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Chapter 5

Aristotle on Space, Time, and Motion

I. Aristotle: Life and Times

Aristotle was born in Stagira in Thrace in 384 B.C. He studied with Plato at the Academy from 368-348 B.C. On Plato's death, he left Athens and in 343 B.C. became the tutor of the young Alexander (later: the Great) of Macedon. In 335 B.C., he returned to Athens to form his own school at the Lyceum. When Alexander the Great died in 323 B.C., he left Athens and died in 322 B.C.

Aristotle was associated with Plato for over 20 years both as a student and as a colleague. His own views reflect his Platonic heritage, although he rejects both the details and the spirit of the Platonic world view. The range of Aristotle's work was enormous. He wrote extensively on a wide variety of topics including metaphysics, ethics, politics, biology, psychology, and the philosophy of science, as well as on the physics and philosophy of space, time, and motion.

II. Aristotle's Scientific Philosophy

Aristotle's significance for the history and philosophy of science rests on two fundamental achievements. First, he developed a comprehensive philosophical system which overshadowed anything in ancient times and, when rediscovered in the 12th century A.D., fashioned the medieval world view. Second, Aristotle developed a method of scientific investigation. He was, in effect, the first philosopher of science; the first to study the logic of scientific reasoning and investigation.

If we think of Plato as an "other worldly" philosopher (the ultimate rationalist), then Aristotle must be counted as an empiricist, and a common sense realist. As Aristotle developed his own views, and turned more and more to empirical biological investigations, he found Plato's world of Forms more and more offensive to common sense. In particular, he felt that the interaction which Plato postulated between the world of Forms and the sensible world was unexplained. To call the sensible world a "copy" of the world of Forms was merely a metaphor (Plato agreed with him on this point). Secondly, Aristotle felt that Plato did not give an adequate account of motion and change. As mentioned before, Aristotle shared with Plato the two fundamental theses that: (1) knowledge is possible; (2) knowledge is of Forms (Universals). But whereas, for Plato, the Forms exist independently of the objects of experience, for Aristotle, the Forms only exist embodied in the particular objects which exemplify them.

Aristotle considers each object, e.g., this table, to consist of both matter and form. The matter is what makes it this table rather than that table (in the next room, for example). The forms are the universal properties which this table shares in common with all tables. Thus, for Aristotle, there is only one world, the world of everyday experience. However, the objects in that world exhibit common characteristics which can be discerned by reason and it is these common characteristics that science studies. In fact, Aristotle distinguishes the sciences on the basis of which characteristics they study. This solves the first of Aristotle's difficulties with the Platonic view. Since there is only one world rather than two the alleged interaction of the two worlds ceases to be a problem. Also, one can see why Aristotle places so much emphasis on observation and experiment: Science is knowledge of this world of experience.

A second problem Aristotle found with the Platonic view was how to account for motion. Aristotle accounts for motion by making a distinction of fundamental importance between Potentiality and Actuality. This distinction survives in modern physics in the notion, e.g., of "potential energy" and, in fact, is fundamental throughout science. When we say, for example, that an egg is fertile, what we are saying, in essence, is that it has the potential to become an embryo. Similarly, when we say that a piece of metal is malleable, what we are saying is that it has the potential to be hammered into different shapes. In general, physical terms which end "-ible", or "-able" attribute potentialities of various sorts to the objects to which they apply.

How does Aristotle use this to explain change? Consider this table top. It is now actually cold. What happens if I build a fire under the table? The table top then becomes hot. The pre-Socratic philosophers found this puzzling because it seemed to them that this meant that "coldness" itself became "hotness" itself. Since they considered these to be opposite natures, change seemed to be self contradictory. Aristotle's two basic distinctions, between matter and form on the one hand, and potentiality and actuality on the other hand, allow him to overcome this difficulty. It is the table which is first cold and then becomes hot. How can the same thing be both hot and cold? Because, when it is actually cold (hot) it is only potentially hot (cold). This may seem like a trivial and obvious point, but to the Greeks it was a great insight and required a tremendous amount of intellectual effort to get straight.

Aristotle now defines change as the actualizing of something which has a potentiality. Consider an acorn. An acorn, properly nurtured, ultimately turns into an oak. The acorn, according to Aristotle, has the potentiality to become an oak. The acorn changes into an oak insofar as this potentiality becomes actualized. Once the potentiality is fully actualized an oak exists and the change is over. The change is the process leading from the beginning (the acorn) to the end (the oak), and it takes place only so long as there remains a potentiality to be actualized. Thus, Aristotle defines change as the actualization of what exists potentially, insofar as (or as long as) it exists potentially.

For Aristotle, natural objects are those which "contain within themselves a principle of motion and rest." The task of natural philosophy (physics) is to discover these principles. The principles are all such that they are to account for how this body with such and such perceivable qualities comes to have such and such other perceivable qualities. Thus, how for example, do we account for the fact that a heavy object which is held 5 feet above the floor when released will fall to the floor? What we are trying to account for is its change in position from up there to down here. Aristotle does this by arguing that heavy objects have within themselves a principle of motion which tends to make them move in a downward motion. We will have more to say about this in the remaining sections of this chapter.

