LECTURE 12 (215 a 24-216 a 26)

IT IS SHOWN FROM THE SPEED AND SLOWNESS IN MOTION THAT THERE IS NO SEPARATED VOID

             527. Here he shows from the speed and slowness in motion that there is no void.

             Concerning this he makes two points. First he names the causes of the speed and slowness in motion. Secondly, where he says, 'Now the medium causes . . .' (215 a 28), he argues from these causes to what was proposed.

             He says, therefore, first that one and the same heavy body, or anything else, for example, a stone or some such thing, is moved faster because of two reasons--either because of a difference in the medium through which it is moved, for example, through air or earth or water; or because of a difference in the mobile thing itself, in that it is lighter or heavier, other things being equal.

             528. Next where he says, 'Now the medium causes . . .' (215 a 28), he argues from these causes to what was proposed. He argues first from the difference in the medium, and secondly, where he says, '. . . the following depend upon . . .' (216 a 13), from the difference in the mobile thing.

             Concerning the first part he makes two points. First he gives the argument, and secondly he summarizes by repeating it, where he says, 'To sum the matter up . . .' (216 a 8).

             Concerning the first part he makes two points. First he gives the argument, and secondly, where he says, 'For let F be void . . .' (215 b 24), he shows that the conclusion follows from the premises.

             529. First, therefore, he gives the following argument. The proportion of motion to motion in speed is as the proportion of medium to medium in thinness. But there is no proportion of void space to full space. Therefore motion through a void is not proportioned to motion through a plenum.

             He clarifies the first proposition of this argument. He says that the medium through which a thing is moved is the cause of the speed and slowness because it impedes the body which is moved. And the medium especially impedes when it is moved in the opposite direction, as is clear in a ship whose motion is impeded by the wind. However it secondarily impedes even if it is at rest. For if it were moved together with the mobile thing, it would not impede it, but would rather help it, as a river which moves a ship from below. Now among things that impede, that which is not easily divided impedes more. Such a body is more dense. He explains this with an example. A is a body which is moved; B is the space through which it is moved; and C is the time in which A is moved through B. Moreover let us posit a space D which is the same length as B. But D is filled with a thinner body than B, according to some 'analogy', that is, according to a proportion with the bodily medium which impedes the motion of the body. For example, let the space B be filled with water and the space D be filled with air. Therefore, as much as air is thinner and less dense than water, so much will the mobile body A move faster through space D than through space B. Hence the proportion of speed to speed is the same as the proportion of air to water in thinness. And as much as the speed is greater, so much is the time smaller. For that motion is called faster which goes through an equal space in less time, as will be said in Book VI. Hence, if air is twice as thin as water, it follows that the time in which A is moved through B, which is filled with water, is twice the time in which it is moved through D, which is filled with air. And thus the time C, in which it crosses the space B, will be twice the time E, in which it crosses the space D. Hence we can say universally that in whatever proportion a medium through which something is moved is thinner and less impeding and easily divisible, in the same proportion the motion will be faster.

             530. Next where he says, 'Now there is no ratio . . .' (215 b 12), he clarifies the second proposition. He says that a void is not exceeded by a plenum according to any proportion.

             He proves this as follows. A number does not exceed zero by any proportion. A proportion is found only between number to number or to unity. Thus four exceeds three by one, and it exceeds two by more, and it exceeds one by still more. Thus there is a greater proportion of four to one than to two or to three. But four does not exceed zero by any proportion.

             Therefore it is necessary that anything which exceeds be divided into that which it exceeds and the excess, that is, that by which it exceeds. Thus four is divided into three and into one, by which it exceeds. If, therefore, four exceeds zero, it would follow that four is divided into several and zero, which is unsuitable. Hence it also cannot be said that a line exceeds a point, unless it were composed of points and were divided into them. And likewise it cannot be said that a void has any proportion to a plenum. For a void does not enter into the composition of a plenum.

             531. Next where he says, '. . . therefore neither can movement . . .' (215 b 21), he concludes that there cannot be a proportion between motion through a void and motion through a plenum. Even if a body is moved through something that is very thin in a certain space and time, motion through a void transcends every given proportion.

             532. Next where he says, 'For let F be void . . .' (215 b 24), in order to proceed more certainly he proves the same conclusion by deducing to impossibility. He does this because the above conclusion was clearly deduced from posited principles and some questions might arise concerning these principles.

             If it be said that motion through a void has some proportion of speed to motion through a plenum, then let there be a void space F which is equal in magnitude to the space B, which is filled with water, and to the space D, which is filled with air.

