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The first attempts to develop comprehensive and systematic accounts of natural phenomena can be traced to the Greek cosmologists writing between 600-400 B.C. In the light of these initial efforts, Greek thinkers came to recognize that the concepts of space, time and motion, which lay at the heart of any view of natural phenomena, presented a number of conceptual and theoretical difficulties. Some of the problems and paradoxes associated with the ideas of space, time and motion were set out by Zeno of Elea (fl. 450 B.C.). These paradoxes, according to Bertrand Russell, served as the framework for all subsequent Western thinking about space and time. Zeno's paradoxes are treated in the next chapter. They form the watershed separating the groping thought of the early Greek cosmologists from the more systematic treatments of Plato (429-348 B.C.: see Chapter 4) and Aristotle (384-322 B.C.: see Chapter 5).
In this chapter, our purpose is to, first, outline some of the basic themes underlying the early Greek cosmologies, themes which set off their attempts from the earlier mythopoeic efforts and which survived to form the initial basis of science and rational inquiry as we know it today. Second, we give a brief sketch of the development of rational cosmology from Thales (fl. 585 B.C.) to Plato, with a particular emphasis on the contributions of these thinkers to the development of a coherent view of the nature of space and time. We close with some brief remarks on the legacy of the early Greek cosmologists both for the development of science, in general, and for the development of views about the nature of space and time, in particular.
II. Basic Themes of the Greek Cosmologists
As far as we can tell, the birth of rational cosmology, that is, the systematic attempt to describe and explain natural phenomena in rational terms, was initiated by the Greeks around 600 B.C. These thinkers have become known as pre-Socratics, in virtue of the fact that, with Socrates (469-399 B.C.), Greek speculative thinking shifted from a concern with nature to a concern with man. Although these early cosmologists represent the first attempts to develop systematic views about the universe, causality, space, time and other physical concepts, what have come down to us are only fragmentary remnants of their writings.
Interpreting the pre-Socratics is a major industry for classical scholars. The picture we develop below does not pretend to be complete or comprehensive. It is mainly intended to highlight those special features of Greek speculative thinking which have been incorporated into our modern vision of what a rational inquiry amounts to. Our interpretation and summaries of the efforts of these thinkers, it must be realized, are based upon a limited number of scattered references. It must also be kept in mind that even to Plato and Aristotle, barely 200 years after the first beginnings of rational cosmology, it was not clear what some of the earlier cosmologists were trying to say. How much more difficult, then, is it for us today, 2600 years after the beginnings, to try to piece together a coherent picture of early cosmological speculations.
Despite these difficulties, the effort at trying to understand the Greek contribution is, we feel, worthwhile. A fundamental premise of this book is that our understanding of basic concepts of physical science is enhanced by a careful study of their origins and historical development. In a sense, we appreciate more deeply where we are when we realize whence we came and by what paths. The pre-Socratics provide these origins and many of the paths which bring us to the present conceptual age.
Despite differences in detail between the early competing cosmologies, a number of characteristic themes common to the mainstream of Greek speculative thought emerge. These common themes serve to mark off the Greek speculative thinkers from their mythopoeic predecessors. We isolate eight important themes.
1. The demythologization of nature.
For the first time, we find a conscious attempt to explain physical phenomena in naturalistic terms, instead of appealing to the actions and desires of willfull gods. Thus, the pre-Socratics asked questions like: What are things made of? How do things change? Adequate answers to these questions had to be framed in terms of the natures of things and their properties rather than by the whims of gods.
2. The idea of a cosmos.
A second theme which emerges in pre-Socratic thinking is that the world is viewed as an ordered cosmos. The basic idea of seeing the world as a cosmos is that the world is viewed as a unity, as an intelligible whole whose workings are regulated by principles which can be understood by human reason. Today such an idea seems commonplace. In order to appreciate its revolutionary significance, you should contrast it with the mythic approach from which it emerged. The fundamental insight is that nature has a rational order. The major thrust of early Greek thought is the attempt to discover that rational order.
3. The search for general explanations.
That the universe had a rational order meant, for the Greeks, that there were general principles which could be invoked to give general explanations of natural phenomena. Their aim was to find explanations for each and every occurrence of a phenomenon of a given kind, as opposed to giving a special explanation for each particular occurrence. Consider, for example, some natural event such as an earthquake. For the mythopoeic thinkers, each earthquake was different and unique. Each, therefore, had to be explained and understood in its own particular way. One earthquake, for example, might be the result of the anger of one particular god but a second earthquake might be the result of a game played by some other god. The idea that there might be a common explanation for all earthquakes does not seem to have occurred to these earlier thinkers.