Aristotle's cosmology dominated thinking about space, time and the physical universe until the scientific revolution in the 1600's. We present here a brief sketch of the most important features of Aristotle's view of the universe.

Figure 5-1

The diagram represents a two dimensional cross section of Aristotle's model of the universe. Note that Aristotle's universe is basically spherical. In fact, there are three spheres of fundamental importance. The first is the earth itself in the center of the diagram. The second is the sphere that encloses what is called the "sub-lunar realm." This is the area between the orbit of the moon and the earth. The third sphere is the shell that encloses the heavens and everything else in the universe. This is the sphere of the fixed stars. The orbits of the sun and the other planets lie in between the sphere of the fixed stars and the orbit of the moon.

Several important aspects of Aristotle's view can be read off of the diagram.

1. Aristotle has a geocentric model of the universe. The planet Earth is at rest in the center of the Universe. This implies that the universe is finite in extent, since an infinite space can have no center. In the 2nd century A.D., the Aristotelian model was used to estimate the size of the universe. Since the earth is at rest, the motion of heavenly objects, the moon, the sun, the planets, and the stars, is explained in terms of their revolving around the stationary earth.

2. Physical objects, for Aristotle, are made up of various combinations of five fundamental elements: Earth, Air, Fire, Water, and Aether. The objects in the sublunar realm, including the moon, are composed of Earl and Water. Those objects in the heavens are composed of the fifth element (the quint-essence) Aether. Associated with each one of these five elements is a natural place and a natural motion. It is in the nature of each of these elements to move, if it is not restricted in some say, to its natural place. The natural motions of the sublunar elements are straight line Up and Down motions towards or away from the center of the Earth, which is also, of course, the center of the universe. The natural motion of the heavy elements Earth, and Water, is down. The natural motion of the light elements, Air, and Fire, is up. If the universe should separate into its component parts then all the Earth would accumulate at the very center of the universe. It, in turn, would be covered by Water, the Water, in turn, would be covered by a layer of Air, and the layer of Air would be covered by a sphere of Fire, and these elements would fill up the entire sublunar realm. Thus the natural place of Earth is the very center of the universe, the natural place of Fire is the inner surface of the sublunar sphere, and the natural places of Water and Air are the appropriate intermediate positions.

This closed finite world with the planet Earth at its center was the dominant cosmological model until 1600. In that year, Giordano Bruno was burned at the stake by Calvin in Geneva for advocating the view that the universe was infinite in extent, among other heresies.

The sharp distinction in the Aristotelian model between the sublunar realm, on the one hand, and the heavenly realm, on the other, was a major obstacle to the development of the "new science" ushered in by the scientific revolution. It was not fully overcome until the publication of Newton's Principia in 1687. Newton's Principia was the coup de grace to the Aristotelian world view. From an Aristotelian point of view, a single physics would be impossible because not only is the stuff of the universe different in the sublunar realm from the stuff of the universe in the heavenly realm but the laws of motion themselves are different. Sublunar objects tend to execute straight line motions whereas heavenly objects tend to execute circular and eternal motions.

Reflection on the Aristotelian model throws new light on the story of Newton and the apple. As the story goes, Newton was sitting under an apple tree when an apple fell from the tree and struck him on the forehead. The traditional story has it that this event triggered Newton to the discovery of gravity. But, of course, that makes the story highly implausible, for even Aristotle was aware that if you sat under an apple tree you were liable, now and then, to be hit on the head by a piece of fruit. The true significance of Newton's achievement, however, was to realize that the force which drew the apple from the tree to the earth was in fact the same force that drew the moon to the earth, and was also the same force that held planets in their orbits around the sun. This is an extremely revolutionary idea, since it suggests that there might be a single physics descriptive and explanatory not only of the sublunar realm but of the heavens as well.

We turn now to a detailed analysis of Aristotle's views on place and time.

III. Aristotle on Place and Void

Physics, for Aristotle, is the study of the principles whereby objects move. The primary and most important kind of motion is loco-motion, or change of place. An object moves from one place to another place insofar as it is first (earlier) at the one place and then (later) at the other place. Thus, consideration of motion leads us directly to an examination of the nature of place and time. Aristotle professes himself dissatisfied with the efforts of his predecessors to explain motion, space and time and he seeks to provide a better understanding of these key ideas.

Aristotle's discussion of place is complicated in several respects. First, Aristotle does not seem to have a full fledged theory of spatiality as such. What he talks about instead, for the most part, is the notion of place, in the sense of the specific location of a thing. It is tempting (for us) to consider space, as a totality, as the collection of all places, but Aristotle does not seem inclined to think along these lines. Thus, when we come to abstract a general theory of spatiality from Aristotle's remarks we must be careful not to distort his meaning. The second complication concerns Aristotle's discussion of place itself. He seems to be trying to weld two different ideas into a single concept. On the one hand, he takes place to be something associated with particular objects, as one might talk about the place of this book, or the place one was born, or the like. On the other hand, his doctrine of motion leads him to talk about 'natural places,' i.e. places where certain kinds of objects tend to go, according to their natures. The result of trying to define a concept which satisfies both these requirements is not completely satisfactory. With these cautions in mind, we may proceed.

