1 · When the objects of an inquiry, in any department, have principles, [184a10] causes, or elements, it is through acquaintance with these that knowledge and understanding is attained. For we do not think that we know a thing until we are acquainted with its primary causes or first principles, and have carried our analysis as far as its elements. Plainly, therefore, in the science of nature too our first task [15] 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 clear 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 we must follow this method and advance from what is more obscure by nature, but clearer to us, towards what is more clear and [20] more knowable by nature.
Now what is to us plain and clear at first is rather confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from universals to particulars; for it is a whole that is more knowable to sense-perception, and a universal is a kind of whole, comprehending many things [25] within it, like parts. Much the same thing happens in the relation of the name to the [184b10] formula. A name, e.g. ‘circle’, means vaguely a sort of whole: its definition analyses this into particulars. 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 one or more than one. If one, it [15] must be either motionless, as Parmenides and Melissus assert, or in motion, as the physicists hold, some declaring air to be the first principle, others water. If more than one, then either a finite or an infinite plurality. If finite (but more than one), then either two or three or four or some other number. If infinite, then either as [20] Democritus believed one in kind, but differing in shape; 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 [25] many, and if many, whether a finite or an infinite plurality. So they are inquiring whether the principle or element is one or many.
Now to investigate whether what exists is one and motionless is not a [185a1] 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 one common to all—so a man investigating principles cannot argue with one who denies their existence. For if what exists 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.
[5] To inquire therefore whether what exists 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 what exists 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 [10] not follow. Or rather the argument of Melissus is gross and offers no difficulty at all: accept one ridiculous proposition and the rest follows—a simple enough proceeding.
We, 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 one is bound to solve every kind of difficulty that may be [15] 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 [20] 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 ways. 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 [25] 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, what exists will be many.
If on the other hand it is asserted that all things are quality or quantity, then, [30] whether substance exists or not, an absurdity results, if indeed the impossible can properly be called absurd. For none of the others can exist independently except substance; for everything is predicated of substance as subject. Now Melissus says that what exists is infinite. It is then a quantity. For the infinite is in the category of [185b1] quantity, whereas substance or quality or affection cannot be infinite except accidentally, 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 what exists is both substance and quantity, it is two, not one; if only substance, it is [5] not infinite and has no magnitude; for to have that it will have to be a quantity.
Again, ‘one’ itself, no less than ‘is’, is used in many ways, so we must consider in what way the word is used when it is said that the universe is one.
Now we say that the continuous is one or that the indivisible is one, or things are said to be one, when the account of their essence is one and the same, as liquor and drink.
If their One is one in the sense of continuous, it is many; for the continuous is [10] 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 in what way they can be one or many, and, if they are more than one, in what way they are more than one. (Similarly with the parts of wholes which are not continuous.) Further, if each of [15] 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 their One is one as indivisible, nothing will have quantity or quality, and so what exists 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 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 [20] 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 quantity. [25]
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 [30] if they added the word ‘is’ they should be making the one to be many—as if ‘one’ and ‘is’ were always used in one and the same way. What is may be many either in definition (for example to be white is one thing, to be musical another, yet the same thing may 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 [186a1] 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 what is one may be 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 [5] 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 offers no difficulty at all: admit one ridiculous proposition and the rest follows—a simple enough proceeding.]1 [10]
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 [15] coming to be simpliciter but also in the case of qualitative change—as if change never took place all at once. Again, does it follow that what is, 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, what is cannot be one in form, though it may be in what it is made of. (Even some of [20] 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 ‘is’ is used in a single way only is false, [25] 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 [30] 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 ‘is’ has the same meaning, of whatever it is predicated, but further that it means what just is and what is just one. For an attribute is predicated of some subject, so that the subject to which ‘is’ is attributed will not be, as it is something different from being. Something, therefore, [186b1] which is not will be. Hence what just is will not belong to anything else. For the subject cannot be a being, unless ‘is’ means several things, in such a way that each is something. But ex hypothesi ‘is’ means only one thing.
If, then, what just is is not attributed to anything, but other things are [5] attributed to it, how does what just is mean what is rather than what is not? For suppose that what just is is also white, and that being white is not what just is (for being cannot even be attributed to white, since nothing is which is not what just is), it follows that what is white is not—and that not in the sense of not being something [10] or other, but in the sense that it is not at all. Hence what just is is not; for it is true to say that it is white, and we found this to mean what is not. So ‘white’ must also mean what just is; and then ‘is’ has more than one meaning.
In particular, then, what is will not have magnitude, if it is what just is. For each of the two parts must be in a different way.
What just is is plainly divisible into other things which just are, if we consider [15] the mere nature of a definition. For instance, if man is, what just is, animal and biped must also be what just is. For if not, they must be attributes—and if attributes, attributes either of man or of some other subject. But neither is possible.
For 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 [20] 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, [25] 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. [30]
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 what just is, then man too will be an attribute of something else. But we must assume that what just is is not the attribute of anything, and that the subject of which both biped and animal are predicated is the subject also of the complex. Are we then to say that the universe is composed of indivisibles?
Some thinkers did, in point of fact, give way to both arguments. To the [187a1] argument that all things are one if being means one thing, they conceded that what is not is; to that from bisection, they yielded by positing atomic magnitudes. But obviously it is not true that if being means one thing, and nothing can at the same time both be and not be, 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 something or [5] other. To say that all things will be one, if there is nothing besides what is itself, is absurd. For who understands ‘what is itself’ to be anything but some particular thing? But if this is so, there is still nothing to prevent there being many beings, as [10] has been said.
It is, then, clearly impossible for what is 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 three2 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. [15] (Now these are contraries, which may be generalized into excess and defect. Compare Plato’s ‘Great and Small’—except that he makes 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 [20] 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 homogeneous substances and his [25] contraries infinite, whereas Empedocles posits only the so-called elements.
The theory of Anaxagoras that the principles are infinite was probably due to his acceptance of the common opinion of the physicists that nothing comes into being from what is not. (For this is the reason why they use the phrase ‘all things [30] 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 come into being 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, [35] 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, [187b1] but imperceptible to our senses because of the smallness of their bulk. So they assert that everything has been mixed in everything, because they saw everything arising out of everything. But things, as they say, appear different from one another and receive different names according to what is numerically predominant among the innumerable constituents of the mixture. For nothing, they say, is purely and [5] entirely white or black or sweet, or bone or flesh, but the nature of a thing is held to be that of which it contains the most.
Now 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 [10] 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, if the parts of a whole may be indefinitely big or small (by parts I [15] 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 also be of any size. Clearly, therefore, if 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 [20] 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, 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 [25] 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 is evident 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 [30] 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 parts in a finite quantity—which is impossible. Another proof may be added: [35] 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 [188a1] would be less than the minimum of flesh.
Again, 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,3 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 [5] 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 something white or healthy which was nothing but white or healthy, i.e. was not the predicate of a subject. So his Mind absurdly aims at the impossible, if it is supposed to wish to separate them, and it is [10] 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 [15] 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.
All thinkers then agree in making the contraries principles, both those who describe the universe as one and unmoved (for even Parmenides treats hot and cold [20] 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, he 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, [25] 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 [30] contraries.
But we must see how this can be arrived at as a reasoned result. 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 accidentally. For how could white come from musical, unless musical [35] happened to be an attribute of the not-white or of the black? No, white comes from [188b1] not-white—and not from any not-white, but from black or some intermediate. Similarly, musical comes to be from non-musical, but not from any thing other than musical, but from unmusical or any intermediate state there may be.
Nor again do things pass away into the first chance thing; white does not pass [5] into musical (except, it may be, accidentally), but into not-white—and not into any chance thing which is not white, but into black or an intermediate; 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 [10] complex follow the same principle, but the opposite state has not received a name, so we fail to notice the fact. For 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, [15] 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 anything else. 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 [20]—each of these objects being partly order and partly composition.
