Democritus was born in Abdera, the leading Greek city on the northern coast of the Aegean Sea. Although the ancient accounts of Democritus’s career differ widely, they all agree that he lived to a ripe old age, 90 being the lowest figure. During that long career Democritus wrote many books. Little Cosmology, a veritable encyclopedia, has perished because its contents displeased those, such as the philosopher Plato, whose decisions determined which works should be preserved. Of all of Democritus’s many-sided interