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Chapter 4

Plato's Universe

I. Plato: Life and Times

Plato (429-348 B.C.) is one of the two most significant ancient Greek philosophers in the Western intellectual tradition. (The other is Aristotle, whose physical system is discussed in the next chapter.) His significance for the story of the development of the concepts of space and time is that his dialogue, the Timaeus, is an early attempt to give a systematic account of the nature of space and time. Plato was born into an aristocratic Athenian family. As a youth, he was a follower of Socrates. The major contribution of Socrates was to shift the focus of intellectual attention away from issues of natural philosophy and the nature of the physical universe to a concern for moral issues and the nature of man. Socrates himself never wrote anything. He taught by engaging people in dialogue and he devoted his life to trying to persuade people to live better lives by becoming more self aware of their purposes and interests. For his trouble, he was put to death by the Athenian state in 399 B.C., ostensibly for corrupting the youth of Athens and undermining the authority of the state, although political revenge was part of the motive. (Guthrie, 1975, chapter 4)

Plato decided to go into philosophy instead of politics when he saw what the state did to his friend and teacher. He founded a school, the Academy, in c. 387 B.C., which survived until 529 A.D., when it was shut down by Justinian. Unlike the pre-Socratics and Socrates himself, Plato left a large number of complete works which still survive. Plato was a master of the dialogue form and most of his works aredialogical conversations imitative of the teaching style of Socrates. In the dialogues, Plato developed a systematic philosophical view on the nature of man, the state, morality, knowledge, language and a wide range of diverse subjects (see e.g. Taylor, 1927).

II. Being and Becoming

The problem of permanence and change, or the relation between Being and Becoming, was one of the central problems emerging from the speculations of the pre-Socratic philosophers. The correlative problem of the distinction between what was Real and what was mere Appearance impressed upon Greek thinkers that there were fundamental conflicts between what could be known by reason and what could be known by the senses.

The world, as known by the senses, appeared to be extended in space, enduring through time, and subject to constant change. The arguments of Parmenides and Zeno, on the other hand, suggested that these features were only apparent, and that following reason would persuade us that neither space, nor time nor motion was real.

In addition, the conflicting theories of the pre-Socratics about the nature of the world seemed dogmatic and arbitrary. How was one to know which of these theories, if any, was correct? A sense of skepticism about the very possibility of knowledge filled the air (Guthrie, 160 , chapter IV). Out of this situation, in Athens, in the 4th century B.C., two philosophical systems were developed which, between them, were to have an enormous influence on the subsequent development of scientific thought: that of Plato, which we consider now, and that of Aristotle, which we consider in Chapter 5.

The basic problems of Permanence and Change can be stated as three questions:

(1) What is the nature of that which is Permanent (Being)?

(2) How are we to understand Becoming or Change?

(3) Can we have true knowledge of what is (Being) and the nature of Change?

On two fundamental points, Plato and Aristotle agreed. They agreed, against the skeptics of the day, that knowledge is possible. Secondly, they agreed that

knowledge involves understanding and grasping the universal or essential features of things. The philosophical systems they built on this common base, however, were radically different.

III. Plato's Solution to the Problem of Permanence and Change

We are, of course, primarily interested in Plato's views on space and time. In order to properly understand them, however, it is necessary to briefly consider the general outline of Plato's metaphysics (theory of Being) and epistemology (theory of knowledge). In this way we can correctly situate Plato's cosmological picture and his view of space and time within the wider framework of his total philosophy.

Plato's metaphysics and epistemology is an attempt to come to grips with the paradox of Parmenides: that, what truly is, is unchanging, although the evidence of our senses suggests that the world we experience is a world of objects which are impermanent and subject to change. Plato's solution to the paradox of Parmenides was to distinguish between

(1) The World of Forms


(2) The Sensible World.

(1) The World of Forms: The world of Forms was, for Plato, a world of permanent unchanging essences or true Beings. True knowledge of these Forms was possible through the use of reason. What were these Forms? Consider two individual tables (men, bluebirds, oaks, trumpets, atoms, what have you). According to Plato, these two individual tables, e.g., must share some properties in common in virtue of which they are both tables. What they share that makes them both tables is an essence of table-ness, or, a Form of "table-hood." Although an individual table may suffer the ravages of time, and become defaced, decay, or perhaps wind up as firewood, its essence, that which makes it a table,

remains inviolate and unchanging.