If then this is true, everything that comes to be or passes away comes 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, [25] 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 [30] theory, but constrained as it were by the truth itself. They differ, however, from one another in that some assume contraries which are prior, others contraries which are posterior; 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 causes of [35] 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 [189a1] 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 [5] what is more knowable in the order of explanation, others what is more familiar to sense. (The universal is 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.
[10] 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, what is 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 [15] an infinite multitude; for Empedocles professes to obtain all that Anaxagoras obtains from his innumerable principles. Again, some contraries are prior to 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. [20]
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 [25] 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 posit some other nature under the contraries may be added. We do not find that the contraries constitute the substance of any thing. But what is a first principle ought not to be predicated of [30] 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, 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-substance be prior to substance?
If then we accept both the former argument and this one, we must, to preserve both, posit some third thing, such as is spoken of by those who describe the universe [189b1] 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 [5] 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 [10] 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 [15] 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 one thing is sufficient to be acted on; but if we have four contraries, there [20] 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 [25] a single genus of being, so that the principles can differ only as prior and posterior, not in genus; for 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.
[30] 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 something from something different, in the case both of simple and of complex things. I mean the following. We can say the man becomes musical, or what is not-musical becomes [190a1] musical, or the not-musical man becomes a musical man. Now what becomes in the first two cases—man and not-musical—I call simple, and what each becomes—musical—simple also. But when we say the not-musical man becomes a musical man, both what becomes and what it becomes are complex.
[5] In some cases, we say not only this becomes so-and-so, but also from being this, it comes to be so-and-so (e.g.: from being not-musical he comes to be musical); but we do not say this in all cases, as we do not say 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 it survives [10] through the process, in the other it does not. For the man remains a man and is such even when he becomes musical, whereas what is not musical or is unmusical does not survive, 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 there must always be an underlying [15] something, namely that which becomes, and that this, though always one numerically, in form at least is not one. (By ‘in form’ I mean the same as ‘in account’.) For to be a man is not the same as to be unmusical. One part survives, the other does not: what is not an opposite survives (for the man survives), but [20] not-musical or unmusical does not survive, nor does the compound of the two, namely the 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 we sometimes use the latter form of expression even of what [25] 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 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 from an unmusical [30] man’, and ‘an unmusical man becoming musical’.
Things are said to come to be in different ways. 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 without qualification.
Now in all cases other than substance it is plain that there must be something underlying, namely, that which becomes. For when a thing comes to be of such a quantity or quatity or in such a relation, time,4 or place, a subject is always [35] presupposed, since substance alone is not predicated of another subject, but everything else of substance.
But that substances too, and anything that can be said to be without [190b1] qualification, come to be from some underlying thing, 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.
Things which come to be without qualification, come to be in different ways: [5] by change of shape, as a statue; by addition, as things which grow; by taking away, as the Hermes from the stone; by putting together, as a house; by alteration, as things which turn in respect of their matter.
It is plain that these are all cases of coming to be from some underlying [10] thing.
Thus, from what has been said, whatever comes to be is always complex. There is, on the one hand, something which comes to be, and again something which becomes that—the latter 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 [15] subject.
Plainly then, if there are causes 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 substance, not what each is accidentally—plainly, I say, everything comes to be from both subject and form. For the musical man is [20] 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 there is the man, the gold—in general, the countable matter; for it is more of the nature of a [25] ‘this’, and what comes to be does not come from it accidentally; the privation, on the other hand, and the contrariety are accidental.) And the form is one—the order, the 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 [30] 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 what underlies is different from the contraries; for it is itself not a [35] 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 [191a1] being, 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 [5] be something underlying 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 absence and presence.)
The underlying nature can be known by analogy. For as the bronze is to the [10] statue, the wood to the bed, or the matter and5 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’); one is the form or definition;6 then further there is its contrary, the privation. [15] In what sense these are two, and in what sense more, has been stated above. We explained first that only the contraries were principles, and later that something else underlay them, 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 what underlies. Whether the form or what underlies is [20] the substance 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.
[25] The first of those who studied philosophy 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 [30] (because it is already), and from what is not nothing could have come to be (because something must be underlying). 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 what is itself is. Such then was their opinion, and such the reason for its adoption.
[35] Our explanation on the other hand is that for something to come to be from what is or from what is not, or what is not or what is to do something or have something done to it or become some particular thing, are in one way no different from a doctor doing something or having something done to him, or being or [191b1] becoming something from being a doctor. These expressions may be taken in two ways, and so too, clearly, may ‘from what is’, and ‘what is acts or is acted on’. A doctor builds a house, not qua doctor, but qua housebuilder, and turns gray, not qua [5] 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 what is not means ‘qua what is not’.
It was through failure to make this distinction that those thinkers gave the [10] 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 what is 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 in a qualified sense, i.e. accidentally. For a [15] thing comes to be from the privation, which in its own nature is something which is not—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 what is, and that what is does not come to be except accidentally. 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 dog, or a horse [20] 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 accidentally, it will not be from animal; and if what is, not from what is—nor from what is not either, for it has been explained that [25] by ‘from what is not’ we mean qua what is not.
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 spoken of in terms of potentiality and actuality. But this has been done with greater precision elsewhere.7
So, as we said, the difficulties which constrain people to deny the existence of [30] 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 [35] adequately.
In the first place they allow that a thing may come to be without qualification [192a1] from what is not, accepting on this point the statement of Parmenides. Secondly, they think that if it 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 [5] the matter, accidentally is not, while the privation in its own nature is not; 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 what is not, and that whether they are taken together as one or separately. Their triad is therefore of [10] 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 philosopher8 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 other part of the contrariety may often [15] seem, if you concentrate your attention on it as an evil agent, not to exist at all.
For admitting 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 [20] contrary desires its own extinction. 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 in itself but accidentally.
[25] 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 [30] substratum from which it should come and which should persist in it; but this is its own very 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, and which persists in the result, not accidentally.) 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 first philosophy; so [192b1] 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.
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, [10] fire, air, water)—for we say that these and the like exist by nature.
All the things mentioned plainly differ from things which are not constituted by nature. For 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 [15] 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 [20] extent—which seems to indicate that nature is a principle or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not accidentally.
I say ‘not accidentally’, because (for instance) a man who is a doctor might himself be a cause of health to himself. Nevertheless it is not in so far as he is a [25] 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 principle of its own production. But while in some cases (for instance houses and the [30] 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 accidentally—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 is always in a subject.
The term ‘according to nature’ is applied to all these things and also to the [35] 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 [193a1] 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 [5] 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 [10] 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 [15] rules of the art is merely an accidental attribute, whereas the substance is the other, which, further, persists continuously through the process.
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, [20] that (they say) would be their nature and substance. 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 [25] 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 primary underlying matter of things which have in themselves a principle of motion or change.
[30] 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 [35] 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 [193b1] own nature, and does not exist by nature, until it receives the form specified in the definition, which we name in defining what flesh or bone is. Thus on the second account of nature, it would be the shape or form (not separable except in statement) [5] of things which have in themselves a principle of motion. (The combination of the two, e.g. man, is not nature but by nature.)
The form indeed is nature rather than the matter; for a thing is more properly said to be what it is when it exists in actuality than when it exists potentially. Again man is born from man but not bed from bed. That is why people say that the shape is [10] 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 shape is art,9 then on the same principle the shape of man is his nature. For man is born from man.
Again, nature in the sense of a coming-to-be proceeds towards nature. For it is not like doctoring, which leads not to the art of doctoring but to health. Doctoring [15] must start from the art, not lead to it. But it is not in this way that nature is related to nature. 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 are used in two ways. For the privation too is in a way form. [20] But whether in unqualified coming to be there is privation, i.e. a contrary, 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 student of nature; for natural bodies contain surfaces and volumes, lines and points, and these are the subject-matter of mathematics. [25]
Further, is astronomy different from natural science or a department of it? It seems absurd that the student of nature 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 nature obviously do discuss their shape and whether the earth and the [30] 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 natural 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, [35] though they are not aware of it; for they separate the objects of natural science, which are less separable than those of mathematics. This becomes plain if one tries [194a1] 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, [5] not like curved.
