International Catholic University
Thus far in our course on the philosophy of nature we have treated matter and form as the intrinsic principles of nature's operations. In our last lecture we examined motion or change as the pervasive property of the world of nature. This has taken us through the first three books of Aristotle's Physics. In this lecture we move on to the fourth book of the Physics, where Aristotle takes up what he refers to as nature's measures: place as the measure of the moveable body, and time as the measure of the motions moveable bodies undergo. We shall also take up some additional topics, from the fourth through the sixth book, relating to space and the void, and to the properties of the continuum as related to both time and motion.
The Latin word for place is locus, and it is the root from which we derive the word "local" as used in the expression local motion. From our previous lecture we know that local motion is very important, for it provides the paradigm in terms of which we understand other types of successive motion or change. Thus if we do not know what place is, we will have difficulty grasping change of place, the most common motion in the universe. Again, the category of location, the answer to the question "where?" (in Latin, ubi), would be very difficult to determine if we had no grasp of the meaning of place.
The most important thing to note about place is that it is a physical or natural concept, not a mathematical concept. The mathematical concept that is most closely related to place is the concept of space, which we shall also be discussing. Whereas the natural philosopher studies place and time as natural measures in the universe, the physicist studies space and time as the mathematical measures most used in his discipline. The two concepts, place and space, should not be confused, for they refer to quite different entities.
When I say that place is a physical or natural concept I mean that it is closely tied to the nature of a thing. Every natural body has a place or environment to which it is properly suited -- what we refer to as its natural place. As we have seen, natural bodies have powers that initiate and sustain their activities, and these powers are in many cases directed outside the body to other bodies in their surroundings. An important instance of this is gravitational force, which is found in all natural bodies, both living and non-living. Another significant instance, and this for living things, is homeostatic control. This power is essential to survival, for it regulates the responses of plants and animals to the entities and circumstances making up their ecology.
In defining place we should bear in mind the following three points. First, for local motion to be possible there must be places in the world in which bodies can succeed one another. Second, places must be real and must be something distinct from the body or bodies that are in them. If the place of a body were not distinct from the body, a moving body would take its place along with it and would have the same place after the motion as before. And third, for local motion to occur the place previously occupied by a body must remain unchanged when the body leaves it, and that the new place must also be unchanged as the body moves into it.
A good model for place is some type of vessel or container. Place is like a container that can be emptied of one thing and filled with another, and remains distinct from the things it successively contains. One may ask, for example, "Where is the honey?" and get the reply, "It is in the jar." The jar is, in a sense, the place of the honey. But the jar is an artifact, and now we are concerned with finding a containing place in nature that will fill the same function as the jar in the cupboard. Perhaps before being in the jar the honey was in a honeycomb, and how would we go about defining that kind of place?
Well, for one, place should state the environment in which a natural body exists. Again, place should be seen as surrounding the object in place. Yet again, this surrounding environment should be distinct from the located body. And finally, the exact place of a thing should be physically equal to the thing located in that place. For example, in a jar filled with honey the place that surrounds the honey is neither larger nor smaller than the volume of the honey itself. The volume of a place should be equal to the volume of the body in place.
To meet these requirements Aristotle proposed a definition of place that has been much debated through the centuries. He proposed his definition, of course, in the context of a spherical geocentric universe of finite size that is very different from the universe we conceive in the present day. We shall first explain the definition he offered in its original context, and then see how it may be adapted to the modern context.
The definition is succinct. In English it reads as follows: Place is the primary motionless boundary of that which contains. In his commentary on this definition St. Thomas divides it into two parts. He identifies the expression "boundary of that which contains" as the genus of the definition and the expression "primary motionless" as its difference. Let us examine each in detail.
Place is "the boundary of that which contains." This is the genus. Another term for boundary is surface, so place is in some way similar to the outermost surface of the body that is in place. Actually it encloses this outermost surface of the body in place, for place is the surface immediately outside that surface. This will be the innermost surface "of that which contains," namely, the innermost surface of the medium that immediately surrounds the body. Thus place will be the first surface outside the body in place.