A. Aristotle on Place

Aristotle's main discussion of place is in the Physics 208a27-213a10. His procedure is, typically, to first "review the literature," i.e., to examine the doctrines and problems on a given question which have been formulated by his predecessors. In the light of this, he then sets forth his own doctrine. This is the method he employs here. He is concerned, primarily, with two basic questions: (1) Do places exist?; (2) If so, what is a place?

Aristotle gives two arguments to show that there is such a thing as place. What he is concerned to show is that places are distinct from bodies.

The Replacement Argument (208bl): That places exist and are distinct from what occupies them is held to be proved by the fact that different bodies can be and are said to occupy the same place. If places were not something different from the bodies that occupy them, this would not be so.

The Location Argument (208b8f): That places exist and that they exert a certain influence over bodies is taken by Aristotle to be established by the locomotion of the elementary natural bodies, i.e., Earth, Air, Fire, and Water. Aristotle's doctrine of natural motions entails that there are natural places, i.e., that places cannot only be located in relation to us but that they also have, in some sense, an absolute location in nature. At 208bl9, Aristotle remarks: "It is not any chance direction which is 'up,' but where fire and what is light are carried; similarly, too, 'down' is not any chance direction but where what has weight and what is made of earth are carried." The implication is that these places do not differ merely in relative position, but that they also differ insofar as they possess distinct potencies.[*]

The fact that a place possesses a potency means that it is an existent. That the simple elements (Earth, Air, Fire, and Water) move (i.e., change places) towards their natural place, if unhindered, suffices to establish that the places are distinct from the bodies that occupy them.

Having established that a place is something, Aristotle reviews the literature as to the nature of place (209a-210alO).

Having surveyed the views of his predecessors, Aristotle now turns to the problem of providing an adequate definition or concept of "place." Before we can come up with the definition, however, we must have some idea of what the definition is supposed to accomplish, i.e., of what would make it "adequate." Thus, before considering various definitions, Aristotle suggests that any adequate definition of place must satisfy a number of (adequacy) conditions.[*] These adequacy conditions are conditions which constrain the kind of definition that he will ultimately find acceptable. Aristotle arrived at these conditions by examining what the traditional accounts had to say about places.

From these accounts, he selected out features that everyone agreed were characteristic of places. To these, he added constraints imposed by his own theories. The result is a list of characteristics that will help to weed out inadequate conceptions of place.

Any adequate definition of place must, Aristotle suggests, satisfy the following conditions (210b34-211a6):

ACl. A place contains that whose place it is.

AC2. A place is not itself a part of that whose place it is.

AC3. The immediate place of a thing, as distinct from larger places in which the thing is contained, is neither less nor greater than the thing.

AC4. A place may be left behind by that whose place it is.

AC5. Every place has the characteristic of being up or down, and every thing naturally (i.e., by its nature) moves to and stays in its proper place, i.e., up or down.

These adequacy conditions are supposed to reflect our intuitions about the nature of place. Clearly, they are based both on considerations of linguistic usage (i.e., how the term 'place' is used) and on common sense observation (e.g., AC4 and AC5).

Aristotle now considers four likely candidates for the definition of place:

Pl. A place is the shape of a thing.

This definition violates AC2, and is, accordingly rejected.

P2. Place is the matter of a thing.

This definition violates ACl and AC2. Hence, it is rejected.

P3. A place is an interval stretching between the inner

extremities of the container of a thing.

Aristotle rejects this definition on the grounds that "There would be an infinity of places coinciding, since, when water and air replaced one another, each part of either would be constantly moving from one self-subsistent interval, one inside the other and therefore, partially coincident . . . " A diagram should make the objection clear.

Figure 5-2

Let A be a jug filled with water. If the cap is removed, then the water will flow out. If places were self subsistent intervals stretching between the inner extremities of the jug, then, as the water flows out of the jug, there will be an infinite succession of places each contained within the other. The place of the air at stage B is contained within the place of the air at stage C, etc. Since the interval from the bottom of the jar to the mouth is infinitely divisible, this definition entails that there are an actual infinite number of places nested within each other in the jar. But this is impossible, since, on Aristotle's view there cannot be an actual infinite number of anything.

A second objection to this proposal is that it would commit us to the view that places, themselves, would have places. But, this would mean two different places would be in the same place, and that strikes Aristotle as absurd (211a25). The basic idea behind this objection seems to be Aristotle's concern that if the place of a body is the interval of the container of the body, then when the container moves from one place to another, the interval will move (with the container) from the first place to the second (see Figure 5-3).

Figure 5-3

The object O is contained in C (which in turn is contained in the air). Suppose the place of O is the interval I determined by the extremities of C. When C moves (with respect to the surrounding atmosphere) from A to B, the interval I moves as well. Aristotle does not seem to have considered the possibility that the 'interval' which is the place occupied by 0, is (or could be) left behind when the container moves from A to B. Aristotle's discussion reflects both his failure to think of space as a container (as Plato did) and his insistence on treating place as a local concept tied to the notion of container. Aristotle's failure to recognize the full implications of motion as relative to some frame of reference or other also seems to be coloring his view here (cf. Chapter 3 - 18).

The final alternative is

P4. A place is the extremities of the container of the thing.