Although it may seem obvious to us now, it is not necessarily obvious on the face of it when you begin to think about such kinds of natural phenomena. For example, no two earthquakes have exactly the same qualitative features, that is, exactly the same set of characteristics such as length of tremor, time of day of occurrences, location, amount of destruction, emotional impact on victims, and so on. It takes a fairly sophisticated degree of abstraction to be able to think away all the differences between any two particular examples of an earthquake and to see, instead, the common general characteristics which are shared by both and in virtue of which both are earthquakes. This emphasis on the ability and necessity to abstract away from the particular and see the general unifying theme was one of the great achievements of Greek thought.
4. Man as a spectator.
In mythopoeic thinking, man was often seen as an integral part of natural phenomena through his involvement in ritual. The Greeks saw man as essentially a spectator of natural processes rather than as a participant in natural processes. We see a shift in Greek thought to the view of man as an observer and knower, one who seeks to understand natural phenomena, which occur more or less independently of the actions or desires of human agents.
5. Critical debate.
Greek thinking differed from its predecessors not only in content but also in its methodology. Certain characteristics of the Greeks as a people seem to be reflected not only in the kinds of theories they produced but also in the way they discussed their theories. The Greeks were great individualists. One important difference between the Greek thinkers and those who came before them is that the Greek philosophers were private individuals and not members of a priestly class. The views that they produced were idiosyncratically their own. The Mesopotamic and Egyptian myths, on the other hand, were the products of a priestly class whose job, in part, was to put forth an official state doctrine.
The net effect of the individualistic strain in Greek thought is that alternative cosmological accounts are considered as competitors that need to be reconciled with one another or rejected. Thus, Greek theorists criticize each other's views as being inadequate to the facts or incomplete or inconsistent.
The argumentative strain that one finds in Greek philosophy, and which has become a characteristic of the Western intellectual tradition, is a reflection of the fact that the Greeks themselves were a very argumentative and competitive people. One sees this exemplified in non-intellectual areas in the fact that it was the Greeks, recall, who instituted the Olympic games. Just as athletes could compete on the Olympic field to see who was the best sportsman, so Greek philosophers competed with each other to see who could produce the best and most complete account of natural phenomena. Although there were no Olympic contests devoted to philosophic competitions, there were quasi-Olympic contests in theatre. Thus, most, if not all, of the dramas and comedies that come down to us from classical Greece were initially written as competitive pieces to be performed in front of judges, where prizes were awarded for the best plays.
These are all manifestations of a sense of individualism which one finds lacking in mythopoeic thinking. Among all the myths that come down to us from Egypt and Mesopotamia, for example, not a single author's name is included. Mythological thinking is anonymous in a way that Greek thinking and modern thinking is not. The important result of this individualism, for our purposes, is that it gave rise to the view that alternative physical theories were to be subject to critical evaluation. This, in turn, gave rise to questions concerning standards of proof and the development of formal logic and the philosophy of science by Aristotle. These methodological standards then served to shape the development of scientific theories in general and theories about the nature of space and time in particular.
The interest of the Greeks in criticizing each other's views is also a reflection of their desire to produce a consistent theory of physical phenomena. Where consistency is not valued, the mere fact that alternative views conflict with one another is no cause for concern. However, given that there is a rational order to nature, then accounts which are inconsistent with one another cannot all be correct. Since the Greek cosmologists were committed to the discovery of that rational order, inconsistencies could not be tolerated. Conflicting views either had to be reconciled or one (or all) rejected.
7. The distinction between Appearances and Reality.
The desire for a consistent world picture, coupled with the search for general principles, leads to the idea that the diversity of human experience masks a fundamental underlying unity of nature. This idea becomes a key focus for the Italian school of pre-Socratic philosophers. It is formalized as the distinction between the Appearances (what appears to be the case) and Reality (what actually is the case). This distinction is fundamental to the development of Greek thought about nature and is fundamental to modern scientific thinking as well.
Such a distinction is a natural consequence of the attempt to arrive at a comprehensive and consistent picture of reality. In order to achieve such a picture, the data of experience must be organized in such a way that some of it must either be ignored or reinterpreted. For example, if we are to argue that all earthquakes are fundamentally alike and can be treated as exemplifications of a single pattern, then the individuality of different earthquakes must be suppressed. In order to achieve a general picture, one must think away the individual peculiarities of each particular earthquake and focus, instead, on those features shared by all. Or consider the concept of space. In order to reach the view of space as essentially a container of physical objects and events, one must be willing to suppress the emotive feelings associated with different places as inessential.
Thus, in general, certain features of the phenomena under investigation are seen to be inessential (mere appearances), whereas other features are seen to be fundamental (real). The distinct;on between Appearance and Reality is fundamentally the distinction between that which is unimportant and that which is important. One thing that makes the history of science interesting is that different ages have had different ideas as to what was or was not important.
