this to a clod or
common fragment of earth or to the earth as a whole. The fact
indicated does not depend upon degrees of size but applies universally
to everything that has the centripetal impulse. Therefore earth in
motion, whether in a mass or in fragments, necessarily continues to
move until it occupies the centre equally every way, the less being
forced to equalize itself by the greater owing to the forward drive of
the impulse.

  If the earth was generated, then, it must have been formed in this
way, and so clearly its generation was spherical; and if it is
ungenerated and has remained so always, its character must be that
which the initial generation, if it had occurred, would have given it.
But the spherical shape, necessitated by this argument, follows also
from the fact that the motions of heavy bodies always make equal
angles, and are not parallel. This would be the natural form of
movement towards what is naturally spherical. Either then the earth is
spherical or it is at least naturally spherical. And it is right to
call anything that which nature intends it to be, and which belongs to
it, rather than that which it is by constraint and contrary to nature.
The evidence of the senses further corroborates this. How else would
eclipses of the moon show segments shaped as we see them? As it is,
the shapes which the moon itself each month shows are of every kind
straight, gibbous, and concave-but in eclipses the outline is always
curved: and, since it is the interposition of the earth that makes the
eclipse, the form of this line will be caused by the form of the
earth's surface, which is therefore spherical. Again, our observations
of the stars make it evident, not only that the earth is circular, but
also that it is a circle of no great size. For quite a small change of
position to south or north causes a manifest alteration of the
horizon. There is much change, I mean, in the stars which are
overhead, and the stars seen are different, as one moves northward
or southward. Indeed there are some stars seen in Egypt and in the
neighbourhood of Cyprus which are not seen in the northerly regions;
and stars, which in the north are never beyond the range of
observation, in those regions rise and set. All of which goes to
show not only that the earth is circular in shape, but also that it is
a sphere of no great size: for otherwise the effect of so slight a
change of place would not be quickly apparent. Hence one should not be
too sure of the incredibility of the view of those who conceive that
there is continuity between the parts about the pillars of Hercules
and the parts about India, and that in this way the ocean is one. As
further evidence in favour of this they quote the case of elephants, a
species occurring in each of these extreme regions, suggesting that
the common characteristic of these extremes is explained by their
continuity. Also, those mathematicians who try to calculate the size
of the earth's circumference arrive at the figure 400,000 stades. This
indicates not only that the earth's mass is spherical in shape, but
also that as compared with the stars it is not of great size.

                              Book III

                                 1

  WE have already discussed the first heaven and its parts, the moving
stars within it, the matter of which these are composed and their
bodily constitution, and we have also shown that they are
ungenerated and indestructible. Now things that we call natural are
either substances or functions and attributes of substances. As
substances I class the simple bodies-fire, earth, and the other
terms of the series-and all things composed of them; for example,
the heaven as a whole and its parts, animals, again, and plants and
their parts. By attributes and functions I mean the movements of these
and of all other things in which they have power in themselves to
cause movement, and also their alterations and reciprocal
transformations. It is obvious, then, that the greater part of the
inquiry into nature concerns bodies: for a natural substance is either
a body or a thing which cannot come into existence without body and
magnitude. This appears plainly from an analysis of the character of
natural things, and equally from an inspection of the instances of
inquiry into nature. Since, then, we have spoken of the primary
element, of its bodily constitution, and of its freedom from
destruction and generation, it remains to speak of the other two. In
speaking of them we shall be obliged also to inquire into generation
and destruction. For if there is generation anywhere, it must be in
these elements and things composed of them.

  This is indeed the first question we have to ask: is generation a
fact or not? Earlier speculation was at variance both with itself
and with the views here put forward as to the true answer to this
question. Some removed generation and destruction from the world
altogether. Nothing that is, they said, is generated or destroyed, and
our conviction to the contrary is an illusion. So maintained the
school of Melissus and Parmenides. But however excellent their
theories may otherwise be, anyhow they cannot be held to speak as
students of nature. There may be things not subject to generation or
any kind of movement, but if so they belong to another and a higher
inquiry than the study of nature. They, however, had no idea of any
form of being other than the substance of things perceived; and when
they saw, what no one previously had seen, that there could be no
knowledge or wisdom without some such unchanging entities, they
naturally transferred what was true of them to things perceived.
Others, perhaps intentionally, maintain precisely the contrary opinion
to this. It has been asserted that everything in the world was subject
to generation and nothing was ungenerated, but that after being
generated some things remained indestructible while the rest were
again destroyed. This had been asserted in the first instance by
Hesiod and his followers, but afterwards outside his circle by the
earliest natural philosophers. But what these thinkers maintained
was that all else has been generated and, as they said, 'is flowing
away, nothing having any solidity, except one single thing which
persists as the basis of all these transformations. So we may
interpret the statements of Heraclitus of Ephesus and many others. And
some subject all bodies whatever to generation, by means of the
composition and separation of planes.

  Discussion of the other views may be postponed. But this last theory
which composes every body of planes is, as the most superficial
observation shows, in many respects in plain contradiction with
mathematics. It is, however, wrong to remove the foundations of a
science unless you can replace them with others more convincing.
And, secondly, the same theory which composes solids of planes clearly
composes planes of lines and lines of points, so that a part of a line
need not be a line. This matter has been already considered in our
discussion of movement, where we have shown that an indivisible length
is impossible. But with respect to natural bodies there are
impossibilities involved in the view which asserts indivisible
lines, which we may briefly consider at this point. For the impossible
consequences which result from this view in the mathematical sphere
will reproduce themselves when it is applied to physical bodies, but
there will be difficulties in physics which are not present in
mathematics; for mathematics deals with an abstract and physics with a
more concrete object. There are many attributes necessarily present in
physical bodies which are necessarily excluded by indivisibility;
all attributes, in fact, which are divisible. There can be nothing
divisible in an indivisible thing, but the attributes of bodies are
all divisible in one of two ways. They are divisible into kinds, as
colour is divided into white and black, and they are divisible per
accidens when that which has them is divisible. In this latter sense
attributes which are simple are nevertheless divisible. Attributes
of this kind will serve, therefore, to illustrate the impossibility of
the view. It is impossible, if two parts of a thing have no weight,
that the two together should have weight. But either all perceptible
bodies or some, such as earth and water, have weight, as these
thinkers would themselves admit. Now if the point has no weight,
clearly the lines have not either, and, if they have not, neither have
the planes. Therefore no body has weight. It is, further, manifest
that their point cannot have weight. For while a heavy thing may
always be heavier than something and a light thing lighter than
something, a thing which is heavier or lighter than something need not
be itself heavy or light, just as a large thing is larger than others,
but what is larger is not always large. A thing which, judged
absolutely, is small may none the less be larger than other things.
Whatever, then, is heavy and also heavier than something else, must
exceed this by something which is heavy. A heavy thing therefore is
always divisible. But it is common ground that a point is indivisible.
Again, suppose that what is heavy or weight is a dense body, and
what is light rare. Dense differs from rare in containing more
matter in the same cubic area. A point, then, if it may be heavy or
light, may be dense or rare. But the dense is divisible while a
point is indivisible. And if what is heavy must be either hard or
soft, an impossible consequence is easy to draw. For a thing is soft
if its surface can be pressed in, hard if it cannot; and if it can
be pressed in it is divisible.

