Prof. Fred L. Wilson
Rochester Institute of Technology
Science and Human Values
Pre-Socratic Philosophers
Original Source
Introduction
Rationalism, for what ever its value, appears to have emerged from mythology with the Greeks. In engaging in this intellectual exercise, the Greeks assumed, of course, that nature would play fair; that, if attacked in the proper manner, it would yield its secrets and would not change position or attitude in midplay. Over two thousand years later, Albert Einstein expressed this feeling when he said, "God may be subtle, but He is not malicious." There was also the feeling that the natural laws, when found, would be comprehensible. This Greek optimism has never entirely left the human race.
With confidence in the fair play of nature, human beings needed to work out an orderly system for learning how to determine the underlying laws from the observed data. To progress from one point to another by established rules of argument is to use "reason." A reasoner may use "intuition" to guide the search for answers, but must rely on sound logic to test particular theories. To take a simple example: if brandy and water, whiskey and water, vodka and water, and rum and water are all intoxicating beverages, one may jump to the conclusion that the intoxicating factor must be the ingredient these drinks hold in common -- namely, water. There is something wrong with this reasoning, but the fault in the logic is not immediately obvious, and in more subtle cases, the error may be hard indeed to discover.
According to Greek tradition, the first of the Greeks to devote himself to the exciting intellectual exercise of trying to discover just what the laws of nature might be was Thales of Miletus, (born: Miletus, 624 B.C., died: Miletus, 546 B.C.) The later Greeks considered Thales the founder of Greek science, mathematics, and philosophy, and they credited to him the origin of almost every branch of knowledge. It is hard to say how much of this is later embroidery.
He is supposed to have been born of a Phoenician mother, though this is doubted by some. Perhaps the legend only signifies that he was educated in Eastern science. Certainly he visited Egypt and probably Babylonia. It may be that what seemed to the Greeks a multiplicity of achievement was simply the lore of the more ancient peoples.
For instance, the single deed that most secured his reputation, according to the tale told a century and a half later by the Greek historian Herodotus, was his prediction of an eclipse of the sun, an eclipse which then proceeded to take place in the very year for which it was predicted. When it occurred it frightened the Medes and Lydians, who were on the point of advancing into battle, and convinced them of the beauties of peace. They signed a treaty and the armies returned home. Modern astronomical research showed that the only eclipse that took place in Asia Minor in Thales' time was on May 28, 585 B.C., to that the aborted battle is the first historical event that can be dated with certainty to the exact day.
Nevertheless Thales' feat seems not so miraculous when we consider that the Babylonians had worked out systems for the accurate prediction of lunar eclipses at least two centuries before his time. His ability to predict this solar eclipse, and to the year rather than to the day, was, therefore, almost certainly acquired in the East. Thales was the first Greek to maintain that the moon shone by reflected sunlight and this, too, may represent Babylonian lore.
Thales also borrowed Egyptian geometry, but here he made a fundamental advance. He converted it into an abstract study, being the first man we know of to consider it as dealing with imaginary lines of zero thickness and perfect straightness, rather than with actual lines, thick and imperfect, scraped in the sand or scratched on wax. (If the Egyptians or Babylonians had already made this advance, it is still true that Thales was the first to place such views on record in a form that has reached us, via the works of later philosophers.)
Thales seems also to have been the first to go about proving mathematical statements by a regular series of arguments, marshaling what was already known and proceeding step by step to the desired proof as inevitable consequence. In other words, he invented deductive mathematics, which was to be systematized and brought to a high polish two and a half centuries later by Euclid.
He is also supposed to have discovered certain specific geometric theorems; for instance, that the diameter of a circle divides it into two equal parts, that vertical angles are equal, and that the base angles of an isosceles triangle are equal. He was also supposed to have measured the height of an Egyptian pyramid by comparing the length of its shadow to that of the shadow of a stick of known size -- which represents the concept of trigonometry.
In the physical sciences, he was the first to study magnetism. More important, he is the first man we know of who asked the question: Of what is the Universe made? and to answer it without introducing gods or demons.