The distinction between Appearance and Reality is still central to modern scientific thinking. Anyone who has ever taken a laboratory course in a science has come up against its present day significance. At some point the experimental data is subject to interpretation. When data is thrown out as spurious or doubtful, one is invoking a version of the distinction between appearance and reality. Even "clean" data never gives a perfect fit to a smooth curve. Drawing a smooth curve through a set of data points is an implicit reinterpretation of the data and a recognition that its real significance is not what initially it may have appeared to be.
8. The problem of permanence and change.
The world as we experience it is a world of diversity and change. The early Greek cosmologists (as we shall see in the next section) tended to try to account for the unity of nature by postulating a fundamental permanent stuff as the basis for all things. The idea that underlying this diversity and change is a permanent unity of some kind raised some fundamental problems for the Greek cosmologists. In particular, if reality consists of some basic stuff which is everywhere and always the same, how does one account for change? The problem of motion, or change in general, was at the forefront of ancient Greek intellectual activity. Change of place or loco-motion appeared to be fundamental. This problem naturally led the later Greek philosophers to focus on an analysis of space (or place) and time since loco-motion is just change of place in time. Given that one of the essential features of a physical process is that it involves change or motion, it is easy to understand why space and time came to be seen as fundamental concepts of natural philosophy.
These eight themes served to define the problems and set the standards for the development of scientific thinking in early Greece. The contrast with the mythopoeic views is instructive. The Greek ideal, which, with some modifications coincides with our present day ideal, is that natural phenomena are to be explained in terms of general principles subject to rational criticism. Science is beginning to stir. We turn now to a brief consideration of the views of the early cosmologists which set the stage for the more extensive critiques of space, time and motion by Plato, Aristotle and their successors.
III. The Greek Cosmologists
The pre-Socratic cosmologists can be profitably divided into three groups. The earliest speculative philosophers were from Asia Minor and came to be known as the Ionian school. They were characterized by Aristotle as "philosophers of matter" because they tended to focus on the problem of characterizing the fundamental material stuff out of which the universe was made. The second group originated in Italy and came to be known as the Italian school. An influential philosopher from Elea in Italy, Parmenides, (fl. 500 B.C.) gave rise to a school known as the Eleatics. The philosophers of the Italian school were characterized by Aristotle as "philosophers of form," since they tended to focus on the formal aspects of the universe, and in particular the role of reason in discovering those formal principles.
The Eleatic position, as developed by Parmenides and his disciples, was that Reality was basically One and Unchanging. Ordinary experiences to the contrary was dismissed as illusory. Since everything on this view is fundamentally "one," it is labeled Monism. Eleatic Monism generated the third major school of pre-Socratic philosophers, the Pluralists, which included, among others, the ancient atomists. We turn to a brief survey of the major figures in these schools.
1. Thales of Miletus (c. 624-547 B.C.)
Traditionally, the first pre-Socratic philosopher is reckoned to be Thales. Thales' cosmology can be summarized by the claim "all is water." No one whose writings we still possess knew exactly what he meant by this. Aristotle's guess was that he meant that everything was made up of water, which turns out to be one of the four basic elements, according to Aristotle. Another guess is that he was trying to answer the question: what came first? His answer would be that everything originated in water.
Whichever of the two questions Thales was trying to address it is clear that his answer does not go far enough. If the point is that everything is made up of water, Thales gives us no clue as to how things which are apparently quite different from water, could really be water nonetheless. If the point is that everything came from water, we are left in the dark about how what is not now water came to be from what was originally water.
We know little more about Thales' views than this one claim that all is water. He is reputed to have predicted an eclipse in 585 B.C., but if he did so, it is not clear how he did it. We know nothing about his views, if any, on space and time as such. One tradition has it that his view of the universe was that the earth floats on water like a log.
Figure 2-1: Thales' Cosmology
2. Anaximander of Miletus (610-545 B.C.)
According to Anaximander, the basic stuff of the Universe was something he called "apeiron." In Greek, "apeiron" means something like "unlimited" or "undifferentiated." Again, exactly what Anaximander had in mind is somewhat unclear. One reading is that he was trying to answer the question: Where did everything come from? By postulating the apeiron as the source of everything, Anaximander might have been trying to account for how the many diverse things with different properties could originate from one thing. The trick is this one thing, being unlimited, has, as it were, all properties which might then separate out to form different things with different sets of properties. This position is superior to that of Thales because if everything is (or came from) water (which has a definite nature) we are faced with the problem of explaining how things whose nature is different from that of water could either come from or be made up of water. But even Anaximander's apeiron leaves much unanswered. The problem of how different things with different natures evolved from this undifferentiated stuff remains. Anaximander has the further distinction of being the author of what many consider to be the first philosophical fragment on time.