Similar evidence is supplied by the more natural of the branches of mathematics, such as optics, harmonics, and astronomy. These are in a way the converse of geometry. While geometry investigates natural lines but not qua natural, optics [10] investigates mathematical lines, but qua natural, not qua mathematical.
Since two sorts of thing are called nature, the form and the matter, we must investigate its objects as we would the essence of snubness, that is neither independently of matter nor in terms of matter only. Here too indeed one might [15] raise a difficulty. Since there are two natures, with which is the student of nature 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, natural science would seem to be concerned with the matter. (It was only very slightly that Empedocles and Democritus touched on form [20] and 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 [25] beams, and so forth): if this is so, it would be the part of natural science 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 toward some end, that last stage10 is [30] actually 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 [35] 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’ may be taken in two ways, as we said in [194b1] 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,11 whereas the art which is directive as being [5] 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 thing—for different forms there is different matter.
[10] How far then must the student of nature 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);12 and the student of nature 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 [15] separable it is the business of first 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 [20] it (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 natural change, in order that, knowing their principles, we may try to refer to these principles each of our problems.
In one way, then, that out of which a thing comes to be and which persists, is [25] called a 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 way, the form or the archetype, i.e. the definition 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.
[30] Again, the primary source of the change or rest; e.g. the man who deliberated is a cause, the father is cause of the child, and generally what makes of what is made and what changes of what is changed.
Again, 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 [35] 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 [195a1] 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 things are called causes in many ways, it follows that there are several causes of the same thing (not merely accidentally), e.g. both the art of the sculptor [5] 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 principle of [10] motion. 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 [15] the causes of syllables, the material of artificial products, fire and the like 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 what underlies, e.g. the parts, the other set in the sense of essence—the whole and the combination and the [20] form. But the seed and the doctor and the deliberator, and generally the maker, are all sources whence the change or stationariness originates, which the others are causes in the sense of the end or the good of the rest; for that for the sake of which tends to be what is best and the end of the things that lead up to it. (Whether we call [25] it good or apparently 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 things are called causes in many ways and even within the same kind one may be prior to another: e.g. the doctor and the expert are [30] 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 accidental and its genera, e.g. in one way Polyclitus, in another a sculptor is the cause of a statue, because being Polyclitus and a sculptor are accidentally conjoined. Also the classes [35] in which the accidental attribute is included; thus a man could be said to be the cause of a statue or, generally, a living creature. An accidental attribute too may be [195b1] 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 accidental, may be spoken of either as potential or as actual; e.g. the cause of a house being built is either a house-builder or a [5] house-builder building.
Similar distinctions can be made in the things of which the causes are causes, e.g. of this statue or of a statue or of an image generally, of this bronze or of bronze [10] or of material generally. So too with the accidental attributes. Again we may use a complex expression for either and say, e.g., neither ‘Polyclitus’ nor a ‘sculptor’ but ‘Polyclitus, the sculptor’.
All these various uses, however, come to six in number, under each of which again the usage is twofold. It is either what is particular or a genus, or an accidental [15] attribute or a genus of that, and these either as a complex or each by itself; and all 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 housebuilding [20] 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 a 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 [25] 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 [30] causation.
4 · But chance and spontaneity are also 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 [35] among the causes enumerated, and whether they are the same or different, and generally what chance and spontaneity are.
Some people even question whether there are such things or not. They say that [196a1] 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 [5] wish to go and buy in the market. Similarly, in other so-called 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 [10] 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 all know that each of them can be ascribed to some cause (as the old [15] argument said which denied chance), nevertheless they all speak of some of these things as happening by chance and others not. For this reason 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 [20] 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’.13 He tells us also that most of the parts of animals came to be by chance.
There are some who actually ascribe this heavenly sphere and all the worlds to [25] spontaneity. They say that the vortex arose spontaneously, i.e. the motion that separated and arranged the universe in its present order. 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 [30] 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 [35] 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 [196b1] 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 believe that chance is a cause, but that it is inscrutable to [5] 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 [10] way, and others for the most part. It is clearly of neither of these that chance, or the result of chance, is said to be the cause—neither of that which is by necessity and always, nor of that which is 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 [15] 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.
Of things that come to be, some come to be for the sake of something, others not. Again, some of the former class are in accordance with 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 what is necessary and what is for [20] the most part, there are some in connexion with which the phrase ‘for the sake of something’ is applicable. (Things 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 accidentally are said to be by chance. For just as a thing is something either in virtue of itself or accidentally, so may it be a cause. For [25] instance, the housebuilding faculty is in virtue of itself a cause of a house, whereas the pale or the musical is an accidental cause. That which is per se cause is determinate, but the accidental cause is indeterminable; for the possible attributes of an individual are innumerable. As we said, then, when a thing of this kind comes [30] 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 collecting14 subscriptions for a feast. He would have gone to such and such a place for the purpose of getting the money, if he had [35] known. He actually went there for another purpose, and it was only accidentally that he got his money by going there;15 and this was not due to the fact that he went [197a1] 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 objects of choice and the result of thought. It is when these conditions are satisfied that the man is said to have gone by chance. If he had chosen and gone for the sake of this—if he always or normally went there when he was collecting payments—he would not be said to [5] have gone by chance. It is clear then that chance is an accidental cause in the sphere of those actions for the sake of something which involve choice. Thought, then, and chance are in the same sphere, for choice implies thought.
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 [10] 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, as might be expected. Things do, in a way, occur by chance, for they occur accidentally and chance is an accidental cause. But it is not the cause without qualification of anything; for [15] instance, a housebuilder is the cause of a house; accidentally, 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 unaccountable is correct. For an account is of [20] what holds always or for the most part, whereas chance belongs to a third type of event. Hence, since causes of this kind are indefinite, chance too is indefinite. (Yet in some cases one might raise the question whether any chance 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 accidental causes are more relevant to the effect than others.)
[25] Chance 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 presence of the attribute, ignoring the hair’s breadth of difference. Further, it is with reason that good fortune [30] is regarded as unstable; for chance is unstable, as none of the things which result from it can hold always or for the most part.
Both are then, as I have said, accidental causes—both chance and spontaneity—in the sphere of things which are capable of coming to pass not simply, nor for the most part and with reference to such of these as might come to pass for the sake [35] of something.
6 · They differ in that spontaneity is the wider. 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 [197b1] capable of good fortune and of action generally. Therefore necessarily chance is in the sphere of 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 action, [5] since it is well-doing. Hence what is not capable of action cannot do anything by chance. Thus an inanimate thing or a beast or a child cannot do anything by chance, because it is incapable of choice; nor can good fortune or ill fortune be ascribed to them, except metaphorically, as Protarchus, for example, said that the stones of [10] 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 beasts and in many inanimate objects. We say, for example, that the horse came spontaneously, [15] because, though his coming saved him, he did not come for the sake of safety. Again, the tripod fell spontaneously, because, though it stood on its feet so as to serve for a seat, it did not fall so as to serve for a seat.
Hence it is clear that events which belong to the general class of things that may come to pass for the sake of something, when they come to pass not for the sake of what actually results, and have an external cause, may be described by the phrase [20] ‘from spontaneity’. These spontaneous events are said to be from chance if they have the further characteristics of being the objects of choice and happening to agents capable of choice. This is indicated by the phrase ‘in vain’, which is used when one thing which is for the sake of another, does not result in it.16 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 [25] implies that what is naturally for the sake of an end is in vain, when it does not effect the end for the sake of 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 for the sake of the other. Thus the spontaneous is even according to its derivation17 the case in which the thing itself happens in vain. The stone that struck the man did not fall for the sake of striking him; therefore it fell [30] spontaneously, because it might have fallen by the action of an agent and for the sake 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 [35] strictly this too is different from the spontaneous proper; for the cause of the latter is external, that of the former internal.
[198a1] 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.
