Physics / Aristotle

                                     350 BC

                                    PHYSICS

                                  by Aristotle

                   translated by R. P. Hardie and R. K. Gaye

                              Book I

                                 1

  WHEN the objects of an inquiry, in any department, have
principles, conditions, or elements, it is through acquaintance with
these that knowledge, that is to say scientific knowledge, is
attained. For we do not think that we know a thing until we are
acquainted with its primary conditions or first principles, and have
carried our analysis as far as its simplest elements. Plainly
therefore in the science of Nature, as in other branches of study, our
first task will be to try to determine what relates to its principles.

  The natural way of doing this is to start from the things which
are more knowable and obvious to us and proceed towards those which
are clearer and more knowable by nature; for the same things are not
'knowable relatively to us' and 'knowable' without qualification. So
in the present inquiry we must follow this method and advance from
what is more obscure by nature, but clearer to us, towards what is
more clear and more knowable by nature.

  Now what is to us plain and obvious at first is rather confused
masses, the elements and principles of which become known to us
later by analysis. Thus we must advance from generalities to
particulars; for it is a whole that is best known to sense-perception,
and a generality is a kind of whole, comprehending many things
within it, like parts. Much the same thing happens in the relation
of the name to the formula. A name, e.g. 'round', means vaguely a sort
of whole: its definition analyses this into its particular senses.
Similarly a child begins by calling all men 'father', and all women
'mother', but later on distinguishes each of them.

                                 2

  The principles in question must be either (a) one or (b) more than
one. If (a) one, it must be either (i) motionless, as Parmenides and
Melissus assert, or (ii) in motion, as the physicists hold, some
declaring air to be the first principle, others water. If (b) more
than one, then either (i) a finite or (ii) an infinite plurality. If
(i) finite (but more than one), then either two or three or four or
some other number. If (ii) infinite, then either as Democritus
believed one in kind, but differing in shape or form; or different
in kind and even contrary.

  A similar inquiry is made by those who inquire into the number of
existents: for they inquire whether the ultimate constituents of
existing things are one or many, and if many, whether a finite or an
infinite plurality. So they too are inquiring whether the principle or
element is one or many.

  Now to investigate whether Being is one and motionless is not a
contribution to the science of Nature. For just as the geometer has
nothing more to say to one who denies the principles of his
science-this being a question for a different science or for or common
to all-so a man investigating principles cannot argue with one who
denies their existence. For if Being is just one, and one in the way
mentioned, there is a principle no longer, since a principle must be
the principle of some thing or things.

  To inquire therefore whether Being is one in this sense would be
like arguing against any other position maintained for the sake of
argument (such as the Heraclitean thesis, or such a thesis as that
Being is one man) or like refuting a merely contentious argument-a
description which applies to the arguments both of Melissus and of
Parmenides: their premisses are false and their conclusions do not
follow. Or rather the argument of Melissus is gross and palpable and
offers no difficulty at all: accept one ridiculous proposition and the
rest follows-a simple enough proceeding.

  We physicists, on the other hand, must take for granted that the
things that exist by nature are, either all or some of them, in motion
which is indeed made plain by induction. Moreover, no man of science
is bound to solve every kind of difficulty that may be raised, but
only as many as are drawn falsely from the principles of the
science: it is not our business to refute those that do not arise in
this way: just as it is the duty of the geometer to refute the
squaring of the circle by means of segments, but it is not his duty to
refute Antiphon's proof. At the same time the holders of the theory of
which we are speaking do incidentally raise physical questions, though
Nature is not their subject: so it will perhaps be as well to spend
a few words on them, especially as the inquiry is not without
scientific interest.

  The most pertinent question with which to begin will be this: In
what sense is it asserted that all things are one? For 'is' is used in
many senses. Do they mean that all things 'are' substance or
quantities or qualities? And, further, are all things one
substance-one man, one horse, or one soul-or quality and that one
and the same-white or hot or something of the kind? These are all very
different doctrines and all impossible to maintain.

  For if both substance and quantity and quality are, then, whether
these exist independently of each other or not, Being will be many.

  If on the other hand it is asserted that all things are quality or
quantity, then, whether substance exists or not, an absurdity results,
if the impossible can properly be called absurd. For none of the
others can exist independently: substance alone is independent: for
everything is predicated of substance as subject. Now Melissus says
that Being is infinite. It is then a quantity. For the infinite is
in the category of quantity, whereas substance or quality or affection
cannot be infinite except through a concomitant attribute, that is, if
at the same time they are also quantities. For to define the
infinite you must use quantity in your formula, but not substance or
quality. If then Being is both substance and quantity, it is two,
not one: if only substance, it is not infinite and has no magnitude;
for to have that it will have to be a quantity.

  Again, 'one' itself, no less than 'being', is used in many senses,
so we must consider in what sense the word is used when it is said
that the All is one.

  Now we say that (a) the continuous is one or that (b) the
indivisible is one, or (c) things are said to be 'one', when their
essence is one and the same, as 'liquor' and 'drink'.

  If (a) their One is one in the sense of continuous, it is many,
for the continuous is divisible ad infinitum.

  There is, indeed, a difficulty about part and whole, perhaps not
relevant to the present argument, yet deserving consideration on its
own account-namely, whether the part and the whole are one or more
than one, and how they can be one or many, and, if they are more
than one, in what sense they are more than one. (Similarly with the
parts of wholes which are not continuous.) Further, if each of the two
parts is indivisibly one with the whole, the difficulty arises that
they will be indivisibly one with each other also.

  But to proceed: If (b) their One is one as indivisible, nothing will
have quantity or quality, and so the one will not be infinite, as
Melissus says-nor, indeed, limited, as Parmenides says, for though the
limit is indivisible, the limited is not.

  But if (c) all things are one in the sense of having the same
definition, like 'raiment' and 'dress', then it turns out that they
are maintaining the Heraclitean doctrine, for it will be the same
thing 'to be good' and 'to be bad', and 'to be good' and 'to be not
good', and so the same thing will be 'good' and 'not good', and man
and horse; in fact, their view will be, not that all things are one,
but that they are nothing; and that 'to be of such-and-such a quality'
is the same as 'to be of such-and-such a size'.

  Even the more recent of the ancient thinkers were in a pother lest
the same thing should turn out in their hands both one and many. So
some, like Lycophron, were led to omit 'is', others to change the mode
of expression and say 'the man has been whitened' instead of 'is
white', and 'walks' instead of 'is walking', for fear that if they
added the word 'is' they should be making the one to be many-as if
'one' and 'being' were always used in one and the same sense. What
'is' may be many either in definition (for example 'to be white' is
one thing, 'to be musical' another, yet the same thing be both, so the
one is many) or by division, as the whole and its parts. On this
point, indeed, they were already getting into difficulties and
admitted that the one was many-as if there was any difficulty about
the same thing being both one and many, provided that these are not
opposites; for 'one' may mean either 'potentially one' or 'actually
one'.

                                 3

  If, then, we approach the thesis in this way it seems impossible for
all things to be one. Further, the arguments they use to prove their
position are not difficult to expose. For both of them reason
contentiously-I mean both Melissus and Parmenides. [Their premisses
are false and their conclusions do not follow. Or rather the
argument of Melissus is gross and palpable and offers no difficulty at
all: admit one ridiculous proposition and the rest follows-a simple
enough proceeding.] The fallacy of Melissus is obvious. For he
supposes that the assumption 'what has come into being always has a
beginning' justifies the assumption 'what has not come into being
has no beginning'. Then this also is absurd, that in every case
there should be a beginning of the thing-not of the time and not
only in the case of coming to be in the full sense but also in the
case of coming to have a quality-as if change never took place
suddenly. Again, does it follow that Being, if one, is motionless? Why
should it not move, the whole of it within itself, as parts of it do
which are unities, e.g. this water? Again, why is qualitative change
impossible? But, further, Being cannot be one in form, though it may
be in what it is made of. (Even some of the physicists hold it to be
one in the latter way, though not in the former.) Man obviously
differs from horse in form, and contraries from each other.

  The same kind of argument holds good against Parmenides also,
besides any that may apply specially to his view: the answer to him
being that 'this is not true' and 'that does not follow'. His
assumption that one is used in a single sense only is false, because
it is used in several. His conclusion does not follow, because if we
take only white things, and if 'white' has a single meaning, none
the less what is white will be many and not one. For what is white
will not be one either in the sense that it is continuous or in the
sense that it must be defined in only one way. 'Whiteness' will be
different from 'what has whiteness'. Nor does this mean that there
is anything that can exist separately, over and above what is white.
For 'whiteness' and 'that which is white' differ in definition, not in
the sense that they are things which can exist apart from each
other. But Parmenides had not come in sight of this distinction.

  It is necessary for him, then, to assume not only that 'being' has
the same meaning, of whatever it is predicated, but further that it
means (1) what just is and (2) what is just one.

  It must be so, for (1) an attribute is predicated of some subject,
so that the subject to which 'being' is attributed will not be, as
it is something different from 'being'. Something, therefore, which is
not will be. Hence 'substance' will not be a predicate of anything
else. For the subject cannot be a being, unless 'being' means
several things, in such a way that each is something. But ex hypothesi
'being' means only one thing.

  If, then, 'substance' is not attributed to anything, but other
things are attributed to it, how does 'substance' mean what is
rather than what is not? For suppose that 'substance' is also 'white'.
Since the definition of the latter is different (for being cannot even
be attributed to white, as nothing is which is not 'substance'), it
follows that 'white' is not-being--and that not in the sense of a
particular not-being, but in the sense that it is not at all. Hence
'substance' is not; for it is true to say that it is white, which we
found to mean not-being. If to avoid this we say that even 'white'
means substance, it follows that 'being' has more than one meaning.

  In particular, then, Being will not have magnitude, if it is
substance. For each of the two parts must he in a different sense.

  (2) Substance is plainly divisible into other substances, if we
consider the mere nature of a definition. For instance, if 'man' is
a substance, 'animal' and 'biped' must also be substances. For if
not substances, they must be attributes-and if attributes,
attributes either of (a) man or of (b) some other subject. But neither
is possible.

  (a) An attribute is either that which may or may not belong to the
subject or that in whose definition the subject of which it is an
attribute is involved. Thus 'sitting' is an example of a separable
attribute, while 'snubness' contains the definition of 'nose', to
which we attribute snubness. Further, the definition of the whole is
not contained in the definitions of the contents or elements of the
definitory formula; that of 'man' for instance in 'biped', or that
of 'white man' in 'white'. If then this is so, and if 'biped' is
supposed to be an attribute of 'man', it must be either separable,
so that 'man' might possibly not be 'biped', or the definition of
'man' must come into the definition of 'biped'-which is impossible, as
the converse is the case.

  (b) If, on the other hand, we suppose that 'biped' and 'animal'
are attributes not of man but of something else, and are not each of
them a substance, then 'man' too will be an attribute of something
else. But we must assume that substance is not the attribute of
anything, that the subject of which both 'biped' and 'animal' and each
separately are predicated is the subject also of the complex 'biped
animal'.

  Are we then to say that the All is composed of indivisible
substances? Some thinkers did, in point of fact, give way to both
arguments. To the argument that all things are one if being means
one thing, they conceded that not-being is; to that from bisection,
they yielded by positing atomic magnitudes. But obviously it is not
true that if being means one thing, and cannot at the same time mean
the contradictory of this, there will be nothing which is not, for
even if what is not cannot be without qualification, there is no
reason why it should not be a particular not-being. To say that all
things will be one, if there is nothing besides Being itself, is
absurd. For who understands 'being itself' to be anything but a
particular substance? But if this is so, there is nothing to prevent
there being many beings, as has been said.

  It is, then, clearly impossible for Being to be one in this sense.

                                 4

  The physicists on the other hand have two modes of explanation.