His own answer was that the fundamental stuff (the "element," we would now say) of the Universe was water, and the earth was only a flat disc floating on an infinite ocean. This answer was a most reasonable guess for the times, since it was clear that life, at least, depended on water. But the question itself was far more important than the answer, for it inspired later philosophers, who flourished in the same region, near Miletus, among them Anaximander, Anaximenes, and Heraclitus, to speculate on the same subject. It was this line of thought that led eventually, after two thousand years of painful intellectual struggle, to modern chemistry.
Thales, in addition to being a philosopher was, according to later tradition, a practical man of affairs. In politics he shrewdly urged a political union of the various Greek Cities of lonia (the modem southwest coast of Turkey), of which Miletus was one, for self-defense against the encroaching non-Greek kingdom of Lydia. This, the following centuries amply demonstrated, was the only way the Greeks could defend themselves against the surrounding nations. However, the Greek passion for disunity rose triumphant over all and was the cause of the country's ruin.
Plato invented another tale to point another moral. While walking along and studying the stars, Plato said, Thales fell into a well. An old woman coming in response to his cries, helped him out, but said with contempt, "Here is a man who would study the stars and cannot see what lies at his feet."
Already in the time of Plato and Aristotle, two and a half centuries after Thales, the old philosopher's views were remembered imperfectly and made the subject of legend.
In valuing philosophical speculation over the practical applications of science, Thales set the tone for later Greek thinking. As a result the work of Greek engineers and inventors was largely ignored by later Greek writers and badly underestimated, in consequence, by all later generations. We have only very slight information about Thales' younger contemporary, Eupalinus, who in his way may have been as accomplished a sage.
In later centuries, when the Greeks made up lists of the "seven wise men," Thales was invariably placed first.
Ionian Philosophers
In addition to Thales there were other Ionian philosophers, Anaximander, and Anaximenes. These philosophers parted with everything they inherited from the Homeric phase of Greek culture. When they did not raise questions about the beginning and end of the world, they simply imitated Hesiod. Their assumption about things developing from the primitive state by successive differentiations and by the interaction of opposing forces repulsion and attraction, was also a borrowing from poetical cosmogonies. Other thoughts of Hesiod, such as the role of mind, love, and strife in the physical universe, also keep turning up in the statements of other philosophers, Anaxagoras, Parmenides, and Empedocles. The occurrence of analogies taken from the organic world is not absent even in the fragments ascribed to Democritus, that resolute champion of a rigidly mechanistic interpretation of nature. He used organic analogy to explain the preferential grouping of the same kinds of units of matter, as if it were an attraction, as among animals:
Living creatures consort with their kind, as doves with doves, and cranes with cranes, and similarly with the rest of the animal world. So it is with inanimate things, as one can see with the sieving of seeds and with the pebbles on beaches. In the former, though the circulation of the sieve, beans are separated and ranged with beans, barley-grains with barley, and wheat with wheat; in the latter, with the motion of the wave, oval pebbles are driven to the same place as oval, and round to round, as if the similarity in these things had a sort of power over them which had brought them together. [Note 1]
In all this there was, however, far more of a semantic accommodation than of a return to a personalistic representation of the universe. After all, the Ionians and Democritus too had to speak a language in which the same words still retained human and superhuman, animalistic as well as mechanistic, nuances. How could they avoid using such basic terms as thymos, pneuma, psyche, and a number of others that resisted any strict definition? Their stylistic inconsistencies notwithstanding, the basic orientation of both the Ionians and the atomists is unmistakable. Their principal aim was not the cultivation of the personalistic texture of the Homeric outlook, but rather an experimentation in bold aphorisms that preferred to speak of the impersonal world of matter, motion, and space. For them, as Aristotle summed up their views, there was only one permanent element in the universe
Of the first philosophers, most thought the principles which were of the nature of matter were the only principles of all things; that of which all things that are consist, and from which they first come to be, and into which they are finally resolved..., this they say is the element and the principle of things, and therefore they think nothing is either generated or destroyed, since this sort of entity is always conserved.... [Note 2]
Like Thales, whose pupil he was, Anaximander (Born: Miletus, 610 B.C. Died: Miletus, about 546 B.C.) helped introduce the science of the ancient East to Greece. He was the first Greek to make use of the sundial, for instance, which had been known for centuries both in Egypt and Babylonia. No better timekeeper was to he found until the days of Clesibius, over three centuries later. Anaximander was also the first to attempt to draw a map of the whole earth as he knew it.