[5] Spontaneity and chance are causes of effects which, though they might result from intelligence or nature, have in fact been caused by something accidentally. Now since nothing which is accidental is prior to what is per se, it is clear that no accidental cause can be prior to a cause per se. Spontaneity and chance, therefore, [10] 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 universe and of many things in it besides.
7 · It is clear then that there are causes, and that the number of them is what [15] we have stated. The number is the same as that of the things comprehended under the question ‘why’. The ‘why’ is referred ultimately either, in things which do not involve motion, e.g. in mathematics, to the ‘what’ (to the definition of straight line or commensurable or the like); or to what initiated a motion, e.g. ‘why did they go to war?—because there had been a raid’; or we are inquiring ‘for the sake of [20] what?’—‘that they may rule’; or 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 student of nature 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 [25] 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, with all things which cause movement by being themselves moved; and such as are not of this kind are no longer inside the province of natural science, for they cause motion not by possessing motion or a source of motion in themselves, but being themselves incapable of [30] 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 [35] primary agent or patient?’ and so at each step of the series. Now the principles which cause motion in a natural way are two, of which one is not [198b1] natural, as it has no principle of motion in itself. Of this kind is whatever causes movement, not being itself moved, such as that which is completely unchangeable, the primary reality, and the essence of a thing, 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 [5] senses of the term, namely, that from this that will necessarily result (‘from this’ either without qualification or for the most part); that this must be so if that is to be so (as the conclusion presupposes the premisses); that this was the essence of the thing; and because it is better thus (not without qualification, but with reference to the substance in each case).
8 · We must explain then first why nature belongs to the class of causes [10] which act for the sake of something; and then about the necessary and its place in nature, for all writers ascribe things to this cause, arguing that since the hot and the cold and the like are of such and such a kind, therefore certain things necessarily are and come to be—and if they mention any other cause (one friendship and strife, [15] another 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.) [20] 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 [25] 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 to be for an end, such things survived, being [30] organized spontaneously in a fitting way; whereas those which grew otherwise perished and continue to perish, as Empedocles says his ‘man-faced oxprogeny’ did.18
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 for the most part come about in a given way; but of not one of the results of chance or spontaneity is this true. We do not [199a1] ascribe to chance or mere coincidence the frequency of rain in winter, but frequent rain in summer we do; nor heat in summer but only if we have it in winter. If then, it is agreed that things are either the result of coincidence or for the sake of something, and these cannot be the result of coincidence or spontaneity, it follows [5] that they must be for the sake of something; 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 there is an end, all the preceding steps are for the sake of that. [10] Now surely as in action, so in nature; and as in nature, so it is in each action, if nothing interferes. Now 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 not only by nature but also by art, they would come to be in the same [15] way as by nature. The one, then, is for the sake of the other; and generally art in some cases completes what nature cannot bring to a finish, and in others imitates nature. 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 items is the same in both.
[20] This is most obvious in the animals other than man: they make things neither by art nor after inquiry or deliberation. That is why people wonder 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 [25] 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 [30] of cause is operative in things which come to be and are by nature. And since nature is twofold, 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 occur even in the operations of art: the literate man makes a mistake in writing and the doctor pours out the wrong dose. Hence clearly mistakes [199b1] 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 [5] original combinations the ‘ox-progeny’, if they failed to reach a determinate end must have arisen through the corruption of some principle, as happens now when the seed is defective.
Further, seed must have come into being first, and not straightway the animals: what was ‘undifferentiated first’19 was seed.
[10] Again, in plants too we find that for the sake of which, 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 come to be at random. But the [15] 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 end: the same end is not reached from every principle; nor any chance end, 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, [20] when he does so as if he had come for that purpose, though it was not for that that he came. This is accidental, for chance is an accidental cause, as I remarked before. But when an event takes place always or for the most part, it is not accidental or by [25] 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: [30] 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 [200a1] necessarily comes to be because what is heavy is naturally carried downwards and what is light to the top, so that 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, [5] 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 that for the sake of which: 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 [10] end, however, cannot be realized unless the saw is made of iron. It is, therefore, necessary for it to be of iron, if we are to have a saw and perform the operation of sawing. What is necessary then, is necessary on a hypothesis, not as an end. 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 [15] 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 [20] exist; otherwise just as there, if the conclusion is not true, the principle will not be true, so here the end or that for the sake of which will not exist. For this too is itself a principle, but of the reasoning, not of the action. (In mathematics the principle is the principle 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 [25] 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 principles will not be true, if the angles of the triangle are not equal to two right angles. [30]
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 student of nature, 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 principle starts from the definition or essence: as [200b1] 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, so too if man is this, then these; if these, then those. Perhaps the necessary is present also in the definition. For if one defines [5] 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 stand as matter.
1 · Nature is a principle of motion and change, and it is the subject of our inquiry. We must therefore see that we understand what motion is; for if it were unknown, nature too would be unknown.
[15] When we have determined the nature of motion, our task will be to attack in the same way the terms which come next in order. 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 the account of the infinite is often used in definitions of the continuous; for what is infinitely divisible is [20] 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 everything and universal, 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.
[25] To begin then, as we said, with motion.
Some things are in fulfilment only, others in potentiality and in fulfilment—one being a ‘this’, another so much, another such and such, and similarly for the other categories of being. The term ‘relative’ is applied sometimes with reference to [30] excess and defect, sometimes to agent and patient, and generally to what can move and what can be moved. For what can cause movement is relative to what can be moved, and vice versa.
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 [201a1] is neither ‘this’ nor quantity nor quality 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, substance—the one is its form, the other privation; in quality, white and black; in [5] quantity, complete and incomplete. Similarly, in respect of locomotion, upwards and downwards or light and heavy. Hence there are as many types of motion or change as there are of being.
We have distinguished in respect of each class between what is in fulfilment [10] and what is potentially; thus the fulfilment of what is potentially, as such, is motion—e.g. the fulfilment of what is alterable, as alterable, is alteration; of what is increasable and its opposite, decreasable (there is no common name for both), increase and decrease; of what can come to be and pass away, coming to be and passing away; of what can be carried along, locomotion.
That this is what motion is, is clear from what follows: when what is buildable, [15] in so far as we call it such, is in fulfilment, it is being built, and that is building. Similarly with learning, doctoring, rolling, jumping, ripening, aging.
The same thing can be both potential and fulfilled, not indeed at the same time [20] or not in the same respect, but e.g. potentially hot and actually cold. Hence 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 acting and of being acted upon. Hence, too, what effects motion as a natural 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 [25] moved. But this question depends on another set of arguments, and the truth will be made clear later.20 It 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 fulfilled 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. [30] 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 be 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 [201b1] 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 colour and visible are different—and clearly it is the fulfilment of what is potential as potential that is [5] motion.
It is evident that this is motion, and that motion occurs just when the fulfilment itself occurs, and neither before nor after. For each thing is capable of being at one time actual, at another not. Take for instance the buildable: the actuality of the buildable as buildable is the process of building. For the actuality must be either [10] this or the house. But when there is a house, the buildable is no longer there. On the other hand, it is the buildable which is being built. Necessarily, then, the actuality is the process of building. But building is a kind of motion, and the same account will apply to the other kinds also. [15]
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 [20] we consider where some people put it: they identify motion with difference 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 [25] something indefinite, and the principles in the second column21 are indefinite because they are privative: none of them is either a ‘this’ or such or comes under any of the other categories. The reason why motion is thought to be indefinite is that is cannot be classed as a potentiality or as an actuality—a thing that is merely capable [30] of having a certain size is not necessarily 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 simple actuality, yet none of these seems [202a1] 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.
Every mover too is moved, as has been said—every mover, that is, which is capable of motion, and whose immobility is rest (for when a thing is subject to [5] 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 motion is the fulfilment of the movable as movable, the cause being contact with what can move, so that the mover is also acted on. The mover will always transmit a form, [10] either a ‘this’ or such or so much, which, when it moves, will be the principle and cause of the motion, e.g. the actual man begets man from what is potentially man.
3 · The solution of the difficulty is plain: motion is in the movable. It is the fulfilment of this potentiality by the action of that which has the power of causing [15] 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, [20] although their definitions are not one. So it is with the mover and the moved.