  Moreover, no weight can consist of parts not possessing weight.
For how, except by the merest fiction, can they specify the number and
character of the parts which will produce weight? And, further, when
one weight is greater than another, the difference is a third
weight; from which it will follow that every indivisible part
possesses weight. For suppose that a body of four points possesses
weight. A body composed of more than four points will superior in
weight to it, a thing which has weight. But the difference between
weight and weight must be a weight, as the difference between white
and whiter is white. Here the difference which makes the superior
weight heavier is the single point which remains when the common
number, four, is subtracted. A single point, therefore, has weight.

  Further, to assume, on the one hand, that the planes can only be put
in linear contact would be ridiculous. For just as there are two
ways of putting lines together, namely, end to and side by side, so
there must be two ways of putting planes together. Lines can be put
together so that contact is linear by laying one along the other,
though not by putting them end to end. But if, similarly, in putting
the lanes together, superficial contact is allowed as an alternative
to linear, that method will give them bodies which are not any element
nor composed of elements. Again, if it is the number of planes in a
body that makes one heavier than another, as the Timaeus explains,
clearly the line and the point will have weight. For the three cases
are, as we said before, analogous. But if the reason of differences of
weight is not this, but rather the heaviness of earth and the
lightness of fire, then some of the planes will be light and others
heavy (which involves a similar distinction in the lines and the
points); the earthplane, I mean, will be heavier than the
fire-plane. In general, the result is either that there is no
magnitude at all, or that all magnitude could be done away with. For a
point is to a line as a line is to a plane and as a plane is to a
body. Now the various forms in passing into one another will each be
resolved into its ultimate constituents. It might happen therefore
that nothing existed except points, and that there was no body at all.
A further consideration is that if time is similarly constituted,
there would be, or might be, a time at which it was done away with.
For the indivisible now is like a point in a line. The same
consequences follow from composing the heaven of numbers, as some of
the Pythagoreans do who make all nature out of numbers. For natural
bodies are manifestly endowed with weight and lightness, but an
assemblage of units can neither be composed to form a body nor possess
weight.

                                 2

  The necessity that each of the simple bodies should have a natural
movement may be shown as follows. They manifestly move, and if they
have no proper movement they must move by constraint: and the
constrained is the same as the unnatural. Now an unnatural movement
presupposes a natural movement which it contravenes, and which,
however many the unnatural movements, is always one. For naturally a
thing moves in one way, while its unnatural movements are manifold.
The same may be shown, from the fact of rest. Rest, also, must
either be constrained or natural, constrained in a place to which
movement was constrained, natural in a place movement to which was
natural. Now manifestly there is a body which is at rest at the
centre. If then this rest is natural to it, clearly motion to this
place is natural to it. If, on the other hand, its rest is
constrained, what is hindering its motion? Something, which is at
rest: but if so, we shall simply repeat the same argument; and
either we shall come to an ultimate something to which rest where it
is or we shall have an infinite process, which is impossible. The
hindrance to its movement, then, we will suppose, is a moving thing-as
Empedocles says that it is the vortex which keeps the earth still-:
but in that case we ask, where would it have moved to but for the
vortex? It could not move infinitely; for to traverse an infinite is
impossible, and impossibilities do not happen. So the moving thing
must stop somewhere, and there rest not by constraint but naturally.
But a natural rest proves a natural movement to the place of rest.
Hence Leucippus and Democritus, who say that the primary bodies are in
perpetual movement in the void or infinite, may be asked to explain
the manner of their motion and the kind of movement which is natural
to them. For if the various elements are constrained by one another to
move as they do, each must still have a natural movement which the
constrained contravenes, and the prime mover must cause motion not
by constraint but naturally. If there is no ultimate natural cause
of movement and each preceding term in the series is always moved by
constraint, we shall have an infinite process. The same difficulty
is involved even if it is supposed, as we read in the Timaeus, that
before the ordered world was made the elements moved without order.
Their movement must have been due either to constraint or to their
nature. And if their movement was natural, a moment's consideration
shows that there was already an ordered world. For the prime mover
must cause motion in virtue of its own natural movement, and the other
bodies, moving without constraint, as they came to rest in their
proper places, would fall into the order in which they now stand,
the heavy bodies moving towards the centre and the light bodies away
from it. But that is the order of their distribution in our world.
There is a further question, too, which might be asked. Is it possible
or impossible that bodies in unordered movement should combine in some
cases into combinations like those of which bodies of nature's
composing are composed, such, I mean, as bones and flesh? Yet this
is what Empedocles asserts to have occurred under Love. 'Many a head',
says he, 'came to birth without a neck.' The answer to the view that
there are infinite bodies moving in an infinite is that, if the
cause of movement is single, they must move with a single motion,
and therefore not without order; and if, on the other hand, the causes
are of infinite variety, their motions too must be infinitely
varied. For a finite number of causes would produce a kind of order,
since absence of order is not proved by diversity of direction in
motions: indeed, in the world we know, not all bodies, but only bodies
of the same kind, have a common goal of movement. Again, disorderly
movement means in reality unnatural movement, since the order proper
to perceptible things is their nature. And there is also absurdity and
impossibility in the notion that the disorderly movement is infinitely
continued. For the nature of things is the nature which most of them
possess for most of the time. Thus their view brings them into the
contrary position that disorder is natural, and order or system
unnatural. But no natural fact can originate in chance. This is a
point which Anaxagoras seems to have thoroughly grasped; for he starts
his cosmogony from unmoved things. The others, it is true, make things
collect together somehow before they try to produce motion and
separation. But there is no sense in starting generation from an
original state in which bodies are separated and in movement. Hence
Empedocles begins after the process ruled by Love: for he could not
have constructed the heaven by building it up out of bodies in
separation, making them to combine by the power of Love, since our
world has its constituent elements in separation, and therefore
presupposes a previous state of unity and combination.

  These arguments make it plain that every body has its natural
movement, which is not constrained or contrary to its nature. We go on
to show that there are certain bodies whose necessary impetus is
that of weight and lightness. Of necessity, we assert, they must move,
and a moved thing which has no natural impetus cannot move either
towards or away from the centre. Suppose a body A without weight,
and a body B endowed with weight. Suppose the weightless body to
move the distance CD, while B in the same time moves the distance
CE, which will be greater since the heavy thing must move further. Let
the heavy body then be divided in the proportion CE: CD (for there
is no reason why a part of B should not stand in this relation to
the whole). Now if the whole moves the whole distance CE, the part
must in the same time move the distance CD. A weightless body,
therefore, and one which has weight will move the same distance, which
is impossible. And the same argument would fit the case of
lightness. Again, a body which is in motion but has neither weight nor
lightness, must be moved by constraint, and must continue its
constrained movement infinitely. For there will be a force which moves
it, and the smaller and lighter a body is the further will a given
force move it. Now let A, the weightless body, be moved the distance
CE, and B, which has weight, be moved in the same time the distance
CD. Dividing the heavy body in the proportion CE:CD, we subtract
from the heavy body a part which will in the same time move the
distance CE, since the whole moved CD: for the relative speeds of
the two bodies will be in inverse ratio to their respective sizes.
Thus the weightless body will move the same distance as the heavy in
the same time. But this is impossible. Hence, since the motion of
the weightless body will cover a greater distance than any that is
suggested, it will continue infinitely. It is therefore obvious that
every body must have a definite weight or lightness. But since
'nature' means a source of movement within the thing itself, while a
force is a source of movement in something other than it or in
itself qua other, and since movement is always due either to nature or
to constraint, movement which is natural, as downward movement is to a
stone, will be merely accelerated by an external force, while an
unnatural movement will be due to the force alone. In either case
the air is as it were instrumental to the force. For air is both light
and heavy, and thus qua light produces upward motion, being
propelled and set in motion by the force, and qua heavy produces a
downward motion. In either case the force transmits the movement to
the body by first, as it were, impregnating the air. That is why a
body moved by constraint continues to move when that which gave the
impulse ceases to accompany it. Otherwise, i.e. if the air were not
endowed with this function, constrained movement would be
impossible. And the natural movement of a body may be helped on in the
same way. This discussion suffices to show (1) that all bodies are
either light or heavy, and (2) how unnatural movement takes place.