  The first set make the underlying body one either one of the three
or something else which is denser than fire and rarer than air then
generate everything else from this, and obtain multiplicity by
condensation and rarefaction. Now these are contraries, which may be
generalized into 'excess and defect'. (Compare Plato's 'Great and
Small'-except that he make these his matter, the one his form, while
the others treat the one which underlies as matter and the
contraries as differentiae, i.e. forms).

  The second set assert that the contrarieties are contained in the
one and emerge from it by segregation, for example Anaximander and
also all those who assert that 'what is' is one and many, like
Empedocles and Anaxagoras; for they too produce other things from
their mixture by segregation. These differ, however, from each other
in that the former imagines a cycle of such changes, the latter a
single series. Anaxagoras again made both his 'homceomerous'
substances and his contraries infinite in multitude, whereas
Empedocles posits only the so-called elements.

  The theory of Anaxagoras that the principles are infinite in
multitude was probably due to his acceptance of the common opinion
of the physicists that nothing comes into being from not-being. For
this is the reason why they use the phrase 'all things were
together' and the coming into being of such and such a kind of thing
is reduced to change of quality, while some spoke of combination and
separation. Moreover, the fact that the contraries proceed from each
other led them to the conclusion. The one, they reasoned, must have
already existed in the other; for since everything that comes into
being must arise either from what is or from what is not, and it is
impossible for it to arise from what is not (on this point all the
physicists agree), they thought that the truth of the alternative
necessarily followed, namely that things come into being out of
existent things, i.e. out of things already present, but imperceptible
to our senses because of the smallness of their bulk. So they assert
that everything has been mixed in every. thing, because they saw
everything arising out of everything. But things, as they say,
appear different from one another and receive different names
according to the nature of the particles which are numerically
predominant among the innumerable constituents of the mixture. For
nothing, they say, is purely and entirely white or black or sweet,
bone or flesh, but the nature of a thing is held to be that of which
it contains the most.

  Now (1) the infinite qua infinite is unknowable, so that what is
infinite in multitude or size is unknowable in quantity, and what is
infinite in variety of kind is unknowable in quality. But the
principles in question are infinite both in multitude and in kind.
Therefore it is impossible to know things which are composed of
them; for it is when we know the nature and quantity of its components
that we suppose we know a complex.

  Further (2) if the parts of a whole may be of any size in the
direction either of greatness or of smallness (by 'parts' I mean
components into which a whole can be divided and which are actually
present in it), it is necessary that the whole thing itself may be
of any size. Clearly, therefore, since it is impossible for an
animal or plant to be indefinitely big or small, neither can its parts
be such, or the whole will be the same. But flesh, bone, and the
like are the parts of animals, and the fruits are the parts of plants.
Hence it is obvious that neither flesh, bone, nor any such thing can
be of indefinite size in the direction either of the greater or of the
less.

  Again (3) according to the theory all such things are already
present in one another and do not come into being but are constituents
which are separated out, and a thing receives its designation from its
chief constituent. Further, anything may come out of anything-water by
segregation from flesh and flesh from water. Hence, since every finite
body is exhausted by the repeated abstraction of a finite body, it
seems obviously to follow that everything cannot subsist in everything
else. For let flesh be extracted from water and again more flesh be
produced from the remainder by repeating the process of separation:
then, even though the quantity separated out will continually
decrease, still it will not fall below a certain magnitude. If,
therefore, the process comes to an end, everything will not be in
everything else (for there will be no flesh in the remaining water);
if on the other hand it does not, and further extraction is always
possible, there will be an infinite multitude of finite equal
particles in a finite quantity-which is impossible. Another proof
may be added: Since every body must diminish in size when something is
taken from it, and flesh is quantitatively definite in respect both of
greatness and smallness, it is clear that from the minimum quantity of
flesh no body can be separated out; for the flesh left would be less
than the minimum of flesh.

  Lastly (4) in each of his infinite bodies there would be already
present infinite flesh and blood and brain- having a distinct
existence, however, from one another, and no less real than the
infinite bodies, and each infinite: which is contrary to reason.

  The statement that complete separation never will take place is
correct enough, though Anaxagoras is not fully aware of what it means.
For affections are indeed inseparable. If then colours and states
had entered into the mixture, and if separation took place, there
would be a 'white' or a 'healthy' which was nothing but white or
healthy, i.e. was not the predicate of a subject. So his 'Mind' is
an absurd person aiming at the impossible, if he is supposed to wish
to separate them, and it is impossible to do so, both in respect of
quantity and of quality- of quantity, because there is no minimum
magnitude, and of quality, because affections are inseparable.

  Nor is Anaxagoras right about the coming to be of homogeneous
bodies. It is true there is a sense in which clay is divided into
pieces of clay, but there is another in which it is not. Water and air
are, and are generated 'from' each other, but not in the way in
which bricks come 'from' a house and again a house 'from' bricks;
and it is better to assume a smaller and finite number of
principles, as Empedocles does.

                                 5

  All thinkers then agree in making the contraries principles, both
those who describe the All as one and unmoved (for even Parmenides
treats hot and cold as principles under the names of fire and earth)
and those too who use the rare and the dense. The same is true of
Democritus also, with his plenum and void, both of which exist, be
says, the one as being, the other as not-being. Again he speaks of
differences in position, shape, and order, and these are genera of
which the species are contraries, namely, of position, above and
below, before and behind; of shape, angular and angle-less, straight
and round.

  It is plain then that they all in one way or another identify the
contraries with the principles. And with good reason. For first
principles must not be derived from one another nor from anything
else, while everything has to be derived from them. But these
conditions are fulfilled by the primary contraries, which are not
derived from anything else because they are primary, nor from each
other because they are contraries.

  But we must see how this can be arrived at as a reasoned result,
as well as in the way just indicated.

  Our first presupposition must be that in nature nothing acts on,
or is acted on by, any other thing at random, nor may anything come
from anything else, unless we mean that it does so in virtue of a
concomitant attribute. For how could 'white' come from 'musical',
unless 'musical' happened to be an attribute of the not-white or of
the black? No, 'white' comes from 'not-white'-and not from any
'not-white', but from black or some intermediate colour. Similarly,
'musical' comes to be from 'not-musical', but not from any thing other
than musical, but from 'unmusical' or any intermediate state there may
be.

  Nor again do things pass into the first chance thing; 'white' does
not pass into 'musical' (except, it may be, in virtue of a concomitant
attribute), but into 'not-white'-and not into any chance thing which
is not white, but into black or an intermediate colour; 'musical'
passes into 'not-musical'-and not into any chance thing other than
musical, but into 'unmusical' or any intermediate state there may be.

  The same holds of other things also: even things which are not
simple but complex follow the same principle, but the opposite state
has not received a name, so we fail to notice the fact. What is in
tune must come from what is not in tune, and vice versa; the tuned
passes into untunedness-and not into any untunedness, but into the
corresponding opposite. It does not matter whether we take attunement,
order, or composition for our illustration; the principle is obviously
the same in all, and in fact applies equally to the production of a
house, a statue, or any other complex. A house comes from certain
things in a certain state of separation instead of conjunction, a
statue (or any other thing that has been shaped) from
shapelessness-each of these objects being partly order and partly
composition.

  If then this is true, everything that comes to be or passes away
from, or passes into, its contrary or an intermediate state. But the
intermediates are derived from the contraries-colours, for instance,
from black and white. Everything, therefore, that comes to be by a
natural process is either a contrary or a product of contraries.

  Up to this point we have practically had most of the other writers
on the subject with us, as I have said already: for all of them
identify their elements, and what they call their principles, with the
contraries, giving no reason indeed for the theory, but contrained
as it were by the truth itself. They differ, however, from one another
in that some assume contraries which are more primary, others
contraries which are less so: some those more knowable in the order of
explanation, others those more familiar to sense. For some make hot
and cold, or again moist and dry, the conditions of becoming; while
others make odd and even, or again Love and Strife; and these differ
from each other in the way mentioned.

  Hence their principles are in one sense the same, in another
different; different certainly, as indeed most people think, but the
same inasmuch as they are analogous; for all are taken from the same
table of columns, some of the pairs being wider, others narrower in
extent. In this way then their theories are both the same and
different, some better, some worse; some, as I have said, take as
their contraries what is more knowable in the order of explanation,
others what is more familiar to sense. (The universal is more knowable
in the order of explanation, the particular in the order of sense: for
explanation has to do with the universal, sense with the
particular.) 'The great and the small', for example, belong to the
former class, 'the dense and the rare' to the latter.

  It is clear then that our principles must be contraries.

                                 6

  The next question is whether the principles are two or three or more
in number.

  One they cannot be, for there cannot be one contrary. Nor can they
be innumerable, because, if so, Being will not be knowable: and in any
one genus there is only one contrariety, and substance is one genus:
also a finite number is sufficient, and a finite number, such as the
principles of Empedocles, is better than an infinite multitude; for
Empedocles professes to obtain from his principles all that Anaxagoras
obtains from his innumerable principles. Lastly, some contraries are
more primary than others, and some arise from others-for example sweet
and bitter, white and black-whereas the principles must always
remain principles.

  This will suffice to show that the principles are neither one nor
innumerable.

  Granted, then, that they are a limited number, it is plausible to
suppose them more than two. For it is difficult to see how either
density should be of such a nature as to act in any way on rarity or
rarity on density. The same is true of any other pair of contraries;
for Love does not gather Strife together and make things out of it,
nor does Strife make anything out of Love, but both act on a third
thing different from both. Some indeed assume more than one such thing
from which they construct the world of nature.

  Other objections to the view that it is not necessary to assume a
third principle as a substratum may be added. (1) We do not find
that the contraries constitute the substance of any thing. But what is
a first principle ought not to be the predicate of any subject. If
it were, there would be a principle of the supposed principle: for the
subject is a principle, and prior presumably to what is predicated
of it. Again (2) we hold that a substance is not contrary to another
substance. How then can substance be derived from what are not
substances? Or how can non-substances be prior to substance?

  If then we accept both the former argument and this one, we must, to
preserve both, assume a third somewhat as the substratum of the
contraries, such as is spoken of by those who describe the All as
one nature-water or fire or what is intermediate between them. What is
intermediate seems preferable; for fire, earth, air, and water are
already involved with pairs of contraries. There is, therefore, much
to be said for those who make the underlying substance different
from these four; of the rest, the next best choice is air, as
presenting sensible differences in a less degree than the others;
and after air, water. All, however, agree in this, that they
differentiate their One by means of the contraries, such as density
and rarity and more and less, which may of course be generalized, as
has already been said into excess and defect. Indeed this doctrine too
(that the One and excess and defect are the principles of things)
would appear to be of old standing, though in different forms; for the
early thinkers made the two the active and the one the passive
principle, whereas some of the more recent maintain the reverse.

  To suppose then that the elements are three in number would seem,
from these and similar considerations, a plausible view, as I said
before. On the other hand, the view that they are more than three in
number would seem to be untenable.

  For the one substratum is sufficient to be acted on; but if we
have four contraries, there will be two contrarieties, and we shall
have to suppose an intermediate nature for each pair separately. If,
on the other hand, the contrarieties, being two, can generate from
each other, the second contrariety will be superfluous. Moreover, it
is impossible that there should be more than one primary
contrariety. For substance is a single genus of being, so that the
principles can differ only as prior and posterior, not in genus; in
a single genus there is always a single contrariety, all the other
contrarieties in it being held to be reducible to one.

  It is clear then that the number of elements is neither one nor more
than two or three; but whether two or three is, as I said, a
question of considerable difficulty.

                                 7

  We will now give our own account, approaching the question first
with reference to becoming in its widest sense: for we shall be
following the natural order of inquiry if we speak first of common
characteristics, and then investigate the characteristics of special
cases.

