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.
The infinite, then, exists in no other way, but in this way it
does exist, potentially and by reduction. It exists fully in the sense
in which we say 'it is day' or 'it is the games'; and potentially as
matter exists, not independently as what is finite does.
By addition then, also, there is potentially an infinite, namely,
what we have described as being in a sense the same as the infinite in
respect of division. For it will always be possible to take
something ah extra. Yet the sum of the parts taken will not exceed
every determinate magnitude, just as in the direction of division
every determinate magnitude is surpassed in smallness and there will
be a smaller part.
But in respect of addition there cannot be an infinite which even
potentially exceeds every assignable magnitude, unless it has the
attribute of being actually infinite, as the physicists hold to be
true of the body which is outside the world, whose essential nature is
air or something of the kind. But if there cannot be in this way a
sensible body which is infinite in the full sense, evidently there can
no more be a body which is potentially infinite in respect of
addition, except as the inverse of the infinite by division, as we
have said. It is for this reason that Plato also made the infinites
two in number, because it is supposed to be possible to exceed all
limits and to proceed ad infinitum in the direction both of increase
and of reduction. Yet though he makes the infinites two, he does not
use them. For in the numbers the infinite in the direction of
reduction is not present, as the monad is the smallest; nor is the
infinite in the direction of increase, for the parts number only up to
the decad.
The infinite turns out to be the contrary of what it is said to
be. It is not what has nothing outside it that is infinite, but what
always has something outside it. This is indicated by the fact that
rings also that have no bezel are described as 'endless', because it
is always possible to take a part which is outside a given part. The
description depends on a certain similarity, but it is not true in the
full sense of the word. This condition alone is not sufficient: it
is necessary also that the next part which is taken should never be
the same. In the circle, the latter condition is not satisfied: it
is only the adjacent part from which the new part is different.
Our definition then is as follows:
A quantity is infinite if it is such that we can always take a
part outside what has been already taken. On the other hand, what
has nothing outside it is complete and whole. For thus we define the
whole-that from which nothing is wanting, as a whole man or a whole
box. What is true of each particular is true of the whole as
such-the whole is that of which nothing is outside. On the other
hand that from which something is absent and outside, however small
that may be, is not 'all'. 'Whole' and 'complete' are either quite
identical or closely akin. Nothing is complete (teleion) which has
no end (telos); and the end is a limit.
Hence Parmenides must be thought to have spoken better than
Melissus. The latter says that the whole is infinite, but the former
describes it as limited, 'equally balanced from the middle'. For to
connect the infinite with the all and the whole is not like joining
two pieces of string; for it is from this they get the dignity they
ascribe to the infinite-its containing all things and holding the
all in itself-from its having a certain similarity to the whole. It is
in fact the matter of the completeness which belongs to size, and what
is potentially a whole, though not in the full sense. It is
divisible both in the direction of reduction and of the inverse
addition. It is a whole and limited; not, however, in virtue of its
own nature, but in virtue of what is other than it. It does not
contain, but, in so far as it is infinite, is contained. Consequently,
also, it is unknowable, qua infinite; for the matter has no form.
(Hence it is plain that the infinite stands in the relation of part
rather than of whole. For the matter is part of the whole, as the
bronze is of the bronze statue.) If it contains in the case of
sensible things, in the case of intelligible things the great and
the small ought to contain them. But it is absurd and impossible to
suppose that the unknowable and indeterminate should contain and
determine.
7
It is reasonable that there should not be held to be an infinite
in respect of addition such as to surpass every magnitude, but that
there should be thought to be such an infinite in the direction of
division. For the matter and the infinite are contained inside what
contains them, while it is the form which contains. It is natural
too to suppose that in number there is a limit in the direction of the
minimum, and that in the other direction every assigned number is
surpassed. In magnitude, on the contrary, every assigned magnitude
is surpassed in the direction of smallness, while in the other
direction there is no infinite magnitude. The reason is that what is
one is indivisible whatever it may be, e.g. a man is one man, not
many. Number on the other hand is a plurality of 'ones' and a
certain quantity of them. Hence number must stop at the indivisible:
for 'two' and 'three' are merely derivative terms, and so with each of
the other numbers. But in the direction of largeness it is always
possible to think of a larger number: for the number of times a
magnitude can be bisected is infinite. Hence this infinite is
potential, never actual: the number of parts that can be taken
always surpasses any assigned number. But this number is not separable
from the process of bisection, and its infinity is not a permanent
actuality but consists in a process of coming to be, like time and the
number of time.
With magnitudes the contrary holds. What is continuous is divided ad
infinitum, but there is no infinite in the direction of increase.
For the size which it can potentially be, it can also actually be.
Hence since no sensible magnitude is infinite, it is impossible to
exceed every assigned magnitude; for if it were possible there would
be something bigger than the heavens.
The infinite is not the same in magnitude and movement and time,
in the sense of a single nature, but its secondary sense depends on
its primary sense, i.e. movement is called infinite in virtue of the
magnitude covered by the movement (or alteration or growth), and
time because of the movement. (I use these terms for the moment. Later
I shall explain what each of them means, and also why every
magnitude is divisible into magnitudes.)
Our account does not rob the mathematicians of their science, by
disproving the actual existence of the infinite in the direction of
increase, in the sense of the untraversable. In point of fact they
do not need the infinite and do not use it. They postulate only that
the finite straight line may be produced as far as they wish. It is
possible to have divided in the same ratio as the largest quantity
another magnitude of any size you like. Hence, for the purposes of
proof, it will make no difference to them to have such an infinite
instead, while its existence will be in the sphere of real magnitudes.
In the fourfold scheme of causes, it is plain that the infinite is a
cause in the sense of matter, and that its essence is privation, the
subject as such being what is continuous and sensible. All the other
thinkers, too, evidently treat the infinite as matter-that is why it
is inconsistent in them to make it what contains, and not what is
contained.
8
It remains to dispose of the arguments which are supposed to support
the view that the infinite exists not only potentially but as a
separate thing. Some have no cogency; others can be met by fresh
objections that are valid.
(1) In order that coming to be should not fail, it is not
necessary that there should be a sensible body which is actually
infinite. The passing away of one thing may be the coming to be of
another, the All being limited.
(2) There is a difference between touching and being limited. The
former is relative to something and is the touching of something
(for everything that touches touches something), and further is an
attribute of some one of the things which are limited. On the other
hand, what is limited is not limited in relation to anything. Again,
contact is not necessarily possible between any two things taken at
random.
(3) To rely on mere thinking is absurd, for then the excess or
defect is not in the thing but in the thought. One might think that
one of us is bigger than he is and magnify him ad infinitum. But it
does not follow that he is bigger than the size we are, just because
some one thinks he is, but only because he is the size he is. The
thought is an accident.
(a) Time indeed and movement are infinite, and also thinking, in the
sense that each part that is taken passes in succession out of
existence.
(b) Magnitude is not infinite either in the way of reduction or of
magnification in thought.
This concludes my account of the way in which the infinite exists,
and of the way in which it does not exist, and of what it is.
Book IV
1
THE physicist must have a knowledge of Place, too, as well as of the
infinite-namely, whether there is such a thing or not, and the
manner of its existence and what it is-both because all suppose that
things which exist are somewhere (the non-existent is nowhere--where
is the goat-stag or the sphinx?), and because 'motion' in its most
general and primary sense is change of place, which we call
'locomotion'.
The question, what is place? presents many difficulties. An
examination of all the relevant facts seems to lead to divergent
conclusions. Moreover, we have inherited nothing from previous
thinkers, whether in the way of a statement of difficulties or of a
solution.
The existence of place is held to be obvious from the fact of mutual
replacement. Where water now is, there in turn, when the water has
gone out as from a vessel, air is present. When therefore another body
occupies this same place, the place is thought to be different from
all the bodies which come to be in it and replace one another. What
now contains air formerly contained water, so that clearly the place
or space into which and out of which they passed was something
different from both.
Further, the typical locomotions of the elementary natural
bodies-namely, fire, earth, and the like-show not only that place is
something, but also that it exerts a certain influence. Each is
carried to its own place, if it is not hindered, the one up, the other
down. Now these are regions or kinds of place-up and down and the rest
of the six directions. Nor do such distinctions (up and down and right
and left, &c.) hold only in relation to us. To us they are not
always the same but change with the direction in which we are
turned: that is why the same thing may be both right and left, up
and down, before and behind. But in nature each is distinct, taken
apart by itself. It is not every chance direction which is 'up', but
where fire and what is light are carried; similarly, too, 'down' is
not any chance direction but where what has weight and what is made of
earth are carried-the implication being that these places do not
differ merely in relative position, but also as possessing distinct
potencies. This is made plain also by the objects studied by
mathematics. Though they have no real place, they nevertheless, in
respect of their position relatively to us, have a right and left as
attributes ascribed to them only in consequence of their relative
position, not having by nature these various characteristics. Again,
the theory that the void exists involves the existence of place: for
one would define void as place bereft of body.