I should note that I am using graphical aids throughout these lectures, and they are available to those taking the course for credit. If you have these, consider the first diagram in the upper portion of Fig. 5.1. It shows a rubber balloon filled with helium that is floating in air, attached to the ground with a string. Here the boundary of that which contains, or the container, is the surface of the air that immediately surrounds the balloon. This surface is directly in contact with the outside of the rubber of which the balloon is made. That suffices to answer the question, "Where is the balloon?" It is in the air. The second diagram there is similar. It shows a table in a room. Supposing that the only surface we know that surrounds the table is that defined by the walls of the rooms, we can answer the question "Where is the table?" The table is in the room. That is its place, taking place in a general way.
This brings us to the difference of Aristotle's definition, expressed in the words "primary motionless." There are two further precisions we can now make about our first determination. One relates to specifying more precisely where the table is located within the room. The other relates to the surface of the air in contact with the balloon when that surface may be continually changing. If the air is blowing, for example, and different air keeps touching the balloon's surface, does that make the place of the balloon change also? The words "primary" and "motionless" are added to take care of problems such as these.
Assume now that there is air in the room and the air is circulating. In such a case, as is shown in the lower portion of Fig. 5.1, there is always a layer of air touching the table on all sides. Then the "primary motionless" surface refers to the air that is touching and circulating around the table's surface. It refers, however, not to the particular air that is moving, but rather to this layer of air as it is related to the walls of the room that are at rest. The walls are motionless, and they are the primary referent for fixing the table's place. A specific place always involves a relationship to something stationary. This is indicated by the layer of air outlined around the table, with arrows drawn from it to the walls of the room. This particular relationship further specifies the table's location within the room.
The same reply applies to the balloon in the air when the air is blowing, also shown in the lower portion of Fig. 5.1. It is not the particular air contacting the balloon that determines its place, but rather the changing layer of air that is continually being related to the ground below the balloon. The ground is at rest and it remains as the stationary surface of reference. It provides what Aristotle would call the "primary motionless boundary" of the air that determines the balloon's proper place.
The universe of Aristotle and Thomas Aquinas was more orderly and more static than the universe of the twenty-first century. With regard to the elements, gravity was the basic force that dictated the natural order of the sublunary region. The ideal order was that of concentric orbs arranged around a center of gravity, which was also the center of the earth, as shown in Fig. 5.2. The innermost sphere was that of the Earth itself, earth being the heaviest element. Next to it was the sphere of the next heaviest element, water. After that came the sphere of air, which was lighter, and finally the sphere of fire, the lightest of all, extending to the sphere of the moon.
These spheres also determined the natural places of the bodies whose natures we have been considering in previous lectures. The natural places of plants and land animals were on and in the surface of the earth, those of fishes were in the waters, those of birds in the air, and those of meteors and shooting stars in the sphere of fire.
In the heavenly regions, beginning with the sphere of the moon, came respectively the orbs of the planets Mercury and Venus, then the orb of the sun, and after it, in succession, the orbs of Mars, Jupiter, and Saturn. The outermost sphere, finally, was the sphere of the fixed stars. This sphere, with its majestic and uniform daily rotation, served as the timepiece for humans. It also provided the ultimate frame of reference for locating every creature or nature within the universe, from the inorganic to the organic, from earthly bodies to those in the farthermost reaches of the heavens.
Our universe of the twenty-first century is much more dynamic and changing than this pre-Copernican universe. Yet we have no difficulty locating within it every object known to human beings. Surprisingly, Aristotle's gravity is still an important determinant of place, particularly for the regions within which we humans live. What is new is the notion of the "Big Bang" and the expanding universe it seems to have produced. This has introduced a new reference point, a new "primary motionless" that is different from a center of gravity, and is almost its opposite. The Big Bang introduces a kind of levity within the universe, one that causes objects to flee from the center rather than be drawn to it.
But from this point of "galactic recession," as it has been called, we can now locate star systems and galaxies, including our own galaxy, the Milky Way. And within galaxies we find our more familiar centers of gravity. Galaxies have their own centers of gravity and of galactic rotation. So do individual stars such as our sun, whose gravitational force enables us to situate the Earth (and ourselves) within the solar system.
Thus we can talk about the table being in the room on Earth, rotating with the Earth in its daily rotation, revolving around the sun. The sun in its turn is changing its place in our galaxy, and our galaxy too is changing its place, as it participates in the cosmic expansion -- all carrying our table along with them. In this way a center of galactic expansion, plus all of these local centers of gravity, provide the "primary motionless" referents in terms of which we still speak of places in our universe.