  We say that one thing comes to be from another thing, and one sort
of thing from another sort of thing, both in the case of simple and of
complex things. I mean the following. We can say (1) 'man becomes
musical', (2) what is 'not-musical becomes musical', or (3), the
'not-musical man becomes a musical man'. Now what becomes in (1) and
(2)-'man' and 'not musical'-I call simple, and what each
becomes-'musical'-simple also. But when (3) we say the 'not-musical
man becomes a musical man', both what becomes and what it becomes
are complex.

  As regards one of these simple 'things that become' we say not
only 'this becomes so-and-so', but also 'from being this, comes to
be so-and-so', as 'from being not-musical comes to be musical'; as
regards the other we do not say this in all cases, as we do not say
(1) 'from being a man he came to be musical' but only 'the man
became musical'.

  When a 'simple' thing is said to become something, in one case (1)
it survives through the process, in the other (2) it does not. For man
remains a man and is such even when he becomes musical, whereas what
is not musical or is unmusical does not continue to exist, either
simply or combined with the subject.

  These distinctions drawn, one can gather from surveying the
various cases of becoming in the way we are describing that, as we
say, there must always be an underlying something, namely that which
becomes, and that this, though always one numerically, in form at
least is not one. (By that I mean that it can be described in
different ways.) For 'to be man' is not the same as 'to be unmusical'.
One part survives, the other does not: what is not an opposite
survives (for 'man' survives), but 'not-musical' or 'unmusical' does
not survive, nor does the compound of the two, namely 'unmusical man'.

  We speak of 'becoming that from this' instead of 'this becoming
that' more in the case of what does not survive the change-'becoming
musical from unmusical', not 'from man'-but there are exceptions, as
we sometimes use the latter form of expression even of what
survives; we speak of 'a statue coming to be from bronze', not of
the 'bronze becoming a statue'. The change, however, from an
opposite which does not survive is described indifferently in both
ways, 'becoming that from this' or 'this becoming that'. We say both
that 'the unmusical becomes musical', and that 'from unmusical he
becomes musical'. And so both forms are used of the complex, 'becoming
a musical man from an unmusical man', and unmusical man becoming a
musical man'.

  But there are different senses of 'coming to be'. In some cases we
do not use the expression 'come to be', but 'come to be so-and-so'.
Only substances are said to 'come to be' in the unqualified sense.

  Now in all cases other than substance it is plain that there must be
some subject, namely, that which becomes. For we know that when a
thing comes to be of such a quantity or quality or in such a relation,
time, or place, a subject is always presupposed, since substance alone
is not predicated of another subject, but everything else of
substance.

  But that substances too, and anything else that can be said 'to
be' without qualification, come to be from some substratum, will
appear on examination. For we find in every case something that
underlies from which proceeds that which comes to be; for instance,
animals and plants from seed.

  Generally things which come to be, come to be in different ways: (1)
by change of shape, as a statue; (2) by addition, as things which
grow; (3) by taking away, as the Hermes from the stone; (4) by putting
together, as a house; (5) by alteration, as things which 'turn' in
respect of their material substance.

  It is plain that these are all cases of coming to be from a
substratum.

  Thus, clearly, from what has been said, whatever comes to be is
always complex. There is, on the one hand, (a) something which comes
into existence, and again (b) something which becomes that-the
latter (b) in two senses, either the subject or the opposite. By the
'opposite' I mean the 'unmusical', by the 'subject' 'man', and
similarly I call the absence of shape or form or order the 'opposite',
and the bronze or stone or gold the 'subject'.

  Plainly then, if there are conditions and principles which
constitute natural objects and from which they primarily are or have
come to be-have come to be, I mean, what each is said to be in its
essential nature, not what each is in respect of a concomitant
attribute-plainly, I say, everything comes to be from both subject and
form. For 'musical man' is composed (in a way) of 'man' and 'musical':
you can analyse it into the definitions of its elements. It is clear
then that what comes to be will come to be from these elements.

  Now the subject is one numerically, though it is two in form. (For
it is the man, the gold-the 'matter' generally-that is counted, for it
is more of the nature of a 'this', and what comes to be does not
come from it in virtue of a concomitant attribute; the privation, on
the other hand, and the contrary are incidental in the process.) And
the positive form is one-the order, the acquired art of music, or
any similar predicate.

  There is a sense, therefore, in which we must declare the principles
to be two, and a sense in which they are three; a sense in which the
contraries are the principles-say for example the musical and the
unmusical, the hot and the cold, the tuned and the untuned-and a sense
in which they are not, since it is impossible for the contraries to be
acted on by each other. But this difficulty also is solved by the fact
that the substratum is different from the contraries, for it is itself
not a contrary. The principles therefore are, in a way, not more in
number than the contraries, but as it were two, nor yet precisely two,
since there is a difference of essential nature, but three. For 'to be
man' is different from 'to be unmusical', and 'to be unformed' from
'to be bronze'.

  We have now stated the number of the principles of natural objects
which are subject to generation, and how the number is reached: and it
is clear that there must be a substratum for the contraries, and
that the contraries must be two. (Yet in another way of putting it
this is not necessary, as one of the contraries will serve to effect
the change by its successive absence and presence.)

  The underlying nature is an object of scientific knowledge, by an
analogy. For as the bronze is to the statue, the wood to the bed, or
the matter and the formless before receiving form to any thing which
has form, so is the underlying nature to substance, i.e. the 'this' or
existent.

  This then is one principle (though not one or existent in the same
sense as the 'this'), and the definition was one as we agreed; then
further there is its contrary, the privation. In what sense these
are two, and in what sense more, has been stated above. Briefly, we
explained first that only the contraries were principles, and later
that a substratum was indispensable, and that the principles were
three; our last statement has elucidated the difference between the
contraries, the mutual relation of the principles, and the nature of
the substratum. Whether the form or the substratum is the essential
nature of a physical object is not yet clear. But that the
principles are three, and in what sense, and the way in which each
is a principle, is clear.

  So much then for the question of the number and the nature of the
principles.

                                 8

  We will now proceed to show that the difficulty of the early
thinkers, as well as our own, is solved in this way alone.

  The first of those who studied science were misled in their search
for truth and the nature of things by their inexperience, which as
it were thrust them into another path. So they say that none of the
things that are either comes to be or passes out of existence, because
what comes to be must do so either from what is or from what is not,
both of which are impossible. For what is cannot come to be (because
it is already), and from what is not nothing could have come to be
(because something must be present as a substratum). So too they
exaggerated the consequence of this, and went so far as to deny even
the existence of a plurality of things, maintaining that only Being
itself is. Such then was their opinion, and such the reason for its
adoption.

  Our explanation on the other hand is that the phrases 'something
comes to be from what is or from what is not', 'what is not or what is
does something or has something done to it or becomes some
particular thing', are to be taken (in the first way of putting our
explanation) in the same sense as 'a doctor does something or has
something done to him', 'is or becomes something from being a doctor.'
These expressions may be taken in two senses, and so too, clearly, may
'from being', and 'being acts or is acted on'. A doctor builds a
house, not qua doctor, but qua housebuilder, and turns gray, not qua
doctor, but qua dark-haired. On the other hand he doctors or fails
to doctor qua doctor. But we are using words most appropriately when
we say that a doctor does something or undergoes something, or becomes
something from being a doctor, if he does, undergoes, or becomes qua
doctor. Clearly then also 'to come to be so-and-so from not-being'
means 'qua not-being'.

  It was through failure to make this distinction that those
thinkers gave the matter up, and through this error that they went
so much farther astray as to suppose that nothing else comes to be
or exists apart from Being itself, thus doing away with all becoming.

  We ourselves are in agreement with them in holding that nothing
can be said without qualification to come from what is not. But
nevertheless we maintain that a thing may 'come to be from what is
not'-that is, in a qualified sense. For a thing comes to be from the
privation, which in its own nature is not-being,-this not surviving as
a constituent of the result. Yet this causes surprise, and it is
thought impossible that something should come to be in the way
described from what is not.

  In the same way we maintain that nothing comes to be from being, and
that being does not come to be except in a qualified sense. In that
way, however, it does, just as animal might come to be from animal,
and an animal of a certain kind from an animal of a certain kind.
Thus, suppose a dog to come to be from a horse. The dog would then, it
is true, come to be from animal (as well as from an animal of a
certain kind) but not as animal, for that is already there. But if
anything is to become an animal, not in a qualified sense, it will not
be from animal: and if being, not from being-nor from not-being
either, for it has been explained that by 'from not being' we mean
from not-being qua not-being.

  Note further that we do not subvert the principle that everything
either is or is not.

  This then is one way of solving the difficulty. Another consists
in pointing out that the same things can be explained in terms of
potentiality and actuality. But this has been done with greater
precision elsewhere. So, as we said, the difficulties which
constrain people to deny the existence of some of the things we
mentioned are now solved. For it was this reason which also caused
some of the earlier thinkers to turn so far aside from the road
which leads to coming to be and passing away and change generally.
If they had come in sight of this nature, all their ignorance would
have been dispelled.

                                 9

  Others, indeed, have apprehended the nature in question, but not
adequately.

  In the first place they allow that a thing may come to be without
qualification from not being, accepting on this point the statement of
Parmenides. Secondly, they think that if the substratum is one
numerically, it must have also only a single potentiality-which is a
very different thing.

  Now we distinguish matter and privation, and hold that one of these,
namely the matter, is not-being only in virtue of an attribute which
it has, while the privation in its own nature is not-being; and that
the matter is nearly, in a sense is, substance, while the privation in
no sense is. They, on the other hand, identify their Great and Small
alike with not being, and that whether they are taken together as
one or separately. Their triad is therefore of quite a different
kind from ours. For they got so far as to see that there must be
some underlying nature, but they make it one-for even if one
philosopher makes a dyad of it, which he calls Great and Small, the
effect is the same, for he overlooked the other nature. For the one
which persists is a joint cause, with the form, of what comes to
be-a mother, as it were. But the negative part of the contrariety
may often seem, if you concentrate your attention on it as an evil
agent, not to exist at all.

  For admitting with them that there is something divine, good, and
desirable, we hold that there are two other principles, the one
contrary to it, the other such as of its own nature to desire and
yearn for it. But the consequence of their view is that the contrary
desires its wtextinction. Yet the form cannot desire itself, for it is
not defective; nor can the contrary desire it, for contraries are
mutually destructive. The truth is that what desires the form is
matter, as the female desires the male and the ugly the beautiful-only
the ugly or the female not per se but per accidens.

  The matter comes to be and ceases to be in one sense, while in
another it does not. As that which contains the privation, it ceases
to be in its own nature, for what ceases to be-the privation-is
contained within it. But as potentiality it does not cease to be in
its own nature, but is necessarily outside the sphere of becoming
and ceasing to be. For if it came to be, something must have existed
as a primary substratum from which it should come and which should
persist in it; but this is its own special nature, so that it will
be before coming to be. (For my definition of matter is just
this-the primary substratum of each thing, from which it comes to be
without qualification, and which persists in the result.) And if it
ceases to be it will pass into that at the last, so it will have
ceased to be before ceasing to be.

  The accurate determination of the first principle in respect of
form, whether it is one or many and what it is or what they are, is
the province of the primary type of science; so these questions may
stand over till then. But of the natural, i.e. perishable, forms we
shall speak in the expositions which follow.

  The above, then, may be taken as sufficient to establish that
there are principles and what they are and how many there are. Now let
us make a fresh start and proceed.

                              Book II

                                 1

  Of things that exist, some exist by nature, some from other causes.

  'By nature' the animals and their parts exist, and the plants and
the simple bodies (earth, fire, air, water)-for we say that these
and the like exist 'by nature'.

  All the things mentioned present a feature in which they differ from
things which are not constituted by nature. Each of them has within
itself a principle of motion and of stationariness (in respect of
place, or of growth and decrease, or by way of alteration). On the
other hand, a bed and a coat and anything else of that sort, qua
receiving these designations i.e. in so far as they are products of
art-have no innate impulse to change. But in so far as they happen
to be composed of stone or of earth or of a mixture of the two, they
do have such an impulse, and just to that extent which seems to
indicate that nature is a source or cause of being moved and of
being at rest in that to which it belongs primarily, in virtue of
itself and not in virtue of a concomitant attribute.