These considerations then would lead us to suppose that place is
something distinct from bodies, and that every sensible body is in
place. Hesiod too might be held to have given a correct account of
it when he made chaos first. At least he says:
'First of all things came chaos to being, then broad-breasted
earth,'
implying that things need to have space first, because he thought,
with most people, that everything is somewhere and in place. If this
is its nature, the potency of place must be a marvellous thing, and
take precedence of all other things. For that without which nothing
else can exist, while it can exist without the others, must needs be
first; for place does not pass out of existence when the things in
it are annihilated.
True, but even if we suppose its existence settled, the question
of its nature presents difficulty-whether it is some sort of 'bulk' of
body or some entity other than that, for we must first determine its
genus.
(1) Now it has three dimensions, length, breadth, depth, the
dimensions by which all body also is bounded. But the place cannot
be body; for if it were there would be two bodies in the same place.
(2) Further, if body has a place and space, clearly so too have
surface and the other limits of body; for the same statement will
apply to them: where the bounding planes of the water were, there in
turn will be those of the air. But when we come to a point we cannot
make a distinction between it and its place. Hence if the place of a
point is not different from the point, no more will that of any of the
others be different, and place will not be something different from
each of them.
(3) What in the world then are we to suppose place to be? If it
has the sort of nature described, it cannot be an element or
composed of elements, whether these be corporeal or incorporeal: for
while it has size, it has not body. But the elements of sensible
bodies are bodies, while nothing that has size results from a
combination of intelligible elements.
(4) Also we may ask: of what in things is space the cause? None of
the four modes of causation can be ascribed to it. It is neither in
the sense of the matter of existents (for nothing is composed of
it), nor as the form and definition of things, nor as end, nor does it
move existents.
(5) Further, too, if it is itself an existent, where will it be?
Zeno's difficulty demands an explanation: for if everything that
exists has a place, place too will have a place, and so on ad
infinitum.
(6) Again, just as every body is in place, so, too, every place
has a body in it. What then shall we say about growing things? It
follows from these premisses that their place must grow with them,
if their place is neither less nor greater than they are.
By asking these questions, then, we must raise the whole problem
about place-not only as to what it is, but even whether there is
such a thing.
2
We may distinguish generally between predicating B of A because it
(A) is itself, and because it is something else; and particularly
between place which is common and in which all bodies are, and the
special place occupied primarily by each. I mean, for instance, that
you are now in the heavens because you are in the air and it is in the
heavens; and you are in the air because you are on the earth; and
similarly on the earth because you are in this place which contains no
more than you.
Now if place is what primarily contains each body, it would be a
limit, so that the place would be the form or shape of each body by
which the magnitude or the matter of the magnitude is defined: for
this is the limit of each body.
If, then, we look at the question in this way the place of a thing
is its form. But, if we regard the place as the extension of the
magnitude, it is the matter. For this is different from the magnitude:
it is what is contained and defined by the form, as by a bounding
plane. Matter or the indeterminate is of this nature; when the
boundary and attributes of a sphere are taken away, nothing but the
matter is left.
This is why Plato in the Timaeus says that matter and space are
the same; for the 'participant' and space are identical. (It is
true, indeed, that the account he gives there of the 'participant'
is different from what he says in his so-called 'unwritten
teaching'. Nevertheless, he did identify place and space.) I mention
Plato because, while all hold place to be something, he alone tried to
say what it is.
In view of these facts we should naturally expect to find difficulty
in determining what place is, if indeed it is one of these two things,
matter or form. They demand a very close scrutiny, especially as it is
not easy to recognize them apart.
But it is at any rate not difficult to see that place cannot be
either of them. The form and the matter are not separate from the
thing, whereas the place can be separated. As we pointed out, where
air was, water in turn comes to be, the one replacing the other; and
similarly with other bodies. Hence the place of a thing is neither a
part nor a state of it, but is separable from it. For place is
supposed to be something like a vessel-the vessel being a
transportable place. But the vessel is no part of the thing.
In so far then as it is separable from the thing, it is not the
form: qua containing, it is different from the matter.
Also it is held that what is anywhere is both itself something and
that there is a different thing outside it. (Plato of course, if we
may digress, ought to tell us why the form and the numbers are not
in place, if 'what participates' is place-whether what participates is
the Great and the Small or the matter, as he called it in writing in
the Timaeus.)
Further, how could a body be carried to its own place, if place
was the matter or the form? It is impossible that what has no
reference to motion or the distinction of up and down can be place. So
place must be looked for among things which have these
characteristics.
If the place is in the thing (it must be if it is either shape or
matter) place will have a place: for both the form and the
indeterminate undergo change and motion along with the thing, and
are not always in the same place, but are where the thing is. Hence
the place will have a place.
Further, when water is produced from air, the place has been
destroyed, for the resulting body is not in the same place. What
sort of destruction then is that?
This concludes my statement of the reasons why space must be
something, and again of the difficulties that may be raised about
its essential nature.
3
The next step we must take is to see in how many senses one thing is
said to be 'in' another.
(1) As the finger is 'in' the hand and generally the part 'in' the
whole.
(2) As the whole is 'in' the parts: for there is no whole over and
above the parts.
(3) As man is 'in' animal and generally species 'in' genus.
(4) As the genus is 'in' the species and generally the part of the
specific form 'in' the definition of the specific form.
(5) As health is 'in' the hot and the cold and generally the form
'in' the matter.
(6) As the affairs of Greece centre 'in' the king, and generally
events centre 'in' their primary motive agent.
(7) As the existence of a thing centres 'in its good and generally
'in' its end, i.e. in 'that for the sake of which' it exists.
(8) In the strictest sense of all, as a thing is 'in' a vessel,
and generally 'in' place.
One might raise the question whether a thing can be in itself, or
whether nothing can be in itself-everything being either nowhere or in
something else.
The question is ambiguous; we may mean the thing qua itself or qua
something else.
When there are parts of a whole-the one that in which a thing is,
the other the thing which is in it-the whole will be described as
being in itself. For a thing is described in terms of its parts, as
well as in terms of the thing as a whole, e.g. a man is said to be
white because the visible surface of him is white, or to be scientific
because his thinking faculty has been trained. The jar then will not
be in itself and the wine will not be in itself. But the jar of wine
will: for the contents and the container are both parts of the same
whole.
In this sense then, but not primarily, a thing can be in itself,
namely, as 'white' is in body (for the visible surface is in body),
and science is in the mind.
It is from these, which are 'parts' (in the sense at least of
being 'in' the man), that the man is called white, &c. But the jar and
the wine in separation are not parts of a whole, though together
they are. So when there are parts, a thing will be in itself, as
'white' is in man because it is in body, and in body because it
resides in the visible surface. We cannot go further and say that it
is in surface in virtue of something other than itself. (Yet it is not
in itself: though these are in a way the same thing,) they differ in
essence, each having a special nature and capacity, 'surface' and
'white'.
Thus if we look at the matter inductively we do not find anything to
be 'in' itself in any of the senses that have been distinguished;
and it can be seen by argument that it is impossible. For each of
two things will have to be both, e.g. the jar will have to be both
vessel and wine, and the wine both wine and jar, if it is possible for
a thing to be in itself; so that, however true it might be that they
were in each other, the jar will receive the wine in virtue not of its
being wine but of the wine's being wine, and the wine will be in the
jar in virtue not of its being a jar but of the jar's being a jar. Now
that they are different in respect of their essence is evident; for
'that in which something is' and 'that which is in it' would be
differently defined.
Nor is it possible for a thing to be in itself even incidentally:
for two things would at the same time in the same thing. The jar would
be in itself-if a thing whose nature it is to receive can be in
itself; and that which it receives, namely (if wine) wine, will be
in it.
Obviously then a thing cannot be in itself primarily.
Zeno's problem-that if Place is something it must be in something-is
not difficult to solve. There is nothing to prevent the first place
from being 'in' something else-not indeed in that as 'in' place, but
as health is 'in' the hot as a positive determination of it or as the
hot is 'in' body as an affection. So we escape the infinite regress.
