Lecture 3 — Mutual transformation of the elements; presence above of the heavenly body

Let us first recall our original principles and the distinctions already drawn and then explain the 'milky way' and comets and the other phenomena akin to these.

Fire, air, water, earth, we assert, originate from one another, and each of them exists potentially in each, as all things do that can be resolved into a common and ultimate substrate.

The first difficulty is raised by what is called the air. What are we to take its nature to be in the world surrounding the earth? And what is its position relatively to the other physical elements.

(For there is no question as to the relation of the bulk of the earth to the size of the bodies which exist around it, since astronomical demonstrations have by this time proved to us that it is actually far smaller than some individual stars.

As for the water, it is not observed to exist collectively and separately, nor can it do so apart from that volume of it which has its seat about the earth: the sea, that is, and rivers, which we can see, and any subterranean water that may be hidden from our observation.)

The question is really about that which lies between the earth and the nearest stars. Are we to consider it to be one kind of body or more than one? And if more than one, how many are there and what are the bounds of their regions?

We have already described and characterized the first element, and explained that the whole world of the upper motions is full of that body. This is an opinion we are not alone in holding: it appears to be an old assumption and one which men have held in the past, for the word ether has long been used to denote that element. Anaxagoras, it is true, seems to me to think that the word means the same as fire. For he thought that the upper regions were full of fire, and that men referred to those regions when they spoke of ether. In the latter point he was right, for men seem to have assumed that a body that was eternally in motion was also divine in nature; and, as such a body was different from any of the terrestrial elements, they determined to call it 'ether'. For the same opinions appear in cycles among men not once nor twice, but infinitely often.

Now there are some who maintain that not only the bodies in motion but that which contains them is pure fire, and the interval between the earth and the stars air: but if they had considered what is now satisfactorily established by mathematics, they might have given up this puerile opinion. For it is altogether childish to suppose that the moving bodies are all of them of a small size, because they so to us, looking at them from the earth. This a matter which we have already discussed in our treatment of the upper region, but we may return to the point now. If the intervals were full of fire and the bodies consisted of fire every one of the other elements would long ago have vanished.

However, they cannot simply be said to be full of air either;

for even if there were two elements to fill the space between the earth and the heavens, the air would far exceed the quantity required to maintain its proper proportion to the other elements. For the bulk of the earth (which includes the whole volume of water) is infinitesimal in comparison with the whole world that surrounds it. Now we find that the excess in volume is not proportionately great where water dissolves into air or air into fire. Whereas the proportion between any given small quantity of water and the air that is generated from it ought to hold good between the total amount of air and the total amount of water.

Nor does it make any difference if any one denies that the elements originate from one another, but asserts that they are equal in power. For on this view it is certain amounts of each that are equal in power, just as would be the case if they actually originated from one another.

So it is clear that neither air nor fire alone fills the intermediate space.

15. Having identified which are the active principles and which the material principles of the passions which he intends to treat, he now begins to determine concerning them. And this is divided into two parts:

in the first he determines concerning the particular transmutations of the elements, whereby they are transmuted according to themselves;

second, he determines about their transmutations accordingly as they enter into composition to form a mixture, in Book IV.

The first part is divided into two parts:

in the first he determines concerning the transmutations or passions of the elements which occur on high;

in the second, about those which occur below, and this in Book II.

The first part is divided into three parts:

in the first he declares what his intention is;

in the second he states certain preliminaries necessary for determining what is to follow, at fire, air, water, earth, we assert (339a36);

in the third he begins to determine concerning his main proposition, at having determined these principles (341b1).

He says therefore first that we must speak of the image of the milk (339a33), i.e., of the appearance of the milky circle, and of comets and of all other like things which are syngeneous, i.e., generable along with them; but in doing so we shall [first] recall the positions laid down by us in the earlier books and the determinations already determined therein, so that we may, when necessary, use them to manifest the proposition.

16. Then when he says, fire, air, water, earth, we assert (339a36), he sets forth certain things needed for what is to follow. About this he does two things:

first, he premises something pertaining to the mutual transmutation of the elements;

second, he speaks of the arrangement of the elements in the world, with special emphasis on air, at the first difficulty is raised (339b2).

He says therefore first that fire and air and water and earth are produced from one another (even though Empedocles thought the contrary). And he restates this as proved in On Generation II. The reason for this which he assigns is that each element exists potentially in another, and that things so related can be generated one from the other. He assigns a further reason, which is that they all have the same common first matter which underlies each of them and into which, as into an ultimate, they are all resolved: for all things whose matter is one and common to all are so related that any one is potentially in any other—as, for example, a knife is potentially in a nail, and a nail potentially in a knife, because they have a common matter, iron.

17. Then when he says, the first difficulty is raised (339b2) he inquires into the order of the elements and into the case of air in particular. About this he does three things.

First he raises the question and says that our first problem is about the body called "air," as to what nature it has in the world surrounding the earth: i.e., is the whole air, and, if not, how it is related to the other elements?

second at for there is no question as to the relation of the bulk (339b6), he proposes certain evident facts about the order of the elements.

The first fact concerns the earth, and it is that we are not entirely ignorant of the size of the earth in comparison to the surrounding magnitudes, namely, those of the heavenly bodies and of the other elements. For it is already plain from the considerations of astronomers that the earth is much smaller than certain stars, and that it is but the size of a point in comparison to the outermost sphere.

The second fact he proposes is about water, at as for the water (339b9). And he says that we do not observe water to exist by itself and isolated from the body located about the earth, namely, from the sea and rivers, which we see, and from the bodies of water which some have asserted to exist hidden from us in the bowels of the earth. For it does not occur to water to be gathered together in this way—since the moistness which is water is contained by some alien terminus.

