BOOK IV

Lecture 1

Place, its existence

406. After treating in Book III of motion, and the infinite, which belongs intrinsically to motion insofar as it is in the genus of continuous things, the Philosopher now intends, in Book IV, to deal with the things that are extrinsically connected with motion.

First, of things that are connected with motion extrinsically as measures of mobile things:

Secondly, of time which is the measure of motion itself, at no.558 (L.15,1.

As to the first he does two things:

First, he studies place;

Secondly, the void, at no. 494 (L.9).

About the first he does two things:

First, he shows that it is the business of the natural philosopher to study place;

Secondly, he carries out his proposition, at no. 411.

As to the first he does two things:

First, [277] he proposes what he intends and says that just as it is the business of the natural philosopher to determine about the infinite; namely, whether it exists or not, and how it exists, and what it is, so also about place;

Secondly, at no. 407, he proves what he had said:

First from the viewpoint of place itself;

Secondly, from our viewpoint [i.e., that of the ones studying place] at no. 409.

407. About the first he gives two reasons, of which the following is the first [278]. Whatever things are common to all natural things pertain especially to the considerations of the natural philosopher; but place is such, for all generally maintain that whatever exists is in some place. They prove it by a sophistic argument consisting of positing the consequent. They argue thus: What does not exist is nowhere, i.e., in no place, for there is no place where the goat-stag or the sphinx exist, which are certain fictions after the manner of chimeras. They argue therefore that if what is found in no place does not exist, then whatever exists is in a place.

But if to be in place belongs to all beings, it seems that place pertains rather to the consideration of metaphysics then that of physics.

And it must be said that Aristotle here argues from the opinion of those who posit that all beings are sensible, on account of their inability to go beyond their imaginations. According to them, natural science is first philosophy, common to all beings, as is mentioned in Metaphysics IV (L.5).

408. Then [279] he gives the second reason: The consideration of motion belongs to the natural philosopher; but the motion which is according to place and is called “change of place” is the most general of all motions. For some things namely, the heavenly bodies, are moved solely according to this motion and nothing is moved with other motions without being moved by this one. Moreover, this motion is more properly so because it alone is truly continuous and perfect, as will be proved in Book VIII. But notion according to place cannot be known without knowing place. The natural philosopher therefore should consider place.

409. Then [280] he arrives at the same conclusion from our viewpoint: Wise men should settle matters about which there is doubt; but there are many doubts about what place is. The cause of these doubts is twofold. One is based on place itself: because not all the properties of place lead to the same opinion about place, but from certain properties of place it seems that place is one thing and from other properties that it is something else. The other cause is based on men, for the ancients neither proposed their doubts about place well nor pursued the truth of the matter well.

410. Then [281] he begins to determine about place.

First in a dialectical manner;

Secondly, by determining the truth, at no. 434.

As to the first he does two things:

First he discusses dialectically whether place exists;

Secondly what it is at no. 422.

About the first he does two things:

First he gives reasons showing that place exists;

Secondly, showing that it does not exist, at no. 415.

As to the first he does two things:

First he shows that place exists, by using reasons based on the truth of things;

Secondly, by reasons based on the opinions of others, at no. 413.

411. In regard to the first, he gives two reasons. In the first of these he proceeds thus: That place is something, is clear from the very transmutation of bodies that are moved according to place. For just as the transmutation which is according to form led men to the knowledge of matter, because there had to be a subject in which the forms could succeed one another, so transmutation according to place led men to a knowledge of place, for there had to be something where bodies could succeed one another. And this is what he adds, namely, that when water goes out from where it now is, i.e., from some vessel, air re-enters. Since, therefore, another body sometimes occupies the same place, it is clear that place is something different from the things that are in place and which are moved according to place. For where air now is there was previously water, and this would not be if place were not something different from both the air and the water. Consequently, place is something: it is a sort of receptacle distinct from any of the things located in it, and it is the term “from which” and “unto which” of local motion.

412. He gives the second reason [282], saying that since the motion of any body whatsoever shows that place exists, as has been said, then the local motion of natural simple bodies, such as fire and earth, and such like heavy and light bodies, not only shows that place is something, but also that place has a certain power and force.

For we observe that each of these bodies is carried to its proper place when it is not prevented, i.e., the heavy are carried down and the light upward. This shows that place has a certain power of pre-serving the thing that is in place. For this reason, an object tends to its own place by a desire of self-preservation. This, however, does not prove that place has the power to attract, except in the sense in which the end is said to attract.

“Up” and “down” and the other directions, namely, “before” and “behind,” “right” and “left,” are the parts and species of place. These directions are determined in the universe according to nature and not merely in relation to ourselves. This is clear from the fact that when we speak of them in relation to ourselves, the same thing is not always “up” or “down,” “right” or “left,” but varies according to our various relations to it. Hence it frequently happens that an immobile object which was “on the right” comes to be “on the left.” The same is true of the other directions, depending on our different relations to them.

But in nature there is a definite “up” and “down” according to the motion of heavy and light bodies, and the other [four] directions are determined by the movements of the heavens, as was said in Book III. It is not just any part of the universe that is “up” and just any part that is “down,” but “up” is always whether light bodies are carried and “down” is whether heavy bodies tend. Now whatever things have according to themselves definite positions must have powers by which they are determined, for in an animal the power of the right is distinct from the power of the left. Accordingly, place exists and has definite powers.

Now, that in certain things the position is assigned only in relation to us is shown in mathematical objects, which, although they are not in place, yet have a position attributed to them solely in relation to ourselves. Hence they have no position according to nature but only according to the intellect, inasmuch as they are understood in some relation to ourselves, either as above or below, or to the right or left.

413. Then [283] he appeals to the opinions of others to show that place exists. First, to the opinion of those who posit a void. For whoever asserts that the void exists must admit that place exists, since the void is nothing more than a place devoid of body. And so from this and from the reasons given above, it is possible to conceive that place is something other than bodies and that all sensible bodies exist in place.

414. Secondly, [284] to confirm the same point he uses the opinion of Hesiod, who was one of the ancient theological poets. It was he who taught that the first thing made was chaos. For he said that the first of all things made was chaos, it being a sort of confusion and a receptacle for bodies; later the extended earth was made to receive various bodies—as if first a receptacle of things had to exist before the things themselves could exist. And he and others posited this because, with many others, they believed that all things that exist are in place. And if this is true, it follows that place not only exists but that it has a remarkable power in that it is the first of all beings. For that can exist without other things but they not without it, seems to be first. But according to them place can exist without bodies—a conjecture they made by observing that place remains even when the things occupying it are destroyed. But things cannot exist without place. It follows, therefore, according to them, that place is the first among all beings.

Lecture 2

Six dialectical reasons showing place does not exist

415. After giving reasons to show that place exists, the Philosopher now gives six reasons showing that place does not exist. Now the way to begin investigating the question “whether a thing exists” is to settle on “what it is,” at least as to what its name means. Therefore he says [285] that although it has been shown that place exists, there is a difficulty, i.e., a question, about what it is, even if it does exist: Is it a bodily mass or a nature of some other kind?

416. Hence, he argues thus: If place is anything it must be a body; for place has three dimensions, namely, length, width and depth; and such things determine a body because whatever has three dimensions is body. But place cannot be a body, because, since place and the body in it are together, there would be two bodies together, which is unacceptable. Therefore, it is impossible for place to be anything.

417. He gives a second reason [286]: If the place of a body is a receptacle distinct from the body, then the place of its surface must be a receptacle distinct from this surface, and similarly for the other limits of quantity, such as the line and the point. He proves this conditional proposition in the following manner: Place was proved to be distinct from bodies on the ground that where the body of air now is, there was the body of water previously; but similarly where the surface of the water was, there is now the surface of the air; therefore the place of the surface is distinct from the surface and the same holds for the line and the point.

He argues therefore by the destruction of the consequent, starting from the fact that there can be no difference between the place of ths point itself. For, since a place is not greater than the thing in place, the place of a point can be only an indivisible. Now two quantitative indivisibles, e.g., two points joined together, are just one point. For the same reason, therefore, neither the place of the surface will be different from the surface itself, nor the place of the body different from the body itself.

418. He gives a third reason [287]: whatever is, either in an element or composed of elements; but place is neither of these; therefore place does not exist. The middle [minor] premise he proves thus: Whatever is an element or composed of elements is either corporeal or incorporeal; but place is not incorporeal, for it has magnitude, nor is it corporeal, because it is not a body, as we have already shown. Therefore it is neither an element nor composed of elements.

Now since someone might say that even though it is not a body, it is nevertheless a bodily element, he excludes this by adding that all sensible bodies have corporeal elements, because the elements are not outside the genus of their compounds. For no magnitude results from intelligible principles which are incorporeal. Hence if place is not a body, it cannot be a corporeal element.

419. He gives the fourth reason [288]: Everything that exists is somehow a cause in relation to something else; but place cannot be a cause in any of the four ways. It is not a cause as matter, because things that exist are not composed out of place and that is implied in the very notion of matter, nor is it a formal cause, for then all things that have the same place would be of the same species, since the principle of the species is the form. It is not like the final cause in things, since places seem to be for the sake of the things in place rather than they for the sake of the places. Finally, it is not an efficient or moving cause, since place is the terminus of a motion. Therefore it seems place is nothing.

420. He gives the fifth reason [289], which is Zeno’s reason: Whatever exists is in place; hence if place is anything it follows that it is itself in place and that place in another place and so on ad infinitum. But this is impossible; consequently, place is not anything.

421. He gives the sixth reason [290]: Every body is in a place and in every place is a body (according to the opinion of many). From this it is taken that place is neither smaller nor larger than the thing in place. When therefore a thing in place grows, its place also should grow. However, this seems impossible, for place is an immobile something. Therefore place is not anything.

In summary he says that for reasons of this sort doubts are raised not only as to the nature of place, but also as to its very existence. However, these reasons will be answered by what follows.

Lecture 3

Is place matter or form?

422. Having inquired dialectically into the question of place’s existence, the Philosopher now attacks the question: what is place?

First he gives dialectical reasons showing that place is form or matter;

Secondly, he gives reasons to the contrary, at no. 429.

As to the first he does three things:

First he gives a reason showing that place is form;

Secondly, that place is matter, at no. 425.

Thirdly, from these he draws a corollary, at no. 428.

423. He says therefore first 52917 that just as in beings some are per se beings and others per accidens, so in regard to place, one place is common, in which all bodies exist, and another is proper and is called “place”, primarily and per se. Now common place is so called only per accidens and in relation to a previous place. He explains this thus: “I can say that you are in the heavens, because you are in the air which is in the heavens, and that you are in the air and in the heavens, because you are on earth and you are said to be on earth, because you are in a place containing nothing but you.”

424. Consequently, what contains a thing primarily and per se is its per se place. Now such a place is the boundary at which a thing is terminated. Therefore, place is properly and per se a boundary of a thing. But the boundary of each thing is its form, because it is through the form that the matter of anything is limited to its own existence and magnitude to a determinate measure. For the quantities of things follow upon their forms. According to this, therefore, it seems that place is the form.

However, it should be noted that in this argument there is the fallacy of consequent; for it is a syllogism in the second figure with two affirmative premises.

425. Then [292] he gives a reason of Plato through which it seemed to him that place is matter. To see this, one must note that the ancients thought that place was the space enveloped by the boundaries of the container, which has the dimensions of length, breadth, and depth. But this space did not seem to be the same as any sensible body, because the space remained the same even when various bodies successively entered it and left. Thus it follows that place is a set of separate dimensions.

426. From this Plato wished to demonstrate that place is matter. This is what he [Aristotle] says: Because some consider that place is the distance of the magnitude of space distinct from every sensible body, place would seem to be matter. For the distance or dimension of a magnitude is distinct from the magnitude. For magnitude signifies something terminated by some species [or form], as a line is terminated by points, and a surface by line, and a body by surface, and these are species of magnitude. But the dimension of space is contained under a determined form as a body is determined by a plane, i.e., by a surface, as, by a definite boundary. Now whatever is contained under boundaries seems to be in itself not determined. What is not determined in itself but by a form and boundary is matter which has the nature of the infinite. For were we to remove from some spherical body its sensible qualities and the boundaries by which the dimension of its magnitude acquires its definite figure, nothing would remain but the matter. Consequently the dimensions themselves, which are not determined by themselves but by something else, are matter.

This followed mainly from the underlying principles of Plato, who posited numbers and quantities as the substance of things.

427. Therefore, because place is dimensions and dimensions are matter, Plato said in the Timaeus that place and matter are the same. For he said that whatever is a receptacle of anything is a place (failing to distinguish between the receptiveness of place and of matter). Hence, since matter receives form, it follows that matter is place.

Yet it should be noted that Plato spoke in various ways about receptacles: for in the Timaeus he said that the receptacle is matter but in his “unwritten teaching,” i.e., his oral teaching in the schools, he said that the receptacle was “the large and the small,” which however he allied with matter, as we have said above. Yet no matter to what he attributed receptivity, he always said that the receptacle and place are the same. Therefore, while many did say that place is something, Plato alone endeavored to say what place is.

428. Then [293] he concludes from the foregoing that if place is either matter or form, it seems reasonable to say that it is difficult to know what place is: because both matter and form involve very lofty and difficult speculation; moreover, it is not easy to know either of them without the other.

429. Then [294] he gives five reasons to the contrary. In the first of these he says that it is not difficult to see that place is neither matter nor form. For form and matter are not separate from the thing of which they are components, whereas place can be separated—in the place where air was, water now is. In like manner, other bodies also mutually change place. Hence it is clear that place is not part of a thing, as matter or form. Nor is place an accident of a thing, because parts and accidents are nor separable from a thing, whereas place is separable. He shows this by an example: place seems to be related to the thing in place as a vessel, the only difference being that place is immobile and the vessel mobile, as will be explained below (L.6). Consequently, since place is separable, it is not form. But that place is not matter is shown not only by the fact that it is separable, but also by the fact that it contains, whereas matter does not contain but is contained.

430. He now gives a second reason [295]. Since he had shown that place is neither matter nor form on the ground that place is separated from the thing in place, he now wishes to show that even if place were never separated from the thing in place, yet the very fact that we say something is in place shows that place is neither form nor matter. For whatever is said to be anywhere seems both to be something and to be distinct from that in which it is. Hence, when something is said to be in place, it follows that place is outside the thing, whereas matter and form are not outside the thing. Therefore, neither matter nor form is place.

431. In the third reason [296] he makes a digression to argue specifically against the position of Plato. For it was said in Book III that Plato posited ideas and numbers as not in place. But logically, according to his opinion about place, they should be in place, because whatever is participated is in the participant—and he said that species and numbers are participated either by matter or by “the large and the small.” Accordingly, species and number exist in matter or in “the large and small,” Therefore, if matter or “the large and the small” are place, it follows that numbers and species are in place.

432. He gives the fourth reason [297]. In this regard he says that no good explanation could be given of how something could be moved according to place, if matter and form are place. For it is impossible to assign a place in things that are not moved up or down or in any direction of place; hence place must be sought in things that are moved according to place. But if place is something intrinsic to what is moved (which would be the case if matter or form were place), it follows that place will be in a place, for whatever is changed in respect to place is itself in place. Now whatever is in a thing, such as its species and the infinite, i.e., its matter, is moved with the thing, since they are not always in the same place, but are wherever the thing is. Therefore, matter and form must be in a place. Therefore, if either of them is place, it follows that place is in a place, which is unacceptable.

433. The fifth reason is then given [298]. Whenever anything is corrupted, the parts of its species are somehow corrupted. Now matter and form are the parts of the species. Therefore, when the thing corrupts, then, at least per accidens, the matter and form are corrupted. Consequently, if matter and form are place, it follows that place is corrupted, if place pertains to the species. Now the body which is generated would not be in the same place, if the place of air pertained to the species of the air, as when water is generated from air. But no explanation can be given of how place is corrupted; hence it cannot be said that matter or form are place.

Finally, he summarizes by asserting that we have stated why it seems place must exist and what causes doubt about its existence.

Lecture 4

Prerequisites to determining the truth about place.

434. After inquiring dialectically into the existence and nature of place, the Philosopher now proceeds to the task of determining the truth.

First he lays down certain things necessary to the consideration of the truth:

Secondly, he determines the truth, at no. 445.

As to the first he does three things:

First he points out the ways in which one thing is said to be in another;

Secondly, he asks whether anything can be in itself, at no. 437;

Thirdly, he settles some difficulties previously raised, at no. 443.

435. He lists [299] eight ways in which something is said to be in something.

The first of these is the way in which a finger is said to be in the hand and in general how any part is in its whole.

The second way is as the whole is said to be in the parts. And because this way is not so customary as the first, he explains it by adding that the whole is not something outside the parts, and thus must be understood as existing in the parts.

The third way is as “man” is said to be in “animal,” and any species in its genus.

The fourth way is as the genus is said to be in the species. And lest this way seem out of place, he gives a reason for mentioning it: the genus is part of the definition of the species as is the difference; hence in some way both the genus and the difference are said to be in the species as parts in the whole.

The fifth way is as health is said to be in hot and cold things, the balance between which constitutes health; and in general as any other form is in matter or a subject, whether it be an accidental or a substantial form.

The sixth way is as the affairs of the Greeks are said to exist in the king of Greece, and generally as everything that is moved is in the first mover. According to this way, I can say that something is in me, because it is in my power to do it.

In the seventh way something is said to be in something as in something supremely loveable and desirable, and generally as in an end. in this way someone’s heart is said to be in what he desires and loves.

Finally in an eighth way something is said to be in something as in a vessel, and in general as a thing in place is in its place.

He seems to have skipped the way in which something is in something as in time. But this is reduced to the eighth way. For just as place is the measure of the mobile thing, so time is the measure of motion.

436. Then he says that it is according to the eighth way that something is in a very proper sense said to be in something. Hence, according to the rule given in Metaphysics IV and V, all the other modes must somehow be reduced to this eighth way, according to which, something is in something as in a place. This is done in the following way.

The thing in place is contained or included by its place and has rest and it has rest and immobility therein. Therefore the way closest to this one is that in which a part is said to be in the integral whole in which it is actually included. Accordingly, it will be said below that a thing in place is as a “separated” part, and a part as a “conjoined” thing in place.

The whole which is according to reason is like this whole; hence it is said that what is in the notion of something is in it, as “animal” in “man.”

Now just as it happens that the part of an integral whole is enclosed in a whole according to act, so the part of a universal whole is enclosed in a whole according to potency for the genus extends to more things potentially than the species does, although the species may have more elements in act. Consequently, species is also said to be in the genus.

And because, just as the species is contained in the potency of the genus, so form is contained in the potency of matter, it is further said that form is in the matter.

And because the whole has the notion of form in relation to the parts, as was said in Book II, consequently the whole is also said to be in the parts. But just as form is enclosed under the passive potency of matter, so the effect is enclosed under the active potency of the agent. Whence it is that something is said to be in a first mover.

Finally, it is clear that the appetite rests in the good it desires and loves and is, indeed, fixed in it, just as the thing in place is fixed in place. Hence the affection of the lover is said to be in the thing loved.

And thus it is evident that all the other ways are derived from the last, which is the most proper.

437. Then [302] he asks whether anything can be in itself, for Anaxagoras said above that the infinite exists in itself.

Therefore, he first raises the question: whether one and the same thing can be in itself; or whether nothing can, but all things either never are or are in something else.

438. Secondly [302] he answers this;

First he shows how something can be in itself;

Secondly, how it cannot, at no. 439.

He says first, therefore [301] that something may be understood to be in itself in two ways: in one way, primarily and per se; in another way, in relation to something else, i.e., in relation to a part. And it is in this second way that something may be said to be in itself. For when two parts of some whole are so related that one part is that in which the other exists and the other is that which is in the first, it follows that the whole is both that “in which” something exists (by reason of one part) and that which is “in this” (by reason of the other), and thus is the whole said to be in itself.

For we observe that something is said of something according to a part, for example, someone is called “white” because his surface is white, and a man is called “knowing” because science is in his rational part. If therefore we take a jug full of wine as a certain “whole” whose parts are jug and wine, neither of the parts will exist in itself, i.e., neither the jug nor the wine, but this whole, which is a jug of wine, will be in itself inasmuch as each is a part of it, i.e., both the wine which is in the jug and the jug in which the wine is. It is in this way, therefore, that one and the same thing can be in itself.

439. Then [302] he shows that nothing can be primarily in itself.

First he proposes what he intends, distinguishing both the way in which something is in itself and the way in which it is not;

Secondly, he proves his proposition, at no. 440.