Another thing is plain: since the vessel is no part of what is in it
(what contains in the strict sense is different from what is
contained), place could not be either the matter or the form of the
thing contained, but must different-for the latter, both the matter
and the shape, are parts of what is contained.
This then may serve as a critical statement of the difficulties
involved.
4
What then after all is place? The answer to this question may be
elucidated as follows.
Let us take for granted about it the various characteristics which
are supposed correctly to belong to it essentially. We assume then-
(1) Place is what contains that of which it is the place.
(2) Place is no part of the thing.
(3) The immediate place of a thing is neither less nor greater
than the thing.
(4) Place can be left behind by the thing and is separable. In
addition:
(5) All place admits of the distinction of up and down, and each
of the bodies is naturally carried to its appropriate place and
rests there, and this makes the place either up or down.
Having laid these foundations, we must complete the theory. We ought
to try to make our investigation such as will render an account of
place, and will not only solve the difficulties connected with it, but
will also show that the attributes supposed to belong to it do
really belong to it, and further will make clear the cause of the
trouble and of the difficulties about it. Such is the most
satisfactory kind of exposition.
First then we must understand that place would not have been thought
of, if there had not been a special kind of motion, namely that with
respect to place. It is chiefly for this reason that we suppose the
heaven also to be in place, because it is in constant movement. Of
this kind of change there are two species-locomotion on the one hand
and, on the other, increase and diminution. For these too involve
variation of place: what was then in this place has now in turn
changed to what is larger or smaller.
Again, when we say a thing is 'moved', the predicate either (1)
belongs to it actually, in virtue of its own nature, or (2) in
virtue of something conjoined with it. In the latter case it may be
either (a) something which by its own nature is capable of being
moved, e.g. the parts of the body or the nail in the ship, or (b)
something which is not in itself capable of being moved, but is always
moved through its conjunction with something else, as 'whiteness' or
'science'. These have changed their place only because the subjects to
which they belong do so.
We say that a thing is in the world, in the sense of in place,
because it is in the air, and the air is in the world; and when we say
it is in the air, we do not mean it is in every part of the air, but
that it is in the air because of the outer surface of the air which
surrounds it; for if all the air were its place, the place of a
thing would not be equal to the thing-which it is supposed to be,
and which the primary place in which a thing is actually is.
When what surrounds, then, is not separate from the thing, but is in
continuity with it, the thing is said to be in what surrounds it,
not in the sense of in place, but as a part in a whole. But when the
thing is separate and in contact, it is immediately 'in' the inner
surface of the surrounding body, and this surface is neither a part of
what is in it nor yet greater than its extension, but equal to it; for
the extremities of things which touch are coincident.
Further, if one body is in continuity with another, it is not
moved in that but with that. On the other hand it is moved in that
if it is separate. It makes no difference whether what contains is
moved or not.
Again, when it is not separate it is described as a part in a whole,
as the pupil in the eye or the hand in the body: when it is
separate, as the water in the cask or the wine in the jar. For the
hand is moved with the body and the water in the cask.
It will now be plain from these considerations what place is.
There are just four things of which place must be one-the shape, or
the matter, or some sort of extension between the bounding surfaces of
the containing body, or this boundary itself if it contains no
extension over and above the bulk of the body which comes to be in it.
Three of these it obviously cannot be:
(1) The shape is supposed to be place because it surrounds, for
the extremities of what contains and of what is contained are
coincident. Both the shape and the place, it is true, are
boundaries. But not of the same thing: the form is the boundary of the
thing, the place is the boundary of the body which contains it.
(2) The extension between the extremities is thought to be
something, because what is contained and separate may often be changed
while the container remains the same (as water may be poured from a
vessel)-the assumption being that the extension is something over
and above the body displaced. But there is no such extension. One of
the bodies which change places and are naturally capable of being in
contact with the container falls in whichever it may chance to be.
If there were an extension which were such as to exist independently
and be permanent, there would be an infinity of places in the same
thing. For when the water and the air change places, all the
portions of the two together will play the same part in the whole
which was previously played by all the water in the vessel; at the
same time the place too will be undergoing change; so that there
will be another place which is the place of the place, and many places
will be coincident. There is not a different place of the part, in
which it is moved, when the whole vessel changes its place: it is
always the same: for it is in the (proximate) place where they are
that the air and the water (or the parts of the water) succeed each
other, not in that place in which they come to be, which is part of
the place which is the place of the whole world.
(3) The matter, too, might seem to be place, at least if we consider
it in what is at rest and is thus separate but in continuity. For just
as in change of quality there is something which was formerly black
and is now white, or formerly soft and now hard-this is just why we
say that the matter exists-so place, because it presents a similar
phenomenon, is thought to exist-only in the one case we say so because
what was air is now water, in the other because where air formerly was
there a is now water. But the matter, as we said before, is neither
separable from the thing nor contains it, whereas place has both
characteristics.
Well, then, if place is none of the three-neither the form nor the
matter nor an extension which is always there, different from, and
over and above, the extension of the thing which is displaced-place
necessarily is the one of the four which is left, namely, the boundary
of the containing body at which it is in contact with the contained
body. (By the contained body is meant what can be moved by way of
locomotion.)
Place is thought to be something important and hard to grasp, both
because the matter and the shape present themselves along with it, and
because the displacement of the body that is moved takes place in a
stationary container, for it seems possible that there should be an
interval which is other than the bodies which are moved. The air, too,
which is thought to be incorporeal, contributes something to the
belief: it is not only the boundaries of the vessel which seem to be
place, but also what is between them, regarded as empty. Just, in
fact, as the vessel is transportable place, so place is a non-portable
vessel. So when what is within a thing which is moved, is moved and
changes its place, as a boat on a river, what contains plays the
part of a vessel rather than that of place. Place on the other hand is
rather what is motionless: so it is rather the whole river that is
place, because as a whole it is motionless.
Hence we conclude that the innermost motionless boundary of what
contains is place.
This explains why the middle of the heaven and the surface which
faces us of the rotating system are held to be 'up' and 'down' in
the strict and fullest sense for all men: for the one is always at
rest, while the inner side of the rotating body remains always
coincident with itself. Hence since the light is what is naturally
carried up, and the heavy what is carried down, the boundary which
contains in the direction of the middle of the universe, and the
middle itself, are down, and that which contains in the direction of
the outermost part of the universe, and the outermost part itself, are
up.
For this reason, too, place is thought to be a kind of surface,
and as it were a vessel, i.e. a container of the thing.
Further, place is coincident with the thing, for boundaries are
coincident with the bounded.
5
If then a body has another body outside it and containing it, it
is in place, and if not, not. That is why, even if there were to be
water which had not a container, the parts of it, on the one hand,
will be moved (for one part is contained in another), while, on the
other hand, the whole will be moved in one sense, but not in
another. For as a whole it does not simultaneously change its place,
though it will be moved in a circle: for this place is the place of
its parts. (Some things are moved, not up and down, but in a circle;
others up and down, such things namely as admit of condensation and
rarefaction.)
As was explained, some things are potentially in place, others
actually. So, when you have a homogeneous substance which is
continuous, the parts are potentially in place: when the parts are
separated, but in contact, like a heap, they are actually in place.
Again, (1) some things are per se in place, namely every body
which is movable either by way of locomotion or by way of increase
is per se somewhere, but the heaven, as has been said, is not anywhere
as a whole, nor in any place, if at least, as we must suppose, no body
contains it. On the line on which it is moved, its parts have place:
for each is contiguous the next.
But (2) other things are in place indirectly, through something
conjoined with them, as the soul and the heaven. The latter is, in a
way, in place, for all its parts are: for on the orb one part contains
another. That is why the upper part is moved in a circle, while the
All is not anywhere. For what is somewhere is itself something, and
there must be alongside it some other thing wherein it is and which
contains it. But alongside the All or the Whole there is nothing
outside the All, and for this reason all things are in the heaven; for
the heaven, we may say, is the All. Yet their place is not the same as
the heaven. It is part of it, the innermost part of it, which is in
contact with the movable body; and for this reason the earth is in
water, and this in the air, and the air in the aether, and the
aether in heaven, but we cannot go on and say that the heaven is in
anything else.