  I say 'not in virtue of a concomitant attribute', because (for
instance) a man who is a doctor might cure himself. Nevertheless it is
not in so far as he is a patient that he possesses the art of
medicine: it merely has happened that the same man is doctor and
patient-and that is why these attributes are not always found
together. So it is with all other artificial products. None of them
has in itself the source of its own production. But while in some
cases (for instance houses and the other products of manual labour)
that principle is in something else external to the thing, in others
those which may cause a change in themselves in virtue of a
concomitant attribute-it lies in the things themselves (but not in
virtue of what they are).

  'Nature' then is what has been stated. Things 'have a nature'which
have a principle of this kind. Each of them is a substance; for it
is a subject, and nature always implies a subject in which it inheres.

  The term 'according to nature' is applied to all these things and
also to the attributes which belong to them in virtue of what they
are, for instance the property of fire to be carried upwards-which
is not a 'nature' nor 'has a nature' but is 'by nature' or
'according to nature'.

  What nature is, then, and the meaning of the terms 'by nature' and
'according to nature', has been stated. That nature exists, it would
be absurd to try to prove; for it is obvious that there are many
things of this kind, and to prove what is obvious by what is not is
the mark of a man who is unable to distinguish what is self-evident
from what is not. (This state of mind is clearly possible. A man blind
from birth might reason about colours. Presumably therefore such
persons must be talking about words without any thought to
correspond.)

  Some identify the nature or substance of a natural object with
that immediate constituent of it which taken by itself is without
arrangement, e.g. the wood is the 'nature' of the bed, and the
bronze the 'nature' of the statue.

  As an indication of this Antiphon points out that if you planted a
bed and the rotting wood acquired the power of sending up a shoot,
it would not be a bed that would come up, but wood-which shows that
the arrangement in accordance with the rules of the art is merely an
incidental attribute, whereas the real nature is the other, which,
further, persists continuously through the process of making.

  But if the material of each of these objects has itself the same
relation to something else, say bronze (or gold) to water, bones (or
wood) to earth and so on, that (they say) would be their nature and
essence. Consequently some assert earth, others fire or air or water
or some or all of these, to be the nature of the things that are.
For whatever any one of them supposed to have this character-whether
one thing or more than one thing-this or these he declared to be the
whole of substance, all else being its affections, states, or
dispositions. Every such thing they held to be eternal (for it could
not pass into anything else), but other things to come into being
and cease to be times without number.

  This then is one account of 'nature', namely that it is the
immediate material substratum of things which have in themselves a
principle of motion or change.

  Another account is that 'nature' is the shape or form which is
specified in the definition of the thing.

  For the word 'nature' is applied to what is according to nature
and the natural in the same way as 'art' is applied to what is
artistic or a work of art. We should not say in the latter case that
there is anything artistic about a thing, if it is a bed only
potentially, not yet having the form of a bed; nor should we call it a
work of art. The same is true of natural compounds. What is
potentially flesh or bone has not yet its own 'nature', and does not
exist until it receives the form specified in the definition, which we
name in defining what flesh or bone is. Thus in the second sense of
'nature' it would be the shape or form (not separable except in
statement) of things which have in themselves a source of motion. (The
combination of the two, e.g. man, is not 'nature' but 'by nature' or
'natural'.)

  The form indeed is 'nature' rather than the matter; for a thing is
more properly said to be what it is when it has attained to fulfilment
than when it exists potentially. Again man is born from man, but not
bed from bed. That is why people say that the figure is not the nature
of a bed, but the wood is-if the bed sprouted not a bed but wood would
come up. But even if the figure is art, then on the same principle the
shape of man is his nature. For man is born from man.

  We also speak of a thing's nature as being exhibited in the
process of growth by which its nature is attained. The 'nature' in
this sense is not like 'doctoring', which leads not to the art of
doctoring but to health. Doctoring must start from the art, not lead
to it. But it is not in this way that nature (in the one sense) is
related to nature (in the other). What grows qua growing grows from
something into something. Into what then does it grow? Not into that
from which it arose but into that to which it tends. The shape then is
nature.

  'Shape' and 'nature', it should be added, are in two senses. For the
privation too is in a way form. But whether in unqualified coming to
be there is privation, i.e. a contrary to what comes to be, we must
consider later.

                                 2

  We have distinguished, then, the different ways in which the term
'nature' is used.

  The next point to consider is how the mathematician differs from the
physicist. Obviously physical bodies contain surfaces and volumes,
lines and points, and these are the subject-matter of mathematics.

  Further, is astronomy different from physics or a department of
it? It seems absurd that the physicist should be supposed to know
the nature of sun or moon, but not to know any of their essential
attributes, particularly as the writers on physics obviously do
discuss their shape also and whether the earth and the world are
spherical or not.

  Now the mathematician, though he too treats of these things,
nevertheless does not treat of them as the limits of a physical
body; nor does he consider the attributes indicated as the
attributes of such bodies. That is why he separates them; for in
thought they are separable from motion, and it makes no difference,
nor does any falsity result, if they are separated. The holders of the
theory of Forms do the same, though they are not aware of it; for they
separate the objects of physics, which are less separable than those
of mathematics. This becomes plain if one tries to state in each of
the two cases the definitions of the things and of their attributes.
'Odd' and 'even', 'straight' and 'curved', and likewise 'number',
'line', and 'figure', do not involve motion; not so 'flesh' and 'bone'
and 'man'-these are defined like 'snub nose', not like 'curved'.

  Similar evidence is supplied by the more physical of the branches of
mathematics, such as optics, harmonics, and astronomy. These are in
a way the converse of geometry. While geometry investigates physical
lines but not qua physical, optics investigates mathematical lines,
but qua physical, not qua mathematical.

  Since 'nature' has two senses, the form and the matter, we must
investigate its objects as we would the essence of snubness. That
is, such things are neither independent of matter nor can be defined
in terms of matter only. Here too indeed one might raise a difficulty.
Since there are two natures, with which is the physicist concerned? Or
should he investigate the combination of the two? But if the
combination of the two, then also each severally. Does it belong
then to the same or to different sciences to know each severally?

  If we look at the ancients, physics would to be concerned with the
matter. (It was only very slightly that Empedocles and Democritus
touched on the forms and the essence.)

  But if on the other hand art imitates nature, and it is the part
of the same discipline to know the form and the matter up to a point
(e.g. the doctor has a knowledge of health and also of bile and
phlegm, in which health is realized, and the builder both of the
form of the house and of the matter, namely that it is bricks and
beams, and so forth): if this is so, it would be the part of physics
also to know nature in both its senses.

  Again, 'that for the sake of which', or the end, belongs to the same
department of knowledge as the means. But the nature is the end or
'that for the sake of which'. For if a thing undergoes a continuous
change and there is a stage which is last, this stage is the end or
'that for the sake of which'. (That is why the poet was carried away
into making an absurd statement when he said 'he has the end for the
sake of which he was born'. For not every stage that is last claims to
be an end, but only that which is best.)

  For the arts make their material (some simply 'make' it, others make
it serviceable), and we use everything as if it was there for our
sake. (We also are in a sense an end. 'That for the sake of which' has
two senses: the distinction is made in our work On Philosophy.) The
arts, therefore, which govern the matter and have knowledge are two,
namely the art which uses the product and the art which directs the
production of it. That is why the using art also is in a sense
directive; but it differs in that it knows the form, whereas the art
which is directive as being concerned with production knows the
matter. For the helmsman knows and prescribes what sort of form a helm
should have, the other from what wood it should be made and by means
of what operations. In the products of art, however, we make the
material with a view to the function, whereas in the products of
nature the matter is there all along.

  Again, matter is a relative term: to each form there corresponds a
special matter. How far then must the physicist know the form or
essence? Up to a point, perhaps, as the doctor must know sinew or
the smith bronze (i.e. until he understands the purpose of each):
and the physicist is concerned only with things whose forms are
separable indeed, but do not exist apart from matter. Man is
begotten by man and by the sun as well. The mode of existence and
essence of the separable it is the business of the primary type of
philosophy to define.

                                 3

  Now that we have established these distinctions, we must proceed
to consider causes, their character and number. Knowledge is the
object of our inquiry, and men do not think they know a thing till
they have grasped the 'why' of (which is to grasp its primary
cause). So clearly we too must do this as regards both coming to be
and passing away and every kind of physical change, in order that,
knowing their principles, we may try to refer to these principles each
of our problems.

  In one sense, then, (1) that out of which a thing comes to be and
which persists, is called 'cause', e.g. the bronze of the statue,
the silver of the bowl, and the genera of which the bronze and the
silver are species.

  In another sense (2) the form or the archetype, i.e. the statement
of the essence, and its genera, are called 'causes' (e.g. of the
octave the relation of 2:1, and generally number), and the parts in
the definition.

  Again (3) the primary source of the change or coming to rest; e.g.
the man who gave advice is a cause, the father is cause of the
child, and generally what makes of what is made and what causes change
of what is changed.

  Again (4) in the sense of end or 'that for the sake of which' a
thing is done, e.g. health is the cause of walking about. ('Why is
he walking about?' we say. 'To be healthy', and, having said that,
we think we have assigned the cause.) The same is true also of all the
intermediate steps which are brought about through the action of
something else as means towards the end, e.g. reduction of flesh,
purging, drugs, or surgical instruments are means towards health.
All these things are 'for the sake of' the end, though they differ
from one another in that some are activities, others instruments.

  This then perhaps exhausts the number of ways in which the term
'cause' is used.

  As the word has several senses, it follows that there are several
causes of the same thing not merely in virtue of a concomitant
attribute), e.g. both the art of the sculptor and the bronze are
causes of the statue. These are causes of the statue qua statue, not
in virtue of anything else that it may be-only not in the same way,
the one being the material cause, the other the cause whence the
motion comes. Some things cause each other reciprocally, e.g. hard
work causes fitness and vice versa, but again not in the same way, but
the one as end, the other as the origin of change. Further the same
thing is the cause of contrary results. For that which by its presence
brings about one result is sometimes blamed for bringing about the
contrary by its absence. Thus we ascribe the wreck of a ship to the
absence of the pilot whose presence was the cause of its safety.

  All the causes now mentioned fall into four familiar divisions.
The letters are the causes of syllables, the material of artificial
products, fire, &c., of bodies, the parts of the whole, and the
premisses of the conclusion, in the sense of 'that from which'. Of
these pairs the one set are causes in the sense of substratum, e.g.
the parts, the other set in the sense of essence-the whole and the
combination and the form. But the seed and the doctor and the adviser,
and generally the maker, are all sources whence the change or
stationariness originates, while the others are causes in the sense of
the end or the good of the rest; for 'that for the sake of which'
means what is best and the end of the things that lead up to it.
(Whether we say the 'good itself or the 'apparent good' makes no
difference.)

  Such then is the number and nature of the kinds of cause.

  Now the modes of causation are many, though when brought under heads
they too can be reduced in number. For 'cause' is used in many
senses and even within the same kind one may be prior to another (e.g.
the doctor and the expert are causes of health, the relation 2:1 and
number of the octave), and always what is inclusive to what is
particular. Another mode of causation is the incidental and its
genera, e.g. in one way 'Polyclitus', in another 'sculptor' is the
cause of a statue, because 'being Polyclitus' and 'sculptor' are
incidentally conjoined. Also the classes in which the incidental
attribute is included; thus 'a man' could be said to be the cause of a
statue or, generally, 'a living creature'. An incidental attribute too
may be more or less remote, e.g. suppose that 'a pale man' or 'a
musical man' were said to be the cause of the statue.