He says, therefore, that there is no case of anything being primarily in itself. And he makes clear what it is for something to be primarily in itself by citing an example of the opposite. For something white is said to be in a body, because the surface is in the body: hence the white is nor primarily in the body but in the surface. In like manner, science is said to be primarily in the soul, and not in the man, in whom science exists by reason of the soul. And it is according to this, i.e., according to the soul and the surface, that the appellations whereby a man is called “white” or “knowing” are verified, since the soul and the surface are as parts of man—not that the surface is a part, but it is like a part, inasmuch as it is something of the man, as The boundary of his body.

Now, if wine and jug are taken as separated one from the other, they are not parts; hence it belongs to neither of them to exist in itself. But when they are together, as when a jug is full of wine, then because both jug and wine are parts, the same thing will be existing in itself (as was explained above), not primarily but through its parts, just as white is not primarily in the man but is there through the body, and in the body through the surface. But it is not in the surface through anything else; hence it is said to be in the surface primarily. Nor is that in which something exists primarily, and that which is in it, the same, as in the case of white and surface. For surface and white are specifically different, and the nature and potency of each is different.

440. Then [303] having pointed out the difference between being primarily in something and not being primarily in something, he now shows that nothing is primarily in itself.

First he shows that nothing is primarily in itself per se;

Secondly, per accidens, at no. 442.

And he explains the first point in two ways: namely, inductively and with an argument. He says therefore first, that by considering inductively all the ways determined above in which something is said to be in itself, it is found that nothing exists in itself primarily and per se: for nothing is the totality of itself, [i.e., in itself as whole in part?], nor as part [in whole?] as genus [in species?], and so on. He lays this down by concluding from what has gone before, because just as it is clear in the case of the white and of the surface (which are related as form and matter) that they differ both in species and in power, the same thing can be considered in all the other modes.

441. Then [304] he proves the same thing with an argument and says that it is clear by reasoning that it is impossible for anything to be primarily and per se in itself. For if there be anything such, necessarily the same thing, in the same way, will have the notion both of that in which something is, and that which is in it. Hence, each would have to be both the container and the content; for example, the jug would be the vessel and the wine, and the wine both the wine and jug, if something could be primarily and per se in itself. Now on this assumption (namely, that the wine is both the jug and wine, and the jug both wine and jug), if anyone were to say that either is in the other, for example, that the wine is in the jug, it would follow that the wine is received into the jug not inasmuch it is wine, but inasmuch as wine is the jug. Wherefore, if to be in the jug primarily and per se is a property of the jug (on the assumption that something is primarily and ptr se in itself), it follows that nothing can be said to be in the jug except inasmuch as that something is the jug. And so, if the wine is said to be in the jug, it follows that to be in the jug belongs to the wine, not inasmuch as it is wine, but inasmuch as the wine is the jug.

For the same reason, if the jug receives the wine, it will receive it not inasmuch as the jug is jug but inasmuch as the jug is wine. Now this is unacceptable. Hence, it is clear that it is under different aspects that something is “that in which” and “that which is in.” For it is one thing to be that which is in something, and another to be that in which something is. Consequently, nothing can be primarily and per se in itself.

442. Then [305] he shows that nothing exists primarily in itself even according to accident. For something is said to be in something according to accident, when it is in it on account of something else existing in it; as, for example, when we say that a man is in the sea because he is in a boat which is in the sea: he is nevertheless said to be in the boat primarily, i.e., not according to a part. If therefore something could be in itself primarily, though not per se but per accidens, it would be in itself on account of something else being in it. And so it follows that two bodies are in the same thing; namely, the body which is in something and that same thing as existing in itself. In this way a jug will be in itself per accidens, if the jug itself, whose nature it is to receive something, is in itself, and again that which it receives, i.e., the wine. Therefore, in the jug will exist both jug and wine, if, because the wine is in the jug it follows that the jug is in itself; and so two bodies would be in the same. Consequently, it is clearly impossible for anything to be primarily in itself.

Notice, however, that sometimes something is said to be “in itself” not according to an affirmation but according to a negation, inasmuch as to be in itself signifies nothing more than not to be in something else.

443. Then [306] he settles certain doubts. First he destroys Zeno’s reason which was appealed to as proof that place does not exist on the assumption that, if it did, it must exist in something else and so on ad infinitum. But this, as he says, is not difficult to answer after one knows the various ways in which something is said to be “in” something else.

For there is nothing to prevent our saying that place is in something: for while it is not in something as in a place, it is in something in some other way, as form is in matter or an accident in a subject, inasmuch as place is a boundary of the container. And this is what he adds: as health is in the hot as a habit, and heat is in a body as a passion or accident. Hence it is not necessary to proceed to infinity.

444. Then [307] he also settles the doubts mentioned above about the nature of place (namely, whether it be form or matter) by appealing to his proof that nothing exists in itself primarily and per se. For it is clear from this proof that nothing can be the vessel or place of that which is contained in it after the manner of a part such as matter or form is: for that which is in something and that in which something is must be primarily and per se distinct, as we have shown. Hence, it follows that neither form nor matter is place; rather place is something entirely different from the thing in place, whereas matter and form belong to the thing in place as intrinsic parts thereof.

Finally he concludes that the things said above about place were said as contesting it. Some of these oppositions have now been solved; others will be solved after the nature of place is manifested.

Lecture 5

Necessary previous notions for the definition of place.

445. After setting forth a preliminary discussion about whether place exists and what it is, and after solving some doubtful points on these matters, the Philosopher now begins the task of determining the truth about place.

First he gives some presuppositions to be used in determining about place;

Secondly, he shows what qualities a definition of place should have, at no. 447;

Thirdly, he begins to determine about place, at no. 448.

446. He says first therefore [308] that it will be clear from the following just what place is. But we must first adopt as it were certain suppositions and self-evident principles, those namely, which appear intrinsic to place. Indeed, there are four such:

For all agree on this maxim, that place contains that of which it is the place, yet in such a way that place is not any part of the thing in place. He says this to exclude the containing force of form, which is part of a thing, but contains in a manner different from place.

The second supposition is that the primary place, i.e., that in which something exists primarily, is equal to, and neither greater nor less than, the thing in place.

The third supposition is that a place exists for everything in place, i.e., that everything in place has a place, but not in the sense that one and the same place is never lost by one and the same thing capable of being in a place; for a place can be separated from a thing in place. However, when one place is lost by a thing in place, it acquires another place.

The fourth supposition is that in all places there is found, as a [specific] difference of place, an “up” and a “down,” and that each body, when it is outside its proper place, naturally seeks it and, when it is in it, naturally remains there. Now the proper places of natural bodies are “up” and down,” to which they are naturally borne and in which they remain. But he says this in keeping with the opinion of those who posited no body other than the four elements: for he has not yet proved the heavenly body to be neither light nor heavy—which he will prove later in De Coelo, I. From these presuppositions he proceeds to the consideration of what remains.

447. He then [309] shows what qualities should be found in a definition of place. And he says that in defining place our attention should be focused on four things which indeed are necessary for a perfect definition:

First, that one show what place is, for a definition is an expression indicating what a thing is.

Secondly, that one resolve conflicting arguments about place: for the knowledge of truth involves the solution of doubts.

Thirdly, that the given definition reveal the properties of place, which inhere in it, because a definition is the middle term in a demonstration, by which the proper accidents are demonstrated of the subject.

Fourthly, that from the definition of place the cause will be clear why there is disagreement about place and of all the conflicting things said about it. Such a procedure is the most beautiful way of defining anything.

448. Then [310] he determines about place;

First he shows what place is;

Secondly, at no. 487, he settles the doubts previously mentioned;

Thirdly, he assigns the cause of the natural properties of place, at no. 492.

About the first he does two things:

First he shows what place is;

Secondly, how something exists iu place, at no. 472(L.7).

As to the first he does two things:

First he mentions some facts preliminary to his hunt for the definition;

Secondly, he begins to investigate the definition of place, at no. 455 (L.6).

449. In regard to the first, be makes four preliminary statements, the first of which is that the question of place would never have arisen were there no motion in regard to place. For it was necessary to posit place as something distinct from the object in place, because two bodies are found successively in the same place, and, in like manner, one body successively in two places. (Similarly, it was the successive change of forms in one and the same matter that led to the knowledge of matter). For this reason some are convinced that the heavens are in place, since they are always in motion. Now, of motions, one is according to place per se, namely, the change of place; another is consequently related to place, namely, increase and decline, beeause as a body grows or decreases, it acquires a larger or a smaller place.

450. He gives the second [311], saying that some things are moved, per se in act as in the case with every body, while others according to accident. This latter can occur in two ways. For some things that could be moved essentially are de facto moved accidentally, as the parts of a body while they are in the whole body are moved per accidens but when they are separated they are moved per se. Thus, a nail, when it is embedded in a ship, is moved per accidens, but when it is extracted it is moved per se. Other things are not be moved per se, but only per accidens, as is the case with whiteness and knowledge, which change place as that in which they are changes place. This point was brought up because things are apt to be in place per se or per accidens, actually or potentially in the same way as they are apt to be moved in those ways.

451. He gives the third [312] when he says that someone is said to be in the heavens as in a place because he is in the air which indeed is in the heavens. Yet we do not say that anyone is in the entire air primarily and per se, but by reason of the ultimate boundary of the air containing him he is said to be in the air. For if the whole air were anything’s place, e.g., a man’s, the place and the thing in place would not be equal—which is against what was supposed above. But that in which something exists primarily is seen to be the boundary of the containing body; and this is what primary place means, i.e., equal.

452. He gives the fourth reason [313]. First, he mentions it; secondly, he proves it, at no. 453.

He says therefore first that whenever the container is not separate from the thing contained but is continuous with it, the latter is not said to be in it as in a place, but as a part in a whole; as, for example, when we say that one part of the air is contained by the totality of air. And he concludes this from what went before, because where there is a continuum there is no ultimate boundary in act, something that is required for place, as was stated above. But when the container is separated, and contiguous to the thing contained, this latter is in place and exists in the ultimate boundary of the container primarily and per se, of a container, that is, which is not a part of the contained and neither greater nor less but equal in dimension. But how the container and the thing contained can be equal he shows by pointing out that the ultimate boundaries of things touching are together: whence, their ultimate boundaries must be equal.

453. Then he proves the fourth point by two arguments [314]. The first of these is that something contained that forms a continuum with the container is not moved in the container but with the container, as the part is moved simultaneously with the whole; but when it is separate from the container, then it can be moved in it, whether the container be moved or not—for a man is moved on a ship whether it be moving or at rest. Therefore, since something can be moved in a place, it follows that place is a separated container.

454. He gives a second argument for the fourth point [315], saying that when the thing contained is not separate from the container but continuous with it, then it is said to be in it as a part in a whole, as sight is in the eye as a formal part and the hand in the body as an organic part. But when the container and the thing contained are separate, then the latter is in it as in a vessel; as water in a barrel or wine in a cup. The difference between the example in the first case and in the second is that the hand is moved with the body, but not in the body, but the water is moved in the barrel.

Therefore, since we have said above that to be in place is to be there as in a vessel but not as a part in a whole, it follows that place is like a separated container.

Lecture 6

The definition of place

455. After positing the preliminary notions required for the search of the definition of place, the Philosopher now begins his search for the definition. About this he does three things:

First, he looks into each part of the definition;

Secondly, he shows that it is a good definition, at no. 471

As to the first he does two things:

First, he searches for the genus of place;

Secondly, for the differentia that will complete the definition, at no.467.

In searching for the genus of place he divides. In connection with this he does three things:

First he gives the division;

Secondly, he excludes three members of the division, at no. 457;

Thirdly, he concludes to the fourth member, at no. 466.

456. He says therefore first [316] that from the previous discussion the nature of place may already be clear. For it seems that according to what is ordinarily said of place that it is one of four things: namely, matter or form or the space between and within the boundaries of the container, or, if there is no space within the boundaries of the container which has its own dimensions over and above the dimensions of the body existing within the confines of the container, then it will be necessary to posit a fourth possibility, namely, that place is the boundary of the containing body.

457. Then [317] he excludes three members of this division.

First, he proposes what he intends, saying that it is clear from what follows that place is not any of these three;

Secondly, he pursues his intention, at no. 458.

First, that it is not form;

Secondly, that it is not space, at no. 460;

Thirdly, that it is not matter, at no. 464.

458. In regard to the first he does two things. First [318] he sets down why form seems to be place: it is because form is a container, and this seems to be a property of place. Now the boundaries of the containing body and those of the contained are together, since the container and the contained are contiguous. Thus it does not seem that the containing boundary, which is place, is separate from that of the body contained. Consequently, there does not seem to be any difference between place and form.

459. Secondly, [319], he shows that form is not place. For although place and form are alike in this, that each is a kind of boundary, nevertheless they are not the boundary of one and the same thing: for form is the boundary of the body of which it is the form, while place is not a boundary of the body of which it is the place, but of the body containing it. So, although the boundaries of the container and of the contained are together, they are not identical.

460. Then [320] he takes up the question of space.

First he sets down why space seems to be place;

Secondly, he shows that it is not place, at no. 461.

He says therefore first that frequently a body contained by place, and distinct from it, is changed from one place to another, and any number of bodies can succeed into its original place (but always in such a way that the container remains immobile) in the way that water goes out of a vessel. For this reason it seems that place is some middle space between the boundaries of the containing body, as though there were something there besides the body moved from one place to another. For if nothing were there besides the contained body, it would follow either that place is not distinct from the thing in place, or that what exists within the confines of the container’s boundaries cannot be place. Now just as place must be something over and above the contained body, so it must be something other than the containing body, due to the fact that place remains immobile, whereas the containing body and everything in it can be changed about. But in addition to the containing body and the contained body there is nothing present except the dimensions of space, which exist in no body. Consequently, because place is immobile, it seems that space is place.

461. Then [321] he shows that space is not place by two arguments. As to the first of these, he states it is not true that there is anything within the confines of the containing body other than the contained body which is transferred from place to place. Rather, within the confines of the containing body there happens a body of some kind, having, nevertheless, the following two characteristics: that it be a mobile body, and be naturally apt to touch the containing body. But if, in addition to the dimensions of the contained body, there were present a space which always remained in the same place, the embarrassing conclusion would follow that there would be infinite places together. The reason is because water and air have their own dimensions, and so does each body, and each part of a body. Now all these parts will do the same thing in the whole body that the whole water does in a vessel. According to those who hold the opinion that space is place, when the entire water is in the vessel there are present, in addition to the dimensions of the water, also other dimensions of space. Now every part of a whole is contained by the whole as a thing in place is contained by a vessel: the only difference being that the part is not separated from the whole, whereas the thing in place is separated frm place. If therefore a part be actually separated within the whole, it will follow that, in addition to the dimensions of the part, also other dimensions of the containing whole will be present.

But it cannot be said that such division would make new dimensions to exist: for division does not cause dimension; rather it divides dimension already existing. Therefore, before that part was divided in the whole, there were present other proper dimensions of the part, in addition to the whole’s dimensions, which also penetrate that part. Now there will be as many sets of dimensions all distinct, some of which interpenetrate others, as there are parts obtainable by division of the whole, parts, namely, so divided that one contains another. But it is possible in a continuous whole to obtain ad infinitum parts which contain other parts, because a continuum can be divided ad infinitum, Consequently, we should have infinite dimensions mutually penetrating themselves. If, therefore, the containing body’s dimensions, penetrating the thing in place, are place, it follows that there are infinite places together—which is impossible.

462. Then [322] he gives a second reason, which is the following. If the dimensions of the space which is between the boundaries of the containing body are place, it follows that place can be transported. For it is clear that when a body is transported, as, for example, a jug, the space within the jug is transported, since that space can never be except where the jug is. Now whatever is transported to another place is penetrated (according to those who hold the doctrine of space as place) by the dimensions of the space into which it is transported. Therefore it follows that other dimensions enter the dimensions of the jug’s space; consequently there would be another place of place, and many places would be existing together.

463. This unacceptable consequence arises from positing one place for the contained body, for example, the water; and another place for the vessel, for example, the jug. For according to the opinion we are discussing, the place of the water is the space within the boundaries of the jug, while the place of the whole jug is the space within the boundaries of the body containing the jug. We, however, do not assign a special place for the part, in which the part moves, as distinct from the whole, when the entire vessel is transported (by “part” he means the body contained in the vessel, as the water contained in the jug): because, according to Aristotle, the water is moved per accidens when the vessel is transported, and it changes place only inasmuch as the jug changes its place. Hence it is not necessary that the place into which the transfer is made, be the place of the part per se, but only inasmuch as it becomes the place of the jug. But according to those who hold the opinion about space as place, it follows that the new place would belong per se both to water and to the jug. Likewise, that space would be transported and would have a place per se, and not only per accidens.

Now although the containing body is sometimes moved, it does not follow according to the opinion of Aristotle, that the place is moved, or that there is a place of a place. For it does indeed happen that a containing body, in which something is contained, is sometimes moved, as are air or water or certain parts of the water, For example, if a boat is in a river, the parts of the water which surround the boat from below are in motion, but the boat’s place is not moved. Hence, he adds, “but not that place where they occur,”, i.e., that in which things occur as in a place is not moved.

How this is true he makes clear by adding, “which is a part of the place which is the place of the whole heavens.” For although this container [e.g., the water surrounding the boat] be moved inasmuch as it is this body, yet in regard to its relation to the whole body of the heavens it is not moved: the body which succeeds it has the same order or position in relation to the whole heavens as had the body which previously flowed on. This therefore is what he says, namely, that although the water or the air be moved, not so the place, considered precisely as a certain part of the place of the whole heavens and as having a definite position in the universe.

464. Then [323] he continues by considering matter.

First he shows why matter seems to be place;

Secondly, that it is not place, at no. 465.

He says therefore first that matter appears to be place, should one consider the transmutation of the bodies which succeed each other in the same place, as this occurs in some, one subject that is at rest in a place, with attention being paid, not to the fact that place is separate, but only to the fact that the transmutation is occurring in one and the same continuum. For some continuous body, at rest according to place, when it is being altered in quality, now white, now black; now hard, while previously soft. Yet it remains one and the same in number. And on account of this transmutation of forms in the subject we say that matter is something that remains one whole change taken place with respect to forms. Because of this, place seems to be something, because in it as remaining different bodies succeed each other. Nevertheless we use different terminology when referring to these two cases: to designate matter or the subject, we say, “What is now water, was previously air”; to designate unity in place, we say, “Where water is now there was air previously.”

465. Then [324] he shows that matter is not place, because, as we said above, matter is not separated from the thing of which it is the matter, nor does it contain the latter: both of which characteristics belong to place. Place, therefore, is not matter.

466. Then [325], having eliminated the first three members, he concludes to the fourth. And he says that since place is not any of these three, i.e., neither form, nor matter, nor some space which is other than the internal distances of the things in place, it must be the fourth of the above named, i.e., the boundary of the containing body. And lest anyone understand that the thing contained or in place is some middle space, he adds that the contained body is what is apt to be moved in respect to change of place.

467. Then [326] he tracks down the specific difference of place; namely, that it is immobile. In regard to this he does two things:

First, he shows that an error arose from improperly considering this difference;

Secondly, how we must understand the immobility of place, at no. 468.

He says therefore that it is a large undertaking and a difficult one to understand what place is, both because some have thought it is matter or form, both of which involve lofty speculation, as was said above (L.3), and because the change that occurs when things change place, occurs in something both at rest and containing, Now, since nothing seems to be containing and immobile except space, it seems that place is a sort of middle space distinct from the magnitudes which are moved in respect to place. And the fact that air seems to be incorporeal helps to make this opinion credible: for where air is there appears to be no body but a certain empty space. Thus place seems to be not only the boundaries of a vessel but something between the boundaries as a vacuum or void.

468. Then [327], in order to exclude the aforesaid opinion, he shows how we must understand the immobility of place. And he says that a vessel and place are seen to differ in this, that a vessel can be transported but place cannot, Hence, just as a vessel can be called “a transportable place,” so place can be called “an immobile (non-transportable) vessel.” Therefore, when something is being moved in a body that is in motion, as a ship in a river, we speak of that in which it is being moved as a vessel rather than of a containing place, because place “wants to-be immobile,” i.e., it is of the very nature and aptitude of the place to be immobile.. On this account it is better to speak of the whole river as being the place of the ship, because the river as a whole is immobile. Thus the whole river inasmuch as it is immobile is the common place.

However, since proper place is a part of common place, we must consider the proper place of the ship in flowing water, not the water inasmuch as it is flowing, but in its relation to the order or position which this flowing water has to the river as a whole: it is this order or position that remains constant, while the water flows on. Therefore, although the water materially passes on, yet, insofar as it has the motion of place, i.e. insofar as it is considered as having a certain order and position with respect to the whole river it does not change.