It is clear, too, from these considerations that all the problems
which were raised about place will be solved when it is explained in
this way:
(1) There is no necessity that the place should grow with the body
in it,
(2) Nor that a point should have a place,
(3) Nor that two bodies should be in the same place,
(4) Nor that place should be a corporeal interval: for what is
between the boundaries of the place is any body which may chance to be
there, not an interval in body.
Further, (5) place is also somewhere, not in the sense of being in a
place, but as the limit is in the limited; for not everything that
is is in place, but only movable body.
Also (6) it is reasonable that each kind of body should be carried
to its own place. For a body which is next in the series and in
contact (not by compulsion) is akin, and bodies which are united do
not affect each other, while those which are in contact interact on
each other.
Nor (7) is it without reason that each should remain naturally in
its proper place. For this part has the same relation to its place, as
a separable part to its whole, as when one moves a part of water or
air: so, too, air is related to water, for the one is like matter, the
other form-water is the matter of air, air as it were the actuality of
water, for water is potentially air, while air is potentially water,
though in another way.
These distinctions will be drawn more carefully later. On the
present occasion it was necessary to refer to them: what has now
been stated obscurely will then be made more clear. If the matter
and the fulfilment are the same thing (for water is both, the one
potentially, the other completely), water will be related to air in
a way as part to whole. That is why these have contact: it is
organic union when both become actually one.
This concludes my account of place-both of its existence and of
its nature.
6
The investigation of similar questions about the void, also, must be
held to belong to the physicist-namely whether it exists or not, and
how it exists or what it is-just as about place. The views taken of it
involve arguments both for and against, in much the same sort of
way. For those who hold that the void exists regard it as a sort of
place or vessel which is supposed to be 'full' when it holds the
bulk which it is capable of containing, 'void' when it is deprived
of that-as if 'void' and 'full' and 'place' denoted the same thing,
though the essence of the three is different.
We must begin the inquiry by putting down the account given by those
who say that it exists, then the account of those who say that it does
not exist, and third the current view on these questions.
Those who try to show that the void does not exist do not disprove
what people really mean by it, but only their erroneous way of
speaking; this is true of Anaxagoras and of those who refute the
existence of the void in this way. They merely give an ingenious
demonstration that air is something--by straining wine-skins and
showing the resistance of the air, and by cutting it off in
clepsydras. But people really mean that there is an empty interval
in which there is no sensible body. They hold that everything which is
in body is body and say that what has nothing in it at all is void (so
what is full of air is void). It is not then the existence of air that
needs to be proved, but the non-existence of an interval, different
from the bodies, either separable or actual-an interval which
divides the whole body so as to break its continuity, as Democritus
and Leucippus hold, and many other physicists-or even perhaps as
something which is outside the whole body, which remains continuous.
These people, then, have not reached even the threshold of the
problem, but rather those who say that the void exists.
(1) They argue, for one thing, that change in place (i.e. locomotion
and increase) would not be. For it is maintained that motion would
seem not to exist, if there were no void, since what is full cannot
contain anything more. If it could, and there were two bodies in the
same place, it would also be true that any number of bodies could be
together; for it is impossible to draw a line of division beyond which
the statement would become untrue. If this were possible, it would
follow also that the smallest body would contain the greatest; for
'many a little makes a mickle': thus if many equal bodies can be
together, so also can many unequal bodies.
Melissus, indeed, infers from these considerations that the All is
immovable; for if it were moved there must, he says, be void, but void
is not among the things that exist.
This argument, then, is one way in which they show that there is a
void.
(2) They reason from the fact that some things are observed to
contract and be compressed, as people say that a cask will hold the
wine which formerly filled it, along with the skins into which the
wine has been decanted, which implies that the compressed body
contracts into the voids present in it.
Again (3) increase, too, is thought to take always by means of void,
for nutriment is body, and it is impossible for two bodies to be
together. A proof of this they find also in what happens to ashes,
which absorb as much water as the empty vessel.
The Pythagoreans, too, (4) held that void exists and that it
enters the heaven itself, which as it were inhales it, from the
infinite air. Further it is the void which distinguishes the natures
of things, as if it were like what separates and distinguishes the
terms of a series. This holds primarily in the numbers, for the void
distinguishes their nature.
These, then, and so many, are the main grounds on which people
have argued for and against the existence of the void.
7
As a step towards settling which view is true, we must determine the
meaning of the name.
The void is thought to be place with nothing in it. The reason for
this is that people take what exists to be body, and hold that while
every body is in place, void is place in which there is no body, so
that where there is no body, there must be void.
Every body, again, they suppose to be tangible; and of this nature
is whatever has weight or lightness.
Hence, by a syllogism, what has nothing heavy or light in it, is
void.
This result, then, as I have said, is reached by syllogism. It would
be absurd to suppose that the point is void; for the void must be
place which has in it an interval in tangible body.
But at all events we observe then that in one way the void is
described as what is not full of body perceptible to touch; and what
has heaviness and lightness is perceptible to touch. So we would raise
the question: what would they say of an interval that has colour or
sound-is it void or not? Clearly they would reply that if it could
receive what is tangible it was void, and if not, not.
In another way void is that in which there is no 'this' or corporeal
substance. So some say that the void is the matter of the body (they
identify the place, too, with this), and in this they speak
incorrectly; for the matter is not separable from the things, but they
are inquiring about the void as about something separable.
Since we have determined the nature of place, and void must, if it
exists, be place deprived of body, and we have stated both in what
sense place exists and in what sense it does not, it is plain that
on this showing void does not exist, either unseparated or
separated; the void is meant to be, not body but rather an interval in
body. This is why the void is thought to be something, viz. because
place is, and for the same reasons. For the fact of motion in
respect of place comes to the aid both of those who maintain that
place is something over and above the bodies that come to occupy it,
and of those who maintain that the void is something. They state
that the void is the condition of movement in the sense of that in
which movement takes place; and this would be the kind of thing that
some say place is.
But there is no necessity for there being a void if there is
movement. It is not in the least needed as a condition of movement
in general, for a reason which, incidentally, escaped Melissus; viz.
that the full can suffer qualitative change.
But not even movement in respect of place involves a void; for
bodies may simultaneously make room for one another, though there is
no interval separate and apart from the bodies that are in movement.
And this is plain even in the rotation of continuous things, as in
that of liquids.
And things can also be compressed not into a void but because they
squeeze out what is contained in them (as, for instance, when water is
compressed the air within it is squeezed out); and things can increase
in size not only by the entrance of something but also by
qualitative change; e.g. if water were to be transformed into air.
In general, both the argument about increase of size and that
about water poured on to the ashes get in their own way. For either
not any and every part of the body is increased, or bodies may be
increased otherwise than by the addition of body, or there may be
two bodies in the same place (in which case they are claiming to solve
a quite general difficulty, but are not proving the existence of
void), or the whole body must be void, if it is increased in every
part and is increased by means of void. The same argument applies to
the ashes.
It is evident, then, that it is easy to refute the arguments by
which they prove the existence of the void.
8
Let us explain again that there is no void existing separately, as
some maintain. If each of the simple bodies has a natural
locomotion, e.g. fire upward and earth downward and towards the middle
of the universe, it is clear that it cannot be the void that is the
condition of locomotion. What, then, will the void be the condition
of? It is thought to be the condition of movement in respect of place,
and it is not the condition of this.
Again, if void is a sort of place deprived of body, when there is
a void where will a body placed in it move to? It certainly cannot
move into the whole of the void. The same argument applies as
against those who think that place is something separate, into which
things are carried; viz. how will what is placed in it move, or
rest? Much the same argument will apply to the void as to the 'up' and
'down' in place, as is natural enough since those who maintain the
existence of the void make it a place.
And in what way will things be present either in place-or in the
void? For the expected result does not take place when a body is
placed as a whole in a place conceived of as separate and permanent;
for a part of it, unless it be placed apart, will not be in a place
but in the whole. Further, if separate place does not exist, neither
will void.
If people say that the void must exist, as being necessary if
there is to be movement, what rather turns out to be the case, if
one the matter, is the opposite, that not a single thing can be
moved if there is a void; for as with those who for a like reason
say the earth is at rest, so, too, in the void things must be at rest;
for there is no place to which things can move more or less than to
another; since the void in so far as it is void admits no difference.
The second reason is this: all movement is either compulsory or
according to nature, and if there is compulsory movement there must
also be natural (for compulsory movement is contrary to nature, and
movement contrary to nature is posterior to that according to
nature, so that if each of the natural bodies has not a natural
movement, none of the other movements can exist); but how can there be
natural movement if there is no difference throughout the void or
the infinite? For in so far as it is infinite, there will be no up
or down or middle, and in so far as it is a void, up differs no whit
from down; for as there is no difference in what is nothing, there
is none in the void (for the void seems to be a non-existent and a
privation of being), but natural locomotion seems to be
differentiated, so that the things that exist by nature must be
differentiated. Either, then, nothing has a natural locomotion, or
else there is no void.
Further, in point of fact things that are thrown move though that
which gave them their impulse is not touching them, either by reason
of mutual replacement, as some maintain, or because the air that has
been pushed pushes them with a movement quicker than the natural
locomotion of the projectile wherewith it moves to its proper place.
But in a void none of these things can take place, nor can anything be
moved save as that which is carried is moved.
Further, no one could say why a thing once set in motion should stop
anywhere; for why should it stop here rather than here? So that a
thing will either be at rest or must be moved ad infinitum, unless
something more powerful get in its way.
Further, things are now thought to move into the void because it
yields; but in a void this quality is present equally everywhere, so
that things should move in all directions.
Further, the truth of what we assert is plain from the following
considerations. We see the same weight or body moving faster than
another for two reasons, either because there is a difference in
what it moves through, as between water, air, and earth, or because,
other things being equal, the moving body differs from the other owing
to excess of weight or of lightness.
Now the medium causes a difference because it impedes the moving
thing, most of all if it is moving in the opposite direction, but in a
secondary degree even if it is at rest; and especially a medium that
is not easily divided, i.e. a medium that is somewhat dense. A,
then, will move through B in time G, and through D, which is
thinner, in time E (if the length of B is egual to D), in proportion
to the density of the hindering body. For let B be water and D air;
then by so much as air is thinner and more incorporeal than water, A
will move through D faster than through B. Let the speed have the same
ratio to the speed, then, that air has to water. Then if air is
twice as thin, the body will traverse B in twice the time that it does
D, and the time G will be twice the time E. And always, by so much
as the medium is more incorporeal and less resistant and more easily
divided, the faster will be the movement.
Now there is no ratio in which the void is exceeded by body, as
there is no ratio of 0 to a number. For if 4 exceeds 3 by 1, and 2
by more than 1, and 1 by still more than it exceeds 2, still there
is no ratio by which it exceeds 0; for that which exceeds must be
divisible into the excess + that which is exceeded, so that will be
what it exceeds 0 by + 0. For this reason, too, a line does not exceed
a point unless it is composed of points! Similarly the void can bear
no ratio to the full, and therefore neither can movement through the
one to movement through the other, but if a thing moves through the
thickest medium such and such a distance in such and such a time, it
moves through the void with a speed beyond any ratio. For let Z be
void, equal in magnitude to B and to D. Then if A is to traverse and
move through it in a certain time, H, a time less than E, however, the
void will bear this ratio to the full. But in a time equal to H, A
will traverse the part O of A. And it will surely also traverse in
that time any substance Z which exceeds air in thickness in the
ratio which the time E bears to the time H. For if the body Z be as
much thinner than D as E exceeds H, A, if it moves through Z, will
traverse it in a time inverse to the speed of the movement, i.e. in
a time equal to H. If, then, there is no body in Z, A will traverse
Z still more quickly. But we supposed that its traverse of Z when Z
was void occupied the time H. So that it will traverse Z in an equal
time whether Z be full or void. But this is impossible. It is plain,
then, that if there is a time in which it will move through any part
of the void, this impossible result will follow: it will be found to
traverse a certain distance, whether this be full or void, in an equal
time; for there will be some body which is in the same ratio to the
other body as the time is to the time.
To sum the matter up, the cause of this result is obvious, viz. that
between any two movements there is a ratio (for they occupy time,
and there is a ratio between any two times, so long as both are
finite), but there is no ratio of void to full.
These are the consequences that result from a difference in the
media; the following depend upon an excess of one moving body over
another. We see that bodies which have a greater impulse either of
weight or of lightness, if they are alike in other respects, move
faster over an equal space, and in the ratio which their magnitudes
bear to each other. Therefore they will also move through the void
with this ratio of speed. But that is impossible; for why should one
move faster? (In moving through plena it must be so; for the greater
divides them faster by its force. For a moving thing cleaves the
medium either by its shape, or by the impulse which the body that is
carried along or is projected possesses.) Therefore all will possess
equal velocity. But this is impossible.
It is evident from what has been said, then, that, if there is a
void, a result follows which is the very opposite of the reason for
which those who believe in a void set it up. They think that if
movement in respect of place is to exist, the void cannot exist,
separated all by itself; but this is the same as to say that place
is a separate cavity; and this has already been stated to be
impossible.
But even if we consider it on its own merits the so-called vacuum
will be found to be really vacuous. For as, if one puts a cube in
water, an amount of water equal to the cube will be displaced; so
too in air; but the effect is imperceptible to sense. And indeed
always in the case of any body that can be displaced, must, if it is
not compressed, be displaced in the direction in which it is its
nature to be displaced-always either down, if its locomotion is
downwards as in the case of earth, or up, if it is fire, or in both
directions-whatever be the nature of the inserted body. Now in the
void this is impossible; for it is not body; the void must have
penetrated the cube to a distance equal to that which this portion
of void formerly occupied in the void, just as if the water or air had
not been displaced by the wooden cube, but had penetrated right
through it.
But the cube also has a magnitude equal to that occupied by the
void; a magnitude which, if it is also hot or cold, or heavy or light,
is none the less different in essence from all its attributes, even if
it is not separable from them; I mean the volume of the wooden cube.
So that even if it were separated from everything else and were
neither heavy nor light, it will occupy an equal amount of void, and
fill the same place, as the part of place or of the void equal to
itself. How then will the body of the cube differ from the void or
place that is equal to it? And if there can be two such things, why
cannot there be any number coinciding?
This, then, is one absurd and impossible implication of the
theory. It is also evident that the cube will have this same volume
even if it is displaced, which is an attribute possessed by all
other bodies also. Therefore if this differs in no respect from its
place, why need we assume a place for bodies over and above the volume
of each, if their volume be conceived of as free from attributes? It
contributes nothing to the situation if there is an equal interval
attached to it as well. [Further it ought to be clear by the study
of moving things what sort of thing void is. But in fact it is found
nowhere in the world. For air is something, though it does not seem to
be so-nor, for that matter, would water, if fishes were made of
iron; for the discrimination of the tangible is by touch.]
It is clear, then, from these considerations that there is no
separate void.
9
There are some who think that the existence of rarity and density
shows that there is a void. If rarity and density do not exist, they
say, neither can things contract and be compressed. But if this were
not to take place, either there would be no movement at all, or the
universe would bulge, as Xuthus said, or air and water must always
change into equal amounts (e.g. if air has been made out of a cupful
of water, at the same time out of an equal amount of air a cupful of
water must have been made), or void must necessarily exist; for
compression and expansion cannot take place otherwise.
Now, if they mean by the rare that which has many voids existing
separately, it is plain that if void cannot exist separate any more
than a place can exist with an extension all to itself, neither can
the rare exist in this sense. But if they mean that there is void, not
separately existent, but still present in the rare, this is less
impossible, yet, first, the void turns out not to be a condition of
all movement, but only of movement upwards (for the rare is light,
which is the reason why they say fire is rare); second, the void turns
out to be a condition of movement not as that in which it takes place,
but in that the void carries things up as skins by being carried up
themselves carry up what is continuous with them. Yet how can void
have a local movement or a place? For thus that into which void
moves is till then void of a void.
Again, how will they explain, in the case of what is heavy, its
movement downwards? And it is plain that if the rarer and more void
a thing is the quicker it will move upwards, if it were completely
void it would move with a maximum speed! But perhaps even this is
impossible, that it should move at all; the same reason which showed
that in the void all things are incapable of moving shows that the
void cannot move, viz. the fact that the speeds are incomparable.
Since we deny that a void exists, but for the rest the problem has
been truly stated, that either there will be no movement, if there
is not to be condensation and rarefaction, or the universe will bulge,
or a transformation of water into air will always be balanced by an
equal transformation of air into water (for it is clear that the air
produced from water is bulkier than the water): it is necessary
therefore, if compression does not exist, either that the next portion
will be pushed outwards and make the outermost part bulge, or that
somewhere else there must be an equal amount of water produced out
of air, so that the entire bulk of the whole may be equal, or that
nothing moves. For when anything is displaced this will always happen,
unless it comes round in a circle; but locomotion is not always
circular, but sometimes in a straight line.