"The source of coming-to-be for existing things is that into which destruction, too happens, 'according to necessity; for they pay penalty and retribution to each other for this injustice according to the assessment of Time,'" (the portion in single quotes is an extant fragment from Anaximander, the rest is a paraphrase by a late Greek commentator of Anaximander's position).
The point of this rather obscure passage is not completely clear. The basic ideas seem to be that things are created out of something and when they die or decay they return to that original something (e.g., living animals are composed of atoms and molecules and when they die, the bodies of the animals decay, leaving the constituent molecules). The point about penalty and retribution may be that the passage of Time wreaks havoc on all things which are created.
Anaximander is also credited with an attempt to give some account of the earth and heavens which we have dubbed his inner tube cosmology.
Figure 2-2: Anaximander's Inner Tube Cosmology
The basic idea is that the earth is a truncated cylinder surrounded by opaque tubes of fires with holes cut in them. What we see as the moon, e.g., is really the fire shining through the hole in such a tube. Eclipses occur when the holes are, for some unstated reason, obscured. There is no indication that Anaximander considered how to handle the stars with this procedure and it is clear that the scheme, although a step in the right direction towards a complete description of the physical universe, leaves much to be desired.
3. Anaximenes of Miletus (588-524 B.C.)
Anaximenes took the basic stuff to be air or mist. He also attempted to give some account of change and motion by appealing to the well known fact that mist or air can be compressed and rarefied. Different things could then be construed as being composed of more or less compressed mist. Change occurs when the mist expands or contracts. This, like the other early cosmologies, is only a stab in the direction of a theory of natural phenomena.
Anaximenes left nothing of his views, if any, on space and time. His cosmology can be illustrated as follows:
Figure 2-3: Anaximenes's Cosmology
The earth, a flat disk, rests at the center of a hemisphere of air. The sun, moon and planets are carried over the top of the hemisphere by rafts. At the end of the day the sun is carried around the perimeter of the hemisphere on a river which circumscribes the universe so as to be ready to rise in the east the next day.
4. Heraclitus of Ephesus (540-480 B.C.)
Heraclitus chose Fire as his basic element. He denied that anything was permanent; everything, he maintained, is in constant flux. In fact, the basic constituent of the universe was flux itself. One corporation has captured this sentiment in a stark poster with the motto "Nothing endures but change."
We have no extant views of Heraclitus on space and time. His cosmology can be diagrammed as follows:
Figure 2-4: Heraclitus' Cosmology
The earth is a globe at the center, surrounded by planets which revolve in orbits through a medium called the aether. The sun and moon are bowls of fire. Eclipses are produced when the bowls of fire rotate so that the opaque bottom is facing the observer on earth.
B The Italian School
Around the middle of the 6th century B.C., the center of intellectual activity shifted from Asia Minor to Italy. The Italian philosophers also shifted their attention from the stuff or matter of the universe to a consideration of its form or rational structure.
5. Pythagoras - The Pythagorean School (C. 550-500 B.C.)
Among those philosophers whom Aristotle classified as philosphers of form, the most important, for our purposes, are the Pythagoreans. The Pythagoreans were a group of thinkers who formed a quasi-religious society following the teachings of the legendary figure, Pythagoras. From our point of view, the fundamental contribution of the Pythagoreans was their conviction that the inherent order in nature is expressible in mathematical terms. Among their important contributions along these lines they
(a) developed a number cosmology,
(b) introduced the notion of proof,
(c) instigated the "Save the appearances" program in astronomy,
(d) discovered irrational numbers.
(a) The development of a number cosmology
The Pythagoreans introduced the use of mathematics into the explanation of natural phenomena, although they went to fantastic lengths to do so. They conceived of numbers as having magical properties and they saw numbers not merely as tools for measuring aspects of reality, as modern physicists and scientists do, but as actually constitutive of reality. From a late source, Diogenes Laertes, we get the following characterization:
"From numbers points, from points line, from lines plain figures, from plain figures solid figures, from these, sensible bodies of which elements are four: fire, water, earth, and air. These change and are wholly transformed; and from them arises a cosmos animate, intelligent, and spherical, embracing earth (itself spherical and inhabited all around) as its center."
The Pythagoreans thus saw numbers not only as explanatory of natural phenomena but as also having a mystical significance and in fact of being causes of various phenomena. The sense in which the Pythagoreans treated numbers as causes is that they saw them as material causes. For example, the number one was associated with a point, the number two with a straight line between two points, the number three with a triangle, and the number four with a square. These simple geometric figures were the atoms in terms of which everything in the material world was supposedly constructed. Thus, the Pythagoreans were numerical atomists.
