Lecture 14 — There is no void within bodies

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 go in and harden.

But, if this were not to take place, either there would be no motion at all or the universe would bulge, as Xuthus said, or air and water must always change into equal amounts (for instance, if air has been made out of a cupful of water, at the same time, out of an equal amount of air, a cupful of water must have been made), or void must necessarily exist.

For compression and expansion cannot take place otherwise.

Now, if they mean by “the rare” that which has many voids existing separately, it is plain that, if void cannot exist separately 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. But, first, the void turns out not to be a cause of all motion, but only of motion upward, for the rare is light, which is the reason they say fire is rare.

Second, the void turns out to be a cause of motion not as that in which it takes place, but as what carries things up, just as skins, by being carried up themselves, carry up what is continuous with them. Yet how can void have a local motion or a place? For thus, that into which void moves is till then void of a void.

Again, how will they explain, in the case of what is heavy as to its motion downward?

And it is plain that, if a thing will move upward more quickly the rarer and more void it is, then, if it were completely void, it would move with a maximum speed. But perhaps it is impossible that it should even move at all; the same reason that showed that, in the void, all things are incapable of moving shows that the void cannot move, which is the fact that the speeds are incomparable.

Since we deny that a void exists, but as for the rest, there are real doubts—either there will be no motion, if there is not to be condensation and rarefaction, or there will be a bulging of the heavens, or a transformation of water into air will always be balanced by an equal transformation of air into water (for it is clear that the air produced from water is bulkier than the water)—

it is necessary, therefore, if compression does not exist, either that the next portion will be pushed outward and make the outermost part bulge, or that there must be an equal amount of water produced somewhere else out of air, such that the entire bulk of the whole may be equal, or it follows that nothing is moved.

For when anything is displaced, this will always happen, unless it comes round in a circle; but locomotion is not always circular, but sometimes in a straight line. These, then, are the reasons for which they might say that there is a void.

Our statement is based on the assumption that (1) there is a single matter for contraries—hot and cold and the other natural contrarieties—and that (2) what exists actually is produced from a potential existent, and that (3) matter is not separable from the contraries, but its being is different, and that (4) a single matter may serve for color 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 not become something different by acquiring an addition to it, but has become actually what it was potentially; again, water is produced from air in the same way, the change being sometimes from smallness to greatness and sometimes from greatness to smallness.

Similarly, therefore, if air that is large in extent comes to have a smaller volume, or if air becomes greater from being smaller, it is the matter that is potentially both that comes to be each of the two.

For as the same matter becomes hot from being cold and cold from being hot because it was potentially both, so too, from hot, it can become more hot, though nothing in the matter has become hot that was not hot when the thing was less hot—just as if the ambit 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 difference of degree do not depend on an intermission of the quality); nor can we get any portion of a flame in which both heat and whiteness are not present.

So too, then, is the earlier heat related to the later. Thus, the greatness and smallness also of the sensible volume are extended not by the matter’s acquiring anything new, but because the matter is potentially matter for both states; in this way, the same thing is dense and rare and the two qualities have one matter.

The dense is heavy, and the rare is light. Again, just as the arc of a circle does not acquire a new part that is convex when it is contracted into a smaller space, but rather what was there has been contracted, and just as any part of fire that one takes will be hot, so too, it is all a question of conduction and expansion of the same matter.

There are two types in each case, both in the dense and in the rare, for both the heavy and the hard are thought to be dense and, contrariwise, both the light and the soft are rare; and weight and hardness fail to coincide in the case of lead and iron.

From what has been said, it is evident, then, that void does not exist either separate (either absolutely separate or as a separate element in the rare) or potentially, unless one is willing to call the cause of motion void, whatever it may be.

At that rate, the matter of the heavy and the light, qua matter, would be the void, for the dense and the rare are productive of locomotion in virtue of this contrariety, and in virtue of their hardness and softness, productive of passivity and impassivity—that is, 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.

544. Having shown that there is no separated void, the Philosopher here shows that there is no void inherent in bodies.

As to this, he does three things:

first, he gives the reason proposed by those who posit such a void;

second, he disproves their position, at now, if they mean (216b30; [546]);

third, he dissolves their argument, at since we deny (217a10; [551]).