This view has a dialectical difficulty. Perhaps it is necessary that there should be an actuality of the agent and of the patient. The one is agency and the other patiency; and the outcome and end of the one is an action, that of the other a passion. Since [25] then they are both motions, we may ask: in what are they, if they are different? Either both are in what is acted on and moved, or 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 the latter case, the motion will be in the mover, for the same account will hold of mover and moved. Hence either every mover will be moved, or, though [30] having motion, it will not be moved.
If on the other hand 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 [35] alterations of quality in one subject towards one form? The thing is impossible: the actualization will be one.
But (someone will say) it is contrary to reason to suppose that there should be [202b1] 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. [5] 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 in something—it is not cut adrift from a subject, but is of one thing in another.
There is nothing to prevent two things having one and the same actualization (not the same in being, but related as the potential is to the actual). [10]
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 respect of the account which states their essence (as raiment and dress), but are the same 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 any way the [15] same that have all their attributes the same, but only those to be which is the same. 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 being here at a distance from there and being there at a distance from here 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 [20] motion; for the actualization of this in that and the actualization of that through the action of this 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 fulfilment of the alterable as alterable (or, more scientifically, the fulfilment of what can act and [25] what can be acted on, as such)—generally and again in each particular case, building, healing. A similar definition will apply to each of the other kinds of motion.
4 · The science of nature is concerned with magnitudes and motion and time, [30] and each of these is necessarily infinite or finite, even if some things are not, e.g. a quality or a point—it is not necessary perhaps that such things should be put under [35] either head. Hence it is incumbent on the person who treats of nature to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, what it is.
[203a1] The appropriateness to the science of this problem is clearly indicated; for 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.
Some, as the Pythagoreans and Plato, make the infinite a principle as a [5] substance in its own right, and not as an accident 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.
[10] 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 [15] 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, 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 [20] 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 seedmass of the atomic shapes according to the other.
Further, Anaxagoras held that any part is a mixture in the same way as the whole, on the ground of the observed fact that anything comes out of anything. For [25] 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 principle of separation, not only for each thing, but for all. Each thing that comes to be comes to be from a similar body, and there is a coming to be of all things, though not, it is true, at the same time. [30] Hence there must also be a principle of coming to be. One such source there is which he calls Mind, and Mind begins its work of thinking from some principle. 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 that no element arises from another element. [203b1] Nevertheless for him the common body is a principle 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 student of nature. Nor is it without reason that they all make it a principle. We cannot say that the infinite exists in vain, and the only power which we can ascribe to it is that [5] of a principle. For everything is either a principle or derived from a principle. But there cannot be a principle of the infinite, for that would be a limit of it. Further, as it is a principle, it is both uncreatable and indestructible. For there must be a point at which what has come to be reaches its end, 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 [10] 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. [15]
Belief in the existence of the infinite comes mainly from five considerations: From the nature of time—for it is infinite; From the division of magnitudes—for the mathematicians also use the infinite; again, if coming to be and passing away do not give out, it is only because that from which things come to be is infinite; again, [20] 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. 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 [25] outside the heaven are supposed to be infinite because they never give out in our thought.
If what is outside is infinite it seems 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 is. [30] 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 [204a1] whether there is a sensible magnitude which is infinite.
We must begin by distinguishing the various ways in which the term ‘infinite’ is used: in one way, it is applied to what is incapable of being gone through, because it is not its nature to be gone through (the way in which the voice is invisible); in another, to what admits of a traversal which cannot be completed, or which can only [5] be completed with difficulty, or what naturally admits of a traversal but does not have a traversal or limit.
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 in itself infinite, separable from sensible objects. If the infinite is neither a magnitude nor an aggregate, but is itself a substance and not an accident, it will be indivisible; for the [10] divisible must be either a magnitude or an aggregate. But if indivisible, then not infinite, except in the way in which the voice is invisible. But this is not the way in which it is used by those who say that the infinite exists, nor that in which we are investigating it, namely as that which cannot be gone through. But if the infinite is [15] accidental, it would not be, qua infinite, an element in things, any more than the invisible would be an element of speech, though the voice is invisible.
Further, how can the infinite be itself something, 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.
[20] 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 [25] 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 fulfilment; for it must be a definite quantity.
[30] Suppose then that infinity belongs accidentally. But, if so, it cannot, as we have said, be described as a principle, but rather that of which it is an accident—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 [204b1] infinite can be present in mathematical objects and things which are intelligible and do not have extension. Our inquiry is limited to our 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.
[5] 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.
[10] 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 can be either compound, or simple.
It will not be compound, 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 [15] 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 [20] the infinite body would be extended in all directions ad infinitum.
Nor can an 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. There are some people who make this the infinite, and not air or water, in [25] 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, [30] water, or anything else—but because there is 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.
Nor can fire or any other of the elements be infinite. For generally, and apart [205a1] from the question how any of them could be infinite, the universe, 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 [5] contrary to contrary, e.g. from hot to cold.)
In each case, we should consider along these lines whether it is or is not possible that it should be infinite. The following arguments give a general demonstration that it is not possible for there to be an infinite sensible body.
It is the nature of every kind of sensible body to be somewhere, and there is a [10] 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 that the infinite sensible body is homogeneous. Then each 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 the place of the body [15] 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 rest everywhere—then it will not be moved; or it will be moved everywhere—then it will not come to rest.
But if the universe has dissimilar parts, the proper places of the parts will be [20] dissimilar also, and the body of the universe will have no unity except that of contact. Then, further, the parts will be either finite or infinite in variety of kind.
Finite they cannot be; for if the universe 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 such an element would destroy what is contrary to it.
But if the parts are infinite in number and simple, their proper places too will [25] 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 [30] nature it is to be nowhere. 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.
[205b1] 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 [5] its own nature. But this is not true: a thing could be somewhere by compulsion, and not where it is its nature to be.
Thus however true it may 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. For it might be not moving because there is nowhere else for it to move, even though there [10] 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, 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 [15] to be infinite, it is at rest, not for this reason, 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.
It is clear at the same time that 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 [20] 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 [25] the doctrine that there is 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 [30] 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 convention, but also in the whole itself. But in the infinite body [206a1] 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 place is somewhere, and what is somewhere is in a 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 a place means that it is somewhere, and that is either up or down or in some [5] 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 [10] 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.
Now things are said to exist both potentially and in fulfilment. Further, a thing is infinite either by addition or by division. Now, as we have seen, magnitude is not [15] 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 we must not construe potential existence in the way we do when we say that it is possible for this to be a statue—this will be a statue, but something [20] infinite will not be in actuality. Being is spoken of in many ways, 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 [25] 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’ is spoken of in several ways, so that we must not regard the infinite as a ‘this’, such as a man or a horse, but must [30] 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, finite, yet always different.]22
But in spatial magnitudes, what is taken persists, while in the succession of [206b1] 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 just as we see division going on ad infinitum, so we see addition being [5] made in the same proportion 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), we shall not [10] 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 in fulfillment in the sense in which we say ‘it is [15] 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 ab extra. Yet the sum of the parts taken will not exceed every determinate magnitude, just as in the direction of division every [20] determinate magnitude is surpassed and there will always be a smaller part.
But in respect of addition there cannot even potentially be an infinite which exceeds every assignable magnitude, unless it is accidentally infinite in fulfillment, as the physicists hold to be true of the body which is outside the world, whose substance is air or something of the kind. But if there cannot be in this way a [25] sensible body which is infinite in fulfilment, 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 [30] 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 he makes numbers only up to the decad.
The infinite turns out to be the contrary of what it is said to be. It is not what [207a1] 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 infinite,23 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 [5] word. This condition alone is not sufficient: it is necessary also that the same part should never be taken twice. In the circle, the latter condition is not satisfied: it is true only that the next part is always different.
Thus something is infinite if, taking it quantity by quantity, we can always take something outside. 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 [10] whole man or box. What is true of each particular is true of the whole properly speaking—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 which has no end and the end is a limit.