  From what has been said earlier it is plain that there cannot be
generation either of everything or in an absolute sense of anything.
It is impossible that everything should be generated, unless an
extra-corporeal void is possible. For, assuming generation, the
place which is to be occupied by that which is coming to be, must have
been previously occupied by void in which no body was. Now it is quite
possible for one body to be generated out of another, air for instance
out of fire, but in the absence of any pre-existing mass generation is
impossible. That which is potentially a certain kind of body may, it
is true, become such in actuality, But if the potential body was not
already in actuality some other kind of body, the existence of an
extra-corporeal void must be admitted.

                                 3

  It remains to say what bodies are subject to generation, and why.
Since in every case knowledge depends on what is primary, and the
elements are the primary constituents of bodies, we must ask which
of such bodies are elements, and why; and after that what is their
number and character. The answer will be plain if we first explain
what kind of substance an element is. An element, we take it, is a
body into which other bodies may be analysed, present in them
potentially or in actuality (which of these, is still disputable), and
not itself divisible into bodies different in form. That, or something
like it, is what all men in every case mean by element. Now if what we
have described is an element, clearly there must be such bodies. For
flesh and wood and all other similar bodies contain potentially fire
and earth, since one sees these elements exuded from them; and, on the
other hand, neither in potentiality nor in actuality does fire contain
flesh or wood, or it would exude them. Similarly, even if there were
only one elementary body, it would not contain them. For though it
will be either flesh or bone or something else, that does not at
once show that it contained these in potentiality: the further
question remains, in what manner it becomes them. Now Anaxagoras
opposes Empedocles' view of the elements. Empedocles says that fire
and earth and the related bodies are elementary bodies of which all
things are composed; but this Anaxagoras denies. His elements are
the homoeomerous things, viz. flesh, bone, and the like. Earth and
fire are mixtures, composed of them and all the other seeds, each
consisting of a collection of all the homoeomerous bodies,
separately invisible; and that explains why from these two bodies
all others are generated. (To him fire and aither are the same thing.)
But since every natural body has it proper movement, and movements are
either simple or mixed, mixed in mixed bodies and simple in simple,
there must obviously be simple bodies; for there are simple movements.
It is plain, then, that there are elements, and why.

                                 4

  The next question to consider is whether the elements are finite
or infinite in number, and, if finite, what their number is. Let us
first show reason or denying that their number is infinite, as some
suppose. We begin with the view of Anaxagoras that all the
homoeomerous bodies are elements. Any one who adopts this view
misapprehends the meaning of element. Observation shows that even
mixed bodies are often divisible into homoeomerous parts; examples are
flesh, bone, wood, and stone. Since then the composite cannot be an
element, not every homoeomerous body can be an element; only, as we
said before, that which is not divisible into bodies different in
form. But even taking 'element' as they do, they need not assert an
infinity of elements, since the hypothesis of a finite number will
give identical results. Indeed even two or three such bodies serve the
purpose as well, as Empedocles' attempt shows. Again, even on their
view it turns out that all things are not composed of homocomerous
bodies. They do not pretend that a face is composed of faces, or
that any other natural conformation is composed of parts like
itself. Obviously then it would be better to assume a finite number of
principles. They should, in fact, be as few as possible,
consistently with proving what has to be proved. This is the common
demand of mathematicians, who always assume as principles things
finite either in kind or in number. Again, if body is distinguished
from body by the appropriate qualitative difference, and there is a
limit to the number of differences (for the difference lies in
qualities apprehended by sense, which are in fact finite in number,
though this requires proof), then manifestly there is necessarily a
limit to the number of elements.

  There is, further, another view-that of Leucippus and Democritus
of Abdera-the implications of which are also unacceptable. The primary
masses, according to them, are infinite in number and indivisible in
mass: one cannot turn into many nor many into one; and all things
are generated by their combination and involution. Now this view in
a sense makes things out to be numbers or composed of numbers. The
exposition is not clear, but this is its real meaning. And further,
they say that since the atomic bodies differ in shape, and there is an
infinity of shapes, there is an infinity of simple bodies. But they
have never explained in detail the shapes of the various elements,
except so far to allot the sphere to fire. Air, water, and the rest
they distinguished by the relative size of the atom, assuming that the
atomic substance was a sort of master-seed for each and every element.
Now, in the first place, they make the mistake already noticed. The
principles which they assume are not limited in number, though such
limitation would necessitate no other alteration in their theory.
Further, if the differences of bodies are not infinite, plainly the
elements will not be an infinity. Besides, a view which asserts atomic
bodies must needs come into conflict with the mathematical sciences,
in addition to invalidating many common opinions and apparent data
of sense perception. But of these things we have already spoken in our
discussion of time and movement. They are also bound to contradict
themselves. For if the elements are atomic, air, earth, and water
cannot be differentiated by the relative sizes of their atoms, since
then they could not be generated out of one another. The extrusion
of the largest atoms is a process that will in time exhaust the
supply; and it is by such a process that they account for the
generation of water, air, and earth from one another. Again, even on
their own presuppositions it does not seem as if the clements would be
infinite in number. The atoms differ in figure, and all figures are
composed of pyramids, rectilinear the case of rectilinear figures,
while the sphere has eight pyramidal parts. The figures must have
their principles, and, whether these are one or two or more, the
simple bodies must be the same in number as they. Again, if every
element has its proper movement, and a simple body has a simple
movement, and the number of simple movements is not infinite,
because the simple motions are only two and the number of places is
not infinite, on these grounds also we should have to deny that the
number of elements is infinite.

                                 5

  Since the number of the elements must be limited, it remains to
inquire whether there is more than one element. Some assume one
only, which is according to some water, to others air, to others fire,
to others again something finer than water and denser than air, an
infinite body-so they say-bracing all the heavens.

  Now those who decide for a single element, which is either water
or air or a body finer than water and denser than air, and proceed
to generate other things out of it by use of the attributes density
and rarity, all alike fail to observe the fact that they are depriving
the element of its priority. Generation out of the elements is, as
they say, synthesis, and generation into the elements is analysis,
so that the body with the finer parts must have priority in the
order of nature. But they say that fire is of all bodies the finest.
Hence fire will be first in the natural order. And whether the
finest body is fire or not makes no difference; anyhow it must be
one of the other bodies that is primary and not that which is
intermediate. Again, density and rarity, as instruments of generation,
are equivalent to fineness and coarseness, since the fine is rare, and
coarse in their use means dense. But fineness and coarseness, again,
are equivalent to greatness and smallness, since a thing with small
parts is fine and a thing with large parts coarse. For that which
spreads itself out widely is fine, and a thing composed of small parts
is so spread out. In the end, then, they distinguish the various other
substances from the element by the greatness and smallness of their
parts. This method of distinction makes all judgement relative.
There will be no absolute distinction between fire, water, and air,
but one and the same body will be relatively to this fire,
relatively to something else air. The same difficulty is involved
equally in the view elements and distinguishes them by their greatness
and smallness. The principle of distinction between bodies being
quantity, the various sizes will be in a definite ratio, and
whatever bodies are in this ratio to one another must be air, fire,
earth, and water respectively. For the ratios of smaller bodies may be
repeated among greater bodies.