545. He first says, therefore (216b22), that there have been some philosophers who believed that there is a void in bodies, basing their argument on the existence of rarity and density. For they believed that rarefaction and condensation took place on account of a void inhering in bodies. If rarity and density did not exist, they say, the parts of bodies could not contract (enter each other) and harden (be compressed by condensation). But, if this does not take place, they deduced certain difficulties both in respect to local motion and in respect to the motions of generation and corruption, or alteration.

Such a difficulty in respect to local motion is that it would be necessary to admit either that motion does not exist at all or that the whole universe is moved with one motion, as says Xuthus, a philosopher. This would be because, if a body were moved locally, when it approached a place full of another body, this body would have to be expelled and tend toward another place, and the body found there would have to go to yet another place, such that, unless there were condensation of bodies, all bodies would have to be in motion.

In regard to generation or alteration, the difficulty arises that there would also be an equal change of air into water and of water into air. For example, if air be generated from one cupful of water, it would be necessary that, from the same amount of air as was generated, an amount of water be generated somewhere else.

The reason is that there is now a greater amount of air than there previously was of water from which it was generated. The generated air, therefore, occupies a greater place than the water from which it was generated.

Consequently, either the whole body of the universe would have to occupy a greater place, or else as much air in some other place would have to be converted into water, or else it must finally be admitted that there is a void within bodies to allow them to be condensed, because these philosophers supposed that bodies could not become condensed and rarefied unless there was a void existing in them.

546. Then, at now, if they mean (216b30), he rejects this position:

first, according to one interpretation;

second, according to another interpretation, at but, if they mean (216b35; [547]).

He says therefore that those who posit a void within bodies can give this two interpretations.

The first is that, in each body, there are, as it were, many empty openings, each with a separate position from the other full parts, as can be seen in a sponge or in pumice or things of this sort.

The second interpretation is that the void is not separate in respect to position from the other parts of the body, as if we should say that the dimensions, which they said were the void, would penetrate all the parts of the body.

The refutation of their claim as to the first way of the void’s being in bodies is evident from what went before. (Lect. 11ff.) For the very argument shows there is not a separate void outside of bodies, nor any place having such a space proper to itself over and above the dimensions of bodies. The same argument can be used to prove that there is no body so rarefied that it would have within itself any empty spaces distinct from the other parts of the body.

547. Then, at but, if they mean (216b35), he disproves the stated position as to the second interpretation and gives four reasons for rejecting it.

He says that, if the void is not in bodies in such a way as to be separable and distinct from the other parts but is nevertheless present in bodies, the situation is less impossible, because the difficulties mentioned above (Lect. 11ff.) against a separate void do not arise; yet against this also certain discrepancies do arise.

First of all, the void will not be the cause of every local motion, as they maintained, but only of upward motion, for the void, according to them, is the cause of rarity, and the rare in turn is found to be light, as is evident in fire, and what is light travels upward. Consequently, the void will be the cause only of upward motion.

548. He gives the second reason at second, the void turns out (217a1), when he says that, according to those who posit a void in bodies, the void is the cause of motion not as that in which something is moved (in the way that those who held a separate empty space posited the void as a cause of motion), but as the cause of motion in such a way that the empty space within the bodies transports them.

It is analogous to the case of inflated wine skins, which, due to the fact that they are carried upward on account of their lightness, also carry upward whatever is attached to them. And, in this way, the void inherent in bodies carries with it the body in which it is.

But this seems impossible, because it would then follow that the void would have to be subject to motion and that there would exist a certain place for the void.

And, since the void and place are the same, it will follow that, of an interior void, there will be an exterior void into which it is transported—which is impossible.

549. He gives the third reason at again, how will they (217a5), when he says that, if the cause of upward motion is the void carrying a body upward, then there would be no explanation of why heavy bodies are carried downwards since there is nothing to carry the body down.

550. He then gives the fourth reason, at and it is plain (217a6), and says that, if the rare causes upward motion on account of emptiness, then the rarer and more empty a thing is, the faster it should be carried upward. And if it were completely empty, it should move with a maximum speed. But this is impossible, because what is completely empty cannot be moved, for the same reason by which it was shown above that motion is impossible in an empty space; (Lect. 12, nn. 529ff., 539.) for there is no way to compare the speeds of the empty and of the full (whether you consider the space or the mobile) according to some definite ratio, because there is no ratio between the full and the empty. Therefore, the void cannot be the cause of upward motion.