This also shows how we ought to consider how the boundaries of natural mobile bodies are place with respect to the entire spherical body of the heavens, which is fixed and immobile on account of the immobility of the center and of the poles. Therefore, although this part of air which contains, or this part of water, flow by and move as this water, yet, insofar as this water has the motion of place, viz., a position and order to the whole spherical body of the heavens, it always remains. This is like the same fire remaining as to its form, although as to its matter it is varied as wood is consumed and other wood added.

469. This removes an objection that could be lodged against positing place as the boundary of the container, for since the container is mobile, its boundary will also be mobile; consequently, a thing at rest will have diverse places. But this does not follow: because the boundary of the container is not place insofar as it is this surface of this particular mobile body, but by reason of the order or position it has in the immobile whole. From which it is evident that the whole notion of place in all containers is taken from the first container and locator, namely, the heavens.

470. Then [328] he concludes form the foregoing the definition of place, namely, that place is the immobile boundary of that which contains first. He says “first” to designate proper place and exclude common place.

471. Then [329] he shows that the definition is well assigned, because the things said about place concur with this definition. And he gives three such things: The first is that, since place is an immobile container, the middle of the heavens, i.e., the center, and the boundary of circular change of place, i.e., of the bodies moved in a circle, namely, the boundary as to us, i.e., te surface of the sphere of the moon, is (namely, the latter) seen as “up”, and the other (namely, the middle) as “down”.

Things absolutely in place, and things in place in a certain respect and this last named (the middle or center) is seen to be said most properly of all. For the center of a sphere is always at rest.

Now that which is the boundary in relation to us of the bodies moved in a circle [namely, the surface of the sphere of the moon], although it moves in a circle, nevertheless remains, insofar as it remains in the same way, i.e., at the same distance from us. Hence, since natural bodies are moved to their proper places, it follows that light bodies naturally move “up”, and heavy bodies “down”—for both the middle (center) and the containing boundary in the direction of the middle are called “down”; and likewise the boundary in the other sense [ the surface of the sphere of the moon], and what is in the direction of that boundary, are called “up”. He uses this manner of speaking, because it is the center that is the place of the earth, which is simply heavy, while toward the center the place of water is found. In like manner, the place of fire, which is simply light, is the outermost, while the place of air is toward the outermost.

He gives the second [330], saying that because place is a boundary, place seems to be like a certain surface and like a containing vessel, but not like the space [or volume] of the containing vessel.

He gives the third [331] when he says that, because place is a boundary, the place and the thing in place are together; for the limits of the thing in place and the boundary of the container, which is place, are together (for the boundaries of things that touch are together). This also explains why place is equal to the thing in place: namely, because they are equated as to their boundaries.

Lecture 7

How something exists in place

472. After defining place, the Philosopher now shows how something exists in place. About this he does two things:

First he shows how something is absolutely in place and how not;

Secondly, how a thing not absolutely in place. is in place in a certain respect, at 482.

473. He concludes therefore first [332] from the foregoing that, since place is the boundary of the container, whenever a body has another body outside it and containing it, it is in place absolutely and per se; if such a body does not have an external body containing it, it is not in place at all. The only body in the universe that exemplifies this second case is the outermost sphere, whatever it may be. Hence, according to this definition, it follows that the outermost orb is not in place.

474. But this seems to be impossible, because the outermost sphere is in motion in place and nothing is moved in place unless it is in place. Now this difficulty does not arise for those who hold the opinion that space is place. For they are not forced to say that, in order to be in place, the outermost sphere must have a body containing it; rather, the space penetrating the entire universe and all its parts is the place of the entire universe and of each of its parts, according to these Philosophers.

But this position is impossible, for one must admit either that place is not distinct from the thing in place, or that space has dimensions existing per se but yet penetrating the dimensions of sensible bodies—both of which positions are impossible.

475. Wherefore Alexander said that the outermost orb is not in place at all: for it is not necessary for every body to be in place, since place is not in the definition of body. For this reason he held that the outermost sphere is not in motion in place, neither as a whole, nor as to its parts.

But since every motion must fit into one of the genera of motion, Avicenna, following him, said that the motion of the outermost sphere is not motion in place but motion in situs [position in place]. This is against Aristotle, who says in Book V (L. 4) that motion is present only in three genera, namely, quality, quantity, and “where.”

Avicenna’s position is untenable because it is impossible that motion strictly speaking be in a genus the notion of whose species consists in an indivisible. For the reason why there is not motion in the genus “substance” is that the nature of every species of substance consists in an indivisible, due to the fact that the species of substances do not admit of more or less; on this account, since motion is successive, a substantial form is not made existent by motion but by generation, which is the terminus of motion. The case is different with whiteness and like things, which can be participated according to more or less. But every species of situs has a nature that consists in an indivisible, so that if anything be added or taken away the original species does not remain. Hence it is impossible for motion to exist in the genus of situs.

Besides, the same difficulty remains. For situs taken as a predicament implies the order of parts in place; although if it be taken as a difference in the genus of quantity it implies merely an order of parts in a whole. Therefore, whatever is moved according to situs, must be moved according to place.

476. Others such as Avempace said that place should be assigned in one way to a body moving in a circle and in another way to a body moving in a straight line. For since a straight line is imperfect, since it can be added to, a body moving in a straight line requires a place externally containing it, but because a circular line is perfect within itself, a body moving in a circle does not require an external place to contain it, but merely a place about w1hich it may revolve; hence it is that circular motion is said to be motion about a center. So therefore they say that the convex surface of the sphere contained is the place of the first sphere. But this is against the common suppositions about place already laid down; namely, that place is a container, and that it is equal to the thing in place.

477. And therefore Averroes said that the outermost sphere is in place per accidens. To understand this, one should consider that everything which has fixity by means of something else, is said to be in place per accidens, due to the fact that that by means of which it is fixed is in place, as it evident in the case of a nail fixed in a ship and of a man at rest in a ship. Now it is clear that bodies moving rotationally are fixed because their center is immobile; hence the outermost sphere is said to be in place per accidens, insofar as the center about which it is revolving has existence in place, The fact that the lower spheres have a per se place in which they are contained is incidental and not essential to a body moving rotationally.

But against this it is objected that, if the outermost sphere is in place per accidens, then it is in motion in place per accidens, and so per accidens motion is prior to per se motion. To this the answer is given that for rotational motion it is not necessary for a body moving per se rotationally to be in place per se, although it is necessary for straight line motion.

But this seems to be against Aristotle’s definition, given above, of what is in place per accidens. For he said that some things exist or are in motion place per accidens, because that in which they exist is in motion. But nothing is said to be in place per accidens because something entirely outside it is in place. Now since the center is completely extrinsic to the outermost sphere, it seems ridiculous to say that the outermost sphere is in place per accidens because the center is in place.

478. And therefore I favor more the opinion of Themistius, who said that the outermost sphere is in place by means of its parts.

To understand this it must be recalled that Aristotle said above that there would be no discussion about place except for the act of motion, which reveals the existence of place from the fact that bodies succeed one another in the same place. Hence, although place is not of the essence of body, yet it is necessary for a body moved according to place. In the case of a body moving locally, the reason it is necessary to assign a place is because in that motion a succession of diverse bodies in the same place is considered. Therefore, in the case of bodies moving in a straight line it is clear that one body succeeds another in the same place according to their totality, for one whole body leaves one whole place which is then occupied by another whole body. Hence a body which is in motion in a straight line must be in place in its entirety.

But in the case of rotational motion, although the whole body comes to be in different places as distinguished by reason, nevertheless the whole body does not change its place as to subject: for the place remains ever the same as to subject; but varies only according to reason, as will be said in Book VI (L.2). Nevertheless the parts change place not only as to reason but as to subject also. Therefore in the case of rotational motion there is not a succession of whole bodies in the same place but of parts of the same body. Therefore a rotating body does not essentially require a place according to its totality but according to its parts.

479. But against this there seems to be the objection that the parts of a continuous body are neither in place nor moved in respect to place; rather, it is the whole that is both moved and in place. But it is clear that the outermost sphere is a continuous body; therefore, its parts are neither in place nor in motion in place. Consequently, it does not seem to be true that place should be attributed to the outermost sphere by reason of its parts.

The answer to this objection is that, although the parts of a continuous body are not actually in place, they are so potentially, insofar as the continuum is divisible. For a part, if it is separated, will be in the whole as in a place; hence, in this manner the parts of a continuum are moved in place. This is clearly evident in liquid continua which are easy to divide—for example, in the case of water, whose parts are found to be in motion within the whole water. Consequently, because something is said of a whole by reason of its parts, insofar as the parts of the outermost sphere are potentially in place the entire outermost sphere is in place per accidens by reason of its parts: and to be in place in that way is enough for rotational motion.

480. If a further objection is raised that what is in act is prior to what is in potency and that consequently it seems Improper that the first local motion be that of a body existing in place by means of its parts which are potentially in place, the reply is that this is most fitting to the first motion. For it is necessary that the descent from the one immobile being to the diversity which is found in mobile things be made step by step. Now the variation based on parts existing in place potentially, is less than that of wholes existing in place actually. Hence the first motion, which is rotational has less deformity and retains greater uniformity, being closer to the immobile substances. Now it is much better to say that the outermost sphere is in place on account of its intrinsic parts, than an account of the center which is entirely extrinsic to its substance; and this is more in agreement with Aristotle’s opinion, as is clear if one considers the passage following, in which Aristotle shows how the heavens are in place.

481. For in regard to this he does two things:

First he shows how the outermost sphere is in place;

Secondly, he draws-a conclusion from what has been said, at 485.

About the first he does three things:

First, he shows that the outermost sphere is in place through its parts;

Secondly, how its parts are in place, at no. 481,

Thirdly, how the parts make the whole to be in place, at no. 434.

482. Therefore, because he had said that if a body does not have something outside of it containing it, it is not in place per se, he concludes [333] that if a body of this kind, such as the outermost sphere is, be water (which will more easily illustrate what we are about to say on account of its easy divisibility), its parts will be in motion inasmuch as one part contains another, thus making it exist in place after a fashion. But the entire water will be in motion in one sense and in another sense not. For it will not be in motion in such a way that the entire water will change its place as though being transferred to another place distinct as to subject, but it will be moved rotationally—a motion that requires place for the parts and not for the whole. And it will be moved, not up and down, but circularly: for some things are moved up and down and change place in their entirety, namely, rare and dense bodies, or light and heavy things.

483. Then [334] he indicates how the parts of the outermost sphere exist in place, saying that, as was mentioned above, some things are actually in place, others potentially. Hence in the case of a continuum of similar parts the parts are in place potentially, as in the case of the outermost sphere; but when the parts are separated and merely contiguous, as occurs in a pile of stones, the parts are in place actually.

484. Then [335] he shows how from this it follows that the entire sphere is in place. And he says that some things are per se in place—as any body that is per se in motion in place, whether it be in respect to local motion or increase, as was said above (L.5). But the heavens, i.e., the outermost sphere, are not in place in this manner, as was said, since no body contains them; but inasmuch as they are moved rotationally, with part succeeding part, place is attributed to the parts potentially, as was said, inasmuch as one part-is “had,” i.e., is consecutive, with respect to another.

Certain things, indeed, are in place per accidens, e.g., the soul, and all forms; and in this manner the heavens, i.e., the outermost sphere, is in place insofar as all its parts are in place, since each of its parts is contained under another in the rotation of the sphere. For in a non-round body the outermost part remains uncontained and merely containing; but in a round body each part is both container and contained, potentially however. Hence it is by reason of all its parts that a found body is in place. And this Aristotle takes to per accidens, namely, what is true of the parts, as above when he said that the parts of a body are in motion per accidens in place.

485. Then [336] he draws a conclusion from the foregoing. For since he had said that a body in rotational motion need not be in place in its entirety but only per accidens by reason of its parts, he concludes that the outermost body is moved only rotationally, because the whole in question is not anywhere; what is somewhere is itself something, and has something outside of it by which it is contained; but there is nothing outside the whole. For this reason all things are said to be in the heavens as in the outermost container, because the heavens are probably the containing whole. He says “probably,” because it has not yet been proved that there is nothing outside the heavens. It is not to be thought that the very body of the heavens is a place; rather, it is a certain final surface of it turned toward us which is as a boundary in contact with the mobile bodies existing in it. For this reason we say that earth is in water which is in air, which is in either, i.e., fire, which is in the heavens, which are not in anything else.

486. However, according to the intention of Aristotle, this passage must be plained differently. For the example of water which he first adduced is not to be referred, according to him, to the outermost sphere only, but to the entire universe, which indeed is moved insofar as its parts are moved—some rotationally, as are the heavenly bodies; some up and down, as are the lower bodies. As to what he said later on, that some things are actually in place and other potentially, this is not to be referred to what he said previously but is to be taken independently. For since he had said that some things are in place according to their parts and others according to their totality, he adds after that, that some things are in place according to act and others according to potency; finally, he says that some things are in place per se and others per accidens.

In this connection note that according to Aristotle “the heavens” are to be taken in two senses here: first, they are taken for the entire universe of bodies and especially of the heavenly; secondly, for the outermost sphere. He says therefore that those things are in place per se which are in motion according to place, whether they are in motion according to their totality or according to their parts, as are the heavens, i.e., the universe; in place per accidens are the soul and the heavens, i.e., the outermost sphere. For it is necessary to say that all the parts of the universe are somehow in place: the outermost sphere per accidens and other bodies per se, inasmuch as they are contained by a body outside of them. And he manifesto this up to the end.

Lecture 8

The definition of place is used to solve the original problems;

the properties of place are justified.

487. After explaining what place is, the Philosopher now uses his definition to resolve the doubts that were raised about place (L.2). Now there were mentioned above six reasons to show that place does not exist. Of these he bypasses two: the one in which it was asked whether place be an element or a composite of elements; the other in which it was shown that place cannot be reduced to any genus of cause. He bypasses them because no one who posited place took it either as an element or as a cause of things. Hence he makes mention only of the four remaining.

488. One of these was that, since place never lacks a body, and a body never lacks a place, it seemed to follow that if the body grew, the place would grow.

Now this would follow if it were supposed that place were a space co-extensive with the dimensions of the body, so that, as the body increased, so would the space. But this does not follow from the aforesaid definition of place, namely, that it is the boundary of the container.

469. Another argument was that, if the place of a body be distinct from the body, then the place of a point would be distinct from the point; wherefore, it did not seem possible for place to be distinct from the body, since the place of a point is not distinct from the point. But this argument was based on the imagining of those who opined, that place, is the space coextensive with the volume of the body, so that a dimension of space would correspond to a dimension of the body and in like manner to each point of the body, This, however, need not be said if we suppose that place is the boundary of the container.

490. Another argument was that, if place is anything, it must be a body, since it has three dimensions. Consequently, there would be two bodies in the same place. But according to those who agree that place is the boundary of the containing body it is not necessary to say that two bodies would be in the same place, or that there is some bodily space intervening between the boundaries of the containing body, but that there is some body there.

491. Likewise another argument was that, if everything that exists is in place, it will follow that even a place is in place. This argument is easy to answer, if we suppose that place is the boundary of the container, For according to this it is clear that place is in something; namely, in the containing body, but it is there, not as in a place, but as a boundary in a finite thing, just as a point is in a line and a surface in a body. For it is not required that everything that is, be in something as in a place; this is required only of a mobile body, for it is motion that led to distinguishing between the thing in place and the place itself.

492. Then [338] he uses his definition to give a reason for the properties of place.

First, as to the fact that a body is naturally borne to its proper place;

Secondly, as to the fact that a body naturally rests in its own place, at no. 493.

He says first therefore, that if place be taken to the boundary of the container, the reason why each body is naturally borne to its own place can be given: it is because the containing body (which is next to the contained and located body, and which is touched by it so that the boundaries of both are together not by compulsion) is akin to it in nature. For the order of situs in the parts of the universe follows upon the order of nature. For the heavenly body, which is supreme, is the most noble; after it, among the other bodies the noblest in nature is fire, and so on down to earth. Hence it is clear that the lower body which is situated according to position, next to the higher body, is akin to it in the order of nature. And therefore he adds, “not by compulsion,” in order to point out the natural order of situs to which the order of nature corresponds and to exclude a compulsive order of situs, as when by compulsion a body of earth is above air or water. Two such bodies next to one another in the natural order of situs and which, in the natural order of natures, are disposed to be together, do not affect each other; i.e., when they are made continuous to each other and become one—and for this they have an aptitude on account of the similarity of their natures—then they do not interact. But when distinct things are in contact, their mutually interact on account of the contrariety of their active and passive qualities. Therefore it is the kinship of nature existing between the container and the thing contained that explains why a body is naturally moved to its own place: because the rank in natural places must correspond to the rank in natures, as was said. But such a reason cannot be assigned if place is taken to be space: because in the separated dimensions of space no order of nature can be considered.

493. Then [330] he gives the reason why bodies naturally rest in their own place. And he says that this happens reasonably, if we grant that place is the boundary of the containing body: because according to this the contained body is related to the containing body after the manner of a part to a whole—a separated part, however. This is abundantly clear in bodies that are easy to divide, such as air or water: for their parts can be moved by something in the whole just as a thing in place is moved in a place. And this also is not only true according to the figure of containing one under the other, but even according to the properties of their nature. For air is related to water as the whole, because water is like matter and air like the form: water is as the matter of air, and air is as the form of water. This is so because water is in potency to air absolutely.

Now while it is true that in some other ways air is in potency to water, as will be explained later in De Generatione, it is necessary for the present to accept this in order that we may explain our proposition. Here it is not declared as a certainty, but in the De Generatione it will be proved with greater certainty. For it will be said there that, when air is generated from water, it is corruption secundum quid and generation simply, because a more perfect form is being introduced and a less perfect one is being put off. But when water is generated from air, it is corruption simply and generation secundum quid, because. a more perfect form is being put off and an imperfect one being introduced. Consequently, water is in potency to air absolutely as the imperfect to the perfect; but air is in potency in water as the perfect to the imperfect. Hence air is as the form, and as the whole which is like the form; water, however, is as the matter and as a part, which pertains to the notion of matter. Therefore, although the same thing is both matter and act, because the water contains both in itself; yet properly speaking, the latter, i.e., the water, is in potency as an imperfect thing, but the former, i.e., the air, in act as a perfect. Hence water will be related to air somewhat as part to whole. And therefore these things, the air and the water, when they are distinct things, they are in contact; but when they form a unity, by one passing into the nature of the other, then coupling, i.e., continuity occurs. Therefore, just as the part naturally is at rest in the whole, so also a body naturally rests in its natural place.

Note, however, that the Philosopher is speaking here of bodies according to the substantial forms which they have under the influence of the heavenly body which is the first place, and which gives to all other bodies the power to act as places. But if we consider active and passive qualities, there is contrariety among the elements and one tends to destroy another.

Finally he concludes in summary that it has been stated that place exists and what place is.

Lecture 9

The void—reasons for and against

494. Having discussed place, the Philosopher now begins to treat of the void. Concerning it he does two things:

First he manifests his intention:

Secondly, he executes it, at no. 497.

As to the first, he does too things:

First he shows that it is proper for the natural philosopher to deal with the void;

Secondly, he shows what order should be followed in determining the matter of the void, at no. 495.

He says therefore, first [346] that it is the task of the natural philosopher to determine about the void just as it was his task to determine about place: whether it exists, what it is. For the same reasons have led to belief or disbelief in the existence both of place and of the void. For those who posit a void think of it as a place and vessel, which vessel or place seems to be full when it has within it the mass of some body; but when it does not it is said to be a void. It is as though the same thing as to subject is place and void and full, any differing among them being only in the mind.

495. Then [341] he shows what order must be followed in determining about the void. And he says that we must begin by giving the reasons of those who claim that the void exists; then the opinions of those who claim it does not exist; and then the general opinions about the void; namely, what belongs to the notion of the void.

496. Then [342] he begins to follow this program:

First sets down preliminary notions that are necessary for discovering the truth about the void;

Secondly, he begins to search for the truth, at no. 520 (L.11).

About the first he does two things:

First he gives the reasons of those who posit or deny the existence of the void;

Secondly, the common opinion about the void, showing what is included in its notion, at no. 506 (L. 10).

As to the first he does two things:

First he gives the reason of those who deny the existence of the void;

Secondly, the reasons of those who affirm it, at no. 499.

497. He says first therefore [342] that some of the earlier philosophers desirous of demonstrating that the void does not exist erred by not arguing against the reasons given for the existence of the void. For they did not show that the void does not exist, but gave their reasons to show that something full of air is not a void, as is evident from Anaxagoras and others who reasoned like him. In order to destroy the void they wanted to demonstrate that air is something, and thus, since te void is that in which nothing exists, it followed that something full of air is not a void.