The basic discovery which traditionally is credited with leading them to this idea, is that the relationship between the notes in the musical scale could be represented in the form of ratios of small whole numbers. Presumably they discovered this empirically by noting that, for example, a string which is stretched to a certain length will sound a note one octave higher when it is pinched in the middle, and so on. The Pythagoreans sought to explain all natural phenomena in terms of such harmonies. For example, they thought that the orbits of the planets were arranged in some harmonious order, and that the revolving planets actually produced tones, which, because they are constantly present, we do not perceive.
Aristotle criticizes their numerological tendencies as follows:
"Why need these numbers be causes? There are seven vowels, the scale consists of seven strings, the Pleides are seven, at [the age of] seven, animals lose their teeth (at least some do, though some do not), and the champions who fought against Thebes were seven. Is it then because the number is the kind of number it is, that the champions were seven or the Pleides consist of seven stars? Surely the champions were seven because there were seven gates or for some other reason, and the Pleides we count as seven, as we count the Bear as twelve, while other people count more stars in both ... These people are like the old-fashioned Homeric scholars, who see small resemblances but neglect great ones. (Aristotle, Metaphysics, 1093al3ff.)
The number mysticism of the Pythagoreans was picked up again later in the 17th century by Kepler. He used the doctrine of the harmony of the spheres, rescued from the Pythagoreans, to help him formulate hypotheses which led to the reduction of the available astronomical data to three laws of planatary motion, which, in turn, were instrumental in promoting the modern concept of the solar system (cf. Kuhn, 1957, 209ff.).
(b) The notion of proof.
A second fundamental contribution of the Pythagoreans was that they introduced the notion of proof. Whether they discovered the Pythagorean theorem or not, they certainly recognized that it was something which had to be proved to hold for all right triangles. Thus, there is some evidence that both the Egyptians and the Babylonians were aware of special cases of right triangles for which the Pythagorean theorem holds, for example, the 3-4-5 triangle. But, unlike the Greeks, the earlier mathematicians made no attempts, as far as we know, to establish the general character of the relationship between the sides and the hypotenuse of any right triangle. The recognition that things like the Pythagorean theorem had to be proved in turn stimulated a discussion among the Greeks of what could legitimately be assumed and what were the conditions under which something could be said to be proved. This discussion culminated in Aristotle's codification of formal logic and axiomatic treatment of geometry in the 4th century B.C.
(c) Save the appearances.
A further contribution of the Pythagoreans consisted in their setting up a research program which guided the development of astronomy for approximately 2000 years. There is some evidence that it was they who defined the problem of astronomy to be that of finding a set of circular motions which together would account for the motions of all of the heavenly bodies (Mason, 1962, 29-30).
The basic idea was to try to find a mathematical model for the motions of the sun, moon, planets and heavenly bodies without considering whether the model was physically real or not. They chose circular motion as the most perfect kind of motion and proposed that the complex motions of the planets, e.g., be reduced to various combinations of simple circular motions. The point was to save the appearances, i.e., to produce a model which would reproduce the apparent motions of the heavenly bodies without concern for whether those motions were actual or not. Thus, astronomy developed for many centuries as a purely mathematical science with little concern for the physical causes which might produce the observed phenomena. It was only after the Copernican revolution and Kepler's discovery that the planetary orbits were ellipses, that astronomers began to speculate about the physical causes producing what they observed.
(d) The discovery of irrational numbers.
The general pythagorean program of providing a geometrical interpretation of natural phenomena was abruptly short-circuited in about 440 B.C. by the discovery that the 2 was an irrational number. The significance of this result can be seen as follows. Consider a unit square, that is, a square whose sides are one unit long:
Figure 2-4a: Pythagorean square
Consider the diagonal of the square. On the diagram, it seems to be a perfectly well defined length. But, what the Pythagoreans discovered was that this length was irrational, that is, could not be represented as the ratio of whole number elements.[*] But, the world picture of the Pythagoreans rested on the supposed universality of these ratios of small whole numbers. In addition, the square, recall, was one of the fundamental building blocks of the numerical atomistic scheme. If it turned out that one of these fundamental building blocks was flawed, in that its features could not all be explained by the basic Pythagorean scheme, then the entire program seemed in deep trouble.
Apparently, the Pythagoreans tried to keep the discovery of the irrationality of [radical]2 secret. But, then as now, security is more easily sought than achieved, and soon the secret was out. It has been argued that the inability to overcome this setback hindered the development of Greek mathematics (Boyer, 1949, 20). One view is that following the discovery of the irrationality of [radical] 2 the Greeks turned away from the development of arithmetic (they never, for example, discovered the power of having "O") and turned their thinking to the development of geometry. This had unfortunate consequences for the development of natural science, because the geometrical approach, in and of itself, can only go so far. Thus, it is no accident that the growth of modern science since the beginning of the 17th century has gone hand-in-hand with the development of that most splendid of arithmetic tools, the integral and differential calculus (Boyer, 1949).