551. Then, at since we deny that (217a10), he answers a previous argument:

first, he repeats it, explaining it more extensively;

second, he solves it, at our statement is based (217a21; [552]).

He says first that, because we do not admit a void either in bodies or outside of them, we must answer the arguments of our opponents, because they present a real difficulty.

First of all, on the side of local motion, either local motion will not be if there is not rarity and density, which they believed could not be produced without the void, or we will be forced to say that, whenever a body is moved, the very heavens or some part of them are borne outward, which he calls the bulging of the heavens.

Second, from the viewpoint of generation and corruption, a transformation of water into air will always have to be balanced by an equal transformation of air into water somewhere else. For since more air is generated from water, it is required (unless condensation takes place, which they thought impossible without a void) either that the body that was held to be outermost according to common opinion—namely, the heavenly body—be pushed outward by the swelling of lower bodies or that there must be an equal amount of air converted into water somewhere else, such that the entire bulk of the universe remain always equal.

But, because one could in a certain way elude what he had said about local motion, he mentions this again in order to exclude it. Thus he repeats, or it follows that nothing is moved. Now, according to the foregoing, a disturbance of the heavens occurs whenever anything is changed. And this is true unless the motion is rotational.

For example, let A be in motion to place B, and B to place C, and C to place D, and again D to place A. In this case, on the assumption of rotational motion, it will not be necessary, if one thing moves, that the whole universe be disturbed. But we do not see every local motion of natural bodies to be rotational, but many are in a straight line. Hence, there will be still disturbance of the heavens unless condensation and the void be admitted. This, then, is the argument that prompted some to posit the void.

552. Then, at our statement is based (217a21), he answers this argument. Now, the entire force of this argument depends on rarefaction and condensation taking place by means of the void. Accordingly, Aristotle meets this by showing that rarefaction and condensation can take place without a void.

First, he reveals his proposition;

second, he introduces the conclusion he mainly intends, at from what has been said (217b20; [557]).

As to the first, he does three things:

first, he explains his proposition by an argument;

second, by examples, at for as the same matter (217a33; [555]);

third, by the effects of rarity and density, at the dense is heavy (217b11; [556]).

As to the first, he does two things:

first, he sets out certain things necessary for his proposition;

second, he proves his proposition, at the same matter also serves (217a26; [386]).

553. Now (217a21), he lays down four preliminary statements that he takes from the subjects, that is, the presuppositions of natural science that were already explained in book 1. (Lect. 12ff.)

The first of these is that the matter of contraries is one (for example, of the hot and the cold, or of any other natural contrariety), for contraries are apt to affect the same thing.

The second is that whatever is in act has to have come into being from what was in potency.

The third is that matter is not separable from contraries such as to exist without them, but yet, according to motion, the matter is distinct from the contraries.

The fourth is that matter is not, by virtue of being, now under one contrary and then under another, different, but numerically one.

554. Then, at the same matter also serves (217a26 [386]), from these preliminaries, he proves his point in this way. The matter of contraries is one in number. But the large and the small are contraries in respect of quantity. Therefore, the matter of the large and the small is numerically the same.

And this is clear in substantial change. For when air is generated from water, the same matter that previously was under the water came to be under air, not receiving anything that it previously lacked, but rather that which was previously in potency in the matter was reduced to act. And the same is true in reverse when water is generated from air.

But there is this difference: when air is generated from water, there is a change from small to large, because the quantity of air generated is larger than the quantity of water from which it was generated.

But, when water is made from air, there is produced, contrariwise, a change from largeness to smallness. Therefore, when a large amount of air is reduced to a smaller amount by condensation, or from a small amount to a larger amount by rarefaction, it is the same matter that becomes both in act (namely, large and small) while being previously in potency to them.