  Those who start from fire as the single element, while avoiding this
difficulty, involve themselves in many others. Some of them give
fire a particular shape, like those who make it a pyramid, and this on
one of two grounds. The reason given may be-more crudely-that the
pyramid is the most piercing of figures as fire is of bodies,
or-more ingeniously-the position may be supported by the following
argument. As all bodies are composed of that which has the finest
parts, so all solid figures are composed of pryamids: but the finest
body is fire, while among figures the pyramid is primary and has the
smallest parts; and the primary body must have the primary figure:
therefore fire will be a pyramid. Others, again, express no opinion on
the subject of its figure, but simply regard it as the of the finest
parts, which in combination will form other bodies, as the fusing of
gold-dust produces solid gold. Both of these views involve the same
difficulties. For (1) if, on the one hand, they make the primary
body an atom, the view will be open to the objections already advanced
against the atomic theory. And further the theory is inconsistent with
a regard for the facts of nature. For if all bodies are quantitatively
commensurable, and the relative size of the various homoeomerous
masses and of their several elements are in the same ratio, so that
the total mass of water, for instance, is related to the total mass of
air as the elements of each are to one another, and so on, and if
there is more air than water and, generally, more of the finer body
than of the coarser, obviously the element of water will be smaller
than that of air. But the lesser quantity is contained in the greater.
Therefore the air element is divisible. And the same could be shown of
fire and of all bodies whose parts are relatively fine. (2) If, on the
other hand, the primary body is divisible, then (a) those who give
fire a special shape will have to say that a part of fire is not fire,
because a pyramid is not composed of pyramids, and also that not every
body is either an element or composed of elements, since a part of
fire will be neither fire nor any other element. And (b) those whose
ground of distinction is size will have to recognize an element
prior to the element, a regress which continues infinitely, since
every body is divisible and that which has the smallest parts is the
element. Further, they too will have to say that the same body is
relatively to this fire and relatively to that air, to others again
water and earth.

    The common error of all views which assume a single element is
that they allow only one natural movement, which is the same for every
body. For it is a matter of observation that a natural body
possesses a principle of movement. If then all bodies are one, all
will have one movement. With this motion the greater their quantity
the more they will move, just as fire, in proportion as its quantity
is greater, moves faster with the upward motion which belongs to it.
But the fact is that increase of quantity makes many things move the
faster downward. For these reasons, then, as well as from the
distinction already established of a plurality of natural movements,
it is impossible that there should be only one element. But if the
elements are not an infinity and not reducible to one, they must be
several and finite in number.

                                 6

  First we must inquire whether the elements are eternal or subject to
generation and destruction; for when this question has been answered
their number and character will be manifest. In the first place,
they cannot be eternal. It is a matter of observation that fire,
water, and every simple body undergo a process of analysis, which must
either continue infinitely or stop somewhere. (1) Suppose it infinite.
Then the time occupied by the process will be infinite, and also
that occupied by the reverse process of synthesis. For the processes
of analysis and synthesis succeed one another in the various parts. It
will follow that there are two infinite times which are mutually
exclusive, the time occupied by the synthesis, which is infinite,
being preceded by the period of analysis. There are thus two
mutually exclusive infinites, which is impossible. (2) Suppose, on the
other hand, that the analysis stops somewhere. Then the body at
which it stops will be either atomic or, as Empedocles seems to have
intended, a divisible body which will yet never be divided. The
foregoing arguments show that it cannot be an atom; but neither can it
be a divisible body which analysis will never reach. For a smaller
body is more easily destroyed than a larger; and a destructive process
which succeeds in destroying, that is, in resolving into smaller
bodies, a body of some size, cannot reasonably be expected to fail
with the smaller body. Now in fire we observe a destruction of two
kinds: it is destroyed by its contrary when it is quenched, and by
itself when it dies out. But the effect is produced by a greater
quantity upon a lesser, and the more quickly the smaller it is. The
elements of bodies must therefore be subject to destruction and
generation.

  Since they are generated, they must be generated either from
something incorporeal or from a body, and if from a body, either
from one another or from something else. The theory which generates
them from something incorporeal requires an extra-corporeal void.
For everything that comes to be comes to be in something, and that
in which the generation takes place must either be incorporeal or
possess body; and if it has body, there will be two bodies in the same
place at the same time, viz. that which is coming to be and that which
was previously there, while if it is incorporeal, there must be an
extra-corporeal void. But we have already shown that this is
impossible. But, on the other hand, it is equally impossible that
the elements should be generated from some kind of body. That would
involve a body distinct from the elements and prior to them. But if
this body possesses weight or lightness, it will be one of the
elements; and if it has no tendency to movement, it will be an
immovable or mathematical entity, and therefore not in a place at all.
A place in which a thing is at rest is a place in which it might move,
either by constraint, i.e. unnaturally, or in the absence of
constraint, i.e. naturally. If, then, it is in a place and
somewhere, it will be one of the elements; and if it is not in a
place, nothing can come from it, since that which comes into being and
that out of which it comes must needs be together. The elements
therefore cannot be generated from something incorporeal nor from a
body which is not an element, and the only remaining alternative is
that they are generated from one another.

                                 7

  We must, therefore, turn to the question, what is the manner of
their generation from one another? Is it as Empedocles and
Democritus say, or as those who resolve bodies into planes say, or
is there yet another possibility? (1) What the followers of Empedocles
do, though without observing it themselves, is to reduce the
generation of elements out of one another to an illusion. They make it
a process of excretion from a body of what was in it all the time-as
though generation required a vessel rather than a material-so that
it involves no change of anything. And even if this were accepted,
there are other implications equally unsatisfactory. We do not
expect a mass of matter to be made heavier by compression. But they
will be bound to maintain this, if they say that water is a body
present in air and excreted from air, since air becomes heavier when
it turns into water. Again, when the mixed body is divided, they can
show no reason why one of the constituents must by itself take up more
room than the body did: but when water turns into air, the room
occupied is increased. The fact is that the finer body takes up more
room, as is obvious in any case of transformation. As the liquid is
converted into vapour or air the vessel which contains it is often
burst because it does not contain room enough. Now, if there is no
void at all, and if, as those who take this view say, there is no
expansion of bodies, the impossibility of this is manifest: and if
there is void and expansion, there is no accounting for the fact
that the body which results from division cfpies of necessity a
greater space. It is inevitable, too, that generation of one out of
another should come to a stop, since a finite quantum cannot contain
an infinity of finite quanta. When earth produces water something is
taken away from the earth, for the process is one of excretion. The
same thing happens again when the residue produces water. But this can
only go on for ever, if the finite body contains an infinity, which is
impossible. Therefore the generation of elements out of one another
will not always continue.