He recognized that the heavens revolved about the Pole star and so he pictured the sky as a complete sphere and not merely as a semispherical arch over the earth. For the first time the notion of spheres invaded astronomy; this was to culminate eventually in the sophisticated (but erroneous) picture of the universe drawn up by Ptolemy.
He also recognized that Earth's surface must be curved, to account for the change in the position of the stars as one traveled. He felt a north-south curvature was enough, however, so he pictured the earth as a cylinder about an east-west axis with a height one-third its diameter. The notion of a spherical earth had to wait several decades for Pythagoras and his followers.
Anaximander's idea of the basic element of the universe was far more mystical than Thales' plain and undramatic notion that it was water. Anaximander envisaged a formless mass that was both the source and the destination of all material things. He called this unobservable substance apeiron, meaning infinite. Nevertheless, he conceded this much to water -- he thought life originated there. In this he was quite correct.
The treatise Anaximander wrote describing his views is thought to be the first work of consequence in Greek prose. His works are now lost.
Thales reduced everything to water, coming very close to formulating the principle of conservation of matter, whereas Anaximander derived everything from air and spoke of never-ending motion. Qualities were explained by quantitative changes. The density scale of the air was to account for fire, water, and earth; and for the first time mechanistic models were adopted to illustrate the dynamics of the universe. The sweeping generalizations reached even the heavens when Anaxagoras described the sun as a flaming stone larger than Peloponnese. There seemed to be simply nothing that could not be reached by a physics that bore all the marks of an unsuspecting, youthful outburst of scientific speculation: from man's soul to the far reaches of the universe there was believed to be only one principle, which produced, governed, and explained everything.
Little is known about Anaximenes ( born: Miletus, about 570 B.C. died: about 500 B.C.) except that he may have been a pupil of Anaximander, and that he believed air to he the fundamental element of the universe. By compression, he supposed, it could take on the form of water and, eventually, earth. He is supposed to have been the first Greek to distinguish clearly between planets (such as Mars and Venus) and stars, and to have maintained that the rainbow was a natural phenomenon rather than a goddess.
Anaximenes contended that,
As our soul, being air, holds us together, so do breath and air surround the whole universe. [Note 3]
True, Anaximenes was quick to qualify his grandiose statement by allowing in living creatures the presence of something other than simple and homogenous air and wind. In so doing, however, he was merely warning simpletons and not making concessions about the unconditional validity of his air-principle.
Pythagoras and the Pythagoreans
Pythagoras (born: Samos -- an Aegean island -- about 582 B.C., died: Metapontum in southern Italy, about 497 B.C.) like the other early sages of Greece, was reputed to have traveled widely in Egypt and the East, and he may well have done so. He is also reported to have studied under Anaximander or even under Thales himself.
However, the first event in his life that seems reasonably certain is his departure from Samos in 529 B.C. and his emigration to Croton in southern Italy. By that time the coasts of southern Italy and eastern Sicily had been colonized by the Greeks and the region remained Greek in culture well Into the Middle Ages. Pythagoras' move, according to tradition, was brought about by the harsh, one-man rule over Samos on the part of the tyrant Polycrates. Whatever the cause, the move extended the philosophic and scientific tradition -- begun by Thales at the eastern rim of the Greek world -- to the far west of the Greek world.
In Croton, Pythagoras broke with the rationalism of the east-Greek tradition and founded a cult marked by secrecy, asceticism, and mysticism. The cult, Pythagoreanism, forbade, for instance, the poking of fire with an iron poker, and the eating of beans. It also taught the doctrine of the transmigration of souls. There is a story, for instance, that Pythagoras ordered a man to stop beating a dog, claiming he recognized the voice of a dead friend of his. This may merely have been a humane impulse on Pythagoras' part -- or it may have been invented by the cult's many enemies to cast ridicule upon it.
In many ways Pythagoreanism was like the mystery cults prevalent in Greece then and afterward, but it differed from them in the interest the followers of Pythagoras had in mathematics and astronomy. The cult achieved important political power in Pythagoras' later years and was usually to be found on the side of the aristocrats. Even during the lifetime of Pythagoras, however, the democrats had started to gain the upper hand in southern Italy and the cult began to suffer persecution. Pythagoras was exiled from Croton about ten years before his death. Pythagoreanism survived as an active cult for only a century after its founder's death.
The unpopularity it brought upon Itself by its political activity resulted in a violent wave of persecution that spread over all the Greek world. By 350 B.C. Pythagoreanism was wiped out. The influence of its ideas, however, has lasted into modem times, and Pythagoras remains the most famous of the earlier Greek philosophers. It is he, indeed, who is supposed to have coined the word "philosopher."
Because of the secrecy shrouding the beliefs of Pythagoreans, it isn't always easy to tell what they were, or how much of what was attributed to them by later Greek writers is correct. In particular, it is hard to say for what Pythagoras himself was responsible, and what was originated by his many disciples.
The greatest scientific success attributed to Pythagoras was in his study of sound. He found that the strings of musical instruments delivered sound of higher pitch as they were made shorter. Furthermore he found that the relationship of pitch could be simply correlated with length. For instance, if one string was twice the length of another, the sound it emitted was just an octave lower. If the ratio of the strings was three to two, the musical interval called a fifth was produced, and if it was four to three, the interval called a fourth was produced. Increasing the tension of the strings also raised the pitch. Thanks to these observations, the study of sound was the one branch of physics in which Greek views remained unaltered in modern times.
This study may have led Pythagoras to the belief that the whole universe rested on numbers and their relationship, for be (or his followers) proceeded to invest numbers with all sorts of mystic significance. Today these notions seem foolish, but they did encourage the investigation of the mathematical properties of the numbers. For instance, it was the Pythagoreans who discovered that the square root of two (that is, the number which, multiplied by itself, gives a product of exactly two) could not be expressed as the ratio of two numbers. No conceivable fraction, however complicated, will give the product of two when multiplied by itself.
Here was a very simple concept that could not be put into whole numbers. How then could numbers account for something as complicated as the whole universe? The Pythagoreans were supposed to have vowed themselves to secrecy concerning such "irrational numbers" lest outsiders scoff. It slipped out anyway and there is a story that the Pythagoreans executed one of their fellows whose tongue had wagged too freely on the subject, though this may be a slander circulated by one of the many enemies of the Pythagoreans.
Pythagoras is most famous, perhaps, for having been the first to work out the proposition (by strict mathematical deduction) that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its sides. This is still known as the Pythagorean theorem.
Pythagoras was the first Greek to recognize that the morning star (Phosphorus) and the evening star (Hesperus) were in fact one star. After his time it was called Aphrodite, and we know it now as the planet Venus. He was also the first to note that the orbit of the moon is not in the plane of the earth's equator but is inclined at an angle to that plane.
He was the first man known to us who taught that Earth was spherical. He was also the first Greek philosopher to point out that the sun, moon, and various planets did not partake of the uniform motion of the stars, but that each had a path of its own. Thus began the notion that in addition to the heavenly sphere that Anaximander had postulated, separate spheres had to be provided for the various planets. For seven hundred years thereafter, the number of spheres necessary to account for the planetary movements was to multiply, and over twenty-one hundred years passed before Kepler wiped them out.
The Pythagoreans believed this ultimate principle to be the unit number. Aristotle was probably reading his own distinctions into the views of the Pythagoreans by saying that for them numbers constituted both the matter and the form of things. Yet, when Aristotle says that for the Pythagoreans "the whole heaven is numbers," he is undoubtedly reporting their genuine conviction. [Note 4] How the heavens could be made of numbers presented no great problem to the Pythagoreans. In their world view lines were derived from points or unit numbers, from lines surfaces, from surfaces simple bodies, from these the elements and the whole world. As an evidence of the explanation of the world by numbers, the Pythagoreans pointed to the strings of musical instruments and to the motions of stars and planets, thereby uniting music, poetry, matter, and mind into a harmonious whole. At least this was their ultimate dream. At any rate, as Philolaus [Note 5] tells us, they held a staunch belief that error and deceit are foreign to the world of numbers. They also held truth, intelligibility, and certitude to be cognate to numbers, which they contrasted with the erroneous world of the undefined, uncounted, senseless, and irrational.