In effect, Aristotle is suggesting that the place of a thing is the surface which contains that thing. Thus, consider a woman standing on a corner. She is surrounded by an envelope of air. Her place is the surface boundary between the air and her body.

Note that this definition clearly satisfies AC1-AC4. Consider the woman again. The surface boundary contains her (AC1). The surface boundary is a layer of air and, hence, not a part of the person (AC2). The immediate place of the woman, i.e., the surface boundary of the surrounding air is just as large, and no larger, than the contained woman (AC3). The surface boundary of the surrounding air remains behind when the woman moves (AC4). This last point is a little difficult to see, since the surrounding air is in constant motion and does not retain its shape as the woman begins to move away. The point is better illustrated by considering a can of split pea soup. The place of the soup, a (relatively) homogenous solid, is the inside boundary of the can. When the can is opened, and the soup slides out, the original place of the soup retains its shape, and is filled with air.

Although ACl-AC4 are clearly satisfied, AC5 is clearly not. The view of place as a container is only partially satisfactory for Aristotle's purposes. It provides the basis for an account of some motions, in that we can understand the motion of an object as a change from one container to another. What it fails to do is provide a basis for Aristotle's view that there are natural places toward which the elementary bodies tend to gravitate. There is no obvious sense in which a place, as a container, has the characteristic of being up or down. Places are up and down, not in virtue of being containers, but rather in virtue of the fact that they can be located in an absolute sense with respect to the (fixed, motionless) earth and the outer sphere (Physics, 212a20f.).

The tension between the container view of place and the 'natural place' view is a result, in part, of the fact that the container view is basically a "local" concept whereas the "natural place" view is a "global" concept. In order to understand a place as a container of what it contains one need only consider the immediate (local) environs of the contained thing. In order to understand a place as the natural place of something, i.e., its being up or down, one must consider the universe (globally) as a collection of places. Aristotle, as we have earlier remarked, is not completely comfortable with this latter idea, and, thus, his view of place (space) is an uneasy comixture of the two views.

There is evidence that Aristotle was aware of and struggling with this issue. Immediately upon proposing his container view, he recognizes that strictly speaking, it is inadequate. The problem is that containers, e.g., cans of soup, can move, but Aristotle does not want the places of things to move (Physics, 212a5 ff.). Places can't be allowed to move for two reasons. One we gave above in conjunction with Aristotle's rejection of P3. The second is that if places as natural places are to serve their intended function, they must remain fixed. Aristotle's discussion is confusing and interpretations vary, but the basic problem seems to be his failure to recognize that place is essentially a relative notion, i.e., a place is characterized with respect to its relation to all other places. The idea of natural place requires this and Aristotle seems aware of it (212a21f). The container view is not so amenable to this, since containers can move with respect to one another. What one needs is a view of places as fixed in some order (as the natural place view provides) in terms of which objects can be located. Unfortunately, this does not fit well with the container view, since if the place of a thing is determined by its relative position in the cosmos, then its local "container" plays no significant role in determining its place. Aristotle never saw this clearly. Perhaps he was constrained by his inability to think of places as mere "intervals," i.e., potential locations which were determined by their relative positions within some overall framework.

Having settled on some notion of what a place is, Aristotle turns to consider the question whether there might be empty places. One would think so since, to consider our can of soup again, it seems that if the soup vacates its place in the can, it might not be replaced by anything. If so, the original place of the soup would now be empty. Aristotle rejects this idea completely, for reasons to which we now turn.

B. Aristotle on the Void

Aristotle argues, 213b32-214al7, that if there is such a thing as a void, then it would be a place with no thing in it. Having defined a void, or a vacuum, as a place with no thing in it, Aristotle goes on to argue that no such voids can exist. Thus, the Aristotelian universe is a so-called plenum. We here find the seeds of the medieval doctrine that "nature abhors a vacuum."

Aristotle gives several arguments against the existence of a void. Since these arguments illustrate important aspects of Aristotle's view of space, it will pay us to examine them with some care. The first is connected with Aristotle's rejection of the characterization of a place as the "interval of a body." We may call it

(i) The Void is not an Interval

If a void is a place with no thing in it, then, no void can exist because that would make a void "the interval of a body." If a void is, in addition, a place, then a place would be an "interval of a body." (Physics, 214al7). Aristotle has already argued that this definition of place leads to difficulties of its own (cf. 211bl4-29).

This argument of Aristotle's against the void trades on Aristotle's unwillingness to think of space as a huge (possibly empty) container, despite the fact that he is willing to think of places as "local" containers. The problem stems possibly from Aristotle's commitment to the view that places (as "local" containers) are nothing more than markers for the distinguishing of different stages of the motion of a body, and his inability to reconcile this "local" requirement with the "global" requirement of the natural place doctrine that requires places to be more than mere markers of the stages of motion of bodies.[*]

(ii ) The Void is not a Condition of Motion

Even so, it had been argued by certain of the pre-Socratics that a void must exist if motion is to take place. Aristotle first points out that not all motions require a void (as some of the followers of Parmenides would have it). For example, qualitative changes (e.g., from hot to cold, which are motions on Aristotle's view) do not require a void. Secondly, some changes of place, or locomotions, such as rotational motions, do not require a void since bodies in such "motion may simultaneously make way for each other although no separate interval apart from them exists." Third, compressions are also explainable without reference to a void. "Things may . . . be condensed, not into any void in them, but because what is in them is squeezed out . . . " Finally, some expansions or contractions, e.g., when water is changed to air (or vice versa) are elemental changes which do not involve one body moving into another.