             Now if it be granted that motion through F has some proportion of speed to motions through B and D, then it is necessary to say that motion through F, which is a void, occurs in some determinate time. For speeds are distinguished in respect to quantities of time, as was said above. Therefore if it be said that the mobile body A crosses a void space F in some time, then let that time be G, which must be less than the time E in which it crosses the space D, which is filled with air. And thus the proportion of the time E to the time G will be the proportion of motion through a void to motion through a plenum. But it will be necessary to admit that in the time G the mobile body A would cross a space filled with a thinner body than is in D. This, indeed, would occur if there could be found some body which differs in thinness from air, which was given as filling the space D, in the same proportion that the time E has to the time G. For example, one might say that this body which fills the space F (formerly given as a void) is fire. If the body which fills the space F is thinner than the body which fills the space D in the same proportion that the time E exceeds the time G, then it would follow that the mobile body A, if it is moved through F (which is a space filled with the thinnest body) and through D (which is a space filled with air), will cross through F on the contrary with a greater speed in the time G. Therefore, if there is no body in F and it is a void space as originally given, the mobile body should be moved faster. But this is contrary to what was granted. For it was granted that the motion would take place through the space F, which is a void, in the time G. And thus, since it would cross the same space in the time G when the space is filled with the thinnest body, it follows that in the same time the same mobile body will cross one and the same space, whether it be a void or a plenum.

             Therefore, it is clear that if there were some time in which a mobile body were moved through any void space, this impossibility would follow: in an equal time it will cross both a plenum and a void. For there will be some body which will have a proportion to another body as one time is proportioned to another.

             533. Next where he says, 'To sum the matter up . . .' (216 a 8), he summarizes the points in which the force of the above argument consists.

             He says that in recapitulating it is clear why the above inconsistency occurs. Each motion is proportioned to every other motion in respect to speed. For every motion is in time, and any two times, if they are finite, have a proportion to each other. But there is no proportion of a void to a plenum, as was proven. Hence, if it be held that there is motion through a void, an inconsistency necessarily follows.

             Finally he concludes that the above inconsistencies occur if the different speeds of motion are taken according to a difference in the media.

             534. But many difficulties arise against this position of Aristotle.

             The first difficulty is that it does not seem to follow that, if there is motion through a void, then there is no proportion in speed to motion through a plenum. For any motion has a determined speed because of the proportion of the power of the mover to the moved, even if there is no impediment.

             This is clear through example and through reason [ratio]. For example, the motion of the celestial bodies is impeded by nothing, nevertheless, they have a determined speed in respect to a determined time. Moreover this is clear through reason [ratio] because, since in the magnitude through which motion occurs there is a prior and a posterior, then there is also a prior and a posterior in the motion. From this it follows that motion occurs in a determined time. And it is true that something can be subtracted from this speed because of an impediment. Therefore, it is not necessary that the proportion of motion to motion in speed be as a proportion of one impediment to another, such that if there is no impediment, then motion occurs in no time. Rather, it is necessary that in respect to the proportion of one impediment to another, there is a proportion of one deceleration to another.

             Hence, granting motion through a void, it follows that there is no deceleration from the natural speed. But it does not follow that motion through a void has no proportion to motion through a plenum.

             535. However Averroes in his commentary tries to overcome this objection.

             First he tries to show that this objection proceeds from a false imagination. He says that those who hold the above objection imagine that an addition occurs in the slowness of motion, just as an addition occurs in the magnitude of a line, because the added part is other than the part to which it is added. The above objection seems to proceed thusly: slowness occurs because some motion is added to another motion such that the quantity of natural motion remains the same when the motion which was added by a retarding impediment is subtracted. But he says that this is not the same case. For when motion is retarded, each part of motion becomes slower; nevertheless, each part of the line does not become greater.

             Next he tries to show how Aristotle's argument has necessity. He says that the speed or slowness of motion does arise from a proportion of the mover to the mobile body. But the mobile body must in some way resist the mover, as a patient in some way is contrary to an agent. This resistance can occur because of three things. First it occurs because of the site of the mobile body. For since the mover intends to move the mobile body to some place, the mobile body itself, existing in another place, resists the intention of the mover. Secondly, this resistance arises because of the nature of the mobile body, as occurs in violent motions, as when a heavy body is thrown upward. Thirdly, this resistance arises because of the medium. All three of these must be taken together as one resistance, so that one cause of the slowness of motion results. Therefore, when a mobile body, considered in itself insofar as it differs from the mover, is some being in act, then the resistance of the mobile body to the mover can be found either in the mobile body alone--as happens with the celestial bodies--or in both the mobile body and the medium--as happens with animated bodies which are here. But in regard to heavy and light bodies, when we subtract that which the mobile body has from the mover (that is, the form, which is a principle of motion and which the generator or mover gives), then nothing remains except matter, in regard to which no resistance to the mover can be considered. Hence it follows that in such things the only resistance is from the medium. Therefore, in celestial bodies there is a difference of speed only in respect to the proportion of the mover to the mobile body. In animated bodies there is a difference of speed in respect to the proportion of the mover to both the mobile body and the resisting medium together. And in regard to such things proceeds the above objection, namely, that when we have removed the deceleration which is due to the impeding medium, there remains a determined quantity of time in motion in respect to the proportion of the mover to the mobile body. But in heavy and light things there can be no deceleration of speed except in respect to the resistance of the medium. And Aristotle's argument deals with these latter things.