  (2) We have now explained that the mutual transformations of the
elements cannot take place by means of excretion. The remaining
alternative is that they should be generated by changing into one
another. And this in one of two ways, either by change of shape, as
the same wax takes the shape both of a sphere and of a cube, or, as
some assert, by resolution into planes. (a) Generation by change of
shape would necessarily involve the assertion of atomic bodies. For if
the particles were divisible there would be a part of fire which was
not fire and a part of earth which was not earth, for the reason
that not every part of a pyramid is a pyramid nor of a cube a cube.
But if (b) the process is resolution into planes, the first difficulty
is that the elements cannot all be generated out of one another.
This they are obliged to assert, and do assert. It is absurd,
because it is unreasonable that one element alone should have no
part in the transformations, and also contrary to the observed data of
sense, according to which all alike change into one another. In fact
their explanation of the observations is not consistent with the
observations. And the reason is that their ultimate principles are
wrongly assumed: they had certain predetermined views, and were
resolved to bring everything into line with them. It seems that
perceptible things require perceptible principles, eternal things
eternal principles, corruptible things corruptible principles; and, in
general, every subject matter principles homogeneous with itself.
But they, owing to their love for their principles, fall into the
attitude of men who undertake the defence of a position in argument.
In the confidence that the principles are true they are ready to
accept any consequence of their application. As though some principles
did not require to be judged from their results, and particularly from
their final issue! And that issue, which in the case of productive
knowledge is the product, in the knowledge of nature is the
unimpeachable evidence of the senses as to each fact.

  The result of their view is that earth has the best right to the
name element, and is alone indestructible; for that which is
indissoluble is indestructible and elementary, and earth alone
cannot be dissolved into any body but itself. Again, in the case of
those elements which do suffer dissolution, the 'suspension' of the
triangles is unsatisfactory. But this takes place whenever one is
dissolved into another, because of the numerical inequality of the
triangles which compose them. Further, those who hold these views must
needs suppose that generation does not start from a body. For what
is generated out of planes cannot be said to have been generated
from a body. And they must also assert that not all bodies are
divisible, coming thus into conflict with our most accurate
sciences, namely the mathematical, which assume that even the
intelligible is divisible, while they, in their anxiety to save
their hypothesis, cannot even admit this of every perceptible thing.
For any one who gives each element a shape of its own, and makes
this the ground of distinction between the substances, has to
attribute to them indivisibility; since division of a pyramid or a
sphere must leave somewhere at least a residue which is not sphere
or a pyramid. Either, then, a part of fire is not fire, so that
there is a body prior to the element-for every body is either an
element or composed of elements-or not every body is divisible.

                                 8

  In general, the attempt to give a shape to each of the simple bodies
is unsound, for the reason, first, that they will not succeed in
filling the whole. It is agreed that there are only three plane
figures which can fill a space, the triangle, the square, and the
hexagon, and only two solids, the pyramid and the cube. But the theory
needs more than these because the elements which it recognizes are
more in number. Secondly, it is manifest that the simple bodies are
often given a shape by the place in which they are included,
particularly water and air. In such a case the shape of the element
cannot persist; for, if it did, the contained mass would not be in
continuous contact with the containing body; while, if its shape is
changed, it will cease to be water, since the distinctive quality is
shape. Clearly, then, their shapes are not fixed. Indeed, nature
itself seems to offer corroboration of this theoretical conclusion.
Just as in other cases the substratum must be formless and
unshapen-for thus the 'all-receptive', as we read in the Timaeus, will
be best for modelling-so the elements should be conceived as a
material for composite things; and that is why they can put off
their qualitative distinctions and pass into one another. Further, how
can they account for the generation of flesh and bone or any other
continuous body? The elements alone cannot produce them because
their collocation cannot produce a continuum. Nor can the
composition of planes; for this produces the elements themselves,
not bodies made up of them. Any one then who insists upon an exact
statement of this kind of theory, instead of assenting after a passing
glance at it, will see that it removes generation from the world.

  Further, the very properties, powers, and motions, to which they
paid particular attention in allotting shapes, show the shapes not
to be in accord with the bodies. Because fire is mobile and productive
of heat and combustion, some made it a sphere, others a pyramid. These
shapes, they thought, were the most mobile because they offer the
fewest points of contact and are the least stable of any; they were
also the most apt to produce warmth and combustion, because the one is
angular throughout while the other has the most acute angles, and
the angles, they say, produce warmth and combustion. Now, in the first
place, with regard to movement both are in error. These may be the
figures best adapted to movement; they are not, however, well
adapted to the movement of fire, which is an upward and rectilinear
movement, but rather to that form of circular movement which we call
rolling. Earth, again, they call a cube because it is stable and at
rest. But it rests only in its own place, not anywhere; from any other
it moves if nothing hinders, and fire and the other bodies do the
same. The obvious inference, therefore, is that fire and each
several element is in a foreign place a sphere or a pyramid, but in
its own a cube. Again, if the possession of angles makes a body
produce heat and combustion, every element produces heat, though one
may do so more than another. For they all possess angles, the
octahedron and dodecahedron as well as the pyramid; and Democritus
makes even the sphere a kind of angle, which cuts things because of
its mobility. The difference, then, will be one of degree: and this is
plainly false. They must also accept the inference that the
mathematical produce heat and combustion, since they too possess
angles and contain atomic spheres and pyramids, especially if there
are, as they allege, atomic figures. Anyhow if these functions
belong to some of these things and not to others, they should
explain the difference, instead of speaking in quite general terms
as they do. Again, combustion of a body produces fire, and fire is a
sphere or a pyramid. The body, then, is turned into spheres or
pyramids. Let us grant that these figures may reasonably be supposed
to cut and break up bodies as fire does; still it remains quite
inexplicable that a pyramid must needs produce pyramids or a sphere
spheres. One might as well postulate that a knife or a saw divides
things into knives or saws. It is also ridiculous to think only of
division when allotting fire its shape. Fire is generally thought of
as combining and connecting rather than as separating. For though it
separates bodies different in kind, it combines those which are the
same; and the combining is essential to it, the functions of
connecting and uniting being a mark of fire, while the separating is
incidental. For the expulsion of the foreign body is an incident in
the compacting of the homogeneous. In choosing the shape, then, they
should have thought either of both functions or preferably of the
combining function. In addition, since hot and cold are contrary
powers, it is impossible to allot any shape to the cold. For the shape
given must be the contrary of that given to the hot, but there is no
contrariety between figures. That is why they have all left the cold
out, though properly either all or none should have their
distinguishing figures. Some of them, however, do attempt to explain
this power, and they contradict themselves. A body of large particles,
they say, is cold because instead of penetrating through the
passages it crushes. Clearly, then, that which is hot is that which
penetrates these passages, or in other words that which has fine
particles. It results that hot and cold are distinguished not by the
figure but by the size of the particles. Again, if the pyramids are
unequal in size, the large ones will not be fire, and that figure will
produce not combustion but its contrary.

  From what has been said it is clear that the difference of the
elements does not depend upon their shape. Now their most important
differences are those of property, function, and power; for every
natural body has, we maintain, its own functions, properties, and
powers. Our first business, then, will be to speak of these, and
that inquiry will enable us to explain the differences of each from
each.

                              Book IV

                                 1

  WE have now to consider the terms 'heavy' and 'light'. We must ask
what the bodies so called are, how they are constituted, and what is
the reason of their possessing these powers. The consideration of
these questions is a proper part of the theory of movement, since we
call things heavy and light because they have the power of being moved
naturally in a certain way. The activities corresponding to these
powers have not been given any name, unless it is thought that
'impetus' is such a name. But because the inquiry into nature is
concerned with movement, and these things have in themselves some
spark (as it were) of movement, all inquirers avail themselves of
these powers, though in all but a few cases without exact
discrimination. We must then first look at whatever others have
said, and formulate the questions which require settlement in the
interests of this inquiry, before we go on to state our own view of
the matter.