Falsehood can in no way breathe on Number; for Falsehood is inimical and hostile to its nature, whereas Truth is related to and in close natural union with the race of numbers. [Note 6]
To reveal the true nature of the cultural change underway the word race was very aptly chosen: the race of impersonal numbers was indeed gaining the upper hand over all other races, human or otherwise. This fascination with numbers, measurement, and calculation suffered only a momentary blow when the Pythagoreans stumbled upon the existence of irrational numbers. The rebound could hardly be more vigorous, and Archytas a hundred years later confidently praised the unexcelled power of mathematics in understanding nature. He boldly asserted that it was the exclusive privilege of the mathematicians to "think correctly about the nature of individual things," for they alone possessed the much coveted knowledge about the whole. What Archytas really meant was that mathematicians succeeded in reaching the very roots of being by giving undivided attention to the realm of numbers. Thus he felt entitled to claim that mathematicians "who are concerned with number and size, these two related primitive forms of being," were alone capable of having
a clear judgment on the speed of the constellations, and their rising and setting, as well as on [plane] geometry and Numbers [arithmetic] and solid geometry, and not least on music; for these mathematical studies appear to be related. [Note 7]
Nature's Hallmark of Intelligibility
The Ionian philosophers, the Pythagorean mystics, and sober geometers had at least one thing in common. They all claimed for their particular approach to nature the exclusive hallmark of intelligibility. Entirely similar was the case with that most influential concept of early Greek science, the atom. The notion of atoms was offered as the bedrock of understanding, and its properties seemed to symbolize the supposedly ultimate form of reasonable questions that could be raised about the universe.
The trust Democritus put in his atoms seems to have been limitless. After all he was their father and as such had to be very partial to their paradoxical though obvious shortcomings. Consequently Democritus suggested a radically mechanistic conception of the world, and he pushed to the extreme, with thorough consistency, the consequences of his basic postulates. In his universe of atoms no place was left for "forces" such as weight, attraction, or repulsion. Nor could the atomists accommodate in their system apparently non-material factors, which, like the "mind" of Anaxagoras, are hardly more than a figure of speech when mentioned by them. But not only spiritual entities were deprived of distinct existence in Democritus' world. Much of what constitutes man's view of the outside world becomes but a subjective illusion in their treatment. In antiquity nobody noted this more strikingly than Galen, who, unlike Democritus, wanted above all to understand man himself and his relation to his surroundings. Truly, if there was a lesson to draw from the atomistic approach to nature, Democritus himself had formulated it with shocking directness:
One must learn by this rule that Man is severed from reality. [Note 8]
But it was not only man's relation to the external world that became meaningless. Man himself as an individual was also to lose his footing in the whirl of atoms. With the cosmos -- the ordered correlation of things -- gone, man's meaning in the universe went too. Of course when Galen noted the pessimism such views had generated, the heyday of atomism had been a thing of the past for almost half a millennium. But in its stage of fresh fascination the atomism of Democritus, which really did not explain any observational phenomena, could not fail to have an overriding impact. Hand in hand with sophism it contributed heavily to a thorough upheaval of the whole set of traditional, humanistic values in pre-Socratic Athens.
Notes:,
Diels,Vorsokratiker, p. 107 [164].
Aristotle, Metaphysics, pp. 1555-6, [983b].
Diels,Vorsokratiker, p. 19, [2].
Aristotle, Metaphysics, 985b.
Philolaus of Tarentum was active in the latyter half of the fifth century B.C. He was said to have written one book, which was the first published account of Pythagoreanism. See Diels, Vorsokratiker, p. 73.
Diels,Vorsokratiker, p. 75, [11].
Diels,Vorsokratiker, p. 78, [1].
Diels,Vorsokratiker, p. 92, [6].
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Fred L. Wilson (shanghai@physics.org)
August 23, 1996