In debating with their adversaries, they showed that air is something by means of wine skins which, when inflated, could support a weight, and which would not happen unless air were something. This also showed that air has strength. Also they showed it by taking the air in clepsydras, i.e., in vessels that absorb water; in these vessels water is drawn in by drawing in air, or water is prevented from entering, unless the air be withdrawn.

It is clear therefore that they are not objecting against those who posit a void, because all such claim it is empty space in which no sensible body exists, for they assume that whatever exists is body perceptible to sense, and thus, where no sensible body exists, they believe nothing exists. Hence, since air is a body scarcely perceptible to sense, they thought that where there was nothing but air the void existed.

498. Therefore, to destroy their position it is not enough to show that air is something, but also one must show that there is no space without a sensible body. Space was supposed to be a void in two ways: first, as something separated from bodies, as though we were to say that the space within the confines of a house is a void; secondly, as something existing In act between bodies, preventing them from being continuous, as Democritus and Leucippus and many of the other natural philosophers held. For they imagined that if the totality of being were continuous, all things would be one: for there would be no more reason for distinguishing bodies at one point rather than another.. Hence between all distinct bodies they posited intervals of empty sapce in whie~i no being existed. And since Democritus posited that bodies are composed of many indivisible bodies, he posited between those indivisibles certain empty places which he called “pores”.- in this way he explained that all bodies are composed of the full and of the empty. Or if the entire body of the world are continuous and no such empty place existed between the parts of the universe, they yet posited a void existing outside the universe.

It is evident therefore that the aforementioned philosophers who tried to reject the void did not answer the problem as laid down by others. For they should have shown that the void does not exist in any of those ways.

499. Then [343] he sets forth the reasons of those who posited a void.

First, those who spoke of the void naturally;

Secondly, of those who spoke of it non-naturally, at no. 505.

As to the first he does two things:

First he mentions the reason given by those who held that the void is a space separated from bodies;

Secondly, by those who held for a void in bodies, at no. 502.

Concerning the first he does two things:

First he gives the reason of those who posited a void;

Secondly, how Melissus used that reason conversely, at no. 501.

500. He says therefore first [343] that those who affirmed the existence of the void gave more opposite reasons. One of which was that motion is respect of place, i.e., change of place and increase, as was said above, would not exist if there were no void. They showed this in the following manner: If something is in motion according to place, it cannot be moved into what is full because a place filled with one body cannot receive another. For, if it received it there would then be two bodies in the same place—and the same would follow for any [additional] body: for there is no reason why many bodies could not be in the same place if two could. And if that were to happen, i.e., that any number of bodies were in the same place, it would follow that the smallest place could receive the largest body—because many small things form one large thing. Hence, if any small equal bodies could exist in the same place, then also many could. And so, having proved this conditional position that there is motion, there is a void, they argue (by positing the antecedent): “But there is motion; therefore, there is a void.”

501. Then [344] he shows how Melissus, supposing the same conditional, argued in a contrary manner from the denial of the consequent, and reasoned thus: if motion exists, there is a void; but there is no void; therefore motion does not exist. Consequently, the totality of being is immobile.

Thus the foregoing is one way in which some proved that the void exists after the fashion of something separate.

502. Then [345] he lists three reasons given by those who held that the void exists in bodies. The first of these is based on things that condense. For in the case of things that can be compressed it seems that the parts come together and fit in together and press down and compress each other so that, as is held, casks will hold as much wine with the wine skins as without, especially if the wine skins are thin, because in the wine skins the wine seems to become condensed. This condensation they believed to take place as though in the condensed body the parts entered into certain empty spaces.

503. The second reason he gives [346] is based on increase: For a body grows on account of food, which is a body. But two bodies cannot exist in the same place. Therefore there must be, in the body which has grown, certain voids in which the food may be received. Consequently, there must be a void in order that food be taken in,

504. The third reason [347] is based on a vessel full of ashes being able to absorb as much water as the empty vessel. This would not be the case unless there were empty spaces between the parts of the ashes.

505. Then [348] he gives the opinions of the non-natural philosophers about the void. And he says that the Pythagoreans also posited a void which entered into the parts of the universe from the heavens, on account of the infinite void which they supposed existed outside the heavens—a void like some infinite air or infinite spirit [i.e. breath]: just as a person who breathes divides by means of his breath certain things that are easy to divide, such as water or similar things, so it was that the things of this world became distinct by some being as though through breathing. They did not understand this to except through a void, as was mentioned in regard to Democritus—as though the void were nothing other than the distinction between things. And because the first distinction and plurality is found in numbers, therefore they first of all posited a void in numbers, so that it is through the nature of the void that one unit would be distinct from another—so that number would not be continuous but would have a discrete nature. But because they spoke of the void in a quasi-equivocal manner, calling the distinction of things “a void” Aristotle does not discuss this opinion below.

Finally, in summary, he concludes that we have given the reasons why some posit a void and why some do not.

Lecture 10

The meaning of “void”—refutation of those positing the void

506. The Philosopher had said above that we I must start with three things. So now, having finished two of them, by giving, namely, the opinions of both of those who posited and of those who rejected the void, he now enters upon the third, by showing, namely, the general notions people have about the void.

Concerning this he does three things:

First he shows what is meant by the word “void”;

Secondly, how some thought that the void exists, at no. 513;

Thirdly, he rejects the reasons given by those who posit that a void exists, at no. 515.

As to the first he does two things:

First he reveals his intention;

Secondly, he executes it, at no. 509.

507. He says first, therefore [349], that since it was pointed out that some people affirmed a void and others denied it, in order to get at the truth we must begin by the meaning of the word “void.” For just as, when there is question about some property existing in a subject, we must begin by agreeing what the thing is, so when there is question about the existence of something, we must begin by taking as the middle form the meaning of the word. For the question of what something is comes after the question of whether it exists.

508. Then [350] he shows that it meant by the word “void”.

First he gives the more common meaning;

Secondly, what the Platonists took it to mean at no. 512.

As to the first he does three things:

First he shows what the word “void” means;

Secondly, what should be added to that meaning at no. 510;

Thirdly, he clears up a doubt, at no. 511.

509. He says therefore that according to common opinion, the void seems to signify nothing more than a place In which there is nothing. The reason for this is because properly that is said to be a void in which there is not any body, and since only a body can be in place, void seems to mean nothing more than a place without any thing in it. But because people suppose that every being is a body, it follows that according to their opinion where there is not body, there is nothing.

And further they believe that every body is tangible, i.e., that it has tactile qualities. And a body of this kind is heavy or light: for in their time it was not yet known that a heavenly body is different in nature from any of the four elements. Hence since it is the very nature of the void to be a place in which there is not a body, it follows that the void is that in which there is neither a light nor a heavy body. However, this is not to say that it belongs to the notion of the void according to the primary meaning of the word, but rather by reason of a certain syllogistic deduction that starts with the general opinion of people that every body is either heavy or light; just as the common opinion of people that every being is a body, leads to the conclusion that the void is that in which there is nothing.

Consequently, the meaning of this word “void” is three-fold: one is proper, namely, that the void is that in which there is not any body; the others come from the general opinion of people: the first is more common, namely, that the void is a place in which nothing exists; the second is more restricted, namely, that the void is a place in which there is neither a heavy nor a light body.

510. Then [351] he shows that must be added to this meaning. For he says that it is not correct to say that a point is a void, even though in a point there is no tangible body. So we must add that the void to a place in which there is not a tangible body, but which has in it space to receive a tangible body, just as a blind person is said to be one who lacks sight but to apt to have it. And so he concludes that in one way the void is called a space which is not full of a body that is sensible by touch, i.e., a body that is heavy or light.

511. Then [352] he clears up the following difficulty; If there is color or sound in a certain space, should it be called a void or not? This question arises because the definition first given says that the void is that in which there is nothing. And he answers by saying that if the space in which there is just sound or color has room for a tangible body, it is a void; if not, not. The reason is that the proper definition of the void is not “that in which there is nothing,” and such a definition is held only by people who believe that where no body is, nothing is.

512. Then [353] he gives the meaning of “void” as used by the Platonists. And he says that there is another meaning of the void: that in which there is no “this something” or any corporeal substance. Now a “this something” comes about on account of the form. Hence some claim that the matter of a body, insofar as it is apart from its form, is the void. These are the same who claim that matter is place, as was stated above (L.3). But this is poor judgment, for matter is not separable from the things of which it is the matter; whereas men inquire about place and the void as being separable from bodies in place.

513. Then [354] he tells how some posited existence of a void;

First, what they said the void was;

Secondly, why they posited it, at no. 514.

He says therefore first that since the void is a place without a body in it, and since we have already decided how place exists and how it does not (for we have said that place is not a space but the boundary of a container), it is clear that the void is neither a space separated from bodies nor intrinsic to them as Democritus supposed. This is so because those who suppose that space exists in either of those two ways, intend the void to be not a body, but the space of a body. For they thought that the void was something because place was something, and just as place seems to be space, so also the void. But if place is not a space outside of bodies, neither can the void be a space outside of bodies. And since it is the very nature of the void to be a bodily space existing outside of bodies, as was said above, it follows that the void does not exist.

514. Then [355] he shows why they posited a void. And he says that they admitted the existence of the void for the same reason that they admitted place, namely, on account of motion, as we said above: for it comes about that local motion is saved, both for those who assert that place is something over and above the bodies which are in place and for those who claim that the void exists. But for those who deny place and the void, there cannot be local motion. Consequently, some believed that the void is a cause of motion in the way that place is, i.e., as that in which motion takes place.

515. Then [356] he rejects the arguments of those who posit existence of the void. He does not, however, intend here to give a true solution to the aforesaid arguments, but to bring an objection which at a glance shows that their arguments do not conclude with necessity.

First therefore he rejects the reasons given by those who posit a separated void;

Secondly, the arguments of those who posit a void existing in bodies, at no. 517.

516. He rejects the first reason in two ways: First, because even though motion exists, it does not necessarily follow that the void exists. And if we speak generally of any species of motion, it is clear that the void is not necessary at all. For nothing prevents the full from being altered [i.e., having motion in quality], since only local motion seems to be excluded if the void is not posited. Yet Melissus did not see this, for he believed that if there were no void, no motion of any kind could exist.

Secondly, he rejects the same reason on the ground that not even local motion is destroyed, if there is no void. For, assuming that there is no separable space over and above moving bodies, local motion can take place, if bodies make room for one another by contracting: thus they would be moving into the full rather than into the empty. This is evident in the generations of continuous bodies, especially in liquids, such as water. For if a stone is thrown into a large surface of water, circles appear around the place of entry as long as one part of the moving water agitates another part and enters it. Hence, because a small portion of water by a process of diffusion enters a larger section, the circles grow from small to large until they cease entirely.

517. Then [357] he rejects the reasons given by those who posit a void in bodies. And first of all the reason based an condensation. And he says that bodies happen to become condensed, and parts of a body mutually penetrate, not because the invading part is entering an empty place but because there were certain openings, full of a more subtle body which escapes under condensation, just when water is compressed and contracted, the air that was present is expelled. This takes place manifestly in a sponge and other like porous bodies. Therefore this solution does not give the reason for condensation (he will give this later [L.14]: but it does show that also in this way, the need of a void can be clearly eliminated.

518. Secondly [358] he rejects the argument based on growth. And he says that growth occurs not only by the addition of some body invading the growing body so as to make the void necessary but also by alteration, as, when air comes to be from water, the quantity of air becomes greater than the quantity of water. This too is not the true solution of their argument but merely an objection showing that it is not necessary to posit a void. The true solution is given in the book “ De Generatione, where it is shown that food does not pass into that which grows as to be a body distinct from it; rather it is converted into its substance, as wood added to fire is converted into fire.

519. Thirdly [351] he rejects together both the argument about increase [in growth] and that about water poured on ashes and says that each of these arguments blocks the other. This is evident as follows. For there is in respect to increase this difficulty: it seems either that the whole body is not being increased, or that increase does not come about by the addition of body but by the addition of something incorporeal, or that two bodies can be in the same place. Now it is this difficulty, which seems to be against both these who posit a void and against those who do not, that they wish to solve. But they do not show that the void exists, or, if increase is due to the void, then they would have to say that the whole body is a void, since the whole body is increased.

Likewise, in regard to the ashes: for if a vessel full of ashes can take as much water as the empty vessel, then one has to say that the whole container must be a void. Therefore this is not due to empty space but to being mixed in with the water. For when water is mixed with ashes it condenses and part of it evaporates; moreover, parts of the ash are condensed on account of the moisture, and a sign of this is that not as much water can be recovered as was put in.

Finally, he concludes that it is clearly easy to solve the arguments by which they prove the existence of a void.

Lecture 11

From motion there is shown to be no separated void

520. Having gone over others’ opinions about the void and having indicated what is meant by the word “void,” he now begins to search for the truth.

First, he shows that the void does not have a separate existence;

Secondly, that there is no void in bodies at no. 544 (L.14).

Concerning the first he does two things:

First he used motion to show that a separate void does not exist;

Secondly, by considering the void in itself, at no. 541.

As to the first he does two things:

First, from the fact of motion he shows there is no void;

Secondly from the fact of faster and slower motions, at no.527 (L.12).

521. In regard to the first point he gives six reasons. In regard to the first of which he says [360] that we must repeat that there is no separated void as some assert. He says “repeat,” because this was already somewhat proved from the notion of place: for if place is not space, it follows that the void is nothing, as was said above. But now he proves the same point again from motion: for void was posited, as we said, on account of motion. But motion does not necessarily require a void. For it would seem especially to be the cause of local motion. But it is not necessary to posit a void in order to explain local motion, because all simple bodies have natural local motions, as the natural motion of fire is upward and that of earth downward toward the center. Thus it is clear that it is the nature of each body that causes its local motion and not the void. The latter would be the cause if any natural bodies were moved due to the necessity of a void. But if it is not set down as the cause of local motion, it cannot be considered the cause of any other motion or of any other thing. The void therefore would exist without a purpose.

522. He then gives the second reason [361]. If a void be postulated, no reason can be assigned for natural motion and rest. For it is clear that a natural body is moved toward its own natural place and rests there naturally on account of the kinship it has with its place and because it has no kinship to the place from which it departs. But the void has no nature by which it could be akin or hostile to a natural body. Therefore, it there were a void, considered as a certain place without a body in it, one could not assign any part to which the body would be naturally moved. For we cannot say that it would be borne to just any part, because observation shows that this is wrong, for a body naturally goes from one place and naturally approaches another.

This same reason is valid against those who posit place as a separate space into which a mobile body is borne. For it would be impossible to explain how a body in such a place could either be moved or be at rest: for the dimensions of space have no nature to which a natural body could be similar or dissimilar. Deservedly, then, the same argument applies to the void as to “up” and “down,” i.e., to place, whose parts are “up” and “down”; for those who posit a void call it place.

Moreover, not only are those who posit a void and those who posit place to be space unable to explain how something is moved and at rest In respect to place, but also how something exists in place or in the void. For if place is supposed to be space, then the whole body would have to be enclosed inside that space, and not as happens with those who agree that place is the boundary of the containing body and that a thing is in place as in something separate and as in a body that contains and sustains it. Indeed, it seems to be of the very nature of place that something be in place as in something separated and existing apart from it: for if any part of a body is not laid down as separated from the body, it will exist in that body not as in a place but as in the whole. Therefore, it pertains to the very nature of place and of the thing in place that one be separated from the other. But this does not happen if place is space into whose entirety the entice body is immersed. Therefore space is not place. And if space is not place it is clear that no void is place.

523. He gives the third reason [362] saying that, whereas the early philosophers claimed that the void had to be, if motion existed, the very opposite is the case: for if there were a void there would be no motion. And this he proves by a simile. For some have said that earth comes to rest at the center on account of the likeness of the parts on the whole circumference: consequently, earth, having no reason to be moved toward one part of the circumference more than another, rests. The same reason would cause rest in a void. For there would be no reason for earth to be moved to one part rather than to another, since the void, as such, does not have differences among its parts—for non-being does not possess differences.

524. He gives the fourth reason [363]as follows. Natural motion is prior to compulsory since compulsory motion is only a departure from natural motion. Therefore, remove natural motion and all other motion is removed; for when the prior is removed, all that follows is removed. But if the void is posited, natural motion is removed; because the differences among the parts of place would be taken away and it is toward such parts that natural motions tend The same holds if the infinite be posited, as we said above.

There is, however, this difference between the void and the infinite, that after granting the infinite there is no way of positing “up” or “down” or “center,” as we pointed out in Book III; but after granting a void, these places could be posited, but it would not be because they were mutually different: for no difference can be assigned in the realm of nothing and non-being and, consequently, of the void, which is a non-being and a privation. Yet natural changes of place do require difference of place, because diverse bodies are moved to diverse places. Consequently, natural places must be different one from the other. Therefore, if a void be posited, nothing could undergo a natural change of place; and if there is no natural change of place, there will be no change of place of any sort. Hence, if there is any change of place, there can be no void.

525. The fifth reason is then given [364]. in regard to this it should be considered that some question exists about projectiles: for the mover and the thing moved must be always together, as will be proved below in Book VII (1-3). Yet a projectile is found to be in motion even after it is separated from the projector, as is evident in the case of a stone that is thrown, or of an arrow shot from a bow. Now on the supposition that there is no void this difficulty is solved by attending to the air with which the medium [the field of trajectory] is filled. And it is solved in two ways. For some assert that projectiles remain in motion even after they are no longer contact with what gave them impulse on account of antiperistasis, i.e., repercussion or counter-resistence: for the air that has been pushed, pushes against other air, and that against other air, and so on, and it is on account of this impact of air against air that the stone is moved.

The other explanation is that the continuum of air that received the impact from the projector pushes the impelled body with more speed than the speed of the motion by which the projectile is naturally borne to its proper place. Hence the speed of the air movement prevents the projectile, for example, the stone, or some other such, from falling downward; but it is carried along by the impulse of the air.

Now neither of these explanations could be alleged if there were a void; consequently, a projectile could be moved only as long as it was carried, for example, in the hand of the one casting it: but as soon as it was released from the hand it would fall. But it is the opposite that happens. Therefore, there is not a void.

526. He then gives the sixth reason [365]. If motion were in a void, no one could give a reason why the moving object should stop anywhere. For there is no reason why it should stop at one part of the void rather than another. This is true both in the case of objects that are moved naturally, because there is no difference among the parts of the void, as we have said, and in the case of objects moved by a compulsory motion. For now we say that a violent compulsory motion ceases when repercussions or impulsions of the air are lacking, on account of the two reasons already given. Therefore it will have to be admitted either that every body is at rest and nothing in motion or that, if anything be in motion, it will remain In motion to infinity unless it runs into a more powerful body that could impede its compulsory motion.

In support of this reasoning, he gives the reason why some posit motion in the void. It is because the void yields to and does not resist the mobile; hence since the void yields in the same way, in all directions, a mobile thing should be moved in all directions ad infinitum.

Lecture 12

From the fastness and slowness of motion, a separated void is disproved

527. Here the Philosopher, arguing from the fast and slow in motion, shows that the void does not exist.

About this he does two things:

First he assigns the causes of fastness and slowness in motion;

Secondly, he uses these reasons to argue to his point, at no. 529.

He says therefore first that one and the same heavy body, and any other thing, for example, a stone or something of this sort, is in faster motion for two reasons: either on account of the medium in which it is being moved, e.g., air or earth or water; or on account of differences in the object, namely, that it is heavier or lighter, all other things being equal.

528. Then [367] he argues to his point from the aforesaid causes.

First from the differences of the medium;

Secondly, from the differences in the mobile object, at no. 539,

As to the first he does two things:

First he gives an argument;

Secondly, he recapitulates, at no. 533.

Concerning the first he does two things:

First he gives his argument;

Secondly, he shows that the conclusion follows from the premises, at no. 532.

529. Therefore, he first gives this argument: The ratio of motion to motion in regard to speed is equal to the ration of medium to medium in respect of subtlety. But there is no ratio between empty space and full space. Therefore, motion in a void has no ratio to motion in the full.