Problems relating to the concept of place still remain, and to address them we must now return to the concept of space. Earlier we said that space is a mathematical concept, and that is certainly true. But Aristotle considered space a physical concept also, one that could be studied by the natural philosopher independently of the mathematician. So let us look briefly at this physical concept.
For Aristotle and St. Thomas space was thought of as an interval or a distance. Real space, for them, would not be identified with the quantity of a body, but it is closely connected with that quantity. The essential element in quantity is that it designates an ordering of parts according to their position in a whole. Immediately flowing from this order are relationships of closeness and distance of these parts, which can be discerned in the three dimensions of length, breadth, and depth. Some parts are immediately close to each other, whereas other parts are distant from each other. Again, by reason of its quantity, one body can be near to or far from another body, by reason of their positioning.
These real relations of distance can be considered in two ways. They can be considered within the same quantity, either from one extreme to the other or from one part to another that is closer to or farther from it. This we may be refer to as an internal distance or as internal space, the space within the body. The relations can also be considered as a distance from one body to another, or from one quantity to another. This is external distance or external space, that outside the bodies, but between them. Fig. 5.3, in the diagram on the left, illustrates these two types of space, and they present no difficulty.
The diagram on the right side of Fig. 5.3 is of interest for its relation to Aristotle's definition of place. In examining the genus of place, Aristotle raised the question whether external space, as we have just defined it, could be used as place's genus. He rejected this possibility for the reason shown in the diagram. The diagram shows a bob suspended from a ceiling and contained within two possible containers. Changing the containers would change the space within which the bob is located, but it would not change the place of the bob, as we have defined it. In fact, an infinite number of containers could be situated around the bob, thus creating an infinite number of spaces, but not one would determine the precise location of the bob.
By way of opposition to the real spaces we have been discussing, it is possible to conceive an imaginary space. An imaginary space may be defined as the relation of distance between a real object and an imagined object that is non-existent. It could also be a relation of distance between two imagined objects, both of which are non-existent. For example, the universe as we now know it has a finite size determined by the limit of its present expansion. It is possible to imagine a space beyond that limit, where nothing exists. This would be our projection beyond what exists. It would not count as real but as imagined space, a "being of reason."
To return now to the mathematical concept of space, this is similar to imaginary space in that it exists in the imagination of the mathematician. It is different from imaginary space in that it is the object of the science of geometry, obtained by abstraction from sensible matter, as we described in our first lecture. In his thought processes the mathematician employs the second degree of abstraction, different from the first degree of abstraction used by the natural philosopher. Mathematical abstraction leaves aside all sensible qualities and natures as found in the physical world, and so arrives at pure extension, abstractly considered. Mathematical space is this pure extension, an ens quantum or quantified being, very different from the ens mobile or moveable being we study in natural philosophy. Physical space, on the other hand, is the space filled by natural bodies, where the concept of place is also applicable. It has a decided advantage over mathematical space in that it can take account of the natures of those bodies, which mathematical space does not.
In conjunction with the concept of space the question arises whether it is possible for there to be a space in the universe that is absolutely empty, a space devoid of any being whatever. This is the problem of the void or the vacuum, which has been discussed by philosophers since the time of Democritus. It is easy, of course, to imagine a space that lacks all being, and this may well be the source of Democritus's conviction that both being and non-being are necessary principles of nature. He saw "being" as atoms and "non-being" as the void. He held that both atoms and the void are necessary to explain motion, for without the void his atoms would have no place to move. All of this he proposed speculatively, for he had no empirical evidence to support either atoms or a void. Aristotle opposed this teaching of Democritus, but likewise on speculative grounds.
In the present day much more is known about atoms and vacuums, and the argument can move to a higher level. As in the case of space, where distinctions had to be made as to the types of space being considered, so in the case of voids or vacuums a few distinctions will be helpful in delineating the state of the question.
Aristotle proposed a basic distinction that is still pertinent to our discussion. This is the difference between a separated void or vacuum, that is, a space or vacuum outside the universe and thus separated from it, and an interior or interstitial void or vacuum, that found in interstices or intervals between the parts of bodies, as in Democritus's atomic hypothesis. Aristotle's arguments were directed against both types of void.
As to the separated vacuum, one can argue that the universe is actually finite, although motions in it may be unbounded or unlimited. This was true of motions in a circle in the Euclidean space of the Ptolemaic universe, and it is also true of many motions in the hyperspaces of modern cosmologies. Again, the notion of a center of gravity in the Ptolemaic system rules at an infinite universe, since an infinite physical body cannot have a center. The same argument applies to a center of galactic recession in the Big Bang theory, and for the same reason.