The Form of a table does not exist in the individual table that we can see, or touch, but, rather, it exists in a realm accessible only to reason--to the mind's eye, as it were.

(2) The Sensible World: The actual individual table that we interact with on the sensory level exists in the sensible world, the world of everyday life and experiences. The objects of this world are subject to constant change. It is a world of Becoming. The world of Becoming, for Plato, is not itself completely real (nor is anything in it) because, for one thing it is a world which is constantly changing and Plato accepts the Parmenidean thesis that what is Real never changes.

Much of the effort in Plato's dialogues is expended towards trying to work out the implications of this distinction in a comprehensive and consistent way. Two problems Plato faced are directly relevant to our concerns: The problem of participation, and the problem of knowledge.

The Problem of Participation: By distinguishing between a world of Forms (Being) and a world of Becoming, Plato tried to salvage both the Parmenidean insights into the nature of the Real and the common sense acceptance of the world as a world of change. The problem Plato faced by separating the essences of things from the things as they are experienced was to explain or account for the relationship between things and their essences. In general, Plato took the world of Becoming to be a copy of the world of Being, but the problem of understanding how an individual object was a copy of its Form plagued Plato for his entire life. The problem became known as the problem of participation, because Plato often suggested that sensible objects somehow "participated" in the Forms. Plato had a difficult time trying to explicate this notion of "participation." The best we can hope for here is to suggest some analogies that Plato employed. One analogy that Plato suggested was that objects in the sensible world stand to their Forms as a picture of an individual stands to the individual.

Form of Table <=> a paritcular table
a particular table a picture of the table

Just as the picture is an imperfect copy of the original, so the object is an imperfect copy of a Form.

Another analogy that Plato suggests is that

Forms (Being) <=> Physical Objects
Physical World (Becoming) table Mirror Images

These metaphors are ultimately somewhat unsatisfactory. It is a credit to Plato's intellectual integrity that he realized this and constantly strove to make his ideas as clear and precise as he could. The relevance of this difficulty for our concern with space and time is that it is constantly in the background of the Timaeus, Plato's dialogue on cosmology, which contains his most detailed views about the nature of physical space and time.

The Problem of Knowledge: According to Plato, following Parmenides, the objects of knowledge (i.e., what can be known) must be Real. Since the world of Becoming, i.e., the physical world, is not completely real, it is a world of which no real knowledge is possible. The best we can do with respect to the physical world is have true opinions and create "likely stories." It follows that natural science, which is the attempt to give an account to the sensible world of Becoming, is not, and never can be, true knowledge. At best, scientific theories can be only "likely stories." In order to appreciate the difference between Plato's perspective on science and the perspective of most modern scientists, one has to realize that for Plato, to say that a scientific theory could only be a 'likely story' was to admit it to be seriously defective. Most modern scientists, on the other hand, would gladly agree that even the best scientific theories of the day are at best "likely stories" insofar as they fail to account for all the (possible) observational evidence or fail to provide a "complete understanding" of the evidence at hand. But, for Plato, what prevents science from being knowledge is neither a lack of observational data nor a lack of complete understanding. For Plato, no empirical account of the physical world, no matter how complete, can count as knowledge because knowledge is always of that which is Real, i.e., of the objects of the eternal, unchanging world of Forms. The objects of the world of Becoming are not the right sort of thing that is capable of being known (see, e.g., Plato's Republic, Book VI). The net effect is that Plato's philosophy has an anti-scientific bias. Despite this, he did produce, in the Timaeus, a cosmological model and an extended attempt to come to grips with the nature of space and time.

IV. Plato's Cosmology

Plato's reasons for writing the Timaeus are somewhat unclear, as it is the first piece in a trilogy which he never finished. However, part of his motivation seems to have been to establish that the physical universe, imperfect as it may be, exemplifies the workings of Reason (Cornford, 1957, 38).