  All causes, both proper and incidental, may be spoken of either as
potential or as actual; e.g. the cause of a house being built is
either 'house-builder' or 'house-builder building'.

  Similar distinctions can be made in the things of which the causes
are causes, e.g. of 'this statue' or of 'statue' or of 'image'
generally, of 'this bronze' or of 'bronze' or of 'material' generally.
So too with the incidental attributes. Again we may use a complex
expression for either and say, e.g. neither 'Polyclitus' nor
'sculptor' but 'Polyclitus, sculptor'.

  All these various uses, however, come to six in number, under each
of which again the usage is twofold. Cause means either what is
particular or a genus, or an incidental attribute or a genus of
that, and these either as a complex or each by itself; and all six
either as actual or as potential. The difference is this much, that
causes which are actually at work and particular exist and cease to
exist simultaneously with their effect, e.g. this healing person
with this being-healed person and that house-building man with that
being-built house; but this is not always true of potential
causes--the house and the housebuilder do not pass away
simultaneously.

  In investigating the cause of each thing it is always necessary to
seek what is most precise (as also in other things): thus man builds
because he is a builder, and a builder builds in virtue of his art
of building. This last cause then is prior: and so generally.

  Further, generic effects should be assigned to generic causes,
particular effects to particular causes, e.g. statue to sculptor, this
statue to this sculptor; and powers are relative to possible
effects, actually operating causes to things which are actually
being effected.

  This must suffice for our account of the number of causes and the
modes of causation.

                                 4

  But chance also and spontaneity are reckoned among causes: many
things are said both to be and to come to be as a result of chance and
spontaneity. We must inquire therefore in what manner chance and
spontaneity are present among the causes enumerated, and whether
they are the same or different, and generally what chance and
spontaneity are.

  Some people even question whether they are real or not. They say
that nothing happens by chance, but that everything which we ascribe
to chance or spontaneity has some definite cause, e.g. coming 'by
chance' into the market and finding there a man whom one wanted but
did not expect to meet is due to one's wish to go and buy in the
market. Similarly in other cases of chance it is always possible, they
maintain, to find something which is the cause; but not chance, for if
chance were real, it would seem strange indeed, and the question might
be raised, why on earth none of the wise men of old in speaking of the
causes of generation and decay took account of chance; whence it would
seem that they too did not believe that anything is by chance. But
there is a further circumstance that is surprising. Many things both
come to be and are by chance and spontaneity, and although know that
each of them can be ascribed to some cause (as the old argument said
which denied chance), nevertheless they speak of some of these
things as happening by chance and others not. For this reason also
they ought to have at least referred to the matter in some way or
other.

  Certainly the early physicists found no place for chance among the
causes which they recognized-love, strife, mind, fire, or the like.
This is strange, whether they supposed that there is no such thing
as chance or whether they thought there is but omitted to mention
it-and that too when they sometimes used it, as Empedocles does when
he says that the air is not always separated into the highest
region, but 'as it may chance'. At any rate he says in his cosmogony
that 'it happened to run that way at that time, but it often ran
otherwise.' He tells us also that most of the parts of animals came to
be by chance.

  There are some too who ascribe this heavenly sphere and all the
worlds to spontaneity. They say that the vortex arose spontaneously,
i.e. the motion that separated and arranged in its present order all
that exists. This statement might well cause surprise. For they are
asserting that chance is not responsible for the existence or
generation of animals and plants, nature or mind or something of the
kind being the cause of them (for it is not any chance thing that
comes from a given seed but an olive from one kind and a man from
another); and yet at the same time they assert that the heavenly
sphere and the divinest of visible things arose spontaneously,
having no such cause as is assigned to animals and plants. Yet if this
is so, it is a fact which deserves to be dwelt upon, and something
might well have been said about it. For besides the other
absurdities of the statement, it is the more absurd that people should
make it when they see nothing coming to be spontaneously in the
heavens, but much happening by chance among the things which as they
say are not due to chance; whereas we should have expected exactly the
opposite.

  Others there are who, indeed, believe that chance is a cause, but
that it is inscrutable to human intelligence, as being a divine
thing and full of mystery.

  Thus we must inquire what chance and spontaneity are, whether they
are the same or different, and how they fit into our division of
causes.

                                 5

  First then we observe that some things always come to pass in the
same way, and others for the most part. It is clearly of neither of
these that chance is said to be the cause, nor can the 'effect of
chance' be identified with any of the things that come to pass by
necessity and always, or for the most part. But as there is a third
class of events besides these two-events which all say are 'by
chance'-it is plain that there is such a thing as chance and
spontaneity; for we know that things of this kind are due to chance
and that things due to chance are of this kind.

  But, secondly, some events are for the sake of something, others
not. Again, some of the former class are in accordance with deliberate
intention, others not, but both are in the class of things which are
for the sake of something. Hence it is clear that even among the
things which are outside the necessary and the normal, there are
some in connexion withwhich the phrase 'for the sake of something'
is applicable. (Events that are for the sake of something include
whatever may be done as a result of thought or of nature.) Things of
this kind, then, when they come to pass incidental are said to be
'by chance'. For just as a thing is something either in virtue of
itself or incidentally, so may it be a cause. For instance, the
housebuilding faculty is in virtue of itself the cause of a house,
whereas the pale or the musical is the incidental cause. That which is
per se cause of the effect is determinate, but the incidental cause is
indeterminable, for the possible attributes of an individual are
innumerable. To resume then; when a thing of this kind comes to pass
among events which are for the sake of something, it is said to be
spontaneous or by chance. (The distinction between the two must be
made later-for the present it is sufficient if it is plain that both
are in the sphere of things done for the sake of something.)

  Example: A man is engaged in collecting subscriptions for a feast.
He would have gone to such and such a place for the purpose of getting
the money, if he had known. He actually went there for another purpose
and it was only incidentally that he got his money by going there; and
this was not due to the fact that he went there as a rule or
necessarily, nor is the end effected (getting the money) a cause
present in himself-it belongs to the class of things that are
intentional and the result of intelligent deliberation. It is when
these conditions are satisfied that the man is said to have gone 'by
chance'. If he had gone of deliberate purpose and for the sake of
this-if he always or normally went there when he was collecting
payments-he would not be said to have gone 'by chance'.

  It is clear then that chance is an incidental cause in the sphere of
those actions for the sake of something which involve purpose.
Intelligent reflection, then, and chance are in the same sphere, for
purpose implies intelligent reflection.

  It is necessary, no doubt, that the causes of what comes to pass
by chance be indefinite; and that is why chance is supposed to
belong to the class of the indefinite and to be inscrutable to man,
and why it might be thought that, in a way, nothing occurs by
chance. For all these statements are correct, because they are well
grounded. Things do, in a way, occur by chance, for they occur
incidentally and chance is an incidental cause. But strictly it is not
the cause-without qualification-of anything; for instance, a
housebuilder is the cause of a house; incidentally, a fluteplayer
may be so.

  And the causes of the man's coming and getting the money (when he
did not come for the sake of that) are innumerable. He may have wished
to see somebody or been following somebody or avoiding somebody, or
may have gone to see a spectacle. Thus to say that chance is a thing
contrary to rule is correct. For 'rule' applies to what is always true
or true for the most part, whereas chance belongs to a third type of
event. Hence, to conclude, since causes of this kind are indefinite,
chance too is indefinite. (Yet in some cases one might raise the
question whether any incidental fact might be the cause of the
chance occurrence, e.g. of health the fresh air or the sun's heat
may be the cause, but having had one's hair cut cannot; for some
incidental causes are more relevant to the effect than others.)

  Chance or fortune is called 'good' when the result is good, 'evil'
when it is evil. The terms 'good fortune' and 'ill fortune' are used
when either result is of considerable magnitude. Thus one who comes
within an ace of some great evil or great good is said to be fortunate
or unfortunate. The mind affirms the essence of the attribute,
ignoring the hair's breadth of difference. Further, it is with
reason that good fortune is regarded as unstable; for chance is
unstable, as none of the things which result from it can be invariable
or normal.

  Both are then, as I have said, incidental causes-both chance and
spontaneity-in the sphere of things which are capable of coming to
pass not necessarily, nor normally, and with reference to such of
these as might come to pass for the sake of something.

                                 6

  They differ in that 'spontaneity' is the wider term. Every result of
chance is from what is spontaneous, but not everything that is from
what is spontaneous is from chance.

  Chance and what results from chance are appropriate to agents that
are capable of good fortune and of moral action generally. Therefore
necessarily chance is in the sphere of moral actions. This is
indicated by the fact that good fortune is thought to be the same,
or nearly the same, as happiness, and happiness to be a kind of
moral action, since it is well-doing. Hence what is not capable of
moral action cannot do anything by chance. Thus an inanimate thing
or a lower animal or a child cannot do anything by chance, because
it is incapable of deliberate intention; nor can 'good fortune' or
'ill fortune' be ascribed to them, except metaphorically, as
Protarchus, for example, said that the stones of which altars are made
are fortunate because they are held in honour, while their fellows are
trodden under foot. Even these things, however, can in a way be
affected by chance, when one who is dealing with them does something
to them by chance, but not otherwise.

  The spontaneous on the other hand is found both in the lower animals
and in many inanimate objects. We say, for example, that the horse
came 'spontaneously', because, though his coming saved him, he did not
come for the sake of safety. Again, the tripod fell 'of itself',
because, though when it fell it stood on its feet so as to serve for a
seat, it did not fall for the sake of that.

  Hence it is clear that events which (1) belong to the general
class of things that may come to pass for the sake of something, (2)
do not come to pass for the sake of what actually results, and (3)
have an external cause, may be described by the phrase 'from
spontaneity'. These 'spontaneous' events are said to be 'from
chance' if they have the further characteristics of being the
objects of deliberate intention and due to agents capable of that mode
of action. This is indicated by the phrase 'in vain', which is used
when A which is for the sake of B, does not result in B. For instance,
taking a walk is for the sake of evacuation of the bowels; if this
does not follow after walking, we say that we have walked 'in vain'
and that the walking was 'vain'. This implies that what is naturally
the means to an end is 'in vain', when it does not effect the end
towards which it was the natural means-for it would be absurd for a
man to say that he had bathed in vain because the sun was not
eclipsed, since the one was not done with a view to the other. Thus
the spontaneous is even according to its derivation the case in
which the thing itself happens in vain. The stone that struck the
man did not fall for the purpose of striking him; therefore it fell
spontaneously, because it might have fallen by the action of an
agent and for the purpose of striking. The difference between
spontaneity and what results by chance is greatest in things that come
to be by nature; for when anything comes to be contrary to nature,
we do not say that it came to be by chance, but by spontaneity. Yet
strictly this too is different from the spontaneous proper; for the
cause of the latter is external, that of the former internal.

  We have now explained what chance is and what spontaneity is, and in
what they differ from each other. Both belong to the mode of causation
'source of change', for either some natural or some intelligent
agent is always the cause; but in this sort of causation the number of
possible causes is infinite.

  Spontaneity and chance are causes of effects which though they might
result from intelligence or nature, have in fact been caused by
something incidentally. Now since nothing which is incidental is prior
to what is per se, it is clear that no incidental cause can be prior
to a cause per se. Spontaneity and chance, therefore, are posterior to
intelligence and nature. Hence, however true it may be that the
heavens are due to spontaneity, it will still be true that
intelligence and nature will be prior causes of this All and of many
things in it besides.

                                 7

  It is clear then that there are causes, and that the number of
them is what we have stated. The number is the same as that of the
things comprehended under the question 'why'. The 'why' is referred
ultimately either (1), in things which do not involve motion, e.g.
in mathematics, to the 'what' (to the definition of 'straight line' or
'commensurable', &c.), or (2) to what initiated a motion, e.g. 'why
did they go to war?-because there had been a raid'; or (3) we are
inquiring 'for the sake of what?'-'that they may rule'; or (4), in the
case of things that come into being, we are looking for the matter.
The causes, therefore, are these and so many in number.

  Now, the causes being four, it is the business of the physicist to
know about them all, and if he refers his problems back to all of
them, he will assign the 'why' in the way proper to his science-the
matter, the form, the mover, 'that for the sake of which'. The last
three often coincide; for the 'what' and 'that for the sake of
which' are one, while the primary source of motion is the same in
species as these (for man generates man), and so too, in general,
are all things which cause movement by being themselves moved; and
such as are not of this kind are no longer inside the province of
physics, for they cause motion not by possessing motion or a source of
motion in themselves, but being themselves incapable of motion.
Hence there are three branches of study, one of things which are
incapable of motion, the second of things in motion, but
indestructible, the third of destructible things.

  The question 'why', then, is answered by reference to the matter, to
the form, and to the primary moving cause. For in respect of coming to
be it is mostly in this last way that causes are investigated-'what
comes to be after what? what was the primary agent or patient?' and so
at each step of the series.

  Now the principles which cause motion in a physical way are two,
of which one is not physical, as it has no principle of motion in
itself. Of this kind is whatever causes movement, not being itself
moved, such as (1) that which is completely unchangeable, the
primary reality, and (2) the essence of that which is coming to be,
i.e. the form; for this is the end or 'that for the sake of which'.
Hence since nature is for the sake of something, we must know this
cause also. We must explain the 'why' in all the senses of the term,
namely, (1) that from this that will necessarily result ('from this'
either without qualification or in most cases); (2) that 'this must be
so if that is to be so' (as the conclusion presupposes the premisses);
(3) that this was the essence of the thing; and (4) because it is
better thus (not without qualification, but with reference to the
essential nature in each case).

                                 8

  We must explain then (1) that Nature belongs to the class of
causes which act for the sake of something; (2) about the necessary
and its place in physical problems, for all writers ascribe things
to this cause, arguing that since the hot and the cold, &c., are of
such and such a kind, therefore certain things necessarily are and
come to be-and if they mention any other cause (one his 'friendship
and strife', another his 'mind'), it is only to touch on it, and
then good-bye to it.

  A difficulty presents itself: why should not nature work, not for
the sake of something, nor because it is better so, but just as the
sky rains, not in order to make the corn grow, but of necessity?
What is drawn up must cool, and what has been cooled must become water
and descend, the result of this being that the corn grows. Similarly
if a man's crop is spoiled on the threshing-floor, the rain did not
fall for the sake of this-in order that the crop might be
spoiled-but that result just followed. Why then should it not be the
same with the parts in nature, e.g. that our teeth should come up of
necessity-the front teeth sharp, fitted for tearing, the molars
broad and useful for grinding down the food-since they did not arise
for this end, but it was merely a coincident result; and so with all
other parts in which we suppose that there is purpose? Wherever then
all the parts came about just what they would have been if they had
come be for an end, such things survived, being organized
spontaneously in a fitting way; whereas those which grew otherwise
perished and continue to perish, as Empedocles says his 'man-faced
ox-progeny' did.

  Such are the arguments (and others of the kind) which may cause
difficulty on this point. Yet it is impossible that this should be the
true view. For teeth and all other natural things either invariably or
normally come about in a given way; but of not one of the results of
chance or spontaneity is this true. We do not ascribe to chance or
mere coincidence the frequency of rain in winter, but frequent rain in
summer we do; nor heat in the dog-days, but only if we have it in
winter. If then, it is agreed that things are either the result of
coincidence or for an end, and these cannot be the result of
coincidence or spontaneity, it follows that they must be for an end;
and that such things are all due to nature even the champions of the
theory which is before us would agree. Therefore action for an end
is present in things which come to be and are by nature.

  Further, where a series has a completion, all the preceding steps
are for the sake of that. Now surely as in intelligent action, so in
nature; and as in nature, so it is in each action, if nothing
interferes. Now intelligent action is for the sake of an end;
therefore the nature of things also is so. Thus if a house, e.g. had
been a thing made by nature, it would have been made in the same way
as it is now by art; and if things made by nature were made also by
art, they would come to be in the same way as by nature. Each step
then in the series is for the sake of the next; and generally art
partly completes what nature cannot bring to a finish, and partly
imitates her. If, therefore, artificial products are for the sake of
an end, so clearly also are natural products. The relation of the
later to the earlier terms of the series is the same in both. This
is most obvious in the animals other than man: they make things
neither by art nor after inquiry or deliberation. Wherefore people
discuss whether it is by intelligence or by some other faculty that
these creatures work,spiders, ants, and the like. By gradual advance
in this direction we come to see clearly that in plants too that is
produced which is conducive to the end-leaves, e.g. grow to provide
shade for the fruit. If then it is both by nature and for an end
that the swallow makes its nest and the spider its web, and plants
grow leaves for the sake of the fruit and send their roots down (not
up) for the sake of nourishment, it is plain that this kind of cause
is operative in things which come to be and are by nature. And since
'nature' means two things, the matter and the form, of which the
latter is the end, and since all the rest is for the sake of the
end, the form must be the cause in the sense of 'that for the sake
of which'.

  Now mistakes come to pass even in the operations of art: the
grammarian makes a mistake in writing and the doctor pours out the
wrong dose. Hence clearly mistakes are possible in the operations of
nature also. If then in art there are cases in which what is rightly
produced serves a purpose, and if where mistakes occur there was a
purpose in what was attempted, only it was not attained, so must it be
also in natural products, and monstrosities will be failures in the
purposive effort. Thus in the original combinations the 'ox-progeny'
if they failed to reach a determinate end must have arisen through the
corruption of some principle corresponding to what is now the seed.

  Further, seed must have come into being first, and not straightway
the animals: the words 'whole-natured first...' must have meant seed.

  Again, in plants too we find the relation of means to end, though
the degree of organization is less. Were there then in plants also
'olive-headed vine-progeny', like the 'man-headed ox-progeny', or not?
An absurd suggestion; yet there must have been, if there were such
things among animals.

  Moreover, among the seeds anything must have come to be at random.
But the person who asserts this entirely does away with 'nature' and
what exists 'by nature'. For those things are natural which, by a
continuous movement originated from an internal principle, arrive at
some completion: the same completion is not reached from every
principle; nor any chance completion, but always the tendency in
each is towards the same end, if there is no impediment.

  The end and the means towards it may come about by chance. We say,
for instance, that a stranger has come by chance, paid the ransom, and
gone away, when he does so as if he had come for that purpose,
though it was not for that that he came. This is incidental, for
chance is an incidental cause, as I remarked before. But when an event
takes place always or for the most part, it is not incidental or by
chance. In natural products the sequence is invariable, if there is no
impediment.

  It is absurd to suppose that purpose is not present because we do
not observe the agent deliberating. Art does not deliberate. If the
ship-building art were in the wood, it would produce the same
results by nature. If, therefore, purpose is present in art, it is
present also in nature. The best illustration is a doctor doctoring
himself: nature is like that.

  It is plain then that nature is a cause, a cause that operates for a
purpose.

                                 9

  As regards what is 'of necessity', we must ask whether the necessity
is 'hypothetical', or 'simple' as well. The current view places what
is of necessity in the process of production, just as if one were to
suppose that the wall of a house necessarily comes to be because
what is heavy is naturally carried downwards and what is light to
the top, wherefore the stones and foundations take the lowest place,
with earth above because it is lighter, and wood at the top of all
as being the lightest. Whereas, though the wall does not come to be
without these, it is not due to these, except as its material cause:
it comes to be for the sake of sheltering and guarding certain things.
Similarly in all other things which involve production for an end; the
product cannot come to be without things which have a necessary
nature, but it is not due to these (except as its material); it
comes to be for an end. For instance, why is a saw such as it is? To
effect so-and-so and for the sake of so-and-so. This end, however,
cannot be realized unless the saw is made of iron. It is, therefore,
necessary for it to be of iron, it we are to have a saw and perform
the operation of sawing. What is necessary then, is necessary on a
hypothesis; it is not a result necessarily determined by
antecedents. Necessity is in the matter, while 'that for the sake of
which' is in the definition.

  Necessity in mathematics is in a way similar to necessity in
things which come to be through the operation of nature. Since a
straight line is what it is, it is necessary that the angles of a
triangle should equal two right angles. But not conversely; though
if the angles are not equal to two right angles, then the straight
line is not what it is either. But in things which come to be for an
end, the reverse is true. If the end is to exist or does exist, that
also which precedes it will exist or does exist; otherwise just as
there, if-the conclusion is not true, the premiss will not be true, so
here the end or 'that for the sake of which' will not exist. For
this too is itself a starting-point, but of the reasoning, not of
the action; while in mathematics the starting-point is the
starting-point of the reasoning only, as there is no action. If then
there is to be a house, such-and-such things must be made or be
there already or exist, or generally the matter relative to the end,
bricks and stones if it is a house. But the end is not due to these
except as the matter, nor will it come to exist because of them. Yet
if they do not exist at all, neither will the house, or the saw-the
former in the absence of stones, the latter in the absence of
iron-just as in the other case the premisses will not be true, if
the angles of the triangle are not equal to two right angles.

  The necessary in nature, then, is plainly what we call by the name
of matter, and the changes in it. Both causes must be stated by the
physicist, but especially the end; for that is the cause of the
matter, not vice versa; and the end is 'that for the sake of which',
and the beginning starts from the definition or essence; as in
artificial products, since a house is of such-and-such a kind, certain
things must necessarily come to be or be there already, or since
health is this, these things must necessarily come to be or be there
already. Similarly if man is this, then these; if these, then those.
Perhaps the necessary is present also in the definition. For if one
defines the operation of sawing as being a certain kind of dividing,
then this cannot come about unless the saw has teeth of a certain
kind; and these cannot be unless it is of iron. For in the
definition too there are some parts that are, as it were, its matter.

                              Book III

                                 1

  NATURE has been defined as a 'principle of motion and change', and
it is the subject of our inquiry. We must therefore see that we
understand the meaning of 'motion'; for if it were unknown, the
meaning of 'nature' too would be unknown.

  When we have determined the nature of motion, our next task will
be to attack in the same way the terms which are involved in it. Now
motion is supposed to belong to the class of things which are
continuous; and the infinite presents itself first in the
continuous-that is how it comes about that 'infinite' is often used in
definitions of the continuous ('what is infinitely divisible is
continuous'). Besides these, place, void, and time are thought to be
necessary conditions of motion.

  Clearly, then, for these reasons and also because the attributes
mentioned are common to, and coextensive with, all the objects of
our science, we must first take each of them in hand and discuss it.
For the investigation of special attributes comes after that of the
common attributes.

  To begin then, as we said, with motion.

  We may start by distinguishing (1) what exists in a state of
fulfilment only, (2) what exists as potential, (3) what exists as
potential and also in fulfilment-one being a 'this', another 'so
much', a third 'such', and similarly in each of the other modes of the
predication of being.

  Further, the word 'relative' is used with reference to (1) excess
and defect, (2) agent and patient and generally what can move and what
can be moved. For 'what can cause movement' is relative to 'what can
be moved', and vice versa.

  Again, there is no such thing as motion over and above the things.
It is always with respect to substance or to quantity or to quality or
to place that what changes changes. But it is impossible, as we
assert, to find anything common to these which is neither 'this' nor
quantum nor quale nor any of the other predicates. Hence neither
will motion and change have reference to something over and above
the things mentioned, for there is nothing over and above them.

  Now each of these belongs to all its subjects in either of two ways:
namely (1) substance-the one is positive form, the other privation;
(2) in quality, white and black; (3) in quantity, complete and
incomplete; (4) in respect of locomotion, upwards and downwards or
light and heavy. Hence there are as many types of motion or change
as there are meanings of the word 'is'.

  We have now before us the distinctions in the various classes of
being between what is full real and what is potential.