             536. But this seems to be completely worthless. For the quantity of speed is not a mode of continuous quantity, so that motion is added to motion, but a mode of intensive quantity, as when something is whiter than another. Nevertheless, the quantity of time, from which Aristotle argues, is a mode of continuous quantity, and time becomes greater by the addition of time to time. Hence, when the time which is added by the impediment is subtracted, the time of the natural speed remains.

             Secondly, when the form which the generator gives is removed from heavy and light things, a quantified body remains only in the understanding. But a body has resistance to a mover because it is quantified and exists in an opposite site. For no other resistance of celestial bodies to their movers can be understood. Hence, not even in regard to heavy and light things does Aristotle's argument follow, as Averroes claims it does.

             Therefore it is better and briefer to say that Aristotle's argument is an argument to contradict a position, and is not a strictly demonstrative argument. For those who posit a void do so in order that motion be not impeded. And thus according to them the cause of motion was due to the medium, which does not impede motion. Therefore against them Aristotle argues as if the whole cause of speed and slowness were due to the medium. He also clearly shows this above when he says that if nature is the cause of the motion of simple bodies, then it is not necessary to posit a void as the cause of their motion. In this way he lets us know that they hold that the whole cause of motion is due to the medium, and not to the nature of the mobile body.

             537. Furthermore, a second objection against Aristotle's argument is that, if the medium which is a plenum impedes, as he says, it follows that in this inferior medium there is no pure, unimpeded motion. But this seems unsuitable.

             To this the Commentator responds that the natural motion of light and heavy things requires this impediment from the medium, so that there might be a resistance of the mobile body to the mover, at least from the medium.

             But it is better to say that all natural motion begins from a nonnatural place and tends to a natural place. Hence, until it reaches the natural place, it is not unsuitable if something unnatural to it be joined to it. For it gradually recedes from that which is against its nature, and tends to that which agrees with its nature. And because of this natural motion is attained in the end.

             538. A third objection is that, since in natural bodies there is a definite limit to rarefaction, it does not seem that there is always a rarer and rarer body in respect to every proportion of time to time.

             But it must be said that determined rarity in natural things is not due to the nature of the mobile body insofar as it is mobile, but is due to the nature of determined forms which require determined rarities or densities. Furthermore in this book mobile body in general is under discussion. And therefore in his arguments in this book Aristotle frequently uses certain things which are false if the determined natures of bodies are considered. But they are possibilities, if the nature of body in general is considered.

             Or it can be said that he proceeds here according to the opinion of the ancient philosophers who posited the rare and the dense as first formal principles. According to them rarity and density can be increased to infinity since they do not follow upon other prior forms by which they are determined as needed.

             539. Next where he says, '. . . the following depend upon . . .' (216 a 13), he shows that there is no separated void by means of the speed and slowness of motion insofar as the cause is completely due to the mobile body.

             He says that that which is said below follows if we consider the difference of speed or slowness insofar as the mobile bodies which are moved exceed one another. For we see that those things which have a greater inclination either in respect to heaviness or lightness are carried more quickly through an equal, finite space. Such things are either greater in quantity and equally heavy or light, or else they are equal in quantity and are heavier or lighter. I say this on the condition that they are similar in respect to shape. For a broad body, if it is lacking in heaviness or magnitude, is moved more slowly than a body of acute shape. And the proportion of speed is the proportion which the moved magnitudes have to each other either in heaviness or magnitude. Hence, if there is motion through a void, then it will also be necessary that the heavier or lighter or more acute body be moved faster through that void. But this cannot be. For one cannot assign any reason why one body is moved faster than another. For if motion occurs through a space filled with some body, it is possible to assign the cause of a greater or lesser speed according to one of the mentioned causes. This happens because that which is moved is larger and divides the medium more quickly by its own strength; or because of the suitability of the shape, for the acute is more penetrating; or because of a greater inclination, which it has either from its heaviness or lightness; or even because of the violence of that which impedes. But a void cannot be divided more slowly or more quickly. Hence it follows that all things are moved through a void with equal speed. But this is clearly impossible. Therefore he shows from the very velocity of motion that there is no void.

             But it must be realized that in the development of this argument there is a difficulty similar to that which appeared in the first argument. For the argument seems to suppose that there is no difference in the speed of motions except the difference of the division of the media. But in the celestial bodies there are diverse speeds for which there is no plenum as a resisting medium which must be divided by the motion of the celestial bodies. This objection must be answered as above.

             540. Finally he concludes that it is clear from what has been said that if a void is posited, then there results the contrary of that which those who hold a void suppose. For they proceeded as if there could be no motion if there were no void. But the contrary has been shown, that is, if there is a void, there is no motion. Therefore the above mentioned philosophers thought that there is a void which is discrete and separated by itself, that is, a certain space having separated dimensions. And they thought that a void of this kind is necessary if there is motion in respect to place. But to posit such a separated void is the same as to say that place is a certain space distinct from bodies. This is impossible, as was shown in the treatment of place.