First of all he explains the first proposition of this argument. And he says that the medium through which a body is in motion is the cause of its fastness or slowness because it acts as an obstacle to the body in motion. The greatest obstacle occurs when the medium is in a contrary motion, as is evident in the case of a ship whose movement is impeded by the wind. The medium is an obstacle in a secondary way even if it is not in motion, because if it were in motion with the object it would not be an obstacle but a help, as the water which carries a ship downstream. But among obstacles a greater impediment is offered by things that are not easy to divide, such as the grosser bodies. He explains this by an example. Let the body in motion be A, and let the space through which it is being moved be B, and the time in which A is being moved through B be C. Let us posit another space, D, of the same length as B, but let D be full of a subtler body than the one in B, so that a certain analogy, i.e., ratio, exists between the bodies which impede the motion (for example, let B be full of water and D full of air). Now to the extent that air is subtler than water and less condensed, to that extent will the mobile A be more quickly moved through D than through B. Therefore the ratio of the velocities will equal the ratio of the subtlety of air to the subtlety of water. And the greater the velocity, the less the time: because that motion is faster which covers the same interval in less time, as will be shown in Book VI (L.3). Hence if air is twice as subtle as water, the time it takes A to be moved through B (full of’ water) will be twice the time for A to pass through D (full of air). Consequently, the time C in which it travels the distance B will be twice the time it takes E to pass through D. Therefore, we can take it as a general rule that in whatever ratio the medium (in which something is in motion) is subtler and less resistant and more easily divisible, in that ratio will the motion be faster.

530. Then [368] he explains the second proposition, and says that the void is not exceeded by the full according to some certain ratio. And he proves this by the fact that a number does not exceed nothing [zero] by any ratio, for ratios can exist only between one number and another, or between a number and unity; as four exceeds three by one, and exceeds two by more yet, and one by still more. Hence there is said to be a greater ratio existing between four and one, than between four and two, or four and three. But four does not exceed nothing according to any ratio.

This is so because anything exceeding is necessarily divided into that which is exceeded and into the excess, i.e., that in which it exceeds; for example, four can be divided into three, and into one, which latter is the amount by which four exceeds 3. But if four exceeds nothing, it will follow that four can be divided into so much and nothing; which is unacceptable. For a same reason one could not say that a line exceeds a point unless it were composed of points and divided into points. In like manner, it cannot be said that the void has any ratio to the full; because the void is not a part of the full.

531. Then [369] he concludes that there can be no ratio between a motion in the void and a motion in the full: but that if any body is in motion in the subtlest of mediums over such and such a distance for such and such a time, the motion in the void will exceed any given ratio.

532. Then [370], because he had deduced the above conclusion in direct line from the assumed principles, he now, lest any doubt arise about those principles, and to make the process more certain, proves the same conclusion by deducing to the impossible.

For if it be claimed that the speed of a motion taking place in the void has a ratio to the speed of a motion taking place in the full, then let the empty space be Z, which shall be equal in magnitude to the space B, full of water, and to the space D, full of air.

Now if it is supposed that a motion through Z has a certain ratio in respect of speed to the motions through B and D, then it must be admitted that the motion through Z (the void) takes place in some definite portion of time, because velocities are distinguished according to the quantities of the times consumed, as was said above. If therefore we say the object A passes through the empty space Z in a definite time, let that time be I, which must be less than the time E required for A to pass through D, which is full of air. Then the ratio of the motion through the empty to the motion through the full will equal the ratio of time E to time I. But during time I, the mobile A will pass through a definite space that is full of a subtler body than exists in D, i.e., than D. And this will happen, if one can find a body which differs in subtlety from air (of which D is full) in the ratio that the time E has to the time I. For example, say the space Z, which had been originally empty space, ir now full of fire. If the body of which Z is full is subtler than the body of which D is full, in the amount that the time E exceeds the time I, it will follow that the mobile A, if it is in motion through Z (which is the space now full of a most subtle body), and through D (which is the space full of air), it will pass through Z conversely at a greater speed in a time I. If therefore no body exists in Z but it is again considered to be empty space, as previously, it will have to move even faster. But this is against what was laid down, namely, that the motion through Z (empty space) required time I. Consequently, since in time I it passes over the same space when it is full of the most subtle of bodies, it follows that during the same time the same mobile passes through one and the same space, when that space is empty and when it is full.

It is clear therefore that if it took a definite time for the mobile to pass through an empty space, the impossibility follows that in equal time it will pass through full and empty space, because there will be some body having the same ratio to some other body as one time has to another time.

533. Then [371] he summarized that in which the force of the previous reasoning consists. And he says that we can now say in recapitulation that the reason why the conflict mentioned in the above occurs is clear: it is because every motion has a ratio to every other motion in respect to speed. For every motion requires time, and any two periods of time, if they are finite, have a ratio one to the other. But there is no ratio between the empty and the full, as we proved. Hence the supposition that motion occurs in the void leads to the conflict mentioned.

In a final summary [372] he concludes that the above mentioned conflicts occur if the different species of motion are taken according to differences of the media.

534. But several difficulties arise against this reasoning of Aristotle. The first is that it does not seem to follow that if motion takes place in the void that it has no ratio to motion in the full. For every motion has its definite velocity from the ratio of the motive energy to the mobile, even if no obstacle exists. And this is evident both from an example and from reason. From an example, indeed, in the heavenly bodies, whose motion encounters no obstacle and yet they have a definite velocity depending on the amount of time. From reason also: for, since it is possible to point out a “before” and “after” in the magnitude through which the motion takes place, so also one can take a “before” and “after” in the motion from which it follows that motion is in a determined time. But it is true that this velocity can be diminished on account of an obstacle. Yet it is not necessary therefore to make the ratio of motion to motion in respect of velocity be as the ratio of obstacle to obstacle, so as to make the motion occur in no time, if there be no obstacle; rather, the ratio of one slowing up to another slowing up must correspond to the ratio of obstacle to obstacle.

Hence on the assumption that motion takes place in the void, it follows that no slowing up happens to the natural speed, but it does not follow that a motion in the void will have no ratio to motion in the full.

535. Averroes attempts to counter this objection in his commentary. First he tries to show that this objection proceeds from false imagination. For he says that those who make the above objection imagine that an addition in slowness of motion occurs just like an addition in the magnitude of a line, where the added part is distinct from the part to which the addition is made. For the above objection seems to proceed as though slowing up takes place by adding one motion to another motion in such a way that if you were to subtract the motion that was added through the obstacle which slows, the quantity of natural motion would then be left. But this is not the case, because when a motion is slowed up, each part of the motion becomes slower, whereas each part of a line does not become larger.

Then he attempts to show how Aristotle’s argument concludes with necessity. And he says that the speed or slowness of a motion does indeed arise from the proportion of the mover to the mobile; but the mobile must in some manner resist the mover, as the patient is in a certain way contrary to the agent. This resistance can arise from three sources: First, from the situs of the mobile; for from the very fact that the mover intends to transfer the mobile to some certain place, the mobile, existing in some other place, resists the intention of the mover. Secondly, from the nature of the mobile, as is evident in compulsory motions, as when a heavy object is thrown upwards. Thirdly, from the medium. All three are taken together as one resistance, to constitute one cause of slowing up in the motion. Therefore when the mobile, considered in isolation as different from the mover, is a being in act, the resistance of the mobile to the mover can be traced either to the mobile only, as happens in the heavenly bodies, or to the mobile and medium together, as happens in the case of animate bodies on this earth. But in heavy and light objects, if you take away what the mobile receives from the mover, viz., the form which is the principle of motion given by the generator, i.e., by the mover, nothing remains but the matter which can offer no resistance to the mover. Hence in light and heavy objects the only source of resistance is the medium. Consequently, in heavenly bodies differences in velocity arise only on account of the ratio between mover and mobile; in animate bodies from the proportion of the mover to the mobile and to the resisting medium—both together. And it is in these latter cases that the given objection would have effect, viz., that if you remove the slowing up caused by the impeding medium, there still remains a definite amount of time in the motion, according to the proportion of the mover to the mobile. But in heavy and light bodies, there can be no slowing up of speed, except what the resistance of the medium causes—and in such cases Aristotle’s argument applies.

536. But all this seems quite frivolous. First, because, although the quantity of slowing up is not parallel to the mode of continuous quantity, so that motion is added to motion, but parallel to the mode of intensive quantity, as when something is whiter than something else, yet the quantity of time from which Aristotle argues is parallel to the manner of continuous quantity—and time becomes greater by the addition of time to time. Hence if you subtract the time which was added on account of the obstacle, the time of the natural velocity remains.

Then, because if you remove the form which the generator gives to light and heavy bodies there still remains in the understanding “quantified body,” which from the very fact that it is a quantified body existing in an opposite situs offers resistance to the mover. For we cannot suppose in heavenly bodies any other resistance to their movers. Hence, as he [Averroes] presents the case, even in the case of heavy and light bodies the reasoning of Aristotle would not follow.

Therefore it is better and briefer to say that the argument brought forward by Aristotle is an argument aimed at contradicting his opponent’s position and not a demonstrative argument in the absolute sense. For those who posited a void did so in order that motion be not prevented. Thus, according to them, the cause of motion was on the part of a medium which did not impede motion. And therefore Aristotle argued against them as though the total cause of fastness and slowness derived from the medium, as he clearly shows above when he says that if nature is the cause of the motion of simple bodies, it is not necessary to posit the void as the cause of their motion. In this way he gives us to understand that they supposed the total cause of the motion to depend on the medium and not on the nature of the mobile.

537. The second difficulty against [Aristotle’s] argument is that if the medium which is full impedes, as he says it does, then it follows that there will not be any pure unimpeded motion in this lower medium—and this seems unfitting. To this the Commentator replies that the impediment that arises from the medium is required by the natural motion of heavy and light bodies, so that there can be resistance of the mobile to the mover, at least on the side of the medium.

But it is better to say that every natural motion begins from a place that is not natural and tends to a natural place. Hence until it reaches its natural place it is not unfitting if something unnatural be attached to it. For it gradually departs from what is against its nature and tends to what is in keeping with its nature. And for this reason a natural motion accelerates as it nears its end.

538. The third objection is that since in natural bodies there is a fixed limit of rarity, it does not seem that one can keep supposing a rarer and rarer body according to any given proportion of time to time.

In reply it should be said that a fixed rarity in natural things is not due to the nature of the mobile body insofar as it is mobile, but to the nature of specific forms that require specific rareness and density. But in this book we are dealing with mobile body in general, and therefore Aristotle frequently uses in his arguments things which are false if the specific natures of bodies are considered, but possible if the nature of body in general is considered.

Or it can be replied that he is here also proceeding according to the opinion of the earlier philosophers who posited the rare and the dense as the first formal principles. According to them, rarity and density could be increased ad infinitum since these did not depend on other previous forms according to whose exigencies they would be determined.

539. Then [373] he shows there is no separated void, arguing from the speed and slowness of motion, insofar as the cause is taken entirely from the viewpoint of the mobile.

And he says that what he is about to say will follow logically, if we attend to the difference of speed and slowness insofar as bodies in motion exceed one another. For we see that over a given equal space, greater speed is shown by bodies having a greater inclination due either to heaviness or lightness, whether they are greater in quantity but equally heavy or light, or whether they are equal in quantity but unequal in heaviness or lightness. And I say this if they are similar in shape. For a wide body is moved more slowly if it be deficient in heaviness or size than a body with a pointed shape. And the ratio of the velocity corresponds to the ratio which the moving magnitudes have to one another in respect to their weight or in respect to their magnitude. And this will have to be true also if the motion occurs in the void, namely, that a heavier body or a lighter body or a more pointed body will be moved faster through an empty medium. But this cannot be, since it is impossible to explain why one body would be moved faster than another. For if the motion takes place within a space filled with some body, an explanation for the greater or lesser speed can be given—it will be due to any of the aforesaid causes. The explanation is that a greater body will on account of its strength divide the medium more quickly, either an account of its shape, because what is sharp has greater penetrating power; or on account of a greater inclination traceable either to the heaviness or lightness of the body; or even to the force imparted by that which projects it. But the void cannot be cleaved faster or slower. Hence it will be moved through a void with equal speed. But this clearly appears as impossible.

And so from a consideration of the velocity of motion, it is evident that the void does not exist.

It should be observed that in this reasoning process there exists the same difficulty as in the first one. For he seems to suppose that difference in velocity in motions is due only to the different ways in which the medium can be cleaved, whereas the fact is that there are differences of velocity among the heavenly bodies in which there is no full medium resisting which has to be cleaved by the motion of the heavenly body. But this difficulty should be solved as the above one was.

540. Finally [347] he summarizes, and concludes that from the foregoing it is clear that in regard to the philosophers who posit a void, the contrary of what they supposed as a reason for proving it occurs. For they proceeded on the assumption that motion could not take place unless there was a void. But the contrary has been proved; namely, that if there be a void, there is no motion. Thus, therefore, those philosophers believe that the void is some distinct and separate thing—a space having separate dimensions—and they believed it was such a space that had to exist if local motion were to be possible. However, to posit such a separated void is the same as saying that place is a kind of space distinct from bodies—which is impossible, as was shown in the treatise on place.

Lecture 13

Non-existence of the void from the void itself

541. Now the Philosopher taking his arguments from the void itself, without any mention of motion, shows that the void does not exist. He shows this by three reasons. He says therefore first [375] that even considering the void on its own merits, without motion, it will be seen that the void spoken of by some is just what the name “void” implies. For “void” means something empty and non-existent—and the claim that it exists is vain and without reason and truth. And he shows this as follows.

If anyone places a cubic body in water (i.e., a body having six square surfaces) an amount of water equal to the quantity of the cube must be displaced. And what is true of water is true of air, although it is not so evident, because water is more perceptible to sense than air. By the same reasoning applied to the case of any body that can be displaced, in some part, it must, if the parts are not compressed, or enter into each other, be dislodged either (1) according to the state of a yielding body (when it has free exit); for example, if it is a heavy body such as earth it will yield downwards, and if it is a light body such as fire it will yield upwards, and if it is a body which is light in relation to one body and heavy in relation to another, it will yield in both directions, such as do air and water; or (2) because the body yields on account of the condition of the newly imposed body, i.e., when the yielding body is prevented by the imposed body, i.e., when the yielding body is prevented by the imposed body from being moved according to its demands but is moved according to the demands of the imposed body. And in general it can be held as true that a body must yield to an inserted one, lest two bodies be in the same place.

But this will not be true in the case of the void, i.e., that it must yield to the inserted body, since the void is not a body, whereas whatever is moved in any manner whatsoever is a body. But if there be empty space and a body inserted therein, then the inserted body must pass through that space which previously was empty and cohabit the same space as the void—just as if water or air were not to yield to a wooden cube, but were to pass into the cube in such a way that the air and water would penetrate that cubic body and cohabit with it.

But it is impossible for a wooden cube to exist with empty space; for the wooden cube has the same magnitude as the empty space, which is supposed to be a certain dimensional space without a sensible body. And even though the wooden cube be hot or cold, heavy or light, nevertheless the cubic body is other in notion from all the sensible qualities, that are its accidents, although it be not separable from them in reality. Now what is in conception distinct from the qualities is the body of a wooden cube, i.e., that which pertains to its corporeity. Now if this body be separated from whatever is distinct from it in notion, so that it is neither heavy nor light, it follows that it will occupy a volume of empty space equal to itself. Thus in the same part equal to it, which is part of the place and of the void, the body of the wooden cube will be.

On this assumption it does not seem possible to find a difference between the body of the cube and the dimensions of the place or void. For just as the dimensions of the place or void exist without sensible qualities, so too the dimensions of the cubic body, at least according to notion, are distinct from its sensible qualities. But two magnitudes of equal quantity can differ only in situs. For we cannot imagine one line as distinct from another of equal length, unless we imagine one in one situs and the other in another. Hence, if two magnitudes are imagined together, it does not seem that they can differ: consequently, if two bodies of equal dimensions are together, whether accompanied by their sensible qualities or not, it follows that two bodies are one, or if the cubic body and the space which is the place or void remain two, but are still together, there is no reason why any number of bodies cannot be there. In that case, just as the cubic body is together with the space of the place or void, along with both a third or even a fourth body ought to be able to be inserted. This, of course, is impossible. For we cannot say that it is because of matter that some other sensible body cannot exist together with the wooden cubic body, for place does not belong to a body because of its matter, except in the sense that the matter is contained under dimensions. Hence the impossibility for two bodies to be together is not on account of the matter or of the sensible qualities, but only on account of the dimensions, in which no diversity can be found if they are equal except a diversity based on situs, as was said. Wherefore since there are dimensions in empty space just as there are in a sensible body, then, just as two sensible bodies cannot be together, so neither can a sensible body be together with empty space. So this is one unacceptable result and impossibility that follows from the aforementioned premiss: namely, that two bodies would be in the same place.

542. He then gives the second reason [376], saying that it is clear that a cube which is transferred to an empty space has what all other bodies have, namely, dimensions. If therefore the dimensions of the cube do not differ from the dimensions of the place according to conception, why is it necessary to find for a body a place distinct from its own body, if place is nothing more than “impossible body,” i.e., a body without sensible qualities? In view of the fact that a body has its own dimensions, there seems to be no necessity for it to be surrounded by other dimensions of a space equal to its own dimensions. Consequently if the void is presumed, or place as a certain separated space, it follows that bodies do not have to be in place.

543. He gives the third reason [377] when he says that if there were a void, it would have to be evident in mobile things. But there is no evidence of a void anywhere in the world, because what is full of air seems to be a void, though it to not. For air is something, although not perceptible to sight. Now if fish were made of iron and had the same appearance as water, our sight would not be able to distinguish them from water; but it would not follow that the water, or even the fish, were non-existent: for it is not only by sight but also by touch that we can discern what is touched. Consequently, it is evident that water is something, because touch can perceive whether it be hot or cold.

From all this it appears that there is no separate void either within or outside the universe.

Lecture 14

There is no void within bodies

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;

Secondly, he disproves their position, at no. 546;

Thirdly, he dissolves their argument, at no. 551.

545. He says therefore first [347] 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 “go in,” i.e., enter each other, and “harden,” i.e., 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.

In respect to local motion, because 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, so that, unless there were condensation of bodies, all bodies would have to be in motion.

In regard to generation or alteration, this 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 a 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 [i.e. volume] 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 finally, it must 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 [379] he rejects this position:

First according to one interpretation;

Secondly, according to another interpretation, at no.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 existing separate in respect to situs 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 situs 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. For the very argument that 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. He then [380] disproves the aforesaid position as to the second interpretation and gives four reasons for rejecting it. He says, therefore, 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 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 the 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 upwards; consequently, the void will be the cause only of upward motion.

548. He gives the second reason [381] 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 for 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 then it would 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. The third reason [382] is given when he says that if the cause of upward motion is the void carrying a body upward, then since there is nothing to carry the body down, there would be no explanation of why heavy bodies are carried downwards.

550. Be then gives the fourth reason [833], 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; 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 [385] be answers a previous argument:

First he repeats it, explaining it more extensively;

Secondly, he solves it, at no. 552.

He says therefore 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 (1) local motion will not be if there is not rarity and density, which they believed could not be produced without the void; or (2) 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.

Secondly, 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 (1) that the body which was held to be outermost according to common opinion, namely, the heavenly body, be pushed outward by the swelling of lower bodies; or (2) that somewhere else there must be an equal amount of air converted into water, so 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 [evasion] 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 transmuted. 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 which prompted some to posit the void.

552. Then 385] he answers this argument. Now the entire force of this argument consists in this, that rarefaction and condensation take 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;

Secondly, he introduces the conclusion be mainly intends, at no. 557.

As to the first he does three things:

First he explains his proposition by an argument;

Secondly, by examples, at no. 555;

Thirdly, by the effects of rarity and density, at no. 556.

As to the first he does two things:

First he premisses certain things necessary for his proposition;

Secondly, he proves his proposition, at no. 554.

553. Now [385] he lays down four preliminary statements which he takes from the “subjects,” i.e., the presuppositions of natural science, and which were already explained in Book I.

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 had to come into being from what was in potency.

The third is that matter is not separable from contraries so 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, now under another, other and other, but numerically one.

554. Then [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 to numerically the same.

And this is clear in substantial transmutation. For when air is generated from water, the same matter which 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 sam is true in reverse, when from air water is generated. 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, from air, water is made, there is produced contrariwise a transmutation 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 which 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, now lesser, quantity: hence, to become rare is nothing other than for matter to receive greater dimensions by being reduced from potency to act; and the opposite for 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 ad infinitum in natural things.

555. Then [387] he makes the same thing clear from examples. And because rarefaction and condensation pertain to the motion of alteration, [i.e., change in quality] 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 previously not hot becomes hot which was not so when It was less 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 in to 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 “defect,” i.e., by subtraction, or addition but by the transmutation 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,” i.e., 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 which was previously in potency to large and small being transmuted 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 [388] 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; namely, in heaviness and lightness, hardness and softness. Consequently, rarity and density diversify qualities and 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; consequently, a heavy body which tends toward the middle [i.e., center]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,” i.e., 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, namely, 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 which 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 actuality. 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 “earth” in it, but what there is of “water” in it is less perfectly congealed and distributed.