In addition to these contributions to the mathematical analysis of nature, the later Pythagoreans (c. 350 B.C.) developed a cosmology which shows a considerable advance over the efforts of the Ionian cosmologists.
Figure 2-5: Pythagorean System
The universe is conceived of as a finite sphere with the stars fixed in the outer shell. The planets, sun, moon and earth revolve around a central fire at the center. This central fire is hidden from our view by a counterearth (CE) which revolves in such a way to block the view of those living in the southern hemisphere.
Finally, the Pythagorean tradition, flawed as it may be, is the first move in a methodological debate which has gone on throughout the centuries. The basic issue concerns the nature of our understanding of physical phenomena, the role of mathematical models, and the role of hypothetical entities, such as the Pythagorean numerical atoms, in science. Regardless of how well numerical atoms seem to explain natural phenomena, they are clearly hypothetical constructs in a sense in which ordinary physical objects like tables and chairs are not. The numerical atoms are the products of reasoning rather than perception. The world, as we experience it, on the other hand, is a world of objects which can be seen, touched, heard, tasted, and smelled. The physical objects of our ordinary experiences seem to be quite different in kind from the numerical atoms postulated by the Pythagoreans. Those who see the aim of science primarily as the construction of mathematical models of physical phenomena, have often been called "Instrumentalists." Those who see the function of science as the discovery of physical causes have often been called "Realists." Their slogan might be "Find the Hidden Structures Underlying the Appearances." This tension between the Instrumentalists, on the one hand, and the Realists, on the other, concerning the nature of the explanatory principles of natural phenomena has continued from antiquity to the present day.
6. Parmenides of Elea. (fl. 500-450 B.C.)
Parmenides of Elea was another influential philosopher from Italy. He is credited with being among the first to consistently use arguments to defend and elaborate his position. The distinction between Appearance and Reality was first drawn clearly by Parmenides.
The Parmenidean school and its followers are called Eleatics. One tradition has it that Parmenides was originally, follower of the Pythagoreans, i.e., a pluralist, but that he came to reject Pythagoreanism and developed a monistic theory that Reality is One. Parmenides presented his view in a poem divided into two parts: the way of Truth and the Way of Opinion. In the Way of Truth, Parmenides argues that Reality is One and Change is unreal. In the Way of Opinion, he apparently tried to deal with the fact that experience seems to suggest otherwise (only fragments of this part of the poem survive).
The fundamental Parmenidean doctrine is that what is truly real, what Parmenides called Being, is One, Indivisible and Unchanging. All change, including apparent temporal and spatial change, as well as the apparent diversity of the sensible world are illusions--mere appearances. As a consequence of this, Parmenides denied that space and time are real.
Despite the apparent absurdity of his views, Parmenides was taken very seriously by Greek philosophers. This was because his views were not mere dogmatic pronouncements but were carefully argued for. In effect, Parmenides was challenging the reliability of sensory evidence--which suggests that the world is pluralistic. Instead, Parmenides argues, if one follows the path of reason, one is led to the view that Reality is One. Faced with a conflict between the evidence of our senses and the conclusions we draw from our powers of reason, Parmenides chose to reject the evidence of the senses and trust the powers of human reason instead. Thus, the distinction between what is Real (known by reason) and what is mere Appearance. This distinction and the correlative conflict between the claims of reason and the claims of the senses have played a fundamental role in the development of subsequent Western philosphy and science.
The Parmenidean position rests on three key premises (Cornford, 1939, 29). These are
P1: Being has a strict and absolute sense. The force of this assumption is that something either is or it is not. No compromise is allowed.
P2: It is if and only if it can be said (named). Thus, what is not cannot be spoken of.
P3: What is One cannot be or become many.
From these assumptions, Parmenides drew a number of devastating conclusions:
Cl: What is cannot come into being or perish (i.e., change is impossible).
C2: The manifold pluralistic world cannot exist.
C3: What is, is immovable, since motion requires a void, but a void is nothing, and, hence, does not exist.
Much of Greek philosophy for the next 150 years was concerned with the ramifications of the Parmenidean position and attempts to salvage the reality of change from the destructive criticism of Parmenides' position.