But if the physical universe is finite or limited in extension, this means that there is nothing physically real existing beyond and outside its limits. This does not prevent us from projecting, beyond the universe we now know, a possible space in regions we may conceive in our imaginations. But this is not the physical space we have just explained, but rather what we have already identified as imaginary space. Imaginary space is a being of reason, an ens rationis or construct of the mind, although it does have a foundation in reality.
On the question of interior voids or vacuums, those in the interstices of physical bodies, it is helpful to make a distinction between a perfect void, a place in which nothing exists, and an imperfect void, one in which something exists, though in a rarified or aetherial state. There is no objection nowadays to the existence of imperfect vacuums, since it is universally admitted that such voids exist. We talk routinely about vacuum tubes and vacuum cleaners, and we know that physicists are trying to produce ever more perfect vacuums. So we need not be concerned with imperfect vacuums since they are not relevant to the problem of the void.
As to a perfect vacuum in the sense of "a place in which nothing exists," this implies a contradiction. A place, by its very definition, is always the place of something, so if it contains nothing, it is not a place. This argument seems to be confirmed by the findings of modern science, which increasingly question the possibility of a perfect void in the universe. These arise from both relativity theory and quantum theory, with their empirical confirmations.
The general theory of relativity, for example, with its notion of space-time, implies that so-called empty space is filled with this hybrid entity that is the cause of gravitational phenomena, and therefore does not qualify as a non-existent. Again, quantum electrodynamics proposes that there is a "quantum vacuum" that "fluctuates," and in so doing produces subatomic particles that interact with other matter. If the quantum vacuum produces particles, it cannot be simply nothing. And finally the Big Bang theory has recently been confirmed by the discovery of a residual energy field known as "cosmic radiation background." This is an electromagnetic field that extends all the way back to the first moments of the universe and is pervasive throughout its extent. It is found in the interiors of atoms, no less than in intergalactic space. And either this field requires a medium, analogous to Aristotle's aether, or it is the medium, which may be aether by a different name.
We turn now to the concept of time. Earlier we said that place and time are measures. Place is the measure of the moveable object, that is, the natural body, and time is the measure of motion, the proper accident of the natural body. It now remains to explain precisely how, and in what sense, time is the measure of motion.
Time is easily associated with motion, and this has led some to think that time is the same thing as motion. That this cannot be so is seen from the fact that motions are particular and of different types, whereas time is physically universal and many motions can take place at the same time. Again, unlike motion, which can be fast or slow, time is uniform in its passage. Therefore time cannot be the same thing as motion.
On the other hand, the awareness of time is very much connected with the awareness of motion. We can easily verify this phenomenon for ourselves. If we sense a changing scene with objects in motion, we immediately connect its changing with the passage of time. And if we are alone, say in a dark room where we can see no motion, it is more difficult to note that passage. But if we have a succession of thoughts or images in our imagination, we become aware that time is passing. Thus there is clearly some kind of link between time and motion.
Aristotle provided an insight into what that link might be by stating that time is the number of motion. Precisely what he means by "number" in this context requires explanation. For example, consider the person in the dark room who has a succession of thoughts or images, and is able to reflect on them. The person then becomes aware that there was a moment, a "now," in which one thought occurred, and then a different moment, another "now," in which a second thought occurred. This situation is diagramed in Fig. 5.4, first by the horizontal line on the left and then by the vertical line on the right.
The horizontal line shows two "now's," one labeled "first" and the other "second." These may be taken to indicate the two moments in which the person in the dark room was aware of the succession of images. The interval between those two "now's" then represents the person's awareness of the passage of time.
Alternatively, the horizontal line may be taken to plot the flight of the bird we discussed in our last lecture. The two "now's" stand for the moments when the bird was first "here" and then "there." The interval between the two indicates the time it took for the bird to fly from here to there.
The vertical line on the right represents a similar example, that of heating the water, from our last lecture. Here again there are two "now's," one, say, representing the water when it was at 27o C., the other when the water was at 65o C. It took time to heat the water, and the passage of this time is represented by the interval along the vertical line between the two "now's."
There is still more to Aristotle's definition of time. In its complete form the definition reads: Time is the number of motion according to before and after. "Number" is frequently translated as "measure," and so an alternate definition reads" "Time is the measure of motion according to before and after." The "according to before and after" we have added is a literal translation of Aristotle's text, which in Latin reads secundum prius et posterius. The phrase is essential to our understanding of the concept of time.