(iii) The Void is Inconsistent with the Natural Motion

of Elementary Bodies

Next, Aristotle argues that the doctrine of natural motion is incompatible with the idea of a void. First, heavy (light) bodies, by nature, move downward (upward). The void, thus, is not needed as a cause of natural motion. Secondly,

a body in a void could not move, because "there would be no direction in which it will have a greater tendency or a lesser tendency to move, for the void in a void has no differentiae [i.e., a void is qualitatively homogeneous]." Aristotle argues that natural motions (up/down) would be impossible in the void, because in the void, qua void, there can be no difference between a place up and a place down. "For just as there can be no differentiae in nothingness [O], so there are none in non-being; and a void is thought to be a non-being and a privation while in a locomotion by nature there is a differentia, and so there will be differentiae in things which exist by nature. Accordingly, either no object can have anywhere a locomotion by nature, or if it can so have, there can be no void." Since Aristotle is committed, on other grounds, to a doctrine of natural place and natural motion, he rejects the alternative of a void. This is a key argument, since it illustrates in part why Aristotle's cosmology survived for as long as it did despite the fact that, from the beginning, specific aspects of the view were under attack. The point is that Aristotle has a cosmology, a unified total picture of the universe. This integrity enabled this picture to survive the piecemeal attacks on it that continued throughout the period down to the time of Galileo. Before Galileo and Newton, no one had a comparable total picture which was plausible enough to replace Aristotle's. One does not throw away a comprehensive model or world view merely because of (apparently) isolated defects unless one has an alternative model of comparable scope in the wings. Modern science works in much the same way, witness the history of Newtonian theory. Newton's total theory and corresponding model of the universe was so successful that, for a long time, its very presence inhibited the development of alternatives despite the occasional failures of the theory to fit the data.

(iv) Projectile Motions Preclude a Void

Aristotle distinguishes between natural motions and unnatural (forced) motions. Natural motions are those motions which objects have in virtue of their natures, such as a tendency to move up or a tendency to move down depending on the composition of the object in question. But, obviously not all motions are straight up and down motions. Projectiles, for example, tend to move more or less parallel to the surface of the earth when thrown or shot by an archer. On Aristotle's view, which is not very well developed on this point, projectile motions and unnatural motions in general occur in virtue of the object in question being pushed by a medium. Thus, what keeps a moving arrow moving on Aristotle's view is that it is continually being pushed in some way, which he never adequately explained, by the medium through which it is moving. If a void existed, then there would be no medium and hence no projectile motion. But, experience clearly tells us that projectiles do move. Therefore, there can be no void. (See discussion in next chapter.)

(v) The Argument from Inertia

Next, there is a very interesting argument which we call, anachronistically, the argument from inertia. It occurs at 215a20f. We call it "the argument from inertia," (although of course the concept of inertia was not known to Aristotle since it was only fully articulated by Newton in the 17th century) for a reason that will become obvious. Against those who argued for the void, Aristotle claims that they cannot say "why a body which has been caused to be in motion will stop somewhere; for why should it stop in one place rather than another? So either it will be resting or it will of necessity be traveling without an end . . . " Aristotle intimates that this last alternative is absurd! The force of this example is a clear indication of how a particular conceptual system can influence the decision about what is or what is not intelligible. Galileo could not refute this view by merely experimenting with the inclined planes, he had to rethink the whole problem of what motion was.

(vi) The Resistance Argument Against The Void

Next, Aristotle presents an argument against the void based on considerations of resistance (215a22). The body moves, so Aristotle seems to hold, insofar as it overcomes resistance. In a void, there is no resistance to be overcome. Hence, there can be no motion in a void. Since the universe is filled with motions, there can be no void. Aristotle's writings suggest the following formula: speed = weight/medium resistance. Hence, if A travels through a medium M and through a medium N, then speed(A through M)/speed(A through N) = resistance (M)/resistance (N). For a void V, the resistance (V) = O. Thus, motion through a void would stand in no determinate ratio to motion through a resisting medium. Movement through a void would not be any determinate ratio faster than motion resisting medium, i.e., would not be k times as fast for any k.

In traveling through resisting media, heavy (light) bodies travel faster, in the ratio of their weights (lightnesses). This is so because a "body that travels or is let go divides the medium either by its shape or by the preponderance of its weight (216al9)." But, in a void, there is nothing to divide, so all bodies would travel with equal speeds. However, Aristotle says, this is impossible. (Compare this argument with the argument from inertia above.) Incidentally, Galileo's demonstration of dropping two weights from the Tower of Pisa may have been designed to refute this argument. (Also, cf. discussion of Philoponous in Chapter 6.) On Aristotle's view, a lead ball 100 times heavier than another should have reached the bottom 100 times quicker. Actually, it would land first, but not in 1/100 the time of the less massive ball.