Plato was unhappy with the "materialistic" cosmologies produced by the pre-Socratics (see Plato's Phaedo). Plato argued that just as the behavior of human beings could not be understood purely in behavioristic or mechanistic terms, but required a knowledge of the human soul and its reasons, so the workings of the physical world could only be understood by appealing to a world soul. Plato's cosmology is, at once, a step forward and a step backward. It is a step forward insofar as it attempts to exploit the mathematical perspective of the Pythagoreans by postulating geometrical figures as the ultimate building blocks of the material universe (Plato, Timaeus, 63C ff.).[*]

It was a step backward in that it reintroduced the idea, gradually eliminated from pre-Socratic cosmologies, that nature was a living being to be understood in terms of the model of a rational agent.

Plato, in fact, suggests that vision was invented to enable men to study the rational order of the universe and so imitate that order in themselves (47B). Thus, Plato's concern is primarily moral rather than scientific.

We turn to a brief summary of the cosmology of the Timaeus. The Timaeus is a creation myth, in which Plato describes, as a "likely story," how the universe was created and what, in general, its structure is. Along with his moral aims, Plato was also wrestling with the problem of participation: how to make sense of the idea that eternal, unchanging archetypes (the Forms) could be the models of impermanent objects in a constantly changing world (see Sayre, forthcoming).

The universe, or Cosmos, is a living being endowed with a soul (30C f.). The Cosmos was fashioned from a pre-existing chaos by a Divine Craftsman, the Demiurge, using the Forms as models for sensible objects (29D f.). Plato does not say what, if anything produced the Demiurge or the chaos. If the myth is a myth of actual creation, then the Platonic story contrasts with the account in Genesis, which is a creation out of nothing. The Demiurge uses a pre-existent chaos and appeals to eternal (and, hence, pre-existent) Forms as models. See section VI below for further qualifications. The Cosmos as a whole is modeled on the Form of a Living Creature (40 C-D) and is unique (31A-B).

There are three irreducible components in the Platonic picture: (1) Being (the Forms), accessible to reason alone; (2) Becoming (sensible objects), accessible to the senses; (3) space (the Nurse of Becoming). Space, in the Platonic sense is a third factor mediating between Being and Becoming. Through a series of metaphors, Plato struggled to make the concept of space clear (see section V below).

The Cosmos is a self-contained sphere which, although alive, does not need any nourishment, since otherwise it would be subject to decay. The sphere uniformly rotates on its axis with the earth at the center. Uniform circular motion is the motion most fitting for a rational being, the closest it can get to not moving at all--i.e. the closest it can get to its eternal archetype. In addition, there are six "irrational" motions, moving to the front or moving to the back, moving up or moving down, and moving to the right or moving to the left (33B-34A). These "irrational" motions are the basic motions possible in a three-dimensional space.

Figure 4-1

The earth, at the center, rotates with the sphere. In order to preserve the succession of day and night, as observed from the earth, the earth must have a counter revolution. All the planets, including the earth, are gods, and each has a motion proper to it (40B-C).

The diurnal (daily) motion of the heavens around the earth is produced by what Plato calls "the motion of the Same" (see Fig. 4-1 above). A further motion, the motion of the Different, is in the opposite direction and at an angle to the motion of the Same. The path of the motion of the Different is through the ecliptic, which is that portion of the sky which contains the orbits of the sun, moon and planets. The motion of the Different accounts for the tendency of these bodies to rotate, with respect to the Earth, in the opposite direction to the daily motion of the stars.

Although the sun, moon and planets revolve in the opposite direction to the motion of the stars, they do not all revolve at the same rate. Plato proposed that the variation in the planetary motions is due to the fact that each planet, as a god, moves, at least partially, in accordance with its own reasons (39E-40B). The Timaeus is the earliest attempt we possess to give a systematic account of the complexities of the motions of the heavenly bodies as seen from the earth. Plato, himself, did not bother to try to work out the details in any systematic way. This task he left to the professional astronomers. (See Heath, 1913; Kuhn, 1957, Chapter 1).