To what do the "before" and "after" refer? They refer primarily to the interval that is traversed in the various motions being measured, and additionally, to the direction in which this interval or distance is being traversed. This is easiest to see in the flight of the bird. Let us say, as before, that the bird is flying from a tree to a church steeple. And let the "here" of the first "now" be when it is leaving the tree, and the "there" of the second "now"when it is arriving at the steeple. The "before and after" of the time is now dictated by the distance that has to be traversed and the direction in which the bird goes. In this case "leaving the tree" has to be the "before" and the "arriving at the steeple" has to be the "after." And the numbering of the two "now's" in this order has to be what defines the time of the bird's flight.
The same example could be adduced for the heating of the water. In this case the water at 27o would be the first "now" and the water at 65o would be the second "now." If the water is to be heating, the 27o obviously has to be the "before" and the 65o the "after," for this is what is meant by its heating. In both the flying and the heating, therefore, the "before" and "after" are dictated by the distance traversed and the direction of the traversal, and these serve to determine the flow of time that elapses in each case.
One further point has to be made, and this is that time, like motion, is a continuum. We have used the term before, and have said that time and motion are "flowing" continuums. It now remains to explain first what a continuum is, and then what is peculiar about continuums that are "flowing."
The continuum is one of the species of quantity, the other being number, which is usually thought of as discrete quantity. The opposite of this, continuous quantity, is best seen in the extension or magnitude found in the lengths of lines, surfaces, and bodies. Both numbers and lengths are composed of parts, but in different ways. Numbers, and here I mean positive whole integers, are composed of units as parts, and we employ these units when calculating with them in a digital way. For Aristotle, the unit or "one" is not a number, but it is a principle of number. In a literal sense "number" signifies a plurality. (If you held only one apple in your hand, you would not say that you were holding a number of apples.) The parts of a continuum are more difficult to specify. One way of approaching a definition is to oppose continuous length to another type of length that also constitutes extension, which may be called contiguous length.
Suppose I have five blocks and put them together so that they are touching end to end and make up a length of, say, five inches. The end of one block is not the beginning of another block, since each block has its own ends. This is an example of a contiguous length. The word "contiguous" means touching, and the ends of the blocks are different but touching each other. Now contrast this with a line segment that is five inches long, along which we designate points at one-inch intervals. These one-inch intervals are the parts of the line, since they make up the length of the line. The parts are joined at the points we have designated, and these points are different from the ends of the blocks. Each point ends one line segment and at the same time it begins another line segment. On this account the line is said to be continuous. The example provides our first definition of a continuum, namely, a continuum is a quantity whose parts share a common boundary, or whose boundaries are one.
Another definition is based on to the divisibility of the continuum. I can take the five blocks apart, and that is as far as I can go in dividing up a contiguous quantity. If I have a line segment that is five inches long, on the other hand, I can designate five parts of the line, as I have already done, but alternatively I can divide the segment in half, and then in half again, and then in half again, and I can do that ad infinitum. Thus we have the second definition of the continuum, namely, a continuum is a quantity that is divisible into parts that are always further divisible.
From this definition one can see that a continuum cannot be composed entirely of indivisibles. In dividing a line segment, one will never come to points. Put another way, a line segment cannot be made up entirely of points. I say "entirely," because the line segment is terminated at both ends by points, and there are points within the line that "tie together" the various parts of the segment, as many as one wishes to designate.
The examples I have been giving are taken from a mathematical continuum, because this is easier for us to understand. There are also physical continuums, an example of which is the natural body. Like the line segment, the natural body is a finite whole and a unit, and it also has parts, but unlike the line it is composed of sensible matter, not imaginable or intelligible matter. Like the mathematical continuum, the physical continuum can be divided to infinity in the imagination. When considered physically, sensible matter is heterogeneous and so has different qualities in its various parts. A natural body can also be divided by a physical cause, but here a difference manifests itself. A piece of lead, for example, can be divided into smaller pieces of lead. But then a question arises: Are all the parts of lead lead, in the same way that all the parts of line segments are line segments?