  Language recognizes (a) an absolute, (b) a relative heavy and light.
Of two heavy things, such as wood and bronze, we say that the one is
relatively light, the other relatively heavy. Our predecessors have
not dealt at all with the absolute use, of the terms, but only with
the relative. I mean, they do not explain what the heavy is or what
the light is, but only the relative heaviness and lightness of
things possessing weight. This can be made clearer as follows. There
are things whose constant nature it is to move away from the centre,
while others move constantly towards the centre; and of these
movements that which is away from the centre I call upward movement
and that which is towards it I call downward movement. (The view,
urged by some, that there is no up and no down in the heaven, is
absurd. There can be, they say, no up and no down, since the
universe is similar every way, and from any point on the earth's
surface a man by advancing far enough will come to stand foot to
foot with himself. But the extremity of the whole, which we call
'above', is in position above and in nature primary. And since the
universe has an extremity and a centre, it must clearly have an up and
down. Common usage is thus correct, though inadequate. And the
reason of its inadequacy is that men think that the universe is not
similar every way. They recognize only the hemisphere which is over
us. But if they went on to think of the world as formed on this
pattern all round, with a centre identically related to each point
on the extremity, they would have to admit that the extremity was
above and the centre below.) By absolutely light, then, we mean that
which moves upward or to the extremity, and by absolutely heavy that
which moves downward or to the centre. By lighter or relatively
light we mean that one, of two bodies endowed with weight and equal in
bulk, which is exceeded by the other in the speed of its natural
downward movement.

                                 2

  Those of our predecessors who have entered upon this inquiry have
for the most part spoken of light and heavy things only in the sense
in which one of two things both endowed with weight is said to be
the lighter. And this treatment they consider a sufficient analysis
also of the notions of absolute heaviness, to which their account does
not apply. This, however, will become clearer as we advance. One use
of the terms 'lighter' and 'heavier' is that which is set forth in
writing in the Timaeus, that the body which is composed of the greater
number of identical parts is relatively heavy, while that which is
composed of a smaller number is relatively light. As a larger quantity
of lead or of bronze is heavier than a smaller-and this holds good
of all homogeneous masses, the superior weight always depending upon a
numerical superiority of equal parts-in precisely the same way, they
assert, lead is heavier than wood. For all bodies, in spite of the
general opinion to the contrary, are composed of identical parts and
of a single material. But this analysis says nothing of the absolutely
heavy and light. The facts are that fire is always light and moves
upward, while earth and all earthy things move downwards or towards
the centre. It cannot then be the fewness of the triangles (of
which, in their view, all these bodies are composed) which disposes
fire to move upward. If it were, the greater the quantity of fire
the slower it would move, owing to the increase of weight due to the
increased number of triangles. But the palpable fact, on the contrary,
is that the greater the quantity, the lighter the mass is and the
quicker its upward movement: and, similarly, in the reverse movement
from above downward, the small mass will move quicker and the large
slower. Further, since to be lighter is to have fewer of these
homogeneous parts and to be heavier is to have more, and air, water,
and fire are composed of the same triangles, the only difference being
in the number of such parts, which must therefore explain any
distinction of relatively light and heavy between these bodies, it
follows that there must be a certain quantum of air which is heavier
than water. But the facts are directly opposed to this. The larger the
quantity of air the more readily it moves upward, and any portion of
air without exception will rise up out of the water.

  So much for one view of the distinction between light and heavy.
To others the analysis seems insufficient; and their views on the
subject, though they belong to an older generation than ours, have
an air of novelty. It is apparent that there are bodies which, when
smaller in bulk than others, yet exceed them in weight. It is
therefore obviously insufficient to say that bodies of equal weight
are composed of an equal number of primary parts: for that would
give equality of bulk. Those who maintain that the primary or atomic
parts, of which bodies endowed with weight are composed, are planes,
cannot so speak without absurdity; but those who regard them as solids
are in a better position to assert that of such bodies the larger is
the heavier. But since in composite bodies the weight obviously does
not correspond in this way to the bulk, the lesser bulk being often
superior in weight (as, for instance, if one be wool and the other
bronze), there are some who think and say that the cause is to be
found elsewhere. The void, they say, which is imprisoned in bodies,
lightens them and sometimes makes the larger body the lighter. The
reason is that there is more void. And this would also account for the
fact that a body composed of a number of solid parts equal to, or even
smaller than, that of another is sometimes larger in bulk than it.
In short, generally and in every case a body is relatively light
when it contains a relatively large amount of void. This is the way
they put it themselves, but their account requires an addition.
Relative lightness must depend not only on an excess of void, but also
an a defect of solid: for if the ratio of solid to void exceeds a
certain proportion, the relative lightness will disappear. Thus
fire, they say, is the lightest of things just for this reason that it
has the most void. But it would follow that a large mass of gold, as
containing more void than a small mass of fire, is lighter than it,
unless it also contains many times as much solid. The addition is
therefore necessary.

  Of those who deny the existence of a void some, like Anaxagoras
and Empedocles, have not tried to analyse the notions of light and
heavy at all; and those who, while still denying the existence of a
void, have attempted this, have failed to explain why there are bodies
which are absolutely heavy and light, or in other words why some
move upward and others downward. The fact, again, that the body of
greater bulk is sometimes lighter than smaller bodies is one which
they have passed over in silence, and what they have said gives no
obvious suggestion for reconciling their views with the observed
facts.

  But those who attribute the lightness of fire to its containing so
much void are necessarily involved in practically the same
difficulties. For though fire be supposed to contain less solid than
any other body, as well as more void, yet there will be a certain
quantum of fire in which the amount of solid or plenum is in excess of
the solids contained in some small quantity of earth. They may reply
that there is an excess of void also. But the question is, how will
they discriminate the absolutely heavy? Presumably, either by its
excess of solid or by its defect of void. On the former view there
could be an amount of earth so small as to contain less solid than a
large mass of fire. And similarly, if the distinction rests on the
amount of void, there will be a body, lighter than the absolutely
light, which nevertheless moves downward as constantly as the other
moves upward. But that cannot be so, since the absolutely light is
always lighter than bodies which have weight and move downward, while,
on the other hand, that which is lighter need not be light, because in
common speech we distinguish a lighter and a heavier (viz. water and
earth) among bodies endowed with weight. Again, the suggestion of a
certain ratio between the void and the solid in a body is no more
equal to solving the problem before us. The manner of speaking will
issue in a similar impossibility. For any two portions of fire,
small or great, will exhibit the same ratio of solid to void, but
the upward movement of the greater is quicker than that of the less,
just as the downward movement of a mass of gold or lead, or of any
other body endowed with weight, is quicker in proportion to its
size. This, however, should not be the case if the ratio is the ground
of distinction between heavy things and light. There is also an
absurdity in attributing the upward movement of bodies to a void which
does not itself move. If, however, it is the nature of a void to
move upward and of a plenum to move downward, and therefore each
causes a like movement in other things, there was no need to raise the
question why composite bodies are some light and some heavy; they
had only to explain why these two things are themselves light and
heavy respectively, and to give, further, the reason why the plenum
and the void are not eternally separated. It is also unreasonable to
imagine a place for the void, as if the void were not itself a kind of
place. But if the void is to move, it must have a place out of which
and into which the change carries it. Also what is the cause of its
movement? Not, surely, its voidness: for it is not the void only which
is moved, but also the solid.