The sphere contains everything in the physical universe. Outside it there is nothing, neither body nor void (33B f.). The Timaeus also contains a discussion of the construction of material objects from the basic geometrical figures and some discussion of the physiology of living creatures (55D ff.). Since it is not relevant to our concerns, we omit discussion of it here.

The only relevant consideration is that Plato adopts, as traditional, the view that the material elements of the Universe are composed of Earth, Air, Fire and Water. He takes the earth (at the center of the cosmos) to be the region where Earth collects and the celestial sphere to be the region of the cosmos where Fire collects (53A, 57C; cf. p. 4-17 below).

In addition to the general cosmological picture summarized above, Plato offered a detailed exposition on the nature of space and time. We turn now to a discussion of those topics.

V. The Nurse of Becoming

In the Timaeus, we find the first systematic account of space, which Plato calls (among other things) "the Nurse of Becoming." It is, in effect, the medium, arena or mirror within which things which change (become) subsists. Plato tries to capture the essence of spatiality through a series of, sometimes conflicting, metaphors. In this section, we briefly review the metaphors and then elicit from the text itself a series of properties characteristic of the Platonic conception of space.[*]

The function of the Nurse of Becoming, for Plato, is to serve as a medium for the Forms to produce sensible objects. The Forms interact with the Nurse of Becoming to produce the sensible objects of the physical world. In four pages, Plato suggests eight metaphors designed to make this idea clear (49A-52D).

(1) The third factor, mediating between Being and Becoming is first identified as a Receptacle--in the sense of something which receives the Forms (49A).

(2) The characterization of the third factor as a passive Receptacle is immediately qualified by calling it the Nurse of Becoming (49A). This suggests an active role for the third factor in the generation and maintenance of the sensible objects of Becoming.

(3) The Receptacle is then likened to a material, gold, which can be molded into any number of distinct figures, but which contributes nothing of its own characteristics to the final product (50C). Plato wants the Receptacle to have no properties of its own, so that it may more faithfully reproduce the properties that objects will possess in virtue of the "imprint" of the Forms. Of course, gold, or any other material does have its own properties and, hence, the analogy breaks down. But, again, the image is that of a passive factor which contributes nothing but a medium within which the objects of Becoming can subsist.

(4) The passive image is reinforced by comparing the Receptacle to the liquid base for a perfume (50D). The perfumer deliberately chooses a liquid which is as odorless as possible in order that the medium will not interfere with the odors that the perfumer is trying to capture.

(5) The Receptacle is characterized, using a biological metaphor, as the Mother of Becoming, the Forms being the Father (51A).

(6) At a later point in the dialogue, the image is shifted to that of foster-mother (88D).

(7) At 52B, the Receptacle is characterized as an arena or container. It is identified explicitly as chora (also 52D). The container metaphor, with some qualification, is the predominant one, mentioned as it is, in the summary to this section of the dialogue (52D).

(8) Finally, space is characterized as analogous to a "winnowing basket," which farmers used to separate chaff from grain (52D). The basket is constantly shaken and the chaff thereby thrown off to the ground while the grain remains behind in the basket. The idea is that the Receptacle is in constant motion jostling the qualities and properties contributed by the Forms. This suggests that the Receptacle, is no mere passive container but is somehow interacting with its contents.

These, then, are the central metaphors that Plato uses to characterize the third factor which mediates between Being and Becoming. We will take this third factor to be Space.

The question is: What are the properties of space, as understood by Plato? The list of metaphors suggests that it is both active and passive with respect to its contents. This suggested-to some, e.g. to Aristotle, that Plato identified space with matter (See Solmsen, 1960). If so, this would make Plato a forerunner of Descartes (see Chapter 6) and Einstein (see Chapter 16; Graves, 1971, Chapter 5). However, there is no indication in Plato's dialogue that such an identification was intended, although it is clear that space, for Plato, is never empty. Thus, to think of space as a container which might not contain anything is alien to Plato's idea (52D-53C).

The following are the basic properties of space, as Plato conceived it.

(S1) Space has no qualities of its own (50E). It is a pure medium within which objects exist and processes take place, but it has no qualities of its own.

(S2) Space is homogeneous (50B). This means that it has the same nature in every region. Since space is a "matrix" for receiving all things and it does not contribute any of its characteristics to the things in it, it would seem to follow that space must be homogeneous. If it weren't, i.e., if its characteristics differed from place to place, then it could not be, at the same time, the pure matrix that Plato (here) says it is. Jammer, it should be pointed out, argues that Platonic space is inhomogeneous, primarily on the basis of a passage at 52D where Plato says

Now the nurse of Becoming, being made watery and fiery and receiving the characters of earth and air, and qualified by all the other affectations that go with these, had every sort of diverse appearance to the sight; . . . [and] . . . was filled with powers that were neither alike nor evenly balanced . . . (Cornford, 1957, 52D-E; cf. Jammer, 1960, 23).

The conflict is only apparent. The passage upon the basis of which Jammer apparently concludes that space is inhomogeneous, clearly indicates that it is not space but its contents which are unevenly distributed throughout space. Thus, we must be extra careful in assigning the property of homogeneity to a particular view of space. A space might be called inhomogeneous if its contents are not evenly distributed throughout every region of space. It is in this sense that Jammer is correct in characterizing space in Plato as "inhomogeneous." However, a space might be called inhomogeneous if the space itself somehow differed from region to region independently of its content. In this latter sense, space in Plato is homogeneous. It is this latter sense that we will generally mean when we talk about the homogeneity or inhomogeneity of space.

(S3) Space is immutable (50B). This means that its "nature" does not change over time, even though the things that enter it, i.e. the sensible objects of Becoming, are constantly changing.

There is something of a difficulty here with Plato's view. At 50B, he suggests that "which receives all bodies . . . must be called always the same; it never departs at all from its own character" (Cornford, 1957, 182). This suggests that space has a character, i.e. a set of essential properties which characterize it. On the other hand, at 50E, it is claimed that space must be "free from all characters" so that it might reproduce the Forms more faithfully (Cornford, 1957, 186). This suggests that space must have no particular character of its own. Thus, space seemingly both has a constant character and has no character. Which is to be? As it stands this concept of space is self-contra-dictory. It is not clear that Plato ever adequately resolves this problem, although the move towards thinking of space as a "container" suggests how it might have a character (i.e., be a place for all things) yet have no particular character of its own.

(S4) Space is spherical (33B). This follows from the fact that every place is in the cosmos, which is itself the interior of a sphere rotating on its axis.

(S5) Space is finite (33B-34A). The extent of space is the extent of the cosmos. There is nothing "outside" of the cosmos, no bodies nor any places or areas for them to exist.

(S6) Space is everlasting and indestructible (52B).

In this respect, Space is like the Forms. It is unlike them, however, in that it is not an object of "rational understanding" (Cornford, 1957, 193). Space is an irreducible, independent factor from which the sensible world is "constructed." It is unlike the objects of Becoming in that there is no Form of Space or Spatiality (compare Time below).

(S7) There are no voids (52D-53C; 58A f.). One would think that if space is a container, then it might be empty, but Plato indicates that this is not, in fact, the case. Even with no empty spaces, motion is still possible. Consider a ring of material revolving in a circle. As one part moves, the next fills up the space left by the first, and so on (58A f.). The fact that Plato's space is always 'full' coupled with the suggestion that space (somehow) interacts with its contents (the Nurse and Mother metaphors), has led some commentators to see, in Plato's view, a foreshadowing of modern theories of matter where space and matter apparently interact (cf. Graves, 1971, Chapter 5).

(S8) Finally, Plato's space is isotropic (62D f.). What this means is that all directions in space are equivalent. But, equivalent in what respect? Evidently there are several different respects in which one might claim that space is isotropic, and a given space might be isotropic in one respect but not in another. We first note a sense in which space is not isotropic for Plato. The fact that space, for Plato, fills a finite sphere with the earth at the center automatically singles out certain positions, namely, the center and the surface shell, as special. They are special in that an observer on the shell will not "see" space to be the same in all directions. For example, the maximal length in any given direction will, in general, be different. For an observer at the center, however, all directions have the same maximal distance. Thus, if isotropic means that all the geometric properties of space are the same for all observers, then Plato's space is not isotropic.