557. Then [389] he concludes his chief proposition. And he says it is clear from the foregoing 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, according to 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 [the motion called] “alteration.”

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

Lecture 15

Does time exist, and is there the same “now” in the whole of time?

558. Having arrived at conclusions concerning Place and the Void, the Philosopher now concluded concerning Time.

First he tells what his intention is and the order he will follow;

Secondly, he carries out his proposal, at no. 559.

He says therefore first [390] that our plan now calls for us to “attack” time, by which he signifies how difficult the subject is. And as in previous discussions, so in the case of time one must begin by presenting extraneous reasons, i.e., the opinions of others, as well as sophistical arguments, dealing with the question of whether time exists or not and, if it does, what is its nature.

Then [391] he begins the discussion of time:

First by arguing against [existence of time];

Secondly, by presenting the truth, at no. 571 (L.17).

In regard to the first he does two things:

First he inquires whether time exists, arguing against it;

Secondly, what it is, at no. 565 (L.16).

As to the first he does two things:

First he gives two reasons which show that time does not exist;

Secondly, he inquires about the “now”: asking whether there is one “now” in the whole of time or several, at no. 561.

559. He says then [391] that two reasons could lead us to suppose either that time does not exist at all or that it is something that can scarcely and only in an obscure way be conceived. Here is the first reason: anything that is composed of things which do not exist cannot have any existence or any substance; but time is composed of what does not exist—for part of time is the past which no longer exists, and the rest is the future, which does not yet exist (and these two things comprise the whole of time considered as infinite and everlasting). Therefore, it is impossible for time to be anything.

560. The second reason [392] is as follows: As long as any divisible thing is existing there must exist some part of it or a number of parts. But time does not meet these requirements—for some parts of time are already past and others are in the future, so that no divisible part of time is actually existing. And the “now” which is actual is not a part of time: for a part is either a measure of a whole, as two is the measure of six, or at least it is a component of the whole, as four is a part of six (although not its measure) since from it and two, six is composed. Time however does not have “nows” as its parts, as will be proved later (Book VI). Therefore, time is not anything.

561. Then [393] he inquires whether there be the same “now” through the whole of time. About this he does three things:

First, he raises the question;

Secondly, he objects to one side of the question, at no. 562;

Thirdly, he objects to the opposite side, at no. 563.

He says therefore first that it is not easy to be certain whether the “now” which is seen to distinguish the past from the future always remains identical with itself throughout the whole of time or whether it is other and other.

562. Then [394] he gives a reason to show that the “now” is not other and other. Two parts of time which are not the same cannot be existing together unless one contains the other, as a greater period of time contains a smaller, e.g., as a year contains the month and the month the day (for the day and the month and the year exist together). But one “now,” since it is indivisible, does not contain another. If, therefore, we are to accept two “now’s” in time, then that “now” which existed before the present one and no longer exists, ceased to be sometime, and so two “now’s” are never together. However, anything that ceased to be, did so in some “now.” But it cannot be that the prior “now” ceased to be in that prior “now,” because the prior “now” was existing then, and nothing ceases to be while it is. Likewise, it cannot be said that the prior “now” ceases to be in a later one: for it is impossible to have two “now’s” together as “had,” i.e., so as to follow immediately one upon the other, just as the same thing is impossible in the case of two points. (This is supposed now, but will be proved in Book VI). Thus, between any two “now’s” there are an infinity of “nows.” If, therefore, that prior “now” ceases to be in some later “now,” it follows that the prior “now” was existing along with all the intermediate “now’s”—which is impossible, as we have said. It is impossible, therefore, that the “now” be other and other.

563. Then [395] he gives two reasons to show that there cannot be just one “now.” The first is that no finite divisible thing can have just one boundary; whether it be a divisible of one dimension, as a line; or of more than one dimension, as a plane or a solid. For the boundaries of one finite line are two points and of a surface the boundaries are several lines, and of a body several planes. But the “now” is a boundary of time. Since therefore it is possible to conceive of a finite time there must be more than one “now.”

564. He gives a second reason [396].Those things are said to be together in time, and neither previously nor later, which are in the same “now.” If therefore it is the same “now” that persevere throughout time, it follows that things which existed a thousand years ago are together with things that exist today.

Summarizing, he concludes that these are the conflicting opinions about the “now’s” which exist in time.

Lecture 16

Dialectical inquiry into what time is, and how related to motion

565. After inquiring whether time exists, the Philosopher now inquires dialectically what it is.

First he disproves the opinions of others;

Secondly, he inquires how time is related to motion, which seems to be something most akin to time, at no. 568.

About the first he does two things:

First he gives various opinions of others about time;

Secondly, he disproves them, at no. 566.

He says therefore first that what time is and what is the nature of time cannot be gathered from what is handed down from the earlier philosophers nor from any piecing together of what they concluded about it. For some said that time is a motion of the heavens; others that it is a heavenly sphere itself.

566. Then [398] he disproves their opinions, first of all, the first; then the second, at no. 567.

In regard to the first opinion he gives two counter-arguments, of which the first is: If a circular revolution in time then part of that revolution is a circular revolution, because a part of time is time. But part of a circular revolution is not a circular revolution. Therefore time is not a circular revolution.

Then [399] he gives a second argument: The number of motions corresponds to the number of mobiles; if therefore there are many heavens, there are many circular revolutions. And thus if a circular revolution is time, there are many times together—which is impossible. For no two parts of time are together unless one contains the other, as we have said. (Those who posited time as a circular revolution were led to do so because they observed that times occur over and over in a kind of cycle.

567. Then [400] he rejects the second opinion. And he says that some thought the sphere of the heavens in time, because all things are in time and all things are also in the sphere of the whole, because the heavens contain all things. Hence they wished to conclude that the sphere of the heavens is time. But there were two things wrong in their reasoning: first, because something is not said univocally as being in time and in place; secondly, because they were using two affirmative premises in a Second Figure syllogism. Therefore he says that their position is too foolish to consider the impossibilities that follow upon it. For it is clear that all the parts of the sphere exist simultaneously, whereas the parts of time do not.

568. Then [401] he inquires how time is related to motion.

First he shows that time is not motion;

Secondly that time does not exist independently of motion, at no. 570.

In regard to the first he gives two reasons to show that time is not a motion or a change (for it certainly seems to be such). Here is his reason: Every change and motion is certainly only in the thing being changed or in the place where the changer and changed are. The first of these is mentioned because of motion in substance and quantity and quality; the second because of motion in the predicament “where,” called motion in place.” But time is everywhere and exists among all things. Therefore time is not a motion.

569. He gives the second reason [402]: Every change and motion is either slow or fast; but time is not either. Therefore time is neither a motion nor a change. He explains the minor premise thus: Slow and fast are determined by time—because that is fast which is moved a great distance in a short time and that is slow which is moved a short distance in much time. But time is not determined by either according to its quantity or its quality, because nothing is its own measure. Therefore, time is neither slow nor fast. And since he had proposed that change is fast or slow, without mention of motion, he adds that for the present it does not matter whether one says “motion” or “change.” Their difference will be shown in Book V.

570. Then [403] he shows that although time is not motion, it is not independent of motion: for when men are not changing according to what they apprehend, they are changing without being aware of it, then it does not seem to them that time is passing. This is clear in the fable about the city in Asia called Sardo. In Sardo certain people were said to sleep among the Heroes,,i.e., among the gods. For they called the souls of the good and the great “Heroes,” and worshipped them as gods, as in the case of Hercules and Bacchus and the like. Certain ones were rendered insensible by means of incantations and said to sleep among the gods, because then they awoke they claimed to have seen marvelous things and foretold future events. These persons, returning to themselves, were not aware of the time which elapsed while they were thus absorbed; because that first instant in which they began to sleep they joined to the instant in which they awoke, as if it were one instant—but the time that elapsed escaped them. Therefore just as there would be no intervening time between “now’s,” if the “now” of time were always the same and not other and other, so also when two “now’s” are fused in our apprehension, the elapsed time is not apprehended, and there seems to have been no intervening time. If, then, we are apt to think that no time has elapsed when we do not perceive any changes, and that we are in one and the same indivisible “now,” but we then perceive time to be elapsing when we sense and determine, i.e., motion and change, it clearly follows that time is not independent of motion and change.

In summary he concludes that time is not motion, nor is it without motion.

Lecture 17

The definition of time, given and explained

571. After treating of time dialectically, the Philosopher here begins to determine the truth.

First, he determines the truth concerning time;

Secondly, he brings up and solves some objections concerning the truth determined, at no. 625 (L.23).

In regard to the first he does two things:

First he determines concerning time absolutely.

Secondly, in relation to things measured by time, at no. 600 (L.20).

As to the first he does three things:

First he makes clear what time is;

Secondly, what the “now” of time is, at no. 582 (L.18);

Thirdly, from the definition he gives of time, he explains the things said about time, at no. 593 (L.19).

About the first he does two things:

First he gives the definition of time;

Secondly, he explains it, at no. 581.

The first point is divided into three parts according to the three parts which he investigates of the definition; The second part begins at no. 575; The third part at no. 580.

572. First [404] therefore he investigates this part: that time is “something of motion.” He says that since we are investigating what time is, we must begin by understanding what aspect of motion time is. That time is something of motion is manifested by the very fact that we sense motion and time together. For it happens that we perceive the flow of time even though we are not sensing any particular sensible motion; for example, if we are in the dark and do not see any external object moving. And if while we are in this situation, we are not undergoing any bodily changes brought about by an external agent, then we are not sensing any motion of a sensible body. Yet if there is a motion within our soul, such as a succession of thoughts and imaginings, suddenly it appears to us that some time is elapsing. Thus by perceiving any sort of motion we perceive time and, vice-versa, when we perceive time we are simultaneously perceiving a motion. Hence, although time is not a motion, as we have already shown, yet it is somehow connected with motion.

573. What has been just said about the perceiving of time and of motion raises a difficulty. For if time follows upon some sensible motion outside the mind, it follows that whosoever does not sense that motion, does not sense time; whereas the opposite of that is said here. And if time depends upon some motion of the mind, it follows that things are not connected to time except through the medium of the mind: thus time will not be a thing of nature but a notion in the mind like the intention of genus and species. But if time follows upon any and every motion, then there are as many times as there are motions—which is impossible, for there cannot be two times together as we said above.

574. In order to clear up this difficulty it must be remembered that there is one first motion which is the cause of every other motion. Hence whatever is in a transmutable state possesses that state on account of the first motion, which is the motion of the first mobile being. Whosoever, therefore, perceives any motion, whether it exists in sensible things or in the mind, is perceiving transmutable being and consequently is perceiving the first motion, which time follows. Thus anyone who perceives any motion whatsoever is perceiving time, although time follows upon just the one first motion by which all other motions are caused and measured. Consequently, there remains only one time.

575. Then [405] he investigates the second particle placed in the definition of time. For supposing that time is something of motion, namely, that it follows upon motion, there still remains the task of investigating according to what does time follow upon motion; the answer being that it follows upon motion “according to before and after.” As to this then he does three things:

First he shows how “before and after” are found in motion;

Secondly, how they are related to motion, at no. 578;

Thirdly, he shows that time follows motion according to “before and after,” at no. 579.

About the first he does two things:

First he shows that the continuity of time is due to the continuity of motion and magnitude;

Secondly, that the same is true of the “before and after” of time, at no.577.

576. He says therefore first that everything that is being moved is being moved. from something to something. But of motions the first is local motion, which is from place to place along a magnitude. But it is the first motion that time follows upon, and therefore, to investigate time, one must take local motion. Since, then, motion according to place is motion according to a magnitude from one place to another, and since every magnitude is continuous, motion must follow magnitude in regard to its continuity, so that, just as magnitude is continuous, so also is motion. Consequently time also is continuous: for the quantity of the first motion and the quantity of time correspond. For time is not measured according to the quantity of just any motion, since something is being moved over a small distance In a large amount of time, and a fast object, vice-versa. Time however corresponds only to the quantity of the first motion.

577. Then [406] he shows that the same order prevails in respect to “before and after,” saying that “before and after” are first of all in a place or in a magnitude. This is so, because a magnitude is a quantity having position; position, however, implies “before and after.” Hence from its position place has”before and after.” And because there is “before and after” in magnitude, it follows that there is a “before and after” in motion corresponding to the things which are there, i.e., in magnitude and place. Consequently, there is a prior and subsequent also in time: for motion and time are so related that the one always follows the other.

578. Then [407] he shows how “before and after” are related to motion. And he says that the “before and after” of these, namely, of time and of motion is, as to what it is, motion; yet in conception, it is distinct from motion and not motion. For it is the notion of motion that it be the act of a being in potency; but that there be in motion a “before and after” occurs in it by reason of the order of the parts of the magnitude. Accordingly, “before and after” are the same as motion as to subject but they differ from it as to notion. Hence the task remains to inquire, since time follows motion, whether it follows upon it inasmuch as it is motion, or inasmuch as it has a “before and after.”

579. Then [408] he shows that motion follows upon time by reason of “before and after.” For it has been shown that the reason why time follows motion is that we recognize both simultaneously. Therefore time follows motion according to that which, when it is perceived in motion, time is perceived. But it is then that we perceive time, when we distinguish a “before” and “after” in motion; and it is then that we say time is passing when we have a sense of the “before” and “after” in motion. Consequently time follows motion according to “before and after.”

580. Then [409] he shows what aspect of motion time is, and says that it is “the number of motion.” He explains this by using the same means as before, namely, our knowledge of time and motion. For it is clear that when we take in motion something different from something other and understand that there is something between them, then it is that we determine that time exists. For when we perceive the differing boundaries of something and the mind calls them two “now’s,” one being before and the other after, as though the mind were counting the “before’s” and “after’s” in a motion, that is what we call time. For time seems to be determined by the “now.” (This statement is taken for granted at present, but later it will be explained). When therefore we sense one “now” but do not discern a “before” and “after” of motion, or when we in discerning a “before” and “after” take the same “now” as the end of the prior and the beginning of the subsequent, no time seems to exist because no motion seemed to exist. But when we discern a “before” and “after” and count them, then we say that time is produced. This is so because time is nothing less than “the numbering of motion according to before and after”: for we perceive time, as was said, when we count the “before and after” of motion. it is clear there fore that time is not motion, but accompanies motions inasmuch as it is counted. Hence time is the number of motion.

But if someone objects against this definition and says that “before and after” are determined by time, and consequently, that the definition is circular, he should remember that “before and after” are placed in the definition of time inasmuch as they are caused in motion by magnitude, and not inasmuch as they are measured out of time. That is why Aristotle had previously shown that “before and after” are present in magnitude before they are so in motion, and they are in motion before they are in time, to exclude this objection.

581. Then [410] he clarifies the aforesaid definition in two ways, and first by a sign. Now that which is a standard of judging something to be more and less is a number of it. But the standard for judging whether a motion is greater or smaller is time. Therefore, time is a number.

Secondly, [411] he makes clearer what has been stated by distinguishing number, saying there are two. First there is that which is actually numbered which can be, as when we say ten men or 100 horses, and this is called “number numbered,” because it is a number applied to the things that are numbered. Then there is the number by which we count, i.e., number considered absolutely, such as two, three, four [the counting numbers]. Now time is not a counting number; otherwise the number of anything would be time; rather it is a number numbered, because it is the number of before and after in motion that we call “time,” or else the things that are counted before and after.

Therefore, although number is discrete quantity, time is nevertheless a continuous quantity on account of the thing counted, just as ten measures of cloth is a continuous quantity, even though ten is a discrete quantity.

Lecture 18

How the same “now” is or is not in a whole time

582. After explaining what time is, the Philosopher here explains the “now.”

First he determines whether the “now” in a whole time is always the same or other and other, which was brought up as a problem above;

Secondly, after settling this he gives the reason for what is said above the “now,” at no. 588.

As to the first he does three things:

First, he declares that the “now” is somehow always the same and somehow not;

Secondly, he explains this, at no. 584;

Thirdly, he proves it, at no. 585.

583. He says therefore first [412] that since time is the number of motion, then, just as the parts of motion are always other and other, so also the parts of time. But that which always exists throughout the whole of time is the same, namely, the “now,” which as to its nature is always the same. While in conception it varies accordingly as it is prior and subsequent. Thus the “now” measures time, not inasmuch as it is always the same thing, but inasmuch as in conception it is other and other, and “before” and “after”.

584. Then [413] he explains what he had just said and declares that the “now” is somehow always the same and somehow not. For insofar as it is always being considered as being in something other and other in the succession of time and of motion, in that sense it is other and not always the same. And this is what we stated above, namely, that “it is other in motion.” for this is the esse of the “now,” i.e., it is according to this that its notion is taken, namely, as considered in the succession of time and motion. But insofar as the “now” is a certain being, from that viewpoint it is always the same thing.

585. Then [414] he proves what he has just said. First he proves that the “now” is always the same as to subject but other and other in conception; secondly, that it is the “now” that measures time, at no. 587.

He says therefore, first that, as was said above, in respect of continuity and in respect of “before” and “after”, motion follows upon magnitude and time upon motion. Let us imagine, therefore, after the manner of geometers, that a point in motion is making a line: then, just as there is something that remains identical in this motion, so there must be something that remains identical throughout time. If the moving point should make a line, it is by the moving point that we discern the motion and the “before” and “after” in it. For motion is perceived only because the mobile thing is in other and other states: according to what pertains to the previous position of the mobile, we judge something as “before” in motion, and according to what pertains to a subsequent position, we judge something as “after” in motion. Therefore this thing which is being moved, by which we recognize that there is motion and by which we discern a “before” and “after” in it, whether it be a point or a stone or anything else, insofar as it is a certain being, whatever it may be, is the same, namely as to subject—but in conception it is other. And this is the way the Sophists use the term “other” when they say that Coriscus in the forum is other than Coriscus in the theater, arguing thus: according to the fallacy of accident: to be in the forum is other than to be in the theater; but Coriscus is now in the forum and now in the theater; therefore he is other than himself. In like manner, it is plain that that which is being moved is other according to conception insofar as it is now here, now there—while remaining the same as to subject.

Now just as time follows upon motion, so the “now” follows that which is being moved. This is so because it is through the mobile that we know the “before” and “after” in motion. For when we see the mobile in some certain part of a magnitude through which it is being moved, we judge that the motion which passed through one part of the magnitude has ceased to be before and that motion through another part will follow after. In like manner, in the counting of motion (which counting is done by time), that which distinguishes the “before.” and “after” of time is the “now,” which is the end of the past and the beginning of the future. Thus the “now” is related to time as the mobile in to motion. Therefore also, by commuting the proportion, we get that time is to motion as the “now” is to the mobile. Hence, if the mobile remains the same as to subject throughout the entire motion—though differing in conception—the same will be true of the “now”: it too will remain the same as to subject but will be other and other in conception. For that by which “before” and “after” are discerned in a motion is the same as to subject but differing in conception, the mobile; and that according to which “before” and “after” are counted in time is the “now.”

586. This train of thought makes easy an understanding of eternity. For the. “now,” insofar as it corresponds to a mobile that is continually other and other, distinguishes the “before” and “after” in time and by its flow makes time, just as a point makes a line. But if that varying status of the mobile be removed, the substance remains always in the same state; whence the “now” is then understood as always standing still and not as flowing nor as having a “before” and “after.” Therefore, just as the “now” of time is understood as the number of the mobile, so the “now” of eternity is understood as the number, or rather the unity of a thing always remaining in the same state.

587. Then [415] he shows whence the “now” derives its function of measuring time. And he says it is because that which is best known in time is the “now”, and what is best known in any genus is the measure of everything in that genus, as is said in Metaphysics X. He also shows this from the relation of motion to the mobile: for motion is perceived through something being moved and local motion is perceived through observing something being moved locally; after the manner of the better known manifesting the less known. This is so because that which is being moved is “this something,” i.e., a certain thing stable in itself—a characteristic which does not belong to motion. Hence the mobile is more known by us than the motion, and motion is known through the mobile object. In like manner., time is made known through the “now.” Thus, he reaches the conclusion principally intended: that what is called the “now” is always the same in one way, and in another way not, because it is similar to the mobile, as was said.

588. Then [416] he explains the reason for the things which are said of the “now”:

First, why it is said that nothing of time exists but the “now”;

Secondly, why the “now” is said to separate and continue the parts, of time, at no. 590;

Thirdly, why it is said that the “now” is not a part of time, at no. 592.