  Similar difficulties are involved in all other methods of
distinction, whether they account for the relative lightness and
heaviness of bodies by distinctions of size, or proceed on any other
principle, so long as they attribute to each the same matter, or
even if they recognize more than one matter, so long as that means
only a pair of contraries. If there is a single matter, as with
those who compose things of triangles, nothing can be absolutely heavy
or light: and if there is one matter and its contrary-the void, for
instance, and the plenum-no reason can be given for the relative
lightness and heaviness of the bodies intermediate between the
absolutely light and heavy when compared either with one another or
with these themselves. The view which bases the distinction upon
differences of size is more like a mere fiction than those
previously mentioned, but, in that it is able to make distinctions
between the four elements, it is in a stronger position for meeting
the foregoing difficulties. Since, however, it imagines that these
bodies which differ in size are all made of one substance, it implies,
equally with the view that there is but one matter, that there is
nothing absolutely light and nothing which moves upward (except as
being passed by other things or forced up by them); and since a
multitude of small atoms are heavier than a few large ones, it will
follow that much air or fire is heavier than a little water or
earth, which is impossible.

                                 3

  These, then, are the views which have been advanced by others and
the terms in which they state them. We may begin our own statement
by settling a question which to some has been the main
difficulty-the question why some bodies move always and naturally
upward and others downward, while others again move both upward and
downward. After that we will inquire into light and heavy and of the
various phenomena connected with them. The local movement of each body
into its own place must be regarded as similar to what happens in
connexion with other forms of generation and change. There are, in
fact, three kinds of movement, affecting respectively the size, the
form, and the place of a thing, and in each it is observable that
change proceeds from a contrary to a contrary or to something
intermediate: it is never the change of any chance subject in any
chance direction, nor, similarly, is the relation of the mover to
its object fortuitous: the thing altered is different from the thing
increased, and precisely the same difference holds between that
which produces alteration and that which produces increase. In the
same manner it must be thought that produces local motion and that
which is so moved are not fortuitously related. Now, that which
produces upward and downward movement is that which produces weight
and lightness, and that which is moved is that which is potentially
heavy or light, and the movement of each body to its own place is
motion towards its own form. (It is best to interpret in this sense
the common statement of the older writers that 'like moves to like'.
For the words are not in every sense true to fact. If one were to
remove the earth to where the moon now is, the various fragments of
earth would each move not towards it but to the place in which it
now is. In general, when a number of similar and undifferentiated
bodies are moved with the same motion this result is necessarily
produced, viz. that the place which is the natural goal of the
movement of each single part is also that of the whole. But since
the place of a thing is the boundary of that which contains it, and
the continent of all things that move upward or downward is the
extremity and the centre, and this boundary comes to be, in a sense,
the form of that which is contained, it is to its like that a body
moves when it moves to its own place. For the successive members of
the scries are like one another: water, I mean, is like air and air
like fire, and between intermediates the relation may be converted,
though not between them and the extremes; thus air is like water,
but water is like earth: for the relation of each outer body to that
which is next within it is that of form to matter.) Thus to ask why
fire moves upward and earth downward is the same as to ask why the
healable, when moved and changed qua healable, attains health and
not whiteness; and similar questions might be asked concerning any
other subject of aletion. Of course the subject of increase, when
changed qua increasable, attains not health but a superior size. The
same applies in the other cases. One thing changes in quality, another
in quantity: and so in place, a light thing goes upward, a heavy thing
downward. The only difference is that in the last case, viz. that of
the heavy and the light, the bodies are thought to have a spring of
change within themselves, while the subjects of healing and increase
are thought to be moved purely from without. Sometimes, however,
even they change of themselves, ie. in response to a slight external
movement reach health or increase, as the case may be. And since the
same thing which is healable is also receptive of disease, it
depends on whether it is moved qua healable or qua liable to disease
whether the motion is towards health or towards disease. But the
reason why the heavy and the light appear more than these things to
contain within themselves the source of their movements is that
their matter is nearest to being. This is indicated by the fact that
locomotion belongs to bodies only when isolated from other bodies, and
is generated last of the several kinds of movement; in order of
being then it will be first. Now whenever air comes into being out
of water, light out of heavy, it goes to the upper place. It is
forthwith light: becoming is at an end, and in that place it has
being. Obviously, then, it is a potentiality, which, in its passage to
actuality, comes into that place and quantity and quality which belong
to its actuality. And the same fact explains why what is already
actually fire or earth moves, when nothing obstructs it, towards its
own place. For motion is equally immediate in the case of nutriment,
when nothing hinders, and in the case of the thing healed, when
nothing stays the healing. But the movement is also due to the
original creative force and to that which removes the hindrance or off
which the moving thing rebounded, as was explained in our opening
discussions, where we tried to show how none of these things moves
itself. The reason of the various motions of the various bodies, and
the meaning of the motion of a body to its own place, have now been
explained.

                                 4

  We have now to speak of the distinctive properties of these bodies
and of the various phenomena connected with them. In accordance with
general conviction we may distinguish the absolutely heavy, as that
which sinks to the bottom of all things, from the absolutely light,
which is that which rises to the surface of all things. I use the term
'absolutely', in view of the generic character of 'light' and 'heavy',
in order to confine the application to bodies which do not combine
lightness and heaviness. It is apparent, I mean, that fire, in
whatever quantity, so long as there is no external obstacle moves
upward, and earth downward; and, if the quantity is increased, the
movement is the same, though swifter. But the heaviness and
lightness of bodies which combine these qualities is different from
this, since while they rise to the surface of some bodies they sink to
the bottom of others. Such are air and water. Neither of them is
absolutely either light or heavy. Both are lighter than earth-for
any portion of either rises to the surface of it-but heavier than
fire, since a portion of either, whatever its quantity, sinks to the
bottom of fire; compared together, however, the one has absolute
weight, the other absolute lightness, since air in any quantity
rises to the surface of water, while water in any quantity sinks to
the bottom of air. Now other bodies are severally light and heavy, and
evidently in them the attributes are due to the difference of their
uncompounded parts: that is to say, according as the one or the
other happens to preponderate the bodies will be heavy and light
respectively. Therefore we need only speak of these parts, since
they are primary and all else consequential: and in so doing we
shall be following the advice which we gave to those whose attribute
heaviness to the presence of plenum and lightness to that of void.
It is due to the properties of the elementary bodies that a body which
is regarded as light in one place is regarded as heavy in another, and
vice versa. In air, for instance, a talent's weight of wood is heavier
than a mina of lead, but in water the wood is the lighter. The
reason is that all the elements except fire have weight and all but
earth lightness. Earth, then, and bodies in which earth preponderates,
must needs have weight everywhere, while water is heavy anywhere but
in earth, and air is heavy when not in water or earth. In its own
place each of these bodies has weight except fire, even air. Of this
we have evidence in the fact that a bladder when inflated weighs
more than when empty. A body, then, in which air preponderates over
earth and water, may well be lighter than something in water and yet
heavier than it in air, since such a body does not rise in air but
rises to the surface in water.