Therefore, condensation does not take place by certain parts moving into others, or rarefaction by inhering parts being extracted, as those thought who posited a void within bodies. Rather, it is because the matter of the same parts now has greater quantity and then lesser. Hence, to become rare is nothing other than for matter to receive greater dimensions by being reduced from potency to act, and the opposite is becoming dense. For just as matter is in potency to definite forms, so it is in potency to definite quantity. Hence rarefaction and condensation do not proceed to infinity in natural things.

555. Then, at **for as the same matter **(217a33), he makes the same thing clear from examples. And, because rarefaction and condensation pertain to the motion of alteration, he gives an example of other alterations. And he says that, just as the same matter is changed from cold to hot and from hot to cold, because both were in the matter potentially, so also something passes from hot to hotter not because some part of the matter that was previously not hot becomes hot, but because the entire matter is reduced into the act of being more or less hot.

He gives another example of a quality in the matter of quantity. And he says that, if the circumference and convexity of a larger circle are brought into that of a smaller circle, they become more curved. This happens not because an ambit, or curvature, begins to exist in some part that previously was not curved but straight, but because the same that was previously less curved becomes more curved.

For in alterations of this sort, things do not become more and less by difference (that is, by subtraction) or addition, but by the changing of one and the same thing from perfect to imperfect, or from imperfect to perfect. This is evident in the case of what is absolutely and uniformly such and such: it is impossible to find in it any part lacking that quality, just as it is impossible in a flame to find any part lacking heat and whiteness, that is, clarity. So also, prior heat comes to a later heat not because a part previously not hot became hot, but because what was less hot became hotter.

So too, the largeness and smallness of a sensible body is not extended or increased in rarefaction and condensation by the matter receiving some addition, but by the matter that was previously in potency to large and small being changed from one to the other. Therefore, the rare and the dense are not produced by the addition of penetrating parts or by their removal, but by there being one matter of the rare and of the dense.

556. Then, at the dense is heavy (217b11), he manifests his proposition by the effects of the rare and of the dense. For from a difference in rarity and density, there follows a difference in other qualities, such as in heaviness and lightness or hardness and softness. Consequently, rarity and density diversify qualities, not quantities.

He says therefore, that lightness follows rarity, and heaviness density. And with good reason, for rarity arises from matter receiving greater dimensions, density from matter receiving lesser dimensions. Consequently, if you take diverse bodies of equal quantity, one being rare and the other dense, then the dense has more matter. Now, it was said above in the treatise on place that the contained body is related to the container, as is matter to form; (Lect. 8, n. 493.) consequently, a heavy body that tends toward the middle contained is with good reason more dense, because it has more matter. Just as, therefore, the circumference of a larger circle, when it is restricted to a smaller circle, does not receive concavity in a part not previously concave, but rather a part previously concave was reduced to a greater concavity, and just as any part of fire that anyone may take will be hot, so also it is the whole body that becomes rare or dense by the conduction, that is, contraction or expansion of one and the same matter, accordingly as it is moved to greater or smaller dimensions.

This is clear from what follows from rarity and density, which are qualities. For the heavy and the hard follow from density. Why heaviness follows density has already been explained. Why hardness follows is easy to explain: that is hard that is better able to resist both pressure and cleavage, but what has more matter is less divisible, because it is less obedient to something acting upon it, on account of its being more remote from act. Contrariwise, lightness and softness follow upon rarity. But the heavy and the hard fail to coincide in some things, for lead is heavier, but iron is harder. The reason for this is that lead has more of the element of earth in it, but what there is of water in it is less perfectly congealed and distributed.

557. Then, at from what has been said (217b20), he concludes his chief proposition. And he says it is clear from the foregoing (Lect. 11ff.) that there is no separate empty space. It is not anything existing absolutely outside a body, or in a rarefied thing after the manner of empty holes, or in potency in a rarefied body, as say those who did not posit a void that exists in bodies as something separated from the fullness of the body. Consequently, in no way is there a void, unless someone simply wants to call matter the void, since it is somehow the cause of heaviness and lightness, and consequently the cause of motion in respect of place. For density and rarity are causes of motion according to the contrariety of heavy and light, but in regard to the contrariety of hard and soft, passible and non-passible are the causes, for the soft is that which easily suffers division and the hard contrariwise, as was said. However, this does not pertain to local motion, but rather to alteration.

And so he concludes that it has been determined in what way the void exists and in what way it does not.