7. Zeno of Elea (fl. 460 B.C.)
Parmenides' denial of the reality of change did not seem reasonable to many of his contemporaries. We take up these pluralistic reactions in a moment. Here we shall mention, however, Zeno of Elea, a follower of Parmenides, who, through a series of paradoxes, attempted to defend the Parmenidean thesis that Reality is One and that Change is an illusion. These paradoxes, moreover, have a significance that goes far beyond their attempted defense of Parmenides. They raise a number of questions of fundamental importance for our understanding of the nature of space and time. They are so significant that we reserve an entire chapter (Chapter 3) for their discussion. For now, we turn to some of the pluralistic reactions to Parmenides.
C. The Pluralistic Reaction.
The pluralists are not strictly speaking a school, in that they are united by only one common theme--namely, their rejection of the Parmenidean thesis that Reality is One.
8. Empedocles (495-435 B.C.)
Empedocles denied the Eleatic contention that Being is One. He postulated four basic elements: Fire, Air, Earth and Water. Different things were held to be composed of different ratios of these four elements.
Change was explained in terms of two principles of cosmic Love (which drew things together) and cosmic Strife (which drove them apart). Change was then due to the rearrangement of the ratios of these elements due to the competing efforts of Love and Strife.
Empedocles had nothing in particular to say about space and time, but he did put forth a doctrine of cosmic cycles. According to this theory the universe is constantly changing and evolving through distinct stages. When the principle of Love is dominant, (1), the universe is uniform. This stage is unstable and gives rise to a period of transitions whence Love yields to Strife (2). This stage of the universe is characterized by increasing disorder. Eventually, Strife prevails, (3), and the universe is fundamentally chaotic. The force of Love cannot be denied, however, and a further transition stage occurs as Strife gives way to Love (4). Eventually, Love dominates and the cycle begins again. The net effect is to postulate an evolutionary history to the universe which constantly repeats the same pattern.
Figure 2-6: Empedoclean diagram
This has led some to see, in Empedocles, a strong statement of the doctrine of Eternal Return (cf. Barnes, 1979 II, 201).
9. Anaxagoras (500-428 B.C.)
Anaxagoras went even further in rejecting the Parmenidean One. He postulated an infinite number of elementary substances. A new twist was added in that Anaxagoras introduced a principle he called Mind which he claimed to be the source of motion of these substances. Nothing remains concerning Anaxagoras' views about space and time, if any.
l0. Leucippus (fl. 430 B.C.) and Democritus (460-352 B.C.)
The ancient atomists met the Parmenidean challenge head on. They accepted the Eleatic thesis that what is cannot come into being or perish. They denied that this entailed that Being must be one. Instead, they argued that the universe contained an infinite number of such indestructible beings which they called "atoms." These atoms, they argued, are in constant motion. Perceived differences in things were held to be due to differences in the shapes, sizes, and arrangements of the atoms that made them up.
They also agreed with the Eleatic thesis that motion requires a void. To overcome the Eleatic objection that a void (as something which was not) was impossible and could not exist, they took the bull by the horns and postulated the voids did exist. Given that one accepts the premise that voids are necessary for motion, one is faced with two choices:
(1) Deny the existence of voids and argue that what is perceived to be motion does not really occur (the Eleatic option).
(2) Accept the reality of motion as perceived and the consequent necessity of postulating the existence of a void, however odd such a claim may initially appear to be (the Atomist option).
The slogan of the atomists became--"Nothing exists but atoms and the void." The acknowledgement of the existence of a void is, in effect, a recognition of the reality of space. Since the number of atoms was held by the atomists to be infinite, they argued that the void, which served to keep the atoms apart, must be infinite as well.
The ancient atomists vacillated between two views of the nature of the void. Some atomists held what might be called a "container view" of the void or space, namely, that space is an infinite void in which bodies (atoms) can be located. Other atomists, such as the founders Democritus and Leucippus held that space or void was an interval between bodies which is such that the universe as a whole is the sum of all the atoms plus the space or void in between them. On this view, atoms and the void are two distinct kinds of Beings and the atoms themselves are not in the void so much as lying alongside it. To illustrate the difference between these two views, consider the following diagram:
Figure 2-7: 3 x 3 Checkerboard
Imagine that the large square represents the entire universe. The blank squares represent places where no bodies exist and the dark squares represent atoms. Each square (blank or dark) we will take to be one unit. On the container view, the universe consists of 9 units of void, 5 of which happen to be occupied by atoms. On the alternative view, the universe consists of 4 units of void plus 5 atom units. This latter view was the standard interpretation of the atomists' position in 4th century B.C. Greek intellectual circles. The difference between it and the container view needs to be kept in mind if some of the criticisms of atomism by, e.g., Aristotle are to make any sense.
With the atomists, we get one of the first attempts to set out a positive view about space and time as such. If we interpret the atomists' void as a kind of space, then several features of space can be abstracted from their writings.
(1) Space is infinite in extent.
