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 acc