These then are the reasons for which they might say that there is
a void; our statement is based on the assumption that there is a
single matter for contraries, hot and cold and the other natural
contrarieties, and that what exists actually is produced from a
potential existent, and that matter is not separable from the
contraries but its being is different, and that a single matter may
serve for colour and heat and cold.
The same matter also serves for both a large and a small body.
This is evident; for when air is produced from water, the same
matter has become something different, not by acquiring an addition to
it, but has become actually what it was potentially, and, again, water
is produced from air in the same way, the change being sometimes
from smallness to greatness, and sometimes from greatness to
smallness. Similarly, therefore, if air which is large in extent comes
to have a smaller volume, or becomes greater from being smaller, it is
the matter which is potentially both that comes to be each of the two.
For as the same matter becomes hot from being cold, and cold from
being hot, because it was potentially both, so too from hot it can
become more hot, though nothing in the matter has become hot that
was not hot when the thing was less hot; just as, if the arc or
curve of a greater circle becomes that of a smaller, whether it
remains the same or becomes a different curve, convexity has not
come to exist in anything that was not convex but straight (for
differences of degree do not depend on an intermission of the
quality); nor can we get any portion of a flame, in which both heat
and whiteness are not present. So too, then, is the earlier heat
related to the later. So that the greatness and smallness, also, of
the sensible volume are extended, not by the matter's acquiring
anything new, but because the matter is potentially matter for both
states; so that the same thing is dense and rare, and the two
qualities have one matter.
The dense is heavy, and the rare is light. [Again, as the arc of a
circle when contracted into a smaller space does not acquire a new
part which is convex, but what was there has been contracted; and as
any part of fire that one takes will be hot; so, too, it is all a
question of contraction and expansion of the same matter.] There are
two types in each case, both in the dense and in the rare; for both
the heavy and the hard are thought to be dense, and contrariwise
both the light and the soft are rare; and weight and hardness fail
to coincide in the case of lead and iron.
From what has been said it is evident, then, that void does not
exist either separate (either absolutely separate or as a separate
element in the rare) or potentially, unless one is willing to call the
condition of movement void, whatever it may be. At that rate the
matter of the heavy and the light, qua matter of them, would be the
void; for the dense and the rare are productive of locomotion in
virtue of this contrariety, and in virtue of their hardness and
softness productive of passivity and impassivity, i.e. not of
locomotion but rather of qualitative change.
So much, then, for the discussion of the void, and of the sense in
which it exists and the sense in which it does not exist.
10
Next for discussion after the subjects mentioned is Time. The best
plan will be to begin by working out the difficulties connected with
it, making use of the current arguments. First, does it belong to
the class of things that exist or to that of things that do not exist?
Then secondly, what is its nature? To start, then: the following
considerations would make one suspect that it either does not exist at
all or barely, and in an obscure way. One part of it has been and is
not, while the other is going to be and is not yet. Yet time-both
infinite time and any time you like to take-is made up of these. One
would naturally suppose that what is made up of things which do not
exist could have no share in reality.
Further, if a divisible thing is to exist, it is necessary that,
when it exists, all or some of its parts must exist. But of time
some parts have been, while others have to be, and no part of it is
though it is divisible. For what is 'now' is not a part: a part is a
measure of the whole, which must be made up of parts. Time, on the
other hand, is not held to be made up of 'nows'.
Again, the 'now' which seems to bound the past and the future-does
it always remain one and the same or is it always other and other?
It is hard to say.
(1) If it is always different and different, and if none of the
parts in time which are other and other are simultaneous (unless the
one contains and the other is contained, as the shorter time is by the
longer), and if the 'now' which is not, but formerly was, must have
ceased-to-be at some time, the 'nows' too cannot be simultaneous
with one another, but the prior 'now' must always have ceased-to-be.
But the prior 'now' cannot have ceased-to-be in itself (since it
then existed); yet it cannot have ceased-to-be in another 'now'. For
we may lay it down that one 'now' cannot be next to another, any
more than point to point. If then it did not cease-to-be in the next
'now' but in another, it would exist simultaneously with the
innumerable 'nows' between the two-which is impossible.
Yes, but (2) neither is it possible for the 'now' to remain always
the same. No determinate divisible thing has a single termination,
whether it is continuously extended in one or in more than one
dimension: but the 'now' is a termination, and it is possible to cut
off a determinate time. Further, if coincidence in time (i.e. being
neither prior nor posterior) means to be 'in one and the same
"now"', then, if both what is before and what is after are in this
same 'now', things which happened ten thousand years ago would be
simultaneous with what has happened to-day, and nothing would be
before or after anything else.
This may serve as a statement of the difficulties about the
attributes of time.
As to what time is or what is its nature, the traditional accounts
give us as little light as the preliminary problems which we have
worked through.
Some assert that it is (1) the movement of the whole, others that it
is (2) the sphere itself.
(1) Yet part, too, of the revolution is a time, but it certainly
is not a revolution: for what is taken is part of a revolution, not
a revolution. Besides, if there were more heavens than one, the
movement of any of them equally would be time, so that there would
be many times at the same time.
(2) Those who said that time is the sphere of the whole thought
so, no doubt, on the ground that all things are in time and all things
are in the sphere of the whole. The view is too naive for it to be
worth while to consider the impossibilities implied in it.
But as time is most usually supposed to be (3) motion and a kind
of change, we must consider this view.
Now (a) the change or movement of each thing is only in the thing
which changes or where the thing itself which moves or changes may
chance to be. But time is present equally everywhere and with all
things.
Again, (b) change is always faster or slower, whereas time is not:
for 'fast' and 'slow' are defined by time-'fast' is what moves much in
a short time, 'slow' what moves little in a long time; but time is not
defined by time, by being either a certain amount or a certain kind of
it.
Clearly then it is not movement. (We need not distinguish at present
between 'movement' and 'change'.)
11
But neither does time exist without change; for when the state of
our own minds does not change at all, or we have not noticed its
changing, we do not realize that time has elapsed, any more than those
who are fabled to sleep among the heroes in Sardinia do when they
are awakened; for they connect the earlier 'now' with the later and
make them one, cutting out the interval because of their failure to
notice it. So, just as, if the 'now' were not different but one and
the same, there would not have been time, so too when its difference
escapes our notice the interval does not seem to be time. If, then,
the non-realization of the existence of time happens to us when we
do not distinguish any change, but the soul seems to stay in one
indivisible state, and when we perceive and distinguish we say time
has elapsed, evidently time is not independent of movement and change.
It is evident, then, that time is neither movement nor independent
of movement.
We must take this as our starting-point and try to discover-since we
wish to know what time is-what exactly it has to do with movement.
Now we perceive movement and time together: for even when it is dark
and we are not being affected through the body, if any movement
takes place in the mind we at once suppose that some time also has
elapsed; and not only that but also, when some time is thought to have
passed, some movement also along with it seems to have taken place.
Hence time is either movement or something that belongs to movement.
Since then it is not movement, it must be the other.
But what is moved is moved from something to something, and all
magnitude is continuous. Therefore the movement goes with the
magnitude. Because the magnitude is continuous, the movement too
must be continuous, and if the movement, then the time; for the time
that has passed is always thought to be in proportion to the movement.
The distinction of 'before' and 'after' holds primarily, then, in
place; and there in virtue of relative position. Since then 'before'
and 'after' hold in magnitude, they must hold also in movement,
these corresponding to those. But also in time the distinction of
'before' and 'after' must hold, for time and movement always
correspond with each other. The 'before' and 'after' in motion is
identical in substratum with motion yet differs from it in definition,
and is not identical with motion.
But we apprehend time only when we have marked motion, marking it by
'before' and 'after'; and it is only when we have perceived 'before'
and 'after' in motion that we say that time has elapsed. Now we mark
them by judging that A and B are different, and that some third
thing is intermediate to them. When we think of the extremes as
different from the middle and the mind pronounces that the 'nows'
are two, one before and one after, it is then that we say that there
is time, and this that we say is time. For what is bounded by the
'now' is thought to be time-we may assume this.
When, therefore, we perceive the 'now' one, and neither as before
and after in a motion nor as an identity but in relation to a 'before'
and an 'after', no time is thought to have elapsed, because there
has been no motion either. On the other hand, when we do perceive a
'before' and an 'after', then we say that there is time. For time is
just this-number of motion in respect of 'before' and 'after'.