589. He says therefore first that it is plain that if there is no time, there will be no “now,” and if no “now,” no time. This is explained by the relation of motion to the mobile. For just as the change of place and that which is being changed are together, so the count of that which is being changed accompanies the count of the change of place. But time is the number of a local motion, while the “now” is related to what is being moved, not as its number (since the “now” is indivisible), but as the unit of number. It follows therefore that time and the “now” are not one without the other. Notice that time is always compared to a local motion, which is the first of all motions: for time is the number of the first motion, as was said.

590. Then [417] he explains why itis said that time is continued and, divided according to the “now.”

First he explains it by considering motion and the mobile;

Secondly, by considering a line and a point, at no. 591.

He says therefore first that what we have already said makes clear that time is made continuous with the “now,” i.e., by the “now,” and is divided by the “now.” This fact also follows from what is found in local motion (the number of which is time) and in the object that is being moved according to place which corresponds to the ‘how”). For it is clear that every motion derives its unity from the object being moved, since that which is being moved remains one and the same throughout the whole course of the motion. And it is not a matter of indifference whether that which is moved, in the course of one motion, be any being at all, but rather it must be that same being which first began to be moved, for if it were another being that was later moved, the former motion would have failed and there would now be another motion of another mobile. So it is clear that it to the mobile that gives unity to the motion, which unity constitutes its continuity.

But it to true that the mobile is other and other according to conception. And it to in this way that it distinguishes the prior and the subsequent part of motion: because insofar as the mobile is considered under one aspect or disposition it is recognized that whatever disposition was in the mobile previous to its present state pertained to the prior part of the motion; whatever disposition will come after this state will pertain to the subsequent part of the motion. Thus it is that the mobile both continues the motion and distinguishes its parts. And the same holds for the “now” in relation to time.

591. Then [418] he explains a case of the same in the matter of line and point. And he says that the conclusion drawn about time and the “now” in the preceding section follows in a way from what is found in a line and a point; for the point continues the line and distinguishes its parts, inasmuch as it is the beginning of one part and the end of another.

But there is a difference in the case of line and point, and in the case of time and the “now”. For both the point and the line are something stationary; whence a person can consider the same point twice and use it as two [give it two interpretations] namely, as both a beginning and an end. When we thus use the point as two, rest occurs, as is evident in a reflex motion, in which that which was the and of the first motion is the beginning of the second and reflected motion. It is on this basis that we shall prove in Book VIII that a reflex motion is not continuous but that an intermediate pause occurs.

But the “now” is not stationary, because it corresponds to the mobile which is always being carried along during the motion—which also accounts for the “now” having to be always other and other in conception as was said above. Therefore since time is the number of motion, it does not number motion in the sense that some same time is taken as the beginning of one and the end of another, but rather it numbers motion by taking two boundaries of time, namely, two “nows,” which are nevertheless not parts of time.

The reason why this method of counting is used in numbering time, rather than the method used when a point numbers the parts of a line (where the same point is considered both a beginning and an end), is that, as was stated, in the latter method we use the point as two things and this brings about an intermediate pause, which cannot exist in time or in motion. Now this does not mean that the same “‘now” is not the beginning of the future and the end of the past, but that we do not perceive time by counting motion in terms of one “now” but in terms of two, as was said; otherwise, in our counting of motion the same “now” would be employed twice.

592. Then [419] he explains why it is said that the “now” is not a part of time. And he says it is plain that the “now” is not a part of time, just as what distinguishes a motion is not a part of the motion, namely, some disposition in the mobile itself, just as points are not parts of a line. For two lines are the parts of a line.

Now he manifests the properties of time from the properties of motion and of line because, as was said above, motion is continuous on account of the magnitude, and time on account of the motion.

He concludes, therefore, finally that the “now,” insofar as it is a certain boundary, is not time but it happens to time, as a boundary does to that which is bounded; but insofar as time or the “now” numbers other things, the “now” is the number of things other than time. The reason is because a boundary can only be of that of which it is the boundary; but a number can be applied to various thing, as the number of ten horses is also that of other things. Thus therefore the “now” is the boundary only of time, but it is the number of all mobiles that are being moved in time.

Lecture 19

From the definition of time certain things are clarified

593. Having defined time, the Philosopher now, in the light of the definition which he has given, gives an explanation of those things that are said about time. About which he does four things:

First, he shows in what sense there to found in time a smallest part, and in what sense there is not;

Secondly, why time is said to be “much” and “little,” “short” and “long”, but not “fast” and “slow,” at no. 595;

Thirdly, in what sense time is the saw, and in what sense it is not [ever the same again] at no. 596;

Fourthly, how time to known through motion and vice-versa, at no. 597.

594. He says therefore first [420] that the previously given definition of time makes clear that time is “the number of motion according to before and after,” as was expounded above, and that time is a type of continuum, as is likewise manifest from what has gone before. For although it does not have continuity insofar as it is a number, yet it has continuity by reason of that of which it is the number: for it is the number of a continuum, namely, of motion, as was said above. For time to not a number absolutely but a number of something numbered.

Among absolute numbers there is unequivocally a least to be found, namely, two. But if we consider owe certain number, namely, the number of something that is continuous, then there is in one sense a minimum and in one sense no minimum, because in the order of multitude [plurality] there is a least, but not in the order of magnitude. For example, in a plurality of lines there is a minimum according to plurality, i.e., one line or two lines (one if you consider what is the minimum in number absolutely; two if you mean that which is least in the genus of number, having the notion of number). But in respect of magnitude there is no minimum in lines, so that there would be namely, some smallest lines—because it is always possible to divide any line whatsoever.

A parallel situation is found in time, for there is a minimum according to multitude, namely, one or two, for example, one year or two years or two days or two hours. But in the order of magnitude there is no minimum, because of any given time there are parts into which it may be divided.

595. Then [421] he gives a reason why time is not said to be slow or fast, but great and small, short and long. For it has already been shown that time is both a number and a continuum. Insofar, therefore, as it is the latter, time, is said to be “long” and “short”, insofar as it is a number, it is said to be “great” and “small.” But to be “fast” and “slow” in no wise belongs to number, neither to number absolutely, as is plain, not to the number of some things. For to be “fast” or “slow” is said of something accordingly as it is numbered: for a motion is called “fast” insofar as it is counted off in a short time—and “slow” conversely. Hence it is clear that in no sense can time be called “fast” or “slow.”

596. Then [422] he shows how time is the same and how not the same.

First, how it is the same or not the same absolutely;

Secondly, how it is the same in a certain respect, at no. 597.

He says therefore first that the time existing at a given moment is the same everywhere, i.e., it is the same in respect to everything that is being moved anywhere. For it is not diversified by reason of the diverse mobiles, but by reason of the diverse parts of the same motion. For which reason a prior time and a later time are not the same. Why? Because the first and present motion, of which time is primarily and principally the number, is one; but one part of this motion has already taken place and is past, and another will be in the future. Hence there is one time which is past, and another time which is future. This is so because time is not number absolutely but the number of something numbered; namely, of the “before” and “after” in motion. And this number always varies and is “before” and “after,” because the “now’s,” as before and after, are always other. But if time were number absolutely, then the time corresponding to the change which is past and the time corresponding to the change which is to come would be the same, for number absolutely is one and the same of different things counted as, for example, in the case of 100 horses and 100 men. But number numbered varies with different things. For 100 horses are not the same as 100 men. Since time is the number of “before’s and “after” in motion; and since the “before” and “after” of a past motion are not the same as those of that which follow, therefore the past time and the future time are other and other.

597. Then [423] he shows how the same time returns in a certain respect. And he says that in the same way that one and the same motion may be repeated, so may one and the same time. For one and the same motion can be duplicated specifically, but not numerically; for it is from the same sign of the Ram that the sun first moves [at the vernal equinox] and later will move the following year; therefore, just as there has been winter or spring or summer or fall, so also there will be, not, indeed, the same one in number, but in species.

598. Then [424] he shows that just as we know motion from time, so also time from motion.

First, by reason of number and the thing numbered;

Secondly, from the likeness existing between magnitude and motion, at no. 599.

He says therefore first that we not only measure time by motion but motion by time, because each is defined in terms of the other. For one must take the quantity of the one according to the quantity of the other. Now that time should determine motion comes about because it is the number of motion; but conversely, as to us, motion determines time. For we sometimes perceive a quantity of time by means of motion, as when we declare a time to be long or short according to a measure of motion, certain to us; because sometimes we know a number through the things that can be counted, and conversely. For we know by this number a multitude of horses and likewise by one horse we know the number of horses. For we would not know how many thousands there were unless we know what a thousand was. The same holds for time and motion. For when a quantity of time is certain to us, but the quantity of motion unknown, then by the time we measure the motion; but we do the opposite when the motion is known and the time unknown.

599. Then [425] he shows the same thing by comparing motion and magnitude. And he says that what has been just said of time and motion happens reasonably because just as motion imitates magnitude in quantity and continuity and divisibility, so also does time imitate motion; for the latter [quantity, continuity and divisibility] are found in motion on account of their presence in magnitude, and they are found in time on account of their presence in motion. For we measure magnitude by means of motion, and motion by means of magnitude. For we say that a road is long when we notice that our motion over it was long; and conversely, when we consider the magnitude of the road, we say that our motion was long. The same holds when relating time and motion, “ we said above.

Lecture 20

How things are, and are not, in time

600. After determining the question of time in itself, the Philosopher now discusses it in relation to things that are in time. As to this, he does two things:

First he compares time with things that exist in time;

Secondly, with things that exist in the “now,” at no. 612 (L.21).

Concerning the first he does two things:

First he compares time to motion;

Secondly to other things that are in time, at no. 602.

601. In regard to the first, note that motion is related to time in a way different from the way other things are related to it. For motion is measured by time both as to what it is and as to its duration i.e., its existence. But other things, such as a man or a stone, are measured by time as to their existence or their duration insofar as they have a changeable existence; but as to what they are in themselves, they are not measured by time; rather it is the “now” of time that here corresponds, as was said above (L. 18).

He says therefore [426] that time is the measure of motion itself, and “of being moved,” by which he means the duration of motion.

Now time measures motion by a certain part of the motion’s being determined by time, which part then measures the whole motion. And this is necessary, because each thing is measured by something of the same genus, as is said in Metaphysics X. This is evident in the measures of lengths. For a cubit can measure the entire length of a piece of cloth or of a road, because the cubit determines some part of the length—which part then measures the whole. Likewise by means of a part of motion, time measures an entire motion: for by means of the motion of one hour, the motion of a whole day is measured, and by means of the daily motion the yearly motion is measured. Therefore, since motion is measured by times, for motion to be in time is, nothing more than for it to be measured by time, both as to what it is and as to its duration—because according to both aspects it is measured by time, as was said.

602. Then [427] he shows how it is related to other things:

First, how other things are in time;

Secondly, what things belong in time, at no. 603.

He says therefore first [427] that since for motion to be in time is for it to be measured by time, both as to itself and as to its existence, it is clear that it is likewise the same for other things to exist in time and to be measured by time, i.e., not as to what they are, but as to their existence: for motion is essentially measured by time but other things only insofar as they have motion.

He proves, in the following way, that for a thing to exist in time is to have its existence measured by time: To be in time can mean two things; first, as something is said to exist in time, because it co-exists with time; secondly, as something is said to exist in time in the way that things are said to exist in number. And this latter also has two meanings: for in a number something is present (1) as a part, as 2 is in 4; and as a property, such as even and odd, or whatever else that belongs to number; or (2) it can be there, not because it is anything pertaining to number, but because number belongs to it as numbered, as men may be said to be in such and such a number.

But because time is a number something can be present tn time in both ways. For the “now,” and “before” and “after,” and things of this sort, exist in time as unity exists in number, of which it is a part, and as do even and odd, which are properties of number, and as do “superfluous” and “perfect.” (A number is called “perfect,” if the sum of the parts measuring it equals the number; for example, six is measured by one, two, and three, which, added together, equal six. A number is called “superfluous” if its divisors total up to a number which exceeds it: for example, 12 is measured by one, two, three, four, and six, which, when added together equal 16.) And that is the way in which some things exist in time, namely, as being something of time. But things that are not something of time are said to be in time as things numbered exist in number. Consequently these latter things that are in time must be contained under time as under a number, just as things in place are contained under place as under a measure.

Then he explains the very first way of something’s existing in time. And he says it is clear that it is not the same thing to exist in time, and to exist when time exists [i.e., to co-exist] just as it is not the same to be in motion and in place and to be in existence when place and motion exist. Otherwise, it would follow that all things would be in anything; for example, the heavens would be in a grain of millet, because when the millet exists, the heavens exist.

There are two differences between these situations: for when something is said to be when something else exists, it is incidental to the one that it exists at the same time as the other; but that in which something exists as in a measure follows necessarily [upon that which is in it], as time necessarily follows upon that which is in time, and motion upon that which is in motion, so that they are together.

603. Then [428] he shows to what things it belongs to be in time;

First he shows that not all beings exist in time;

Secondly, that not all non-beings do, at no. 611.

As to the first he does two things:

First he shows that things which are always do not exist in time;

Secondly, that nevertheless things that are at rest are, as such, in time, at no. 606.

As to the first he does two things:

First he mentions the facts from which he proceeds to the manifestation of his proposition;

Secondly, he concludes to the proposition, at no. 605.

Now he mentions two things. The first of these [428] is that, when something is in time as the numbered is in a number, then necessarily there is some time that can be taken larger than everything that exists in that time, just as it is possible to take a number larger than everything that is numbered. Consequently, all things that exist in time are of necessity contained under time and comprehended under it just as things in place are comprehended under place.

604. The second thing is then mentioned [429] and it is that whatever exists in time suffers something under time in tl;e- ie-nee of “suffering” fpassic7 as what pertains to defect. And he proves this from the way people ordiiiarily speak. For we are wont to say that length of time “wastes things away,” i.e., decays and corrupts them, and again that on account of time all things that exist in time grow old, and that on account of time forgetting occurs - for things we have recently learned remain in the memory but with length of time they slip away.

And lest anyone should say that perfections also are attributed to time as well as defects, he subsequently forestalls this, giving, in effect, three reasons over and above the three aforesaid.

Complementing his statement that forgetting occurs on account of time, he add-s that no one learns on account of time; for if a person should neglect study for a long time, he does not on that account learn, while he does on account of time forget.

In keeping with his statement that all things grow old in time, he adds that nothing becomes new on account of time; for a thing is not renewed on account of a long existence; rather, it becomes antiquated.

To match his statement that time wastes things away, he adds that time does not make a thing good, i.e., whole, and perfect, but rather wasted and decayed. The reason for this is that time corrupts things even when there is no other manifest corrupting agents. All this is due to the very nature of time: for time is the number of motion—and it is of the nature of motion to put a distance between what now is and the condition it was in previously. Consequently, since time is the number of the first motion, which causes mutability in all things, it follows that length of time causes all things that exist to time to be removed from their former condition.

605. Then [430] he concludes to his proposition from the foregoing premises, and first of all, from the first. For it has been shown that whatever exists in time is contained under time while whatever things are always, are not contained under time as exceeding time. Neither is the being, i.e., the duration, of such things measured under time, since they endure to infinity, and the infinite cannot be measured. Therefore those things that exist forever, are not in time. But this is true insofar as they exist always. For the heavenly bodies exist forever according to the being of their substance, but not in regard to “where” they are; consequently, their duration is not measured by time, yet their local motion is.

Secondly [431] he proves the same point from the second of the points laid down before. And he says that a sign that those things which exist forever do not exist in time is that they do not suffer from time, as though not existing in time. For they neither waste away nor grow old, as was said of things that exist in time.

606. Then [432], because he had shown that those things which exist forever do not exist in time, while those things which are at rest also remain the same way someone might think that things at rest are, as such, not measured by time. Therefore to obviate this, he shows that time is also the measure of rest. And in regard to this he does five things:

First he proposes what he intends, and says that because time is the measure of motion per se, it will also be per accidens the measure of rest; for all rest is in time just as all motion is.

607. Secondly [433] he excludes something that might lead one to think that rest is not measured by time. For since time is the measure of motion, someone might suppose that a thing at rest, because it is not in motion, is not in time. Consequently, to exclude this, he says that not everything in time need be in motion, in the same way that everything in motion has necessarily to be moved. For time is not a motion but the number of motion. Now it occurs that not only what is being moved, but also what is at rest, may be in the number of motion.

608. Thirdly [434] he proves the proposition that a thing at rest is in the number of motion, as to be measured by time. To do this, he adduces that not every immobile thing, i.e., not every thing that is not in motion, is at rest; rather, a thing at rest is something deprived of motion, but which is nevertheless by nature disposed to be moved, as it was said above in Book III that that is moved whose immobility is rest—for rest is not the negation of motion, but its privation. Consequently, it is evident that the being [existence] of a thing at rest is the being of a mobile being. Hence, since the being [existence] of a mobile being is in time and is measured by time, the being of a thing at rest is measured by time. Now here we are saying that a thing is in time as in a number, because there is some number for that thing, and because its existence is measured by the number of time. Thus it is clear that a thing at rest exists in time and is measured by time, no insofar as it is rest but insofar as it is a mobile being. That is why he said in the beginning that time is per se a measure of motion but per accidens a measure of rest.

609. Fourthly, [435] he shows in what sense a mobile and a thing at rest are measured by time. And he says that time measures what is moved and at rest not insofar as it is a stone or a man, but insofar as it is in motion and at rest. For measuring is properly due to quantity; therefore, time is properly the measure of that whose quantity is measured by time. Now, from the measuring done by time, are known both the quantity of motion and the quantity of rest, but not the quantity of the thing in motion. Hence the thing in motion is not measured by time according to its own proper quantity, but according to the quantity of its motion. From this it is clear that time properly is the measure of motion and of rest—of motion per se, but of rest per accidens.

610. Fifthly, [436], he adduces a certain corollary from the foregoing. For if nothing is measured by time except insofar as it is in motion or at rest, it follows that whatsoever things are neither in motion nor at rest, e.g., the separated substances, are not in time; for this is to be in time, namely, to be measured by time. But time is the measure of motion and of rest, as is clear from the foregoing.

611. Then [473] he shows that not all non-beings are in time. He says it is clear from the foregoing that neither is every non-being in time, as in the case of things that cannot be otherwise [whose contradictory cannot be], e.g., that a diagonal be commensurate with the side of a square: for this is impossible, because it can never be true. Now such things are not measured by time. And he proves it in this way: Time is primarily and per se the measure of motion, and anything else is measured by time only per accidens. Consequently whatever is measured by time must be capable of motion and rest. Hence things generable and corruptible, and all things that sometimes exist and sometimes do not, since they are “in motion and rest,” exist in time, for same time can be found that is greater than they are and which exceeds their duration, and for that reason measures their substances, not in regard to the nature of the substances, but in regard to their existence or duration.

But among things that do not exist but are nevertheless contained by time, some things existed at one time, as Homer; others will exist, as some future event; or, if they are contained both by past and present time, they both will be and were. But things that are in no way contained by time neither are, nor were, nor will be. Such are things that forever are not, and whose opposites forever are; for example, that a diagonal be not commensurable to the side, forever is; whence it is not measured by time. And for this reason neither is its contrary measured by time, i.e. that the diagonal is symmetrical, i.e., commensurable. The reason why it forever is not, is that it is the contrary of what forever is.

But of whatever things the contrary does not always exist, such things can exist and not exist, and are subject to generation and corruption; such things are measured by time.

Lecture 21

The meaning of “now” and related terms

612. After showing how time is related to things that exist in time, the Philosopher here shows how, in virtue of their relations to the “now,” certain words derived various meanings with respect to time. About this he does two things:

First he explains the meaning of “now”;

Secondly, the meaning of certain other words that are determined by the “now, “ at no. 615.

As to the first be does two things:

First be gives the proper and principal meaning of “now”;

Secondly, be gives a secondary meaning, at no. 614.

613. In regard to the first be says three things about “now.” The first of these [438] is that the “now” joins past time to the future, insofar as it is the boundary of time—the beginning of the future and the end of the past, although this is not so evident in the “now” as in a point. For a point is stationary and therefore can be considered twice: once as a beginning, and once as an end. But this does not occur with the “now,” as was said above.

Secondly [439], he says that time is divided according to the “now” as a line is divided according to the point. But yet the “now” divides time insofar as it, the “now,” is considered to be many in potency, i.e., as it is, namely, taken separately as the beginning of this time, and separately as the end of that time. And insofar as it is taken in this way, the “now” is taken as other and other; but insofar as it is taken as linking time and giving it continuity, it to taken as one and the same. And he shows this from a similar situation in mathematical lines, in which it is more evident. For in mathematical lines the point in the middle of a line is not always taken as the same: for insofar as the line is divided, there is understood one point which is the end of one line, and one point which is the end of the other. For lines, insofar as they are actually divided, are considered as contiguous—and contiguous things are those whose boundaries are together. But insofar as the point continues the parts of the line, it is one and the same—for continuous things are those whose boundary is the same. And this is the situation with the “now” in respect of time: for it can be taken in one way as potentially dividing time; in another way, as the common boundary of two times, uniting them, and making them continuous.