[15] 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’.24 For to connect the infinite with the universe 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 universe in itself—from its having a certain similarity to the whole. It is in fact the matter of [20] the completeness which belongs to size, and what is potentially a whole, though not in fulfilment. 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 something else. 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 [25] 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 [30] 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 [207b1] reasonable too to suppose that in number there is a limit in the direction of the minimum, and that in the other direction every amount is always surpassed. In magnitude, on the contrary, every magnitude is surpassed in the direction of smallness, while in the other direction there is no infinite magnitude. The reason is [5] 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 derivative terms, and so with each of the other numbers. But in the direction of largeness it is [10] always possible to think of a large 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 definite amount. But this number is not separable, and its infinity does not persist but consists in a process of coming to be, like time and the number of time. [15]
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 actually be. Hence since no sensible magnitude is infinite, it is impossible to exceed every definite magnitude; for if it were possible there [20] 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 the posterior depends on the prior, e.g. 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. [25] 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 [30] untraversable. In point of fact they do not need the infinite and do not use it. They postulate only that a finite straight line may be produced as far as they wish. It is possible to have divided into 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 whether the infinite is found among existent magnitudes.
In the four-fold scheme of causes, it is plain that the infinite is a cause in the [208a1] 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.
[5] 8 · It remains to go through 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 true.
In order that coming to be should not fail, it is not necessary that there should [10] be a sensible body which is actually infinite. The passing away of one thing may be the coming to be of another, the universe being limited.
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 possible between any two things taken at random.
[15] To rely on 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.
[20] Time indeed and movement are infinite, and also thinking; but the parts that are taken do not persist.
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.
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 [30] somewhere (the non-existent is nowhere—where is the goat-stag or the sphinx?), and because motion in its most general and proper 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 different 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 [208b1] replacement. Where water now is, there in turn, when the water has gone out as from a vessel, air is present; and at another time another body occupies this same place. The place is thought to be different from all the bodies which come to be in it [5] 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 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 [10] 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) hold only in relation to us. To us they are not always the same but change with the [15] direction in which we are turned: that is why the same thing is often 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 [20] weight and what is made of earth are carried—the implication being that these places do not differ merely in position, but also as possessing distinct powers. This is made plain also by the objects studied by mathematics. Though they have no place, they nevertheless, in respect of their position relatively to us, have a right and left as these are spoken of merely in respect of relative position, not having by nature these various characteristics. Again, the theory that the void exists involves the existence [25] 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 broadbreasted earth,25 [30]
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 power of place must be a marvellous thing, and be prior to all other things. For that without which nothing else can exist, while it can exist without the others, must needs be first; for [209a1] 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 what it is presents difficulty—whether it is some sort of ‘bulk’ of body or some entity other than that; for we must first determine its genus.
[5] Now it has three dimensions, length, breadth, depth, the dimensions by which all body is bounded. But the place cannot be body; for if it were there would be two bodies in the same place.
Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same argument will apply to them: where the bounding planes [10] 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.
What in the world, then, are we to suppose place to be? If it has the sort of [15] 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.
[20] 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 cause 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.
Further, too, if it is itself an existent, it will be somewhere. Zeno’s difficulty demands an explanation; for if everything that exists has a place, place too will have [25] a place, and so on ad infinitum.
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 [30] place—not only as to what it is, but even whether there is such a thing.
2 · Something can be said of a subject either in virtue of itself or in virtue of something else; and there is place which is common and in which all bodies are, and which is the proper and primary location of each body. I mean, for instance, that you are now in the world because you are in the air and it is in the world; 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.
[209b1] 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 which the magnitude or the matter of the magnitude is defined; for this is the limit of each body.
[5] 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; for when the [10] 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, [15] 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 [20] 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 [25] 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; and in so far as [30] it contains it, 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 has written in the [210a1] 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 [5] 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 [10] resulting body is not in the same place. What sort of destruction then is that?
This concludes my statement of the reasons why place must be something, and again of the difficulties that may be raised about is essential nature.
3 · The next step we must take is to see in how many ways one thing is said to be in another. In one way, as a finger is in a hand, and generally a part in a whole. In [15] another way, as a whole is in its parts; for there is no whole over and above the parts. Again, as man is in animal, and in general a species in a genus. Again, as the genus is in the species, and in general a part of the species in its definition. Again, as [20] health is in the hot and the cold, and in general the form in the matter. Again, as the affairs of Greece are in the King, and generally events are in their primary motive agent. Again, as a thing is in its good, and generally in its end, i.e. in that for the sake of which. And most properly of all, as something is in a vessel, and generally in a place.26
[25] 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 [30] is said to be white because the visible surface of him is white, or to be scientific because his thinking faculty is. 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 [210b1] 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, [5] as white is in man because it is in body, and in body because it resides in the visible surface. But it is not in surface in virtue of something else. And these things—the surface and the white—differ in form, and each has a different nature and power.
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 [10] 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 [15] 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 what they are 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 accidentally; for two things would be at the same time in the same thing. The jar would be in itself—if a thing [20] 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 [25] else—not indeed in that as in a place, but as health is in the hot as a state 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 something primarily is different from what is contained), place could not be either the matter or the form of the thing contained, but must be different—for the latter, [30] 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 first that place is what contains that of which it is the place, and is no part of the thing; again, that the primary place of a [211a1] thing is neither less nor greater than the thing; again, that place can be left behind by the thing and is separable; and in addition that 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. [5] Having laid these foundations, we must complete the theory. We ought to try to conduct our inquiry into what place is in such a way as not only to solve the difficulties connected with it, but also to show that the attributes supposed to belong to it do really belong to it, and further to make clear the cause of the trouble and of [10] the difficulties about it. In that way, each point will be proved in the most satisfactory manner.
First then we must understand that place would not have been inquired into, if there had not been motion 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 motion there are two species—locomotion on the one hand and, on the other, increase and diminution. For these too involve change: what was then in this place [15] has now in turn changed to what is larger or smaller.
Again, things are moved either in themselves, actually, or accidentally. In the latter case it may be either 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 something which is not in [20] itself capable of being moved, but is always moved accidentally, 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 [25] every part of the air, but that it is in the air because of the 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 [30] a part in a whole. But when the thing is separate and in contact, it is primarily 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 [35] 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 [211b1] 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.]27
It will now be plain from these considerations what place is. There are just four [5] things of which place must be one—the shape, or the matter, or some sort of extension between the extremities, or the extremities (if there is no extension over and above the bulk of the body which comes to be in it).
[10] Three of these it obviously cannot be. 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 the same thing: the form is the boundary of the thing, the place is the boundary of the body which contains it.
The extension between the extremities is thought to be something, because [15] 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 [20] 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 [25] 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 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.
[30] The matter, too, might seem to be place, at least if we consider it in what is at rest and is not 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 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 is now [212a1] 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 [5] 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 [10] displacement of the body that is moved takes place in a stationary container, for its 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 [15] which is moved, is moved and changes, 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 the place of a thing is the innermost motionless boundary of what [20] contains it.
This explains why the middle of the world 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 [25] 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 extremity, and the extremity itself, are up.
For this reason 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 [30] 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 will be moved (for one part is contained in another), while 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 [212b1] the place of its parts. And some parts 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 [5] potentially in place: when the parts are separated, but in contact, like a heap, they are actually in place.
Again, 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 world, as has been said, is not anywhere as a whole, nor in any place, if, that is, no body contains it. But the line on which it is moved provides a place for its parts; for [10] each is contiguous to the next.
Other things are in place accidentally, as the soul and the world. The latter is, in a way, in place, for all its parts are; for on the circle one part contains another. That is why the upper part is moved in a circle, while the universe is not anywhere. For what is somewhere is itself something, and there must be alongside it some [15] other thing wherein it is and which contains it. But alongside the universe or the Whole there is nothing outside the universe, and for this reason all things are in the world; for the world, we may say, is the universe. Yet their place is not the same as the world. It is part of it, the innermost part of it, which is in contact with the [20] 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 the world, but we cannot go on and say that the world 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.
