On the Heavens
By Aristotle
Written 350 B.C.E
Translated by J. L. Stocks
Part 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.
Part 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.
Part 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.
Part 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.
Part 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.
Part 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.
Part 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.
Part 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.
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