Hence time is not movement, but only movement in so far as it admits
of enumeration. A proof of this: we discriminate the more or the
less by number, but more or less movement by time. Time then is a kind
of number. (Number, we must note, is used in two senses-both of what
is counted or the countable and also of that with which we count. Time
obviously is what is counted, not that with which we count: there
are different kinds of thing.) Just as motion is a perpetual
succession, so also is time. But every simultaneous time is
self-identical; for the 'now' as a subject is an identity, but it
accepts different attributes. The 'now' measures time, in so far as
time involves the 'before and after'.
The 'now' in one sense is the same, in another it is not the same.
In so far as it is in succession, it is different (which is just
what its being was supposed to mean), but its substratum is an
identity: for motion, as was said, goes with magnitude, and time, as
we maintain, with motion. Similarly, then, there corresponds to the
point the body which is carried along, and by which we are aware of
the motion and of the 'before and after' involved in it. This is an
identical substratum (whether a point or a stone or something else
of the kind), but it has different attributes as the sophists assume
that Coriscus' being in the Lyceum is a different thing from Coriscus'
being in the market-place. And the body which is carried along is
different, in so far as it is at one time here and at another there.
But the 'now' corresponds to the body that is carried along, as time
corresponds to the motion. For it is by means of the body that is
carried along that we become aware of the 'before and after' the
motion, and if we regard these as countable we get the 'now'. Hence in
these also the 'now' as substratum remains the same (for it is what is
before and after in movement), but what is predicated of it is
different; for it is in so far as the 'before and after' is
numerable that we get the 'now'. This is what is most knowable: for,
similarly, motion is known because of that which is moved,
locomotion because of that which is carried. what is carried is a real
thing, the movement is not. Thus what is called 'now' in one sense
is always the same; in another it is not the same: for this is true
also of what is carried.
Clearly, too, if there were no time, there would be no 'now', and
vice versa. just as the moving body and its locomotion involve each
other mutually, so too do the number of the moving body and the number
of its locomotion. For the number of the locomotion is time, while the
'now' corresponds to the moving body, and is like the unit of number.
Time, then, also is both made continuous by the 'now' and divided at
it. For here too there is a correspondence with the locomotion and the
moving body. For the motion or locomotion is made one by the thing
which is moved, because it is one-not because it is one in its own
nature (for there might be pauses in the movement of such a thing)-but
because it is one in definition: for this determines the movement as
'before' and 'after'. Here, too there is a correspondence with the
point; for the point also both connects and terminates the length-it
is the beginning of one and the end of another. But when you take it
in this way, using the one point as two, a pause is necessary, if
the same point is to be the beginning and the end. The 'now' on the
other hand, since the body carried is moving, is always different.
Hence time is not number in the sense in which there is 'number'
of the same point because it is beginning and end, but rather as the
extremities of a line form a number, and not as the parts of the
line do so, both for the reason given (for we can use the middle point
as two, so that on that analogy time might stand still), and further
because obviously the 'now' is no part of time nor the section any
part of the movement, any more than the points are parts of the
line-for it is two lines that are parts of one line.
In so far then as the 'now' is a boundary, it is not time, but an
attribute of it; in so far as it numbers, it is number; for boundaries
belong only to that which they bound, but number (e.g. ten) is the
number of these horses, and belongs also elsewhere.
It is clear, then, that time is 'number of movement in respect of
the before and after', and is continuous since it is an attribute of
what is continuous.
12
The smallest number, in the strict sense of the word 'number', is
two. But of number as concrete, sometimes there is a minimum,
sometimes not: e.g. of a 'line', the smallest in respect of
multiplicity is two (or, if you like, one), but in respect of size
there is no minimum; for every line is divided ad infinitum. Hence
it is so with time. In respect of number the minimum is one (or
two); in point of extent there is no minimum.
It is clear, too, that time is not described as fast or slow, but as
many or few and as long or short. For as continuous it is long or
short and as a number many or few, but it is not fast or slow-any more
than any number with which we number is fast or slow.
Further, there is the same time everywhere at once, but not the same
time before and after, for while the present change is one, the change
which has happened and that which will happen are different. Time is
not number with which we count, but the number of things which are
counted, and this according as it occurs before or after is always
different, for the 'nows' are different. And the number of a hundred
horses and a hundred men is the same, but the things numbered are
different-the horses from the men. Further, as a movement can be one
and the same again and again, so too can time, e.g. a year or a spring
or an autumn.
Not only do we measure the movement by the time, but also the time
by the movement, because they define each other. The time marks the
movement, since it is its number, and the movement the time. We
describe the time as much or little, measuring it by the movement,
just as we know the number by what is numbered, e.g. the number of the
horses by one horse as the unit. For we know how many horses there are
by the use of the number; and again by using the one horse as unit
we know the number of the horses itself. So it is with the time and
the movement; for we measure the movement by the time and vice
versa. It is natural that this should happen; for the movement goes
with the distance and the time with the movement, because they are
quanta and continuous and divisible. The movement has these attributes
because the distance is of this nature, and the time has them
because of the movement. And we measure both the distance by the
movement and the movement by the distance; for we say that the road is
long, if the journey is long, and that this is long, if the road is
long-the time, too, if the movement, and the movement, if the time.
Time is a measure of motion and of being moved, and it measures
the motion by determining a motion which will measure exactly the
whole motion, as the cubit does the length by determining an amount
which will measure out the whole. Further 'to be in time' means for
movement, that both it and its essence are measured by time (for
simultaneously it measures both the movement and its essence, and this
is what being in time means for it, that its essence should be
measured).
Clearly then 'to be in time' has the same meaning for other things
also, namely, that their being should be measured by time. 'To be in
time' is one of two things: (1) to exist when time exists, (2) as we
say of some things that they are 'in number'. The latter means
either what is a part or mode of number-in general, something which
belongs to number-or that things have a number.
Now, since time is number, the 'now' and the 'before' and the like
are in time, just as 'unit' and 'odd' and 'even' are in number, i.e.
in the sense that the one set belongs to number, the other to time.
But things are in time as they are in number. If this is so, they
are contained by time as things in place are contained by place.
Plainly, too, to be in time does not mean to co-exist with time, any
more than to be in motion or in place means to co-exist with motion or
place. For if 'to be in something' is to mean this, then all things
will be in anything, and the heaven will be in a grain; for when the
grain is, then also is the heaven. But this is a merely incidental
conjunction, whereas the other is necessarily involved: that which
is in time necessarily involves that there is time when it is, and
that which is in motion that there is motion when it is.
Since what is 'in time' is so in the same sense as what is in number
is so, a time greater than everything in time can be found. So it is
necessary that all the things in time should be contained by time,
just like other things also which are 'in anything', e.g. the things
'in place' by place.
A thing, then, will be affected by time, just as we are accustomed
to say that time wastes things away, and that all things grow old
through time, and that there is oblivion owing to the lapse of time,
but we do not say the same of getting to know or of becoming young
or fair. For time is by its nature the cause rather of decay, since it
is the number of change, and change removes what is.
Hence, plainly, things which are always are not, as such, in time,
for they are not contained time, nor is their being measured by
time. A proof of this is that none of them is affected by time,
which indicates that they are not in time.
Since time is the measure of motion, it will be the measure of
rest too-indirectly. For all rest is in time. For it does not follow
that what is in time is moved, though what is in motion is necessarily
moved. For time is not motion, but 'number of motion': and what is
at rest, also, can be in the number of motion. Not everything that
is not in motion can be said to be 'at rest'-but only that which can
be moved, though it actually is not moved, as was said above.
'To be in number' means that there is a number of the thing, and
that its being is measured by the number in which it is. Hence if a
thing is 'in time' it will be measured by time. But time will
measure what is moved and what is at rest, the one qua moved, the
other qua at rest; for it will measure their motion and rest
respectively.
Hence what is moved will not be measurable by the time simply in
so far as it has quantity, but in so far as its motion has quantity.
Thus none of the things which are neither moved nor at rest are in
time: for 'to be in time' is 'to be measured by time', while time is
the measure of motion and rest.
Plainly, then, neither will everything that does not exist be in
time, i.e. those non-existent things that cannot exist, as the
diagonal cannot be commensurate with the side.