(vii) The Density Argument Against The Void

Next, Aristotle considers an argument based on considerations of density. The Atomists had argued from the fact that some objects are denser than others, that this indicated that their atoms were packed more closely together. This seemed to them to necessitate the existence of a void between the atoms. Aristotle argues, however, that changes in density are akin to qualitative changes, i.e., are like changes from hot to cold, and these he had already argued do not require a void (compare 216b22ff).

(viii) The Duplication Argument Against The Void

In addition, Aristotle gives the following puzzling argument at 216a27 to 216b20.

"But even if we consider it on its own merits the so-called vacuum will be found to be really vacuous. For as, if one puts a cube in water, an amount of water equal to the cube will be displaced; so too in air; but the effect is imperceptible to sense. And indeed always, in the case of any body that can be displaced, it must, if it is not compressed, be displaced in the direction in which it is its nature to be displaced--always either down, if its locomotion is downwards as in the case of earth, or up, if it is fire, or in both directions--whatever be the nature of the inserted body. Now in the void this is impossible; for it is not body; the void must have penetrated the cube to a distance equal to that which this portion of the void formally occupied in the void, just as if the water or air had not been displaced by the wooden cube, but had penetrated right through it.

"But the cube also has a magnitude equal to that occupied by the void; a magnitude which, if it is also hot or cold, or heavy or light, is none the less different in essence from all its attributes, even if it is not separable from them; I mean the volume of the wooden cube. So that even if it were separated from everything else and were neither heavy nor light, it will occupy an equal amount of void, and fill the same place, as the part of place or of the void equal to itself. How then will the body differ from the void or place that is equal to it? And if there can be two such things, why cannot there be any number coinciding?"

The force of this argument rests on Aristotle's treatment of the void as a thing, rather than as a mere lack of something. If one puts a cube of wood (say) in water, then the cube will displace a certain amount of water. This is because the cube of wood and the water are both bodies and two bodies cannot occupy the same place. Now suppose there were a void, which is not a body. Imagine putting the wooden cube in the void. The void will not be displaced, but will penetrate the cube to the distance that the cube is immersed in the void.

Suppose the cube is totally immersed in the void. The cube has a certain volume which is now occupying an equal amount of void. But, on Aristotle's view, the volume of the cube is a property of the cube whereas the void place that the cube occupies is distinct from it. But, the void has no properties and neither does the volume of the cube. They are, thus, indistinguishable. But, if two such indistinguishables can occupy the same place, why not any number? But, this, Aristotle argues is absurd. It would be like saying of an empty room that there are 27 undetectable, indistinguishable objects with no properties in the room. Why 27? Why not 3? Or, as Aristotle remarks, why not any number?

The only reasonable response is that there is only one such object. Since, on Aristotle's view, each object has a volume with the required characteristics, it is gratuitous to postulate another such object (the void) coinciding with it.

On the basis of these arguments, Aristotle concludes that there are no voids in nature. Basically, his criticism of voids rests on two lines of attack: (1) Those who argue that voids are necessary are mistaken, and (2) The existence of voids is inconsistent with the doctrine of natural motion. This latter point is most important because it illustrates how being wedded to a certain view about one thing can color one's attitude and view about other things as well. The implications of Aristotle's rejection of the void are profound, if one accepts the plausible view that Aristotle's failure to develop a coherent view of spatiality as such is connected, as suggested above, with his failure to recognize the utility of thinking of places as fixed intervals wherein bodies reside. This latter view is clearly influenced by his rejection of the reality of voids. The utility of the fixed interval view is that it appears to be one of the key elements in the development of Newton's theory of space and time from which our modern notion has directly evolved. (cf. Chapter 7 below.)

C. General Features of Aristotle's View of Space

Despite the fact that Aristotle did not develop a full fledged theory of space as such, it will prove helpful for future comparisons for us to consider that he did so. In this section, we want to enumerate a number of properties that space has on Aristotle's view in order to facilitate a comparison with the later views of Newton, Leibniz and Einstein.

1. Space is qualitatively heterogeneous. To say that space is qualitatively heterogeneous, is to say that different spatial locations or different places are physically different merely in virtue of their difference in location. In virtue of Aristotle's doctrine of natural places, it is clear that he is committed to the qualitatively heterogeneity of space (cf. 10 below). In addition, since the Aristotelian universe is finite, there are a number of privileged positions in the universe. One, of course, is the center. An entire group of privileged places are the places at the outer extremities of the Heavenly Sphere. Similarly, the places on the surface of the surface of the Sub-Lunar Sphere are also special because they mark the boundary between the sub-lunar realm (with one set of natural motions, and, hence, one set of physical principles) and the heavens (with a different set of natural motions, and, hence, subject to a different set of physical principles).

2. Space is finite in extent. That the Aristotelian universe is finite follows from the fact that the earth is immobile at the center of the universe (De Caelo, 27lb ff.; 295a8 f.).