18. He further at the question is really about that which lies between the earth (339b13), pursues the question he raised earlier, namely, as to what is the middle between the aforesaid [i.e., the earth and the farthest stars]. About this he does two things:

first, he shows that it is not the case that the entire space from the highest stars to the earth is filled with some one body such as fire or air or both, but that above there is an additional body besides these;

second, he shows how the other bodies are related to that highest body with respect to position, at it remains to explain (340a19).

Regarding the first he proceeds thus.

First he says that there is a problem whether between earth and the farthest stars, which are called "non-wandering" and "fixed," we should posit, according to what is proper to nature, one body or more than one; and if more than one, how many, and where are the boundaries of their regions?

19. second at we have already described (339b16), he repeats something already determined in On the Heavens: this is the condition, as far as its power is concerned, of the first element, namely, the celestial body; and that that entire world which is about the upper motions, i.e., which is moved with a circular motion, is filled with that body—for all the heavenly bodies pertain to the nature of that first element. And since the philosophers supposed the contrary, he therefore, lest his opinion appear novel, adds that not only did he have this opinion, but it was also an ancient opinion of earlier men. For the body which is called aether, and which we call the "heaven," has an ancient name.

But Anaxagoras seems to have supposed that it means the same as "fire"—for he took the word "aether" not to mean always running, i.e., to be in continuous motion, but he derives it from aethein, which is "to burn," because he believed the superior bodies to be filled with fire. And although in this he spoke ill, nevertheless he was right in supposing the name "aether" to befit a corporeal potency over and above those bodies. For all the ancients are seen to have believed, and decided, that the name "aether" should be given to the body which always runs, i.e., is always in motion, and which is a certain divine, i.e., perpetual, something according to its nature. This they did as if that body were like no body that exists around us.

Nor should it seem strange if this opinion, which we appeared to have adopted for the first time, was already held by the ancients. For we hold that the same opinions re-appear among men after dying out through neglect of study, not twice or thrice only, but an infinitude of times. Now he says this in keeping with his opinion that the world and human generation have been going on from eternity, as indicated in previous books. This being supposed, it is also plain that certain opinions and arts have begun from certain definite times; and thus it is necessary to say that these were in turn frequently, nay, an infinitude of times, destroyed by wars or other corrupting factors and again rediscovered.

20. third at now there are some (339b30), he shows that the circularly moved body is not any of the lower bodies. About this he does three things:

first, he shows this with respect to fire;

second, with respect to air, at however, they cannot simply be said (340a3);

third, with respect to both, at for even if there were two (340a3).

With respect to the first it should be kept in mind that some have thought only the "carried" [moved] heavenly bodies, i.e., the sun, moon and stars, to have a fiery nature, and whatever exists between them to be of the nature of air; some on the other hand supposed the entire system to be of the nature of fire, as Anaxagoras said. He says therefore that those who posited not only the moving bodies to be pure fire, but also the whole that surrounds them (i.e., all the spheres), and that which intervenes between earth and the stars to be air, i.e., from the earth to the moon's orb, and that whatever is above is all of it fire—whoever, I say, claim this, would, were they to consider the facts which have now been sufficiently proved by the mathematicians concerning the sizes of bodies, probably give up this childish opinion. Only a simple and unschooled person would believe that the stars are small in size just because they appear small to us looking at them from afar.

This matter has been already discussed in the previous reasonings, i.e., in On the Heavens II; but we shall once more destroy the aforesaid position with the same argument. For, since the bodies of the stars and spheres are immeasurably greater than the size of the earth and of the things near the earth, then, if not only the bodies of the stars were of fire, but all the area between them were full of fire, every one of the elements would have long since been annihilated by virtue of the preponderance of fire over it.

Then he shows the same with regard to air, saying that it is not possible for those distances to be full of air. For it is clear that the quantity of air would still exceed the equality of analogy—that is proportion—which should be common among the elements, so that the elements may be preserved.

21. Then when he says, for even if there were two (340a3), he shows the same thing with respect to both. About this he does two things:

first, he gives the reason;

second, he excludes a certain cavilling objection, at nor does it make any difference (340a13).

He says therefore first that the due proportion among the elements is not kept, if the entire space between the earth and the outermost heaven is full of two elements (340a3), namely, fire and air. For the bulk of the earth, in which the whole quantity of water is also contained, is as no part at all compared to the total size of the bodies surrounding it, since, according to astronomers, even if compared only to the outermost sphere, it is as a mere point. But we see that when, as a result of separation or rarefaction, air comes to be from water, or fire from air, there is not such an immense excess in size. Now it is necessary, if the due proportion prevailing among the elements is to be preserved, that this small quantity of water maintain the same reason, i.e., proportion, to the air made from it, as is maintained between the whole of water and the whole of air. In other words, the extent to which the quantity of air exceeds the quantity of water from which it is made must be proportional to the extent that all the air in the world exceeds all the water in the world.

22. Then when he says, nor does it make any difference (340a13), he refutes a certain cavilling objection and says that it is nothing against our position if someone should maintain, according to the opinion of Empedocles, that the elements are not generated from one another. For it is necessary, according to his opinion, that the elements be proportionally equal in power. Consequently, proportionate equality of power must be kept in the sizes of the elements if they are not generated one from the other, just as if they are.

23. Then he summarizes what has been said, and concludes that it is plain from the foregoing that neither does air fill the intermediate place between the earth and the highest stars, nor does fire; but, in addition to these two elements, there must be above them a heavenly body which is none of the lower elements.