by Aristotle
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 w
hich 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.