3. Space is continuous. By calling space continuous, Aristotle meant that spatial magnitudes were infinitely divisible. We might remind the reader that when Aristotle (or the Greeks) thought of space as infinitely divisible they did not think of that division as something which could be, in principle, carried out. Thus, to say that something was infinitely divisible for Aristotle, or for the Greeks in general, was to say that the division would never end. Recall that Aristotle accepted the idea of a potential infinity, that is, he accepted the idea that some process or activity might go on forever. Thus, for Aristotle, although the universe is finite in extent, it is potentially, infinitely divisible, where this is understood to mean that the division might, in principle, continue indefinitely. Contrasting, recall, with the idea of a potential infinity is the idea of an actual or completed infinity. The idea of an actual or completed infinity was rejected as self-contra-dictory by Aristotle and by many thinkers up until Cantor's theory of sets in the late l900's.[*]

4. Space is anisotropic. To say that space is anisotropic is to say that there are preferred directions in space. That the Aristotelian universe is anisotropic is evidenced by Aristotle's remarks on the directions "up" and "down." If space were isotropic, then there would be no intrinsic difference between directions and any chance direction could be taken as up, etc. In all, Aristotle distinguished six directions: Up/down, right/left, forward/backward. The following diagram illustrates the general relationship between these:

[Insert Figure 5-4]

Figure 5-4

Aristotle's anisotropic view of space should be compared with the isotropic view advocated by Plato (pp. 4-15 above). The basic difference between the two views is a reflection of Aristotle's acceptance of the doctrine of natural motion. Plato explained the motion of fire and earth and the like in terms of the principle that "like attracts like" rather than in terms of the elements moving to a natural place (Plato, Timaeus, 57a).

5. Space is object dependent. Here the issue is, does space exist independently of the existence of objects? If there were no objects, could we still meaningfully talk about empty space? Aristotle's denial of the existence of a void, and his rejection of the idea that place might be a self- subsisting interval, suggests that, for Aristotle, you cannot have places without objects to fill them. If this is the interpretation one takes of Aristotle, then one would say Aristotle's view of space is that space is object dependent.*

6. Space is mind independent. Here the issue is whether or not space or places exist independently of minds which are conscious of them. Again, as far as can be seen, Aristotle does not say one way or the other whether space is mind dependent. But, there is no reason to think, that given the other particulars of his views, place or space is mind dependent in any sense. It is significant to note this here because there is some indication that, for Aristotle, time might be construed as mind dependent (cf. p. 5-46 below). Again, the main reason for raising this question at this point is for the sake of future comparisons. Newton will argue that space is mind independent; Leibniz will argue that space is mind dependent.

7. Space is immutable. Here the issue is whether or not the character or nature or properties of space or places (if any) changes over time. Again, Aristotle's view suggests that, for him, spaces and places are immutable.[*]* This is so whether we consider places as "local" containers (since the place of a thing is the first fixed boundary) or as "global" natural places, whose positions are fixed relative to the earth and the heavenly sphere.

8. Space is incorporeal. Although space (place) is a something for Aristotle, it is not a body.*

9. Aristotelian space admits absolute position. Places in the finite sphere are, for Aristotle, absolute by nature. They are fixed with respect to some standard non-arbitrary frame of reference, i.e., the cosmos as a whole. Thus, one can imagine setting up an absolute frame of reference with axes centered on the center of the earth and the directions determined by certain fixed events such as the position of the north star and the solstices and equinoxes. The fact that the earth is at the center of a finite sphere makes this choice of a coordinate system more "natural" and less arbitrary. All observers in the universe, no matter where they are or how they are moving with respect to the center of the universe, will agree that the earth is the center of the universe. Thus, a coordinate system set up as described above at the center serves as a natural frame of reference upon which all observers can agree. Once a position is fixed with respect to this coordinate system, then there is a clear non-arbitrary sense in which that position retains its relationship to all the positions similarly fixed for all observers.

10. The Causal Activity of Places. Space, for Aristotle, is not merely a receptacle for objects and events, as we have seen. Do places interact with the bodies they contain? Aristotle's discussion of natural places and natural motion suggests that they do. At 208bl7 ff., he says: "It is not every chance direction which is 'up,' but where fire and what is light are carried; similarly, too, 'down' is not any chance direction but where what has weight and what is made of earth are carried--the implication being that these places do not differ merely in relative position, but also as possessing distinct potencies." (emphasis added)

This sounds as if Aristotle is suggesting that the natural place of fire, e.g., in some sense causes fire to move in its direction. But, Aristotle explicitly denies at one point that places are causes (in any of the four senses of "cause" that he allows: material, efficient, formal or final). (Physics, 209a20)[*] On the other hand, the passage cited above just as clearly attributes some sense of potency or power to places. The fact may be that while Aristotle is committed to the idea that places have to be differentiated in some way (so that, e.g., fire will "know" when it is up and, will stop), and, hence, thinks of natural places as "attracting" the natural objects whose places they are, he has no way of fitting this notion clearly into his causal schema.

11. Space is a plenum. This is just another way of saying that, for Aristotle there are no empty places. In this, he is in agreement with Leibniz, but in disagreement with Newton, as we shall see.

This concludes our discussion of Aristotle's views on space, place, and void. Let us now turn to a consideration of Aristotle's views on the nature of time.

IV. Aristotle on Time

Aristotle's extended discussion of time occurs in the Physics (217b30-224al7). In this discussion, he raises a number of questions about the nature of time and attempts to answer them satisfactorily. His treatment here, as in the case of place and space, is somewhat incomplete. Nevertheless, his discussion illuminates the difficulties one faces in trying to pin down the illusive nature of time and temporality.