However, there is a sense in which space is isotropic for Plato. Plato's discussion (63A-63E) is designed to explain the application of the terms "up" and "down." His conclusion is that the terms have relative signification only and will vary depending on where in the universe an observer happens to be. An observer on the earth, which is where the (element) Earth tends to collect, observes the following: Upon taking up a test particle of Earth and letting

go of it, it tends to fall to the planet earth. We call this direction "down", and the opposite direction "up." Now imagine an observer on the inner edge of the celestial sphere. This is, as Plato puts it, "that region of the universe which is specially allotted to fire" (63B). Upon taking up a test particle of Fire and letting go, the test particle will fall to the inner surface of the sphere. For our celestial observer, that direction will be "down," and the opposite "up." On the basis of this thought experiment, Plato concludes that there is no absolute sense of up or down.[*]

In effect, there is no unique answer to the question: Which way is up? To an observer standing on the inner surface of the cosmic sphere, (if one could), up would be in the direction of the earth.

Figure 4-2

Which way is "up" is just whichever way one's arrow happens to be pointing. There is no physical difference between the two directions indicated in Fig. 4-2, both of which could be said by the appropriate observer to be "up." Another way to put the same point is to say that up (and down, or any direction) is purely relative to the person who happens to be making the determination. Space would be anisotropic, if certain directions were not relative to the individual making the determination. For example, if some direction were always "up," independently of the orientation of any observer, then the direction up would have an absolute "sense," and space would be anisotropic. In fact, Aristotle held just such a view, as we will see in the next chapter.

This completes our discussion of Plato's view of space. The contrast with the earlier views is striking. For those earlier views, we had, with the possible exception of the atomists, only the vaguest suggestions concerning the nature of space. In the Timaeus, Plato has given a reasonably complete account of the nature of space given the limitations of what he knew and also the special interests he was pursuing in the dialogue.

VI. The Moving Likeness of Eternity

Time and space have a fundamentally different status in Plato's cosmology. Space, as one of the three factors which constitute the building blocks of the physical Universe, is a self-subsistent entity, not dependent on either Being or Becoming. Time, unlike Space, has an eternal archetype. It is the image of a Form. That Form is Eternity, conceived of as the Model of Everlastingness and Unchangingness (37C-38C).

The world of Becoming, which is constantly changing, can never completely imitate the unchanging Forms which are the Models for sensory objects. The Demiurge is constrained by the materials he has to work with. Nothing in this world is Everlasting or Unchanging. Eternity (the Form) can only be imperfectly mirrored in the physical world by something which is itself changing. The Demiurge, though constrained, tries to produce the most perfect copy that he can. The closest approximation to the unchanging Form of Eternity Plato takes to be the change associated with the uniform flow of time, the measure of the uniform motion of the Sphere. Time is the moving likeness of Eternity, the closest we can get to Eternity in this world. The metaphor is both brilliant and provocative.

From the text, we can discover some of the properties attributed to Time.

(Tl) Time coexists with the Cosmos (37E). As long as the visible universe exists, so does time. As something "created" it comes into being with the creation of the Cosmos.

It would seem that if the Cosmos and time were created, then the amount of lapsed time from the beginning to the present would have to be finite. However, time could be infinite, if the cosmos always existed. It is not completely clear from the text whether Plato took the cosmos to be always existent or not. The case is not settled by appealing to the fact that the Demiurge is portrayed as "creating" the Cosmos, because there is some question as to how literally one is supposed to take this. The reason for the problem is that the chaos, from which the Demiurge is supposed to have created the Cosmos by imposing the Forms, is characterized as possessing a "disorderly" or random motion (30A). The problem is that motion is change of position with respect to time. In order for there to be motion in chaos (before the Cosmos existed), time must have existed before the Cosmos. A further point is that "before" itself is a temporal motion. How can one sensibly speak of chaos (or the Forms or the Demiurge or Space) as existing before the Cosmos was created, given that time only begins at the creation of the Cosmos? Given these problems, the most reasonable solution seems to take the Cosmos (and time) as always existing. The "creation" by the Demiurge is, thus, to be construed as a fanciful way of saying that the Cosmos is composed of a number of distinct factors which can be analytically separated in thought but not in fact. Given this construction of the text, we may conclude that

(T2) Time is infinite.