  Def. The fulfilment of what exists potentially, in so far as it
exists potentially, is motion-namely, of what is alterable qua
alterable, alteration: of what can be increased and its opposite
what can be decreased (there is no common name), increase and
decrease: of what can come to be and can pass away, coming to he and
passing away: of what can be carried along, locomotion.

  Examples will elucidate this definition of motion. When the
buildable, in so far as it is just that, is fully real, it is being
built, and this is building. Similarly, learning, doctoring,
rolling, leaping, ripening, ageing.

  The same thing, if it is of a certain kind, can be both potential
and fully real, not indeed at the same time or not in the same
respect, but e.g. potentially hot and actually cold. Hence at once
such things will act and be acted on by one another in many ways: each
of them will be capable at the same time of causing alteration and
of being altered. Hence, too, what effects motion as a physical
agent can be moved: when a thing of this kind causes motion, it is
itself also moved. This, indeed, has led some people to suppose that
every mover is moved. But this question depends on another set of
arguments, and the truth will be made clear later. is possible for a
thing to cause motion, though it is itself incapable of being moved.

  It is the fulfilment of what is potential when it is already fully
real and operates not as itself but as movable, that is motion. What I
mean by 'as' is this: Bronze is potentially a statue. But it is not
the fulfilment of bronze as bronze which is motion. For 'to be bronze'
and 'to be a certain potentiality' are not the same.

  If they were identical without qualification, i.e. in definition,
the fulfilment of bronze as bronze would have been motion. But they
are not the same, as has been said. (This is obvious in contraries.
'To be capable of health' and 'to be capable of illness' are not the
same, for if they were there would be no difference between being
ill and being well. Yet the subject both of health and of
sickness-whether it is humour or blood-is one and the same.)

  We can distinguish, then, between the two-just as, to give another
example, 'colour' and visible' are different-and clearly it is the
fulfilment of what is potential as potential that is motion. So
this, precisely, is motion.

  Further it is evident that motion is an attribute of a thing just
when it is fully real in this way, and neither before nor after. For
each thing of this kind is capable of being at one time actual, at
another not. Take for instance the buildable as buildable. The
actuality of the buildable as buildable is the process of building.
For the actuality of the buildable must be either this or the house.
But when there is a house, the buildable is no longer buildable. On
the other hand, it is the buildable which is being built. The
process then of being built must be the kind of actuality required But
building is a kind of motion, and the same account will apply to the
other kinds also.

                                 2

  The soundness of this definition is evident both when we consider
the accounts of motion that the others have given, and also from the
difficulty of defining it otherwise.

  One could not easily put motion and change in another genus-this
is plain if we consider where some people put it; they identify motion
with or 'inequality' or 'not being'; but such things are not
necessarily moved, whether they are 'different' or 'unequal' or
'non-existent'; Nor is change either to or from these rather than to
or from their opposites.

  The reason why they put motion into these genera is that it is
thought to be something indefinite, and the principles in the second
column are indefinite because they are privative: none of them is
either 'this' or 'such' or comes under any of the other modes of
predication. The reason in turn why motion is thought to be indefinite
is that it cannot be classed simply as a potentiality or as an
actuality-a thing that is merely capable of having a certain size is
not undergoing change, nor yet a thing that is actually of a certain
size, and motion is thought to be a sort of actuality, but incomplete,
the reason for this view being that the potential whose actuality it
is is incomplete. This is why it is hard to grasp what motion is. It
is necessary to class it with privation or with potentiality or with
sheer actuality, yet none of these seems possible. There remains
then the suggested mode of definition, namely that it is a sort of
actuality, or actuality of the kind described, hard to grasp, but
not incapable of existing.

  The mover too is moved, as has been said-every mover, that is, which
is capable of motion, and whose immobility is rest-when a thing is
subject to motion its immobility is rest. For to act on the movable as
such is just to move it. But this it does by contact, so that at the
same time it is also acted on. Hence we can define motion as the
fulfilment of the movable qua movable, the cause of the attribute
being contact with what can move so that the mover is also acted on.
The mover or agent will always be the vehicle of a form, either a
'this' or 'such', which, when it acts, will be the source and cause of
the change, e.g. the full-formed man begets man from what is
potentially man.

                                3

  The solution of the difficulty that is raised about the
motion-whether it is in the movable-is plain. It is the fulfilment
of this potentiality, and by the action of that which has the power of
causing motion; and the actuality of that which has the power of
causing motion is not other than the actuality of the movable, for
it must be the fulfilment of both. A thing is capable of causing
motion because it can do this, it is a mover because it actually
does it. But it is on the movable that it is capable of acting.
Hence there is a single actuality of both alike, just as one to two
and two to one are the same interval, and the steep ascent and the
steep descent are one-for these are one and the same, although they
can be described in different ways. So it is with the mover and the
moved.

  This view has a dialectical difficulty. Perhaps it is necessary that
the actuality of the agent and that of the patient should not be the
same. The one is 'agency' and the other 'patiency'; and the outcome
and completion of the one is an 'action', that of the other a
'passion'. Since then they are both motions, we may ask: in what are
they, if they are different? Either (a) both are in what is acted on
and moved, or (b) the agency is in the agent and the patiency in the
patient. (If we ought to call the latter also 'agency', the word would
be used in two senses.)

  Now, in alternative (b), the motion will be in the mover, for the
same statement will hold of 'mover' and 'moved'. Hence either every
mover will be moved, or, though having motion, it will not be moved.

  If on the other hand (a) both are in what is moved and acted on-both
the agency and the patiency (e.g. both teaching and learning, though
they are two, in the learner), then, first, the actuality of each will
not be present in each, and, a second absurdity, a thing will have two
motions at the same time. How will there be two alterations of quality
in one subject towards one definite quality? The thing is
impossible: the actualization will be one.

  But (some one will say) it is contrary to reason to suppose that
there should be one identical actualization of two things which are
different in kind. Yet there will be, if teaching and learning are the
same, and agency and patiency. To teach will be the same as to
learn, and to act the same as to be acted on-the teacher will
necessarily be learning everything that he teaches, and the agent will
be acted on. One may reply:

  (1) It is not absurd that the actualization of one thing should be
in another. Teaching is the activity of a person who can teach, yet
the operation is performed on some patient-it is not cut adrift from a
subject, but is of A on B.

  (2) There is nothing to prevent two things having one and the same
actualization, provided the actualizations are not described in the
same way, but are related as what can act to what is acting.

  (3) Nor is it necessary that the teacher should learn, even if to
act and to be acted on are one and the same, provided they are not the
same in definition (as 'raiment' and 'dress'), but are the same merely
in the sense in which the road from Thebes to Athens and the road from
Athens to Thebes are the same, as has been explained above. For it
is not things which are in a way the same that have all their
attributes the same, but only such as have the same definition. But
indeed it by no means follows from the fact that teaching is the
same as learning, that to learn is the same as to teach, any more than
it follows from the fact that there is one distance between two things
which are at a distance from each other, that the two vectors AB and
BA, are one and the same. To generalize, teaching is not the same as
learning, or agency as patiency, in the full sense, though they belong
to the same subject, the motion; for the 'actualization of X in Y' and
the 'actualization of Y through the action of X' differ in definition.

  What then Motion is, has been stated both generally and
particularly. It is not difficult to see how each of its types will be
defined-alteration is the fulfillment of the alterable qua alterable
(or, more scientifically, the fulfilment of what can act and what
can be acted on, as such)-generally and again in each particular case,
building, healing, &c. A similar definition will apply to each of
the other kinds of motion.

                                 4

  The science of nature is concerned with spatial magnitudes and
motion and time, and each of these at least is necessarily infinite or
finite, even if some things dealt with by the science are not, e.g.
a quality or a point-it is not necessary perhaps that such things
should be put under either head. Hence it is incumbent on the person
who specializes in physics to discuss the infinite and to inquire
whether there is such a thing or not, and, if there is, what it is.

  The appropriateness to the science of this problem is clearly
indicated. All who have touched on this kind of science in a way worth
considering have formulated views about the infinite, and indeed, to a
man, make it a principle of things.

  (1) Some, as the Pythagoreans and Plato, make the infinite a
principle in the sense of a self-subsistent substance, and not as a
mere attribute of some other thing. Only the Pythagoreans place the
infinite among the objects of sense (they do not regard number as
separable from these), and assert that what is outside the heaven is
infinite. Plato, on the other hand, holds that there is no body
outside (the Forms are not outside because they are nowhere),yet
that the infinite is present not only in the objects of sense but in
the Forms also.

  Further, the Pythagoreans identify the infinite with the even. For
this, they say, when it is cut off and shut in by the odd, provides
things with the element of infinity. An indication of this is what
happens with numbers. If the gnomons are placed round the one, and
without the one, in the one construction the figure that results is
always different, in the other it is always the same. But Plato has
two infinites, the Great and the Small.

  The physicists, on the other hand, all of them, always regard the
infinite as an attribute of a substance which is different from it and
belongs to the class of the so-called elements-water or air or what is
intermediate between them. Those who make them limited in number never
make them infinite in amount. But those who make the elements infinite
in number, as Anaxagoras and Democritus do, say that the infinite is
continuous by contact-compounded of the homogeneous parts according to
the one, of the seed-mass of the atomic shapes according to the other.

  Further, Anaxagoras held that any part is a mixture in the same
way as the All, on the ground of the observed fact that anything comes
out of anything. For it is probably for this reason that he
maintains that once upon a time all things were together. (This
flesh and this bone were together, and so of any thing: therefore
all things: and at the same time too.) For there is a beginning of
separation, not only for each thing, but for all. Each thing that
comes to be comes from a similar body, and there is a coming to be
of all things, though not, it is true, at the same time. Hence there
must also be an origin of coming to be. One such source there is which
he calls Mind, and Mind begins its work of thinking from some
starting-point. So necessarily all things must have been together at a
certain time, and must have begun to be moved at a certain time.

  Democritus, for his part, asserts the contrary, namely that no
element arises from another element. Nevertheless for him the common
body is a source of all things, differing from part to part in size
and in shape.

  It is clear then from these considerations that the inquiry concerns
the physicist. Nor is it without reason that they all make it a
principle or source. We cannot say that the infinite has no effect,
and the only effectiveness which we can ascribe to it is that of a
principle. Everything is either a source or derived from a source. But
there cannot be a source of the infinite or limitless, for that
would be a limit of it. Further, as it is a beginning, it is both
uncreatable and indestructible. For there must be a point at which
what has come to be reaches completion, and also a termination of
all passing away. That is why, as we say, there is no principle of
this, but it is this which is held to be the principle of other
things, and to encompass all and to steer all, as those assert who
do not recognize, alongside the infinite, other causes, such as Mind
or Friendship. Further they identify it with the Divine, for it is
'deathless and imperishable' as Anaximander says, with the majority of
the physicists.

  Belief in the existence of the infinite comes mainly from five
considerations:

  (1) From the nature of time-for it is infinite.

  (2) From the division of magnitudes-for the mathematicians also
use the notion of the infinite.

  (3) If coming to be and passing away do not give out, it is only
because that from which things come to be is infinite.

  (4) Because the limited always finds its limit in something, so that
there must be no limit, if everything is always limited by something
different from itself.

  (5) Most of all, a reason which is peculiarly appropriate and
presents the difficulty that is felt by everybody-not only number
but also mathematical magnitudes and what is outside the heaven are
supposed to be infinite because they never give out in our thought.

  The last fact (that what is outside is infinite) leads people to
suppose that body also is infinite, and that there is an infinite
number of worlds. Why should there be body in one part of the void
rather than in another? Grant only that mass is anywhere and it
follows that it must be everywhere. Also, if void and place are
infinite, there must be infinite body too, for in the case of
eternal things what may be must be. But the problem of the infinite is
difficult: many contradictions result whether we suppose it to exist
or not to exist. If it exists, we have still to ask how it exists;
as a substance or as the essential attribute of some entity? Or in
neither way, yet none the less is there something which is infinite or
some things which are infinitely many?