(2) Space is an objective feature of the world. By this we mean that even if human perceivers (observers with minds) did not exist, space would still exist. For the atomists, then, space is "mind-independent."
(3) Since both atoms and the void are elementary kinds of Being, the void exists independently of whether or not atoms exist. For the atomists, space or void is "object independent." We shall have occasion later to discuss views which hold that space is not "object-independent (See, e.g., Chapter 7)
(4) For the atomists, space (as void) is not continuous, since where atoms are, void is not. Thus, there are "gaps" in the void, where bodies exist. Only on the later atomistic view of space as a "container," is space continuous.
An interesting point about the atomist's position is that time, unlike space, is not a fundamental objective feature of the universe (Bailey, 1928, 306). The general view is expressed by Lucretius, a late atomist (c. 50 B.C.) in his De Rerum Natura:
" . . . time exists not of itself, but sense
Reads out of things what happened long ago,
What presses now, and what shall follow after:
No man, we must admit, feels time itself,
Disjoined from motion and repose of things.
(Lucretius, 1957, Bk. 1, line 448f.)
In effect, time, unlike space exists only insofar as the motion of things imparts to a conscious observer, a "feeling" of some kind. If objects (atoms) did not move, or if no conscious observers existed, then time would not exist either. Thus, for the atomists,
(4) Time is object-dependent. If there were no objects (in motion) then time would not exist.
(5) Time is mind-dependent. If no conscious observers existed, then time would not exist either.
We point out these attributes because as we survey the history of the development of our concepts of space and time, we will be comparing successive views with respect to these and other relevant features.
One might wonder, since we believe in a form of atomism today, why, if there were atomists 2300 years ago, people ever believed anything different. The key is that the similarity between modern atomic theory and ancient Greek atomism is not much more than a similarity in name only. Ancient atomism flourished from its beginnings around 430 B.C. to roughly 280 B.C. The primary reasons for its decline were not scientific but primarily religious and ethical. In fact, Greek atomism was primarily an ethical and (anti-) religious doctrine and only secondarily an attempt to provide what we would call a legitimate scientific theory of natural phenomena. The primary aim of the atomists in proclaiming that only atoms and the void existed was to free men from the fear of death and the clutches of religious superstition. By the middle of the 3rd century B.C., however, Greek culture was declining and the power of Rome to the west was ascending. In those troubled times, the atheistic materialism offered by atomism was insufficient solace to many and its influence and significance waned.
IV. The Legacy of the Pre-Socratics.
The legacy of the Pre-Socratics to the subsequent development of theories of space and time consisted of three major factors.
(1) A number of important themes characteristic of Greek rational inquiry and which became key features in subsequent philosophies of natures. We isolated eight themes, which we recapitulate here.
(i) The demythologization of nature: This served to mark off Greek rational inquiry from the early mythopoeic attempts to comprehend the universe. The process of demythologization did not occur all at once. The earlier Ionian cosmologies were often imbued with elements of earlier modes of thought. By the time one reaches the pluralists reacting against Parmenides the process is virtually complete.
(ii) The development of the idea of a cosmos.
(iii) The search for general explanations.
(iv) Man becomes a spectator.
(v) The development of rules of critical debate.
(vi) The search for consistent world pictures.
(vii) The distinction between Appearances and Reality.
(viii) The problem of permanence and change.
These themes served to set the standards and define the problems for later Greek philosophy. Attempts to deal with (vii) and (viii), in particular, focused attention on the vexing problems which lay at the heart of the concepts of space, time and motion.
(2) The pre-Socratics began to fashion cosmological models. The early Ionian models are crude and unsophisticated, but as appreciation of the problems grew, the models grew more subtle and refined. The early cosmologists had little, if anything to say about space and time, but the later views of Parmenides and the Atomists serve to push the concerns of space and time to center stage.
(3) Finally, from Zeno of Elea we have a number of profound paradoxes which strike at the very intelligibility of space, time and motion. These paradoxes served as foils against which later philosophers could test their theories of space and time. Not every ancient (or modern) commentator agreed on how profound Zeno's original paradoxes were, but an influential modern view (which we accept) is that they raise a number of important issues about the fundamental structure of space, time, motion, and our understanding of these ideas.
We turn now to a consideration of Zeno's paradoxes and their significance for our story.
[*] The proof of this result is basically very simple. Let the diagonal of the unit square shown above be labeled p. Then, by the Pythagorean theorem we know that p2 = 12 + 12 = 1 + 1 = 2. Thus, p = [radical symbol]2 . One can show that p is not rational indirectly by showing that if we assume that p is rational we are forced to a contradiction. (See Appendix for Proof.) Return to beginning of this chapter or to the Table of Contents.