  The following account will make it plain that there is an absolutely
light and an absolutely heavy body. And by absolutely light I mean one
which of its own nature always moves upward, by absolutely heavy one
which of its own nature always moves downward, if no obstacle is in
the way. There are, I say, these two kinds of body, and it is not
the case, as some maintain, that all bodies have weight. Different
views are in fact agreed that there is a heavy body, which moves
uniformly towards the centre. But is also similarly a light body.
For we see with our eyes, as we said before, that earthy things sink
to the bottom of all things and move towards the centre. But the
centre is a fixed point. If therefore there is some body which rises
to the surface of all things-and we observe fire to move upward even
in air itself, while the air remains at rest-clearly this body is
moving towards the extremity. It cannot then have any weight. If it
had, there would be another body in which it sank: and if that had
weight, there would be yet another which moved to the extremity and
thus rose to the surface of all moving things. In fact, however, we
have no evidence of such a body. Fire, then, has no weight. Neither
has earth any lightness, since it sinks to the bottom of all things,
and that which sinks moves to the centre. That there is a centre
towards which the motion of heavy things, and away from which that
of light things is directed, is manifest in many ways. First,
because no movement can continue to infinity. For what cannot be can
no more come-to-be than be, and movement is a coming to-be in one
place from another. Secondly, like the upward movement of fire, the
downward movement of earth and all heavy things makes equal angles
on every side with the earth's surface: it must therefore be
directed towards the centre. Whether it is really the centre of the
earth and not rather that of the whole to which it moves, may be
left to another inquiry, since these are coincident. But since that
which sinks to the bottom of all things moves to the centre,
necessarily that which rises to the surface moves to the extremity
of the region in which the movement of these bodies takes place. For
the centre is opposed as contrary to the extremity, as that which
sinks is opposed to that which rises to the surface. This also gives a
reasonable ground for the duality of heavy and light in the spatial
duality centre and extremity. Now there is also the intermediate
region to which each name is given in opposition to the other extreme.
For that which is intermediate between the two is in a sense both
extremity and centre. For this reason there is another heavy and
light; namely, water and air. But in our view the continent pertains
to form and the contained to matter: and this distinction is present
in every genus. Alike in the sphere of quality and in that of quantity
there is that which corresponds rather to form and that which
corresponds to matter. In the same way, among spatial distinctions,
the above belongs to the determinate, the below to matter. The same
holds, consequently, also of the matter itself of that which is
heavy and light: as potentially possessing the one character, it is
matter for the heavy, and as potentially possessing the other, for the
light. It is the same matter, but its being is different, as that
which is receptive of disease is the same as that which is receptive
of health, though in being different from it, and therefore
diseasedness is different from healthiness.

                                 5

  A thing then which has the one kind of matter is light and always
moves upward, while a thing which has the opposite matter is heavy and
always moves downward. Bodies composed of kinds of matter different
from these but having relatively to each other the character which
these have absolutely, possess both the upward and the downward
motion. Hence air and water each have both lightness and weight, and
water sinks to the bottom of all things except earth, while air
rises to the surface of all things except fire. But since there is one
body only which rises to the surface of all things and one only
which sinks to the bottom of all things, there must needs be two other
bodies which sink in some bodies and rise to the surface of others.
The kinds of matter, then, must be as numerous as these bodies, i.e.
four, but though they are four there must be a common matter of
all-particularly if they pass into one another-which in each is in
being different. There is no reason why there should not be one or
more intermediates between the contraries, as in the case of colour;
for 'intermediate' and 'mean' are capable of more than one
application.

  Now in its own place every body endowed with both weight and
lightness has weightwhereas earth has weight everywhere-but they
only have lightness among bodies to whose surface they rise. Hence
when a support is withdrawn such a body moves downward until it
reaches the body next below it, air to the place of water and water to
that of earth. But if the fire above air is removed, it will not
move upward to the place of fire, except by constraint; and in that
way water also may be drawn up, when the upward movement of air
which has had a common surface with it is swift enough to overpower
the downward impulse of the water. Nor does water move upward to the
place of air, except in the manner just described. Earth is not so
affected at all, because a common surface is not possible to it. Hence
water is drawn up into the vessel to which fire is applied, but not
earth. As earth fails to move upward, so fire fails to move downward
when air is withdrawn from beneath it: for fire has no weight even
in its own place, as earth has no lightness. The other two move
downward when the body beneath is withdrawn because, while the
absolutely heavy is that which sinks to the bottom of all things,
the relatively heavy sinks to its own place or to the surface of the
body in which it rises, since it is similar in matter to it.

  It is plain that one must suppose as many distinct species of matter
as there are bodies. For if, first, there is a single matter of all
things, as, for instance, the void or the plenum or extension or the
triangles, either all things will move upward or all things will
move downward, and the second motion will be abolished. And so, either
there will be no absolutely light body, if superiority of weight is
due to superior size or number of the constituent bodies or to the
fullness of the body: but the contrary is a matter of observation, and
it has been shown that the downward and upward movements are equally
constant and universal: or, if the matter in question is the void or
something similar, which moves uniformly upward, there will be nothing
to move uniformly downward. Further, it will follow that the
intermediate bodies move downward in some cases quicker than earth:
for air in sufficiently large quantity will contain a larger number of
triangles or solids or particles. It is, however, manifest that no
portion of air whatever moves downward. And the same reasoning applies
to lightness, if that is supposed to depend on superiority of quantity
of matter. But if, secondly, the kinds of matter are two, it will be
difficult to make the intermediate bodies behave as air and water
behave. Suppose, for example, that the two asserted are void and
plenum. Fire, then, as moving upward, will be void, earth, as moving
downward, plenum; and in air, it will be said, fire preponderates,
in water, earth. There will then be a quantity of water containing
more fire than a little air, and a large amount of air will contain
more earth than a little water: consequently we shall have to say that
air in a certain quantity moves downward more quickly than a little
water. But such a thing has never been observed anywhere. Necessarily,
then, as fire goes up because it has something, e.g. void, which other
things do not have, and earth goes downward because it has plenum,
so air goes to its own place above water because it has something
else, and water goes downward because of some special kind of body.
But if the two bodies are one matter, or two matters both present in
each, there will be a certain quantity of each at which water will
excel a little air in the upward movement and air excel water in the
downward movement, as we have already often said.

                                 6

  The shape of bodies will not account for their moving upward or
downward in general, though it will account for their moving faster or
slower. The reasons for this are not difficult to see. For the problem
thus raised is why a flat piece of iron or lead floats upon water,
while smaller and less heavy things, so long as they are round or
long-a needle, for instance-sink down; and sometimes a thing floats
because it is small, as with gold dust and the various earthy and
dusty materials which throng the air. With regard to these
questions, it is wrong to accept the explanation offered by
Democritus. He says that the warm bodies moving up out of the water
hold up heavy bodies which are broad, while the narrow ones fall
through, because the bodies which offer this resistance are not
numerous. But this would be even more likely to happen in air-an
objection which he himself raises. His reply to the objection is
feeble. In the air, he says, the 'drive' (meaning by drive the
movement of the upward moving bodies) is not uniform in direction. But
since some continua are easily divided and others less easily, and
things which produce division differ similarly in the case with
which they produce it, the explanation must be found in this fact.
It is the easily bounded, in proportion as it is easily bounded, which
is easily divided; and air is more so than water, water than earth.
Further, the smaller the quantity in each kind, the more easily it
is divided and disrupted. Thus the reason why broad things keep
their place is because they cover so wide a surface and the greater
quantity is less easily disrupted. Bodies of the opposite shape sink
down because they occupy so little of the surface, which is
therefore easily parted. And these considerations apply with far
greater force to air, since it is so much more easily divided than
water. But since there are two factors, the force responsible for
the downward motion of the heavy body and the disruption-resisting
force of the continuous surface, there must be some ratio between
the two. For in proportion as the force applied by the heavy thing
towards disruption and division exceeds that which resides in the
continuum, the quicker will it force its way down; only if the force
of the heavy thing is the weaker, will it ride upon the surface.

  We have now finished our examination of the heavy and the light
and of the phenomena connected with them.

                            THE END
.

Colophon

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