  The problem, however, which specially belongs to the physicist is to
investigate whether there is a sensible magnitude which is infinite.

  We must begin by distinguishing the various senses in which the term
'infinite' is used.

  (1) What is incapable of being gone through, because it is not in
its nature to be gone through (the sense in which the voice is
'invisible').

  (2) What admits of being gone through, the process however having no
termination, or what scarcely admits of being gone through.

  (3) What naturally admits of being gone through, but is not actually
gone through or does not actually reach an end.

  Further, everything that is infinite may be so in respect of
addition or division or both.

                                 5

  Now it is impossible that the infinite should be a thing which is
itself infinite, separable from sensible objects. If the infinite is
neither a magnitude nor an aggregate, but is itself a substance and
not an attribute, it will be indivisible; for the divisible must be
either a magnitude or an aggregate. But if indivisible, then not
infinite, except in the sense (1) in which the voice is 'invisible'.
But this is not the sense in which it is used by those who say that
the infinite exists, nor that in which we are investigating it, namely
as (2) 'that which cannot be gone through'. But if the infinite exists
as an attribute, it would not be, qua infinite an element in
substances, any more than the invisible would be an element of speech,
though the voice is invisible.

  Further, how can the infinite be itself any thing, unless both
number and magnitude, of which it is an essential attribute, exist
in that way? If they are not substances, a fortiori the infinite is
not.

  It is plain, too, that the infinite cannot be an actual thing and
a substance and principle. For any part of it that is taken will be
infinite, if it has parts: for 'to be infinite' and 'the infinite' are
the same, if it is a substance and not predicated of a subject.
Hence it will be either indivisible or divisible into infinites. But
the same thing cannot be many infinites. (Yet just as part of air is
air, so a part of the infinite would be infinite, if it is supposed to
be a substance and principle.) Therefore the infinite must be
without parts and indivisible. But this cannot be true of what is
infinite in full completion: for it must be a definite quantity.

  Suppose then that infinity belongs to substance as an attribute.
But, if so, it cannot, as we have said, be described as a principle,
but rather that of which it is an attribute-the air or the even
number.

  Thus the view of those who speak after the manner of the
Pythagoreans is absurd. With the same breath they treat the infinite
as substance, and divide it into parts.

  This discussion, however, involves the more general question whether
the infinite can be present in mathematical objects and things which
are intelligible and do not have extension, as well as among
sensible objects. Our inquiry (as physicists) is limited to its
special subject-matter, the objects of sense, and we have to ask
whether there is or is not among them a body which is infinite in
the direction of increase.

  We may begin with a dialectical argument and show as follows that
there is no such thing. If 'bounded by a surface' is the definition of
body there cannot be an infinite body either intelligible or sensible.
Nor can number taken in abstraction be infinite, for number or that
which has number is numerable. If then the numerable can be
numbered, it would also be possible to go through the infinite.

  If, on the other hand, we investigate the question more in
accordance with principles appropriate to physics, we are led as
follows to the same result.

  The infinite body must be either (1) compound, or (2) simple; yet
neither alternative is possible.

  (1) Compound the infinite body will not be, if the elements are
finite in number. For they must be more than one, and the contraries
must always balance, and no one of them can be infinite. If one of the
bodies falls in any degree short of the other in potency-suppose
fire is finite in amount while air is infinite and a given quantity of
fire exceeds in power the same amount of air in any ratio provided
it is numerically definite-the infinite body will obviously prevail
over and annihilate the finite body. On the other hand, it is
impossible that each should be infinite. 'Body' is what has
extension in all directions and the infinite is what is boundlessly
extended, so that the infinite body would be extended in all
directions ad infinitum.

  Nor (2) can the infinite body be one and simple, whether it is, as
some hold, a thing over and above the elements (from which they
generate the elements) or is not thus qualified.

  (a) We must consider the former alternative; for there are some
people who make this the infinite, and not air or water, in order that
the other elements may not be annihilated by the element which is
infinite. They have contrariety with each other-air is cold, water
moist, fire hot; if one were infinite, the others by now would have
ceased to be. As it is, they say, the infinite is different from
them and is their source.

  It is impossible, however, that there should be such a body; not
because it is infinite on that point a general proof can be given
which applies equally to all, air, water, or anything else-but
simply because there is, as a matter of fact, no such sensible body,
alongside the so-called elements. Everything can be resolved into
the elements of which it is composed. Hence the body in question would
have been present in our world here, alongside air and fire and
earth and water: but nothing of the kind is observed.

  (b) Nor can fire or any other of the elements be infinite. For
generally, and apart from the question of how any of them could be
infinite, the All, even if it were limited, cannot either be or become
one of them, as Heraclitus says that at some time all things become
fire. (The same argument applies also to the one which the
physicists suppose to exist alongside the elements: for everything
changes from contrary to contrary, e.g. from hot to cold).

  The preceding consideration of the various cases serves to show us
whether it is or is not possible that there should be an infinite
sensible body. The following arguments give a general demonstration
that it is not possible.

  It is the nature of every kind of sensible body to be somewhere, and
there is a place appropriate to each, the same for the part and for
the whole, e.g. for the whole earth and for a single clod, and for
fire and for a spark.

  Suppose (a) that the infinite sensible body is homogeneous. Then
each part will be either immovable or always being carried along.
Yet neither is possible. For why downwards rather than upwards or in
any other direction? I mean, e.g, if you take a clod, where will it be
moved or where will it be at rest? For ex hypothesi the place of the
body akin to it is infinite. Will it occupy the whole place, then? And
how? What then will be the nature of its rest and of its movement,
or where will they be? It will either be at home everywhere-then it
will not be moved; or it will be moved everywhere-then it will not
come to rest.

  But if (b) the All has dissimilar parts, the proper places of the
parts will be dissimilar also, and the body of the All will have no
unity except that of contact. Then, further, the parts will be
either finite or infinite in variety of kind. (i) Finite they cannot
be, for if the All is to be infinite, some of them would have to be
infinite, while the others were not, e.g. fire or water will be
infinite. But, as we have seen before, such an element would destroy
what is contrary to it. (This indeed is the reason why none of the
physicists made fire or earth the one infinite body, but either
water or air or what is intermediate between them, because the abode
of each of the two was plainly determinate, while the others have an
ambiguous place between up and down.)

  But (ii) if the parts are infinite in number and simple, their
proper places too will be infinite in number, and the same will be
true of the elements themselves. If that is impossible, and the places
are finite, the whole too must be finite; for the place and the body
cannot but fit each other. Neither is the whole place larger than what
can be filled by the body (and then the body would no longer be
infinite), nor is the body larger than the place; for either there
would be an empty space or a body whose nature it is to be nowhere.

  Anaxagoras gives an absurd account of why the infinite is at rest.
He says that the infinite itself is the cause of its being fixed. This
because it is in itself, since nothing else contains it-on the
assumption that wherever anything is, it is there by its own nature.
But this is not true: a thing could be somewhere by compulsion, and
not where it is its nature to be.

  Even if it is true as true can be that the whole is not moved (for
what is fixed by itself and is in itself must be immovable), yet we
must explain why it is not its nature to be moved. It is not enough
just to make this statement and then decamp. Anything else might be in
a state of rest, but there is no reason why it should not be its
nature to be moved. The earth is not carried along, and would not be
carried along if it were infinite, provided it is held together by the
centre. But it would not be because there was no other region in which
it could be carried along that it would remain at the centre, but
because this is its nature. Yet in this case also we may say that it
fixes itself. If then in the case of the earth, supposed to be
infinite, it is at rest, not because it is infinite, but because it
has weight and what is heavy rests at the centre and the earth is at
the centre, similarly the infinite also would rest in itself, not
because it is infinite and fixes itself, but owing to some other
cause.

  Another difficulty emerges at the same time. Any part of the
infinite body ought to remain at rest. Just as the infinite remains at
rest in itself because it fixes itself, so too any part of it you
may take will remain in itself. The appropriate places of the whole
and of the part are alike, e.g. of the whole earth and of a clod the
appropriate place is the lower region; of fire as a whole and of a
spark, the upper region. If, therefore, to be in itself is the place
of the infinite, that also will be appropriate to the part.
Therefore it will remain in itself.

  In general, the view that there is an infinite body is plainly
incompatible with the doctrine that there is necessarily a proper
place for each kind of body, if every sensible body has either
weight or lightness, and if a body has a natural locomotion towards
the centre if it is heavy, and upwards if it is light. This would need
to be true of the infinite also. But neither character can belong to
it: it cannot be either as a whole, nor can it be half the one and
half the other. For how should you divide it? or how can the
infinite have the one part up and the other down, or an extremity
and a centre?

  Further, every sensible body is in place, and the kinds or
differences of place are up-down, before-behind, right-left; and these
distinctions hold not only in relation to us and by arbitrary
agreement, but also in the whole itself. But in the infinite body they
cannot exist. In general, if it is impossible that there should be
an infinite place, and if every body is in place, there cannot be an
infinite body.

  Surely what is in a special place is in place, and what is in
place is in a special place. Just, then, as the infinite cannot be
quantity-that would imply that it has a particular quantity, e,g,
two or three cubits; quantity just means these-so a thing's being in
place means that it is somewhere, and that is either up or down or
in some other of the six differences of position: but each of these is
a limit.

  It is plain from these arguments that there is no body which is
actually infinite.

                                 6

  But on the other hand to suppose that the infinite does not exist in
any way leads obviously to many impossible consequences: there will be
a beginning and an end of time, a magnitude will not be divisible into
magnitudes, number will not be infinite. If, then, in view of the
above considerations, neither alternative seems possible, an arbiter
must be called in; and clearly there is a sense in which the
infinite exists and another in which it does not.

  We must keep in mind that the word 'is' means either what
potentially is or what fully is. Further, a thing is infinite either
by addition or by division.

  Now, as we have seen, magnitude is not actually infinite. But by
division it is infinite. (There is no difficulty in refuting the
theory of indivisible lines.) The alternative then remains that the
infinite has a potential existence.

  But the phrase 'potential existence' is ambiguous. When we speak
of the potential existence of a statue we mean that there will be an
actual statue. It is not so with the infinite. There will not be an
actual infinite. The word 'is' has many senses, and we say that the
infinite 'is' in the sense in which we say 'it is day' or 'it is the
games', because one thing after another is always coming into
existence. For of these things too the distinction between potential
and actual existence holds. We say that there are Olympic games,
both in the sense that they may occur and that they are actually
occurring.

  The infinite exhibits itself in different ways-in time, in the
generations of man, and in the division of magnitudes. For generally
the infinite has this mode of existence: one thing is always being
taken after another, and each thing that is taken is always finite,
but always different. Again, 'being' has more than one sense, so
that we must not regard the infinite as a 'this', such as a man or a
horse, but must suppose it to exist in the sense in which we speak
of the day or the games as existing things whose being has not come to
them like that of a substance, but consists in a process of coming
to be or passing away; definite if you like at each stage, yet
always different.

  But when this takes place in spatial magnitudes, what is taken
perists, while in the succession of time and of men it takes place
by the passing away of these in such a way that the source of supply
never gives out.

  In a way the infinite by addition is the same thing as the
infinite by division. In a finite magnitude, the infinite by
addition comes about in a way inverse to that of the other. For in
proportion as we see division going on, in the same proportion we
see addition being made to what is already marked off. For if we
take a determinate part of a finite magnitude and add another part
determined by the same ratio (not taking in the same amount of the
original whole), and so on, we shall not traverse the given magnitude.
But if we increase the ratio of the part, so as always to take in
the same amount, we shall traverse the magnitude, for every finite
magnitude is exhausted by means of any determinate quantity however
small