There is no necessity that the place should grow with the body in it, nor that a [25] point should have a place; nor that two bodies should be in the same place; 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, place is indeed 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.
[30] Also, 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 is it without reason that each should remain naturally in its proper place. For parts do, and that which is in a place has the same relation to its place as a [213a1] 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 [5] it was necessary to refer to them: what has now been stated obscurely will then be made more clear.28 If the matter and the fulfilment are the same thing (for water is both, the one potentially, the other in fulfilment), 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.
[10] 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 [15] 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 were the same thing, though the essence of the three is different.
[20] 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 common opinions 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 show [25] 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 by void an interval in which there is no sensible body. They hold that everything which is 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 [30] 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 [213b1] 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.
They argue, for one thing, that change in place (i.e. locomotion and increase) would not occur. For it is maintained that motion would seem not to exist, if there [5] 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 small things make a large thing: [10] thus if many equal bodies can be in the same place, so also can many unequal bodies.
Melissus, indeed, actually argues from this that the universe 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. [15] They also reason from the fact that some things are observed to contract and be compressed, as people say that a cask will hold the wine along with the skins, which implies that the compressed body contracts into the voids present in it.
Again increase, too, is thought by everyone to take place by means of void; for nutriment is body, and it is impossible for two bodies to be together. Evidence of this [20] they find also in what happens to ashes, which absorb as much water as the empty vessel.
The Pythagoreans, too, held that void exists and that it enters the world from the infinite air, the world inhaling also the void which distinguishes the natures of [25] things, as if it were 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 [30] meaning of the word.
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 is nothing.
[214a1] Every body, again, they suppose to be tangible; and of this nature is whatever has weight or lightness. Hence, by deduction, what has nothing heavy or light in it, is void.
This result, then, as I have just said, is reached by deduction. It would be [5] 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 [10] 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 not ‘this’ or corporeal substance. So some say that the void is the matter of the body (they identify the place, too, with [15] 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 it does not, it is plain that on this showing void does not exist, either unseparated or separated; for the [20] 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 a cause of movement [25] 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 escaped Melissus; viz. that the full can suffer qualitative change.
But not even movement in respect of place involves a void; for bodies may [30] 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 [214b1] 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 the water [5] 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 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 [10] 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 the void [15] cannot be a cause of locomotion. What, then, will the void be a cause of? It is thought to be a cause of movement in respect of place, and it is not a cause 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, [20] into which things are carried; viz. how will what is placed in it move, or rest? 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 result does not take place when a body is placed as a whole in a place conceived of as [25] 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 studies the matter, is the [30] opposite, that not a single thing can be moved if there is a void; for as with those who say the earth is at rest because of the uniformity, 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 [215a1] 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 [5] 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); but [10] 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 [15] 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; [20] 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 gets 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. [25] 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 [30] it is at rest; and especially a medium that is not easily divided, i.e. a medium that is somewhat dense.
[215b1] A, then, will move through B in time C, and through D, which is thinner, in time E (if the length of B is equal to D), in proportion to the density of the hindering [5] 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 C will be [10] 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 nought to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still [15] 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 and that which is exceeded, so that 4 will be what it exceeds 0 by and 0. For this reason, too, a line does not exceed a [20] 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 thinnest 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 F be void, equal to B and to D. Then if A is to traverse and move through it in a [25] certain time, G, a time less than E, however, the void will bear this ratio to the full. But in a time equal to G, A will traverse the part H of D. And it will surely also traverse in that time any substance F which exceeds air in thinness in the ratio [30] which the time E bears to the time G. For if the body F be as much thinner than D as E exceeds G, A, if it moves through F, will traverse it in a time inverse to the [216a1] speed of the movement, i.e. in a time equal to G. If, then, there is no body in F, A will traverse F still more quickly. But we suppose that its traverse of F when F was void occupied the time G. So that it will traverse F in an equal time whether F be full or void. But this is impossible. It is plain, then, that if there is a time in which it [5] 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. [10]
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 [15] 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 [20] 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 must exist, separated by itself; but this is the same as to say that place is separate; and [25] this has already been stated to be impossible.
But even if we consider it on its own merits the so-called void 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, it must, if it is not [30] 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 [216b1] 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 [5] bulk 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 [10] 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 bulk of each, if their bulk be conceived of as free from attributes? It contributes nothing to [15] 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.]29
[20] 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 [25] 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.
[30] 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 cause of all movement, but only [217a1] 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 cause 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 [5] 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 [10] 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 no 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 [15] more air is produced from 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 [20] 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 is actually is produced from what is potentially, and that matter is not separable from the contraries but its being is different, and that a single matter may serve for colour [25] 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 [30] smallness. Similarly, therefore, if air which is large in extent comes to have a smaller bulk, 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; [217b1] 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 [5] 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 bulk 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 [10] 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 had 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.]30 [15] 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 [20] separate (either absolutely separate or as a separate element in the rare) or potentially, unless one is willing to call the cause 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 [25] 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 [30] 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 [218a1] following considerations would make one suspect that it either does not exist at all or barely, and in the 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 [5] some of its parts must exist. But of time some parts have been, while others are going to be, and no part of it is, though it is divisible. For the ‘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 [10] remain one and the same or is it always other and other? It is hard to say.
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 [15] 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 a point to a point. If then it did not cease [20] 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 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 [25] 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.
[30] 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 the movement of the whole, others that it is the sphere [218b1] itself.
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 [5] would be many times at the same time.
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.
[10] But as time is most usually supposed to be motion and a kind of change, we must consider this view.
Now the change or movement of each thing is only in the thing which changes or where the thing itself which moves or change may chance to be. But time is present equally everywhere and with all things.
Again, change is always faster or slower, whereas time is not; for fast and slow [15] 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.) [20]
11 · But neither does time exist without change; for when the state of our minds does not change at all, or we have not noticed its changing, we do not think 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 [25] 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 mind seems to stay in one indivisible [30] 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 [219a1] 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 [5] we at once suppose that some time has indeed 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 [10] is continuous. Therefore the movement goes with the magnitude. Because the magnitude is continuous, the movement too is continuous, and if the movement, then the time; for the time that has passed is always thought to be as great as the movement.
The distinction of before and after holds primarily, then, in place; and there in [15] 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 identical in substratum with motion yet [20] differs from it in being, 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 one thing is [25] different from another, 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.
[30] When, therefore, we perceive the ‘now’ as one, and neither as before and after in a motion nor as the same element 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 [219b1] 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. An indication of this: we discriminate the more or the less by number, [5] but more or less movement by time. Time then is a kind of number. (Number, we must note, is used in two ways—both of what is counted or countable and also of that with which we count. Time, then, is what is counted, not that with which we count: these are different kinds of thing.)
[10] Just as motion is a perpetual succession, so also is time. But every simultaneous time is the same; for the ‘now’ is the same in substratum—though its being is different—and the ‘now’ determines 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 now was supposed to [15] mean), but its substratum is the same; 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 is different in definition—as [20] 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 [25] before and after in 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 its being is different; for it is in so far as the before and after is that we get the ‘now’. This is what is most knowable; for motion is [30] known because of that which is moved, locomotion because of that which is carried. For what is carried is a ‘this’, the movement is not. Thus the ‘now’ in one sense is always the same, in another it is not the same; for this is true also of what is carried.
[220a1] 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.
[5] 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 substratum (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 [10] 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 [15] 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 [20] 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 being 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 [25] after, and is continuous since it is an attribute of what is continuous.
The smallest number, in the strict sense, 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 [30] 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 [220b1] 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 count is fast or slow. [5]
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 [10] number of a hundred horses and a hundred men is the same, but the things numbered are different—the horses for 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 [15] 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; fo we measure the movement by the time and vice versa. It is reasonable that the [25] 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 then because of the movement. And we measure both the distance by the movement an [30] 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 [221a1] by determining a motion which will measure 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 [5] 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, [10] that their being should be measured by time. To be in time is one of two things: to exist when time exists, and 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, [15] 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 number are contained by number and things in place by place.