The answer would seem to be "no." Water, for example, can be broken down into smaller and smaller parts, but a point will ultimately be reached where the part is no longer water but something else, say, oxygen or hydrogen. This accords with the Aristotelian teaching that there are natural minimums, that is, minimal extensions under which particular natures cannot exist. This is obvious in the case of living substances, since squirrels cannot be as small as cockroaches. It is true of inorganic substances also. We now know that molecules are the natural minimums of chemical compounds and that atoms are the natural minimums of chemical elements. Physical bodies can be divided physically (and chemically) down to their natural minimums. Beyond this, if a further division is effected, that particular nature will no longer persist but will be replaced by a different one.
Natural bodies are physical continuums, and these have a quasi stable, permanent existence. The two other physical continuums we have been considering, time and motion, do not exist in this way, and so are referred to as transient or "flowing" continuums. Earlier we have said that all the parts of a permanent continuum exist together and at the same time, whereas the parts of a flowing continuum do not. Precisely how the parts of time and motion do exist poses a problem, which now attracts our attention.
From our preceding discussion we know that continuums in general are not composed of indivisibles like points as their elements, but of parts that are in turn continuums. These partial continuums are joined together, however, by indivisibles, which have the function of terminating but continuing the parts they join. How they can do this is what I shall now explain.
We have seen that time is the measure of motion and that time and motion are closely associated. It is easier to understand the parts of time and how they are joined, so let us start with that. As illustrated in the upper portion of Fig. 5.5, the parts of time are commonly regarded as the past and the future. The past and the future are joined by the present, which is the moment "now." This moment is actually the indivisible of time. If we compare the flow of time to a line, the "now" is a point that ends the part of the line corresponding to the past and begins the part of the line corresponding to the future. Thus the "now" is an indivisible that joins the past with the future and has the twofold function of terminating the past and originating the future. This is precisely what we said is the role of indivisibles in the continuum generally.
Now consider this. The past is no longer, and the future is not yet. There is a sense, it would seem, that the past has passed out of existence and the future has not yet come into existence. What then can we say about the existence of time, if both of its parts are non-existent? We propose that time is not existent and real by reason of its parts, that is, the past and the future, but it is real and existent by reason of its indivisible, the "now." In ordinary speech, of course, we do not stress this point-like understanding of "now." We tend to spread it out, as it were, and say it is now 1999, or it is now January, or it is now Thursday, or it is now twelve o'clock. In each case we group a little of the past and the future together with the instant that is "now." This illustrates graphically how the "now" gives reality and existence to the past and the future, even though neither exists in the way the natural body exists.
The parts of motion in a flowing continuum are more difficult to describe. Let me begin by saying that motion is a successive continuum. A successive continuum is composed of parts that are continuous. Since every motion is a "coming to be," successive motion is a quasi-extended "coming to be" made up of partial "coming to be's" that are joined together. They are joined by what I shall call "intermediate instants." "Intermediate instants" are the indivisibles of motion, analogous to the "now's" of time, and they are what tie the partial "coming to be's" together. They give reality and existence to the partial "coming to be's" in much the same way as the "now" of time give reality and existence to the past and the future.
Let us now apply this insight to the cases of local motion and heating we have earlier discussed. What is real about the flight of the bird? We can examine that question only while the bird is actually flying, and, of course, flight is a very transitory thing. The best way to describe it is by stopping it down, as it were, to analyze it in the diagram shown in the lower portion of Fig. 5.5. While the bird is in flight, all we have are the intermediate instants that signal that part of the flight has been and that part is yet to be. To say that the bird is flying is therefore to say that the bird has been flying and will be flying. And that will always be at some intermediate instant short of the point at which it ultimately reaches its goal.
To conclude this discussion it is helpful to distinguish between time as duration and time as a measure of motion. As duration, as applied for example to the bird, the bird's time is equated with the bird's existence, and this is fully real. As a measure of the bird's flying, however, time is a formally a "being of reason," since it involves the activity of mind and memory putting the parts of time together to see them as enduring. Yet materially and fundamentally the time of the flight is as real as the motion that is taking place and the distance that is being traversed. If there were no mind and memory to consider motion and time, would the two still exist? In such a circumstance Aristotle would concede them only a sort of imperfect existence, since he thought that mind was necessary to confer on them existence in a formal sense. But fundamentally they exist to the extent that the sensible continuum exists, and that is sufficient to warrant their consideration by the philosopher of nature.
Fig. 5.1 The Definition of Place
Fig. 5.2 The Concentric Spheres of Aristotle's Universe