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On the Heavens
Book III
Chapter 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.
Chapter 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.
Chapter 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.
Chapter 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.