Plainly, too, to be in time does not mean to coexist with time, any more than to [20] be in motion or in place means to coexist with motion or place. For if ‘to be in something’ is to mean this, then all things will be in anything, and the world will be in a grain; for when the grain is, then also is the world. But this is accidental, whereas the other is necessarily involved: that which is in time necessarily involves [25] 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.
[30] 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 people forget owing to the lapse of time, but we do not say the same of getting to know or of [221b1] 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 by time, nor is their being measured by time. An indication of this is [5] that none of them is affected by time, which shows that they are not in time.
Since time is the measure of motion, it will be the measure of rest too. 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 [10] what is at rest 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 [15] 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 measured 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 [20] 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’s being commensurate with the side.
Generally, if time is the measure of motion in itself and of other things [25] accidentally, it is clear that a thing whose being is measured by it will have its being 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 [30] being and beyond the time which measures their being. 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, [222a1] 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 non-existents whose opposites always are, as the incommensurability of the diagonal always is—and this [5] 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 [10] 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 [15] 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 [20] 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 of something is near. 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.
[25] ‘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.
[30] Will time then fail? Surely not, if motion always exists. Is time then always different or does the same time recur? Clearly, it is the same with time as with motion. 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 [222b1] 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 [5] 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.
‘Just now’ refers to the part of future time which is near the indivisible present [10] ‘now’ (When are you walking?—Just now; 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 are you walking?—I have been walking just now). But to say that Troy has just now 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.
[15] ‘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, a cause of destruction [20] rather than of coming into being (for change, in itself, makes things depart from their former condition), and only accidentally 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. [25] Still, time does not work even this change; but this sort of change too happens to occur in time.
We have stated, then, that time exists and what it is, and in how many ways we speak of the ‘now’, and what ‘at some time’, ‘lately’, ‘just now’, ‘long ago’, and ‘suddenly’ mean.
14 · These distinctions having been drawn, it is evident that every change [30] 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 [223a1] 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’ [5] 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’ [10] 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. [15]
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. It is because it is an attribute, or state, of 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 [20] 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 either, 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 [25] reason, is qualified to count, it is impossible for there to be time unless there is soul, but only that of which time is an attribute, i.e. if movement can exist without soul. The before and after are attributes of movement, and time is these qua countable.
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 [30] away, and grow, and are altered, 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 [223b1] 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. [5] 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 it is both equal and [10] 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 counted by some one thing homogeneous with [15] 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 [20] 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.
[25] 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 [30] though to be a circle. And this opinion again is held because time is a 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 [224a1] nothing else is observed in what is measured; 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 [5] 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 [10] same division of it. For a figure of one kind is a circle and a figure of another kind a triangle, and a triangle of one kind is equilateral and a triangle of another kind scalene. They are the same figure, then, and that is a 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 [15] 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.
1 · Everything which changes does so in one of three ways. It may accidentally, as for instance when we say that something musical walks, that which walks being something in which aptitude for music is an accident. Again, a thing is said without qualification to change because something belonging to it changes, i.e. in statements which refer to part of the thing in question: thus the body is restored to [25] health because the eye or the chest, that is to say a part of the whole body, is restored to health. And there is the case of a thing which is in motion neither accidentally nor in respect of something else belonging to it, but in virtue of being itself directly in motion. Here we have a thing which is essentially movable: and that which is so is a different thing according to the particular variety of motion: for instance it may be a thing capable of alteration—and within the sphere of alteration it is again a different thing according as it is capable of being restored to health or [30] capable of being heated. And there are the same distinctions in the case of the mover: one thing causes motion accidentally, another partially (because something belonging to it causes motion), another of itself directly, as, for instance, the physician heals, the hand strikes. We have, then, the following factors: that which directly causes motion, and that which is in motion; further, that in which motion takes place, namely time, and (distinct from these three) that from which and that to which it proceeds (for every motion proceeds from something and to something, [224b1] that which is directly in motion being distinct from that to which it is in motion and that from which it is in motion: for instance, wood, hot, and cold—the first is that which is in motion, the second is that to which the motion proceeds, and the third is that from which it proceeds). This being so, it is clear that the motion is in the wood, not in its form; for the motion is neither caused nor experienced by the form or the [5] place or the quantity. So we are left with a mover, a moved, and that to which the motion proceeds; for it is that to which rather than that from which the motion proceeds that gives its name to the change. Thus perishing is change to not-being, thought it is also true that that which perishes changes from being; and becoming is change to being, though it is also change from not-being. [10]
Now a definition of motion has been given above. Every goal of motion, whether it be a form, an affection, or a place, is immovable, as, for instance, knowledge and heat. Here, however, a difficulty may be raised. Affections, it may be said, are motions, and whiteness is an affection: thus there may be change to a motion. To this we may reply that it is not whiteness but whitening that is a motion. [15] Here also things may hold accidentally, or partially and with reference to something other than itself, or directly and with no reference to anything else: for instance, a thing which is becoming white changes accidentally to an object of thought, the colour being only accidentally the object of thought; it changes to colour, because white is a part of colour (or to Europe, because Athens is a part of [20] Europe); but it changes essentially to white colour. It is now clear in what way a thing is in motion essentially or accidentally, and in respect of something other than itself or itself directly moving—in the case both of the mover and of the moved; and it is also clear that the motion is not in the form but in that which is in motion, that is [25] to say the movable in actuality. Now accidental change we may leave out of account; for it is to be found in everything, at any time, and in any subject. Change which is not accidental on the other hand is not to be found in everything, but only in contraries, in things intermediate between contraries, and in contradictories, as may be shown by induction. An intermediate may be a starting-point of change, [30] since it serves as contrary to either of two contraries; for the intermediate is in a sense the extremes. Hence we speak of the intermediate as in a sense a contrary relatively to the extremes and of either extreme as a contrary relatively to the intermediate: for instance, the central note is low relatively to the highest and high relatively to the lowest, and grey is white relatively to black and black relatively to white.
[225a1] And since every change is from something to something—as the word itself indicates, implying something ‘after’ something else, that is to say something earlier and something later31—that which changes must change in one of four ways: from [5] subject to subject, from subject to non-subject, from non-subject to subject, or from non-subject to non-subject, where by ‘subject’ I mean what is affirmatively expressed. So it follows necessarily from what has been said that there are three kinds of change, that from subject to subject, that from subject to non-subject, and [10] that from non-subject to subject; for that from non-subject to non-subject is not change, as in that case there is no opposition either of contraries or of contradictories.
Now change from non-subject to subject, the relation being that of contradiction, is coming to be—unqualified coming to be when the change takes place in an unqualified way, particular coming to be when the change is change in a [15] particular character: for instance, a change from not-white to white is a coming to be of the particular thing, white, while change from unqualified not-being to being is coming to be in an unqualified way, in respect of which we say that a thing comes to be without qualification, not that it comes to be some particular thing. Change from subject to non-subject is perishing—unqualified perishing when the change is from being to not-being, particular perishing when the change is to the opposite negation, the distinction being the same as that made in the case of coming to be.
[20] Now things are said not to be in several ways; and there can be motion neither of that which is not in respect of the affirmation or negation of a predicate, nor of that which is not in the sense that it only potentially is, that is to say the opposite of that which actually is in an unqualified sense; for although that which is not white or not good may nevertheless be in motion accidentally (for example that which is [25] not white might be a man), yet that which is without qualification not a ‘this’ cannot in any sense be in motion: therefore it is impossible for that which is not to be in motion. This being so, it follows that becoming cannot be a motion; for it is that which is not that becomes. For however true it may be that it accidentally becomes, it is nevertheless correct to say that it is that which is not that in an unqualified sense becomes. And similarly it is impossible for that which is not to be at rest.
[30] There are these difficulties, then, [in the way of the assumption that that which is not can be in motion],32 and it may be further objected that, whereas everything which is in motion is in place, that which is not is not in place; for then it would be somewhere.