Generally, if time is directly the measure of motion and
indirectly of other things, it is clear that a thing whose existence
is measured by it will have its existence in rest or motion. Those
things therefore which are subject to perishing and
becoming-generally, those which at one time exist, at another do
not-are necessarily in time: for there is a greater time which will
extend both beyond their existence and beyond the time which
measures their existence. Of things which do not exist but are
contained by time some were, e.g. Homer once was, some will be, e.g. a
future event; this depends on the direction in which time contains
them; if on both, they have both modes of existence. As to such things
as it does not contain in any way, they neither were nor are nor
will be. These are those nonexistents whose opposites always are, as
the incommensurability of the diagonal always is-and this will not
be in time. Nor will the commensurability, therefore; hence this
eternally is not, because it is contrary to what eternally is. A thing
whose contrary is not eternal can be and not be, and it is of such
things that there is coming to be and passing away.
13
The 'now' is the link of time, as has been said (for it connects
past and future time), and it is a limit of time (for it is the
beginning of the one and the end of the other). But this is not
obvious as it is with the point, which is fixed. It divides
potentially, and in so far as it is dividing the 'now' is always
different, but in so far as it connects it is always the same, as it
is with mathematical lines. For the intellect it is not always one and
the same point, since it is other and other when one divides the line;
but in so far as it is one, it is the same in every respect.
So the 'now' also is in one way a potential dividing of time, in
another the termination of both parts, and their unity. And the
dividing and the uniting are the same thing and in the same reference,
but in essence they are not the same.
So one kind of 'now' is described in this way: another is when the
time is near this kind of 'now'. 'He will come now' because he will
come to-day; 'he has come now' because he came to-day. But the
things in the Iliad have not happened 'now', nor is the flood
'now'-not that the time from now to them is not continuous, but
because they are not near.
'At some time' means a time determined in relation to the first of
the two types of 'now', e.g. 'at some time' Troy was taken, and 'at
some time' there will be a flood; for it must be determined with
reference to the 'now'. There will thus be a determinate time from
this 'now' to that, and there was such in reference to the past event.
But if there be no time which is not 'sometime', every time will be
determined.
Will time then fail? Surely not, if motion always exists. Is time
then always different or does the same time recur? Clearly time is, in
the same way as motion is. For if one and the same motion sometimes
recurs, it will be one and the same time, and if not, not.
Since the 'now' is an end and a beginning of time, not of the same
time however, but the end of that which is past and the beginning of
that which is to come, it follows that, as the circle has its
convexity and its concavity, in a sense, in the same thing, so time is
always at a beginning and at an end. And for this reason it seems to
be always different; for the 'now' is not the beginning and the end of
the same thing; if it were, it would be at the same time and in the
same respect two opposites. And time will not fail; for it is always
at a beginning.
'Presently' or 'just' refers to the part of future time which is
near the indivisible present 'now' ('When do you walk? 'Presently',
because the time in which he is going to do so is near), and to the
part of past time which is not far from the 'now' ('When do you walk?'
'I have just been walking'). But to say that Troy has just been
taken-we do not say that, because it is too far from the 'now'.
'Lately', too, refers to the part of past time which is near the
present 'now'. 'When did you go?' 'Lately', if the time is near the
existing now. 'Long ago' refers to the distant past.
'Suddenly' refers to what has departed from its former condition
in a time imperceptible because of its smallness; but it is the nature
of all change to alter things from their former condition. In time all
things come into being and pass away; for which reason some called
it the wisest of all things, but the Pythagorean Paron called it the
most stupid, because in it we also forget; and his was the truer view.
It is clear then that it must be in itself, as we said before, the
condition of destruction rather than of coming into being (for change,
in itself, makes things depart from their former condition), and
only incidentally of coming into being, and of being. A sufficient
evidence of this is that nothing comes into being without itself
moving somehow and acting, but a thing can be destroyed even if it
does not move at all. And this is what, as a rule, we chiefly mean
by a thing's being destroyed by time. Still, time does not work even
this change; even this sort of change takes place incidentally in
time.
We have stated, then, that time exists and what it is, and in how
many senses we speak of the 'now', and what 'at some time',
'lately', 'presently' or 'just', 'long ago', and 'suddenly' mean.
14
These distinctions having been drawn, it is evident that every
change and everything that moves is in time; for the distinction of
faster and slower exists in reference to all change, since it is found
in every instance. In the phrase 'moving faster' I refer to that which
changes before another into the condition in question, when it moves
over the same interval and with a regular movement; e.g. in the case
of locomotion, if both things move along the circumference of a
circle, or both along a straight line; and similarly in all other
cases. But what is before is in time; for we say 'before' and
'after' with reference to the distance from the 'now', and the 'now'
is the boundary of the past and the future; so that since 'nows' are
in time, the before and the after will be in time too; for in that
in which the 'now' is, the distance from the 'now' will also be. But
'before' is used contrariwise with reference to past and to future
time; for in the past we call 'before' what is farther from the 'now',
and 'after' what is nearer, but in the future we call the nearer
'before' and the farther 'after'. So that since the 'before' is in
time, and every movement involves a 'before', evidently every change
and every movement is in time.
It is also worth considering how time can be related to the soul;
and why time is thought to be in everything, both in earth and in
sea and in heaven. Is because it is an attribute, or state, or
movement (since it is the number of movement) and all these things are
movable (for they are all in place), and time and movement are
together, both in respect of potentiality and in respect of actuality?
Whether if soul did not exist time would exist or not, is a question
that may fairly be asked; for if there cannot be some one to count
there cannot be anything that can be counted, so that evidently
there cannot be number; for number is either what has been, or what
can be, counted. But if nothing but soul, or in soul reason, is
qualified to count, there would not be time unless there were soul,
but only that of which time is an attribute, i.e. if movement can
exist without soul, and the before and after are attributes of
movement, and time is these qua numerable.
One might also raise the question what sort of movement time is
the number of. Must we not say 'of any kind'? For things both come
into being in time and pass away, and grow, and are altered in time,
and are moved locally; thus it is of each movement qua movement that
time is the number. And so it is simply the number of continuous
movement, not of any particular kind of it.
But other things as well may have been moved now, and there would be
a number of each of the two movements. Is there another time, then,
and will there be two equal times at once? Surely not. For a time that
is both equal and simultaneous is one and the same time, and even
those that are not simultaneous are one in kind; for if there were
dogs, and horses, and seven of each, it would be the same number.
So, too, movements that have simultaneous limits have the same time,
yet the one may in fact be fast and the other not, and one may be
locomotion and the other alteration; still the time of the two changes
is the same if their number also is equal and simultaneous; and for
this reason, while the movements are different and separate, the
time is everywhere the same, because the number of equal and
simultaneous movements is everywhere one and the same.
Now there is such a thing as locomotion, and in locomotion there
is included circular movement, and everything is measured by some
one thing homogeneous with it, units by a unit, horses by a horse, and
similarly times by some definite time, and, as we said, time is
measured by motion as well as motion by time (this being so because by
a motion definite in time the quantity both of the motion and of the
time is measured): if, then, what is first is the measure of
everything homogeneous with it, regular circular motion is above all
else the measure, because the number of this is the best known. Now
neither alteration nor increase nor coming into being can be
regular, but locomotion can be. This also is why time is thought to be
the movement of the sphere, viz. because the other movements are
measured by this, and time by this movement.
This also explains the common saying that human affairs form a
circle, and that there is a circle in all other things that have a
natural movement and coming into being and passing away. This is
because all other things are discriminated by time, and end and
begin as though conforming to a cycle; for even time itself is thought
to be a circle. And this opinion again is held because time is the
measure of this kind of locomotion and is itself measured by such.
So that to say that the things that come into being form a circle is
to say that there is a circle of time; and this is to say that it is
measured by the circular movement; for apart from the measure
nothing else to be measured is observed; the whole is just a plurality
of measures.
It is said rightly, too, that the number of the sheep and of the
dogs is the same number if the two numbers are equal, but not the same
decad or the same ten; just as the equilateral and the scalene are not
the same triangle, yet they are the same figure, because they are both
triangles. For things are called the same so-and-so if they do not
differ by a differentia of that thing, but not if they do; e.g.
triangle differs from triangle by a differentia of triangle, therefore
they are different triangles; but they do not differ by a
differentia of figure, but are in one and the same division of it. For
a figure of the one kind is a circle and a figure of another kind of
triangle, and a triangle of one kind is equilateral and a triangle
of another kind scalene. They are the same figure, then, that,
triangle, but not the same triangle. Therefore the number of two
groups also-is the same number (for their number does not differ by
a differentia of number), but it is not the same decad; for the things
of which it is asserted differ; one group are dogs, and the other
horses.
We have now discussed time-both time itself and the matters
appropriate to the consideration of it.