A. Three Questions

Aristotle's discussion focusses on three key problems: (1) Does time exist?, (2) What is the nature of the present moment, the 'now,' as Aristotle calls it?, and (3) What is the nature of time itself? Our treatment will proceed as follows. First, we will try to clarify the significance of Aristotle's three problems for the analysis of time. In so doing, Aristotle's positive view on the nature of time will emerge. Finally, we summarize the key elements of Aristotle's theory of time in a manner which parallels our summary of the key elements of Aristotle's theory of space.

1. Does time exist?


tt> Doubts about whether or not time exists arise from the following considerations. We naturally think of time as somehow comprised of the past, the future and the present moment. But the past no longer exists and the future does not yet exist. The only "part" of time that seems to exist is the present moment. But, Aristotle is not willing to allow that ehe present moment is a part of time. The reason for this is that he thinks of time, as do most of us, as being representable by a straight line extending indefinitely in either direction. The present moment is a "point" on the line separating the past from the future.

Figure 5-5

According to Aristotle, if we allow that the now is a part of time, then we are committed to the view that temporal stretches, e.g., intervals of time such as an hour or a day, are made up of points. But Aristotle argues (and here he exploits the analogy between a temporal interval and a straight line) that a temporal interval is no more composed of points than is a spatial interval, and for the same reasons, namely, that a continuous stretch is not pointlike.

This throws the existence of time into serious doubt. The past and future don't exist and the now, which does exist is not a part of time. How, then, can time exist if none of its parts do?

*These questions are re-echoed in the Confessions by St. Augustine in the following famous passage: "What, is then, time? If no one asks me, I know what it is. If I wish to explain it to him who asks me, I do not know. Yet I say with confidence that I know that if nothing passed away, there would be no past time; and if nothing were still coming, there would be no future time; and if there were nothing at all, there would be no present time.

"But then, how is it that there is the two times, past and future, when even the past is now no longer and the future is now not yet? But if the present were always present, and

[*] Thus, for Aristotle, place has a physical significance. This should be contrasted with some modern views, e.g., the views of Newton and Leibniz where mere difference in place does not constitute a physical difference. For Einstein's General Theory of Relativity which, in some sense identifies space and matter, whether places themselves have causal efficacy (i.e., make a physical difference) is not clear. More on this later.

[*] Adequacy conditions play an important but often unnoticed role in modern science as well. What they do, in effect, is place prior constraints either on the form that a theory may take or the concepts that an adequate explanatory theory might imploy. Usually scientists do not bother to spell out these adequacy conditions explicitly since they are, for the most part, taken for granted. Part of the job of the philosophy of science, in fact, is to make explicit these implicit conditions and assumptions.

[*] In effect, the conflict between Aristotle's two notions of place is a conflict between a tendency to see places (and space) as a relational property of bodies (the container view) and a tendency to see places (and space) as an independently existing arena for bodies (the natural place view). The conflict reemerges with the dispute between Newton and Leibniz in the 17th century (cf. Chapters 7, 8 below). Because Aristotle did not see the issues clearly enough, this way of characterizing his discussion is only approximate.

[*] If you can imagine the totality of all the natural numbers, for example, that would be an example of a completed infinity. Thus, one might say that the natural numbers are infinite in extent in one of two senses: First, one might say that the natural numbers are potentially infinite. By this one would mean that no matter what number one counted to, there would always be a further number. Second, one could speak of the natural numbers as an actual infinity. By this, one would mean that one was considering a set or collection of numbers such that every natural number was a member of this set. Cantor's theory of infinite sets, of which we have spoken earlier, tells us how to deal with such infinities (see Salmon, 1975).

* We have to be careful of our answer to this question because the question we are asking is not one to which Aristotle directly addressed himself. Thus, we must try to tease out a plausible answer based on our interpretation and understanding of the rest of Aristotle's position with respect to the nature of space. The point of asking the question and forcing an Aristotelian answer is that it will facilitate our comparison of the Aristotelian view with the later Newtonian and Leibnizian views. For them, the question of whether space was object dependent or not was a real issue. Thus, Newton will argue that space and places are, at least with respect to what he called Absolute Space, object independent. Leibniz, on the other hand, will argue that space and places are defined in terms of the relations which exist between existent objects. As such, for Leibniz, the concept of space only makes sense insofar as its existence is dependent on the existence of objects. So, if we can agree, that in some sense, Aristotle's view of space is that space is object dependent, then there is some sense in saying that Aristotle's view is closer to that of Leibniz than to that of Newton.

[**] If one construes the geometry of space as a property or character of space then the claim that space is immutable entails, among other things, that the geometry of portions of space do not change over time. Again this was not a direct concern of Aristotle's, but it is important to note that some theories (i.e., certain models of the general theory of relativity) accept the mutability of space.

* It is a matter of some changing historical interpretation as to exactly what one is to understand by the concept of "body." But, if one understands by a "body," something which has material properties, i.e., has a density, has a mass, etc., then one might argue that (certain models of) the general theory of relativity, which assigns such properties to spatial positions is committed to the corporeality, in some sense, of space.

[*] See 194bl6-195b30 for Aristotle's discussion of the four kinds of cause. Return to beginning of this chapter or to the Table of Contents.