(T3) Time is a feature of the visible order of things. Even if we allow that time and the Cosmos have always existed, time, being the image of a Form, is not something, like Space, that exists in and of itself. Time is conceptually dependent upon the motions in the Cosmos. Time and motion are inseparable in a way that Space and the objects in Space are not. One can imagine Space as existing even though no objects existed in Space (although Plato suggests, in fact, that Space is never unoccupied), but one cannot imagine time in the absence of any motion (cf. Atomists, Chapter 2-28).

(T4) Time, unlike space, seems to have a preferred "direction," i.e., towards the future. Time is anisotropic. Plato does not actually say as much, but we believe that one can accept it as a legitimate inference, given that the Demiurge is committed to producing the most rational world (closest to the Forms) under the circumstances.

This concludes our discussion of Plato's concept of Time. The most striking feature of Plato's account is the different status that Space and Time have within his system. Space is, in some sense, Absolute, i.e., it subsists in its own right. Time, on the other hand, exists only insofar as the visible order of motion does.

VII. Conclusion

Plato's account of space and time is a distinct breakthrough when compared with those of his predecessors. However, a number of questions remain unresolved. First, the concept of space is not completely coherent. Second, the view rests on and is intertwined with a metaphysical theory (the Forms) that, as Plato himself recognized, is fraught with difficulties. Nevertheless, Plato's systematic attempt to come to grips with the dilemmas presented by Parmenides led him to formulate view on the nature of space, time and motion which, in failing to be satisfactory served to focus attention on the important questions about the nature of space and time, that had to be answered. The shortcomings of the Platonic view led Aristotle to address these questions anew and attempt to provide better answers.

Finally, the vagaries of the history of thoughts are such that, after the decline of Western civilization that followed the fall of Rome in 410 A.D. Plato's Timaeus was held to be the epitome of the Greek scientific spirit and, thus, his views on space and time played an important role in shaping Western ideas on space and time in the period preceding the rediscovery of Aristotle's work in the 12th century (see Chapter 6 below).

[*] Passages in Plato's dialogues are referred to by citing a page number and letter from a standard Greek edition that is followed by everyone. Thus, 53C indicates page 53 of the standard edition of the Timaeus, paragraph C of that page.

[*] We should note that the ancient Greeks had at least three distinct terms, each of which corresponds in some sense to what we might call "space." They are kenon, chora and topos. Kenon is usually translated as "void." When the atomists argued that all that existed were atoms and the void, they used the word kenon. Plato, for the most part, uses the word chora, which in ordinary Greek meant something like region or area. Topos was usually translated as "place," and was used, in ordinary Greek, when talking about the space occupied by a particular object, such as the place of a chair or table. Aristotle, whose views we take up in the next chapter, mainly spoke about topos. We try to keep the nomenclature clear by using "void" for kenon, "space" for chora, and "place" for topos. The problem unfortunately complicates the discussion of Greek concepts of "space," but it bears remembering when attempting to compare rival views. Part of the source of the problem is, of course, that at the time in question "space," as a scientific concept, did not exist. Even so, the distinction between these terms still survives in English and to a certain extent in the differences between ordinary speech and the technical use of such terms in scientific concepts. This is just a reminder that "space" is not a univocal concept and one must be prepared, to avoid needless arguments, to state just what characteristics one takes "space" to possess.

[*] Plato does not consider the following possible scenario. What would happen if the celestial observer released a particle of Earth at the inner surface of the sphere? This would have a greater appeal to the operational instincts of modern physicists, who would demand that the operational criterion for being "down" be the same for all parts of the Universe. Presumably this did not occur to Plato since he could not conceive of the region where Fire collects containing any Earth. A similar problem faces the modern day scientist who wishes to measure areas on the surface of the sun with a metal ruler. Conditions prohibit the accomplishment of his task. Return to beginning of this chapter or to the Table of Contents.