Thirdly [440], he says that the “now” that divides and continues time is one and the same as to subject, though differing in conception, as the foregoing has made clear. So much for the first meaning of “now.”

614. Then [441] he gives a secondary meaning of “now,” saying that “now” has another meaning, for it can be taken, not as the boundary of time continuing the past with the future, but as the time near to the present “now,” whether that time is past or future, as when we say, “He will come not,” because he will come today, or when we say, “He has come now,” because he came today. But we do not say that the Trojan war has happened “now,” nor that the Flood took place “now,” because, although the whole of the time is continuous [with the present] nevertheless it is not close to the present “now.”

615. Then [442] he explains certain things that are determined by the “now.” And first, what “then” signifies. About this he does two things:

First he gives its meaning;

Secondly, he raises a difficulty, at no. 616.

He says therefore first (442) that “then” signifies a time determined by some previous “now,” whether near or remote. For we can say that Troy was destroyed “then,” and that the Deluge took place “then.” For what is said to have taken place “then” must be included between some preceding “now” or instant [and the present]. For it will be necessary to say that there is a time period of definite quantity from the present time to that “now” which was in the past. In this wise it to evident that “then” differs from the second meaning of “now” in two ways: first, because “then” always refers to the past and it matters not whether it to the near past or the remote past; but “now” refers to the near, and it matters not whether it be past or future.

616. Then [443] he raises a difficulty in the light of the foregoing and solves it. For he had said that the time which is called “then” is included within a past “now” and the present: hence all time called “then” must be finite. But there is no time which cannot be called “then.” Therefore all time is finite. Now all finite time runs out. It seems therefore that one must say that time runs out. But if motion is always and time is the measure of motion, it follows that time will not run out. Therefore, we shall be forced to say, if all time is finite, either that time is always other and other, or that the same time is repeated over and over. And this situation must exist in time just as it is in notion. For if there is some eternally one and the same motion, then there will have to be one and the same time; but if there is not one and the same motion, there will not be one and the same time.

617. According to his opinion, as will be clear in Book VIII, motion never had a beginning, and will never end. Thus one and the same motion is being repeated, not numerically but specifically. For it is not numerically the same revolution that is taking place now and which took place in the past, but it is specifically the same one. Nevertheless, the whole notion is one in continuity, because one revolution is continuous with the next, as will be proved in Book VIII. And what was said of motion must also apply to time.

From this he shows that time will never fail. For it is evident from the foregoing that the “now” is both a beginning and an end, although not in relation to the same thing; but it is an end with respect to the past and a beginning with respect to the future. Accordingly, the situation with respect to the “now” is like that of the circle, in which its concavity and convexity are the same thing in reality, but differ according as they are related to diverse things. For convexity is had in a circle with respect to things outside it, and concavity with respect to things inside it. And because nothing of time can be taken but the “now” (as was said above) it follows that time is always at a beginning and at an end. And for this reason time seems to be other and other, for the “now” is not the beginning and end of the same time, but of different times; otherwise, opposite things would be true of the same thing according to the same aspect. For “beginning” and “end” have opposite notions; consequently, if the same thing were a beginning and an end with respect to the same, opposites would exist in the same thing according to the same aspect.

He further concludes from the foregoing that since the “now” is both a beginning and an end of time, time will never fail: for time cannot be understood without a “now,” and the “now” is the beginning of a time: hence time is always existing in a beginning of itself. But what is at its beginning is not failing; therefore time will not fail. By the same reasoning it can be proved that time did not commence from the point of view of the “now” which is the end of time.

But this reasoning proceeds on the supposition that motion is always, as he says. On this supposition, one would have to say that any “now” of time is a beginning and an end. But if it be said that motion had a beginning, or that it will cease, it follows that some “now” will be a beginning of a period of time and not an end, and some “now” will be an end but not a beginning, as happens also in a line. For if there were an infinite line, any point designated in it would be a beginning and an and. But if the line is finite, some point in it is a beginning only, or an end only. But this will be investigated more in detail in Book VIII.

618. Then [444] he shows what is meant by the words “presently” or “just”; and that they have the same meaning of “now.” For “presently” and “just” refer to what is near the present indivisible “now”, whether it is part of the future or part of the past. It refers to a part of the future, when I say: “When will he leave?” “Presently”—because the time in which this will take place is close. It refers to the past when I say “When are you going?” and it is answered,—“I have just gone”. However in regard to events that are distant, we do not say “presently” or “just”; for example, we do not say that Troy has “just” been destroyed, because this is very remote from the present “now.”

619. Then [445] he explains certain other words referring to time. And he says that “just now” [ modo ] signifies that a period of the past is near the present “now”, as when, if it is asked, “When did so-and-so come?” the answer is “just now,” if the past time is very close to the present. But we say “long ago”, when the time past is far from the present. Finally, we say that something occurs “suddenly”, when the time in which it takes place is imperceptibly small.

Lecture 22

How Corruption is attributed to Time—All Motion and Change are in Time.

620. After comparing time and the “now” to things that exist in time, the Philosopher here explains some things that were touched upon above.

First, how corruption is attributed to time;

Secondly, how every motion and change exist in time, at no. 623.

Concerning the first he does two things:

First he makes his proposition clear by an argument;

Secondly, by a sign, at no. 622.

621. He says therefore first [446] that every change of its very nature removes from its natural disposition the thing that is changed: but both generation and corruption take place in time. And therefore some attributed generations in things to time, as in the case of learning and the like, saying that time is “very wise” because the generation of science takes place in time. But a certain philosopher by the name of Parus, a Pythagorean, claimed on the contrary that time was “wholly unteachable,” because with length of time comes forgetfulness. And he was more right: for, as was said above, time per se is more a cause of corruption than of generation. The reason is that time is the number of motion, and change is per se destructive and corruptive. It does not cause generation and existence except per accidens. For from the fact that something is moved, it departs from the state in which it was. But that it arrive at some disposition is not implied in the notion of motion insofar as it is motion but insofar as it is finished and perfect. And this perfection is brought about by motion on account of the intention of the agent which moves to a predetermined end. Therefore corruption is attributed rather to change and time, whereas generation and being attributed to the agent and generator.

622. Then [447] he explains the same point with a sign, and he says that a sufficient sign of his claim is that nothing is found to come into being independently of an agent and a mover, but that a thing can corrupt without any mover in evidence. And such corruption we are accustomed to attribute to time, as when someone fails through old age from a corrupting internal cause that is not apparent; but when someone is killed with a sword, his corruption is not attributed to time. However, in generation the generator is always evident, because nothing is generated by itself. That is why generation is not attributed to time, as is corruption. Nevertheless, corruption is not laid to time in such a way as that time should cause it; but rather as occurring in time, while the corrupting influence is latent.

Finally [448], he asserts in a summary way that it has been explained that time exists, and what it is, and how “now” is used in various senses, and what are the meanings of “then” and “just now” and “presently” and “long ago” and “suddenly.”

623. Then [449] he above by two arguments that all change occurs in time. The first of these is that in every change is found the distinction of “faster” and “slower.” But these are determined by time—because that is said to be changed “faster,” which is changed first to a designated term, over a same distance, provided that both motions are subject to the same rule; e.g., in the case of local motion, if both motions are circular, or both in a straight line. But if one were along a circle and the other straight, the fact that one reached its terminus before the other would be no reason for saying that one moved “faster” than the other. And the same is to be understood of other types of change. It follows, therefore, that every change exists in time.

624. He then gives a second reason [450], but in this proof he makes use of the proposition that “before” and “after” exist in time. He manifests this proposition in the following way. “Before” and “after” are said according to the distance from the “now,” which is the boundary of the past and of the future. Both “now’s” exist in time; therefore both “before” and “after” exist in time, because that in which the “now” is, and that in which the distance from the “now” is, must be the same; just as it is in the same thing that there are a point and the distance taken in relation to that point, for both are in a line.

And because he had said that “before” and “after” are determined by the distance to the “now,” he shows how this occurs in a contrary manner with the past and the future. For in the past, that is “before” which is farther from the “now” but “after” which is nearer; but in the future it is just the opposite. If therefore “before” and “after” exist in time, and “before” and “after” follow upon every motion, then necessarily every motion exists in time.

Lecture 23

The Problems are Solved as to the Existence and Unity of Time.

625. After determining the truth about time, the Philosopher now settles certain doubts about time:

First in regard to the existence of time;

Secondly, in regard to the unity of time, at no. 630.

As to the first he does two things:

First he raises the doubts;

Secondly, he solves them, at no. 626.

He says therefore first [451] that certain problems require diligent consideration: namely, that of how time is related to the soul; and that of how time seems to be everywhere, i.e., an earth, on the sea, and in the air.

626. Then [452] he answers these questions:

First he answers the second question, because it is easier;

Secondly, he answers the first one, at no. 627.

He says therefore [452] that time is a certain accident of motion, because it is its number (an accident is wont to be called a “possession” [ habitus ] and “property” [ passio ]: hence, wherever there is motion, time must be. Now all bodies are mobile, if not with other motions, at least with respect to local motion, because all things are in place.

And because someone could say that although they are mobile, they are not all being moved, but some are at rest, and thus time does not seem to be in all, to counter this he adds that time accompanies motion, whether motion be actual or potential. For things that are capable of motion, and are not actually being moved, are at rest. But time measures not only motion but rest as well, as was said above. Hence, wherever there is motion either actually or potentially, there time is.

627. Then [453] he answers the first question, and as to this he does three things:

First he raises the question;

Secondly, he gives an objection to the question, at no. 628;

Thirdly, he resolves the question, at no. 629.

The question, therefore, is this: Would time exist if no mind existed?

628. Secondly, [454] he objects, to say it would not. For if it were impossible for something able to count to exist, it would be impossible for some thing countable to exist, i.e., able to be counted. But if there is nothing countable, then there is no number, because number does not exist except in that which is being actually counted or which is potentially countable. Consequently, if there is no one able to count, there is no number. But only the soul is disposed by nature for counting, and among the parts of the soul only the intellect; for counting consists in comparing the things counted with one primary measure, and comparing is a function of reason. Consequently, if there is no intellective soul, there is no number. But time is a number, an was said. If therefore, there is no intellective soul, there is no time.

629. Then [455] he answers the question. And he says that it is necessary to say either that time is not, if the soul is not; or to say what is truer, that time is still some sort of being even without the soul’s existing, similar to motion’s existing without the soul’s existing. For as motion is posited, so is it also necessary to posit time, because “before” and “after” exist in motion, and it is these things, namely, the “before” and “after” in motion, insofar as they are numberable, that are time.

To make this solution more evident it must be considered that once a series of numbered things is posited, it is necessary to posit number. Hence just as counted things depend on someone’s counting, so also their count [or number]. However, the existence of counted things does not depend on an intellect, unless it be an intellect which is the cause of things, as is the divine intellect, It does not depend on the intellect of the same. Hence neither does the number of things depend on the intellect in the human soul; only the counting of them, which counting is an act of the soul, depends on the intellect in the soul. Consequently, just as there can be things perceptible to sense even though no sense exists, and intelligible even though no intelligence exists, so there can exist both numberable [countable] things, and number even though no counter exist.

But perhaps the conditional he first mentioned is true, namely, that if no counter could exist, nothing countable could exist, just as the proposition is true that if there could be no one to sense, there could be nothing sensible. For if there is something sensible, it can be sensed, and if it can be sensed, there can be something to sense it—although it does not follow that if there is something sensible, there is something sensing. In like manner, it follows that if there is something countable, there can be someone to count. Consequently, if no one to count could exist, nothing countable could exist. However, it does not follow that if there is no one counting, there is nothing countable, which is the objection raised by the Philosopher.

Therefore, if motion had a fixed existence in reality, as a stone or a horse has, one could say unqualifiedly that, just as with no soul existing there exists a number of stones, so also with no soul existing, there would exist a number of motion, which is time. However, motion does not have a fixed existence in reality, nor is anything actual of motion found in things but a certain indivisible of motion which divides motion; indeed, the totality of motion comes to be on account of the mind considering and comparing a previous state of the mobile to a subsequent state. According to this, then, time also has no existence outside the soul except according to its indivisible; while the totality of time is had by an ordering process of the mind enumerating the prior and subsequent in motion [i.e., “before” and “after”], as was said above. And therefore the Philosopher said significantly that with no soul existing time is a being “of a sort,” i.e., imperfectly; this is similar to the statement that motion exists imperfectly without a soul existing.

So this answers the arguments mentioned earlier, to show that time does not exist on the ground that it is composed of parts that do not exist. For it is clear from the foregoing that like motion it does not have perfect existence outside the soul.

630. Then [456] he raises a question about the oneness of time, or about the relation of time to motion. As to this he does three things:

First he raises the question;

Secondly, he answers it, at no. 631;

Thirdly, he explains something he took as a presupposition, at no. 637.

So he says first [456] that there is question, since time is the number of motion, of whose, or of what sort of, motion it is the number. Then [457] he answers the question.

First he rejects a false solution;

Secondly, he gives the true one, at no. 634;

In regard to the first he does three things:

First he gives the false answer;

Secondly he disproves it by leading to a discrepancy, at no. 632;

Thirdly, he shows that this discrepancy is really an Impossibility, at no. 633.

631. The first solution, therefore, is that time is the number of any motion whatsoever. To prove this he brings up that every motion exists in time; namely, generation, and increase, and alteration, and local motion. Now what is found in every motion belongs to motion as such. But to exist in time is to be numbered by time. Consequently, it seems that every motion as such has a number; hence, since time is the number of motion, it seems to follow that time is the number of each and every continuous motion and not of some definite motion.

632. Then [458] he disproves this solution. For let us assume two things that are moving together: if, therefore, time to the number of any motion at all, it will follow that of two simultaneous motions each will have its own time, and so it will further follow that two equal times exist at once—e.g., two days or two hours. Now it is not strange for two unequal times to exist at once, e.g., a day and an hour.

633. Then [459] he shows that it is impossible for two equal times to exist at once. For every time that is simultaneous and similar, i.e., equal, is one; but time that is not simultaneous is not numerically one, although it is one in species, as day with day and year with year.

And he explains this by a similarity in other things that are numbered. For if there are seven horses and seven dogs, there is no difference so far as the number is concerned, but the difference is due to the species of the things counted. In like manner, for all motions which have simultaneous terms both as to their beginning and as to their end, there is the same time; yet the motions differ according to their proper notions, in that, perchance, one is fast and the other slow, one is local motion and the other alteration. But the time is the same if the number of the alteration and of the local motion is the same, supposing, of course, that they are simultaneous. Consequently, motions must be distinct from one another, but the time in all of them is the same— because there is one and the same number for all those that are equal and simultaneous, no matter where they occur.

634. Then [460] he gives the true solution. Concerning this he does three things:

First he prefaces certain facts required for the solution;

Secondly, from these he arrives at the solution, at no. 635;

Thirdly, he makes the solution clear by appealing to the statements of others, at no. 636.

In regard to the first he mentions three preliminary facts. The first of these is that among motions, the first and more simple and regular is local motion, and among these, circular motion, as will be proved in Book VIII. The second is that each thing is numbered by something near it, i.e., by something homogeneous with it, as units by a unit and horses by a horse, as is clear in Metaphysics X; hence time must be measured by some definite time, as we see that all times are measured by the day. The third presupposition is that time is measured by motion, and motion by time, as was said above. This is so because it is in terms of some definite motion and some definite time that the quantity of any motion and time is measured.

635. Then [461] he concludes from the foregoing that if something that is first is the measure of all things that are near it, i.e., of all the things in its genus, it is necessary that circular motion, which is regular above all, be the measure of all motions. Now a motion is called “regular,” if it is one and uniform. But such regularity cannot be found in alteration and growth, because they are not incessantly continuous or of equal [constant] speed. But regularity can be found in change of place, because there can be a local motion that is continuous and uniform, and the only such motion is circular motion, as will be proved in Book VIII.

Now among circular motions the most uniform and regular is the first motion which turns the whole firmament in a daily cycle; hence that revolution, as being the first and simplest and most regular, is the measure of all motions. But a regular motion must be the measure and number of the others, because every measure ought to be most certain—and those that are uniform are such. Consequently, from this we can gather that if the first circular motion measures every motion, and motions are measured by time insofar as they are measured by some motion, it has to be said that time is the number of the first circular motion, according to which time is measured, and in relation to which are measured all other motions that are timed.

636. Then [462] he corroborates his solution by appealing to the opinions of others, and first of all by the opinion of those who were led to assert that the movement of the heavenly sphere is time, on the ground that all other motions, and time itself, are measured by that movement; for it is evident that we speak of a complete day or year by reckoning from the motion of the heavens.

Secondly [463] from a common saying. And he says that because of this, namely, that time is the number of the first circular movement, it comes about that people are want to say that there is a cycle in human affairs, and in other things that move naturally and come into being and pass away. This is so because all such things are measured by time, and have a beginning and an end in time, as if time moved in a circle, because time itself seems to be a certain circle. And this again seems to be so because time is a measure of circular movement and is also measured by such a circular movement. And therefore, to say that of things which take place in time there is a certain circle, is nothing other than to say that time is a certain circle—which occurs because time is measured by a circular movement. For that which is measured is not seen to be different from its measure: but rather many measures are seen to make one whole, as many units make one number, and many measures of cloth one quantity of cloth. And this is true when a homogeneous measure is taken.

From all this it is clear that time first measures and numbers the first circular motion and through it measures all other motions. Consequently, there is but one time, due to the oneness of the first motion; and yet whoever perceives any motion whatever, perceives time, because from the first motion there is caused, mutability in all mobile- things, as was said above.

637. Then [464] he explains how something he mentioned above is to be understood. For he said that the number of seven dogs and seven horses is the same number. How this is true he now explains. And he says that it is correct to say, if the number of certain different things is equal, for example, of sheep and dogs, that the number is the same—for example, if the sheep and the dogs are both 10. But it cannot be said that to be 10 is the same for the dogs and sheep, for 10 dogs are not the same 10 as 10 sheep. The reason for this is that a genus can be predicated, with the addition of unity or identity [i.e., as “one genus” or “the same genus”], of several individuals of the same species; and in like manner, the remote genus can be predicated of several species existing under one proximate genus; but neither can the species be predicated of individuals, nor the proximate genus of diverse species, with the addition of unity or identity.

And he then gives an example of what he means. For there are two species of triangle, equilateral, i.e., having three equal sides, and scalene, i.e., having three unequal sides. Now “figure” is the genus for “triangle.” We therefore can not say that equilateral and scalene are the same “triangle,” but we can say that they are the same “figure,” because both are contained under “triangle” which is one species of “figure.” He gives the reason for this, which is that since “identical,” and “diverse” or “different,” are opposed, we can speak of identity whenever no difference is found, but we cannot speak of identity where there is a difference. But it is clear that equilateral and scalene differ mutually by reason of a difference that divides “triangle,” because they are diverse species of triangle. But “equilateral” and “scalene” do not differ in respect of the difference “figure”; rather, they are contained er one and the same difference that divides “figure.”

And this is clear thus. If we divide “figure” into its species which are brought about by differences, it will be found that one species is a circle, another a triangle, and so on for the other species of figure. But if we divide “triangle,” we will find that one species is “equilateral,” another “scalene.” It is clear, therefore, that equilateral and scalene are one “figure,” because they are contained under the one species of “figure,” the species “triangle,” but they are not one “triangle,” because they are diverse species of “triangle.”

The same thing applies to our proposition. For number is divided into diverse species, one of which is 10. Therefore all things that are 10 are said to have one number, because they do not differ from the other in regard to the species of their number, since they are contained under one and the same species of number. But we cannot say that they are the same 10, because the things being called “10” are different, since some are dogs and some horses.

Aristotle seems to have brought up this point so that no one, in trying to uphold the unity of time, would be content with saying that there is one number for things that are equal in number, even though the things be diverse; for although one might have a same 10 or 3 on account of a unity of species, yet it is not the same 10 or 3 on account of the diversity in number as based on matter. Hence, according to this reasoning, it would follow that time would be specifically, but not numerically, one. Therefore to get at the true unity of time, we must have recourse to the unity of the first motion, which is the first thing measured by time, and by which time itself is measured.

Finally, in summary, he concludes that we have finished with our consideration of time, and of the things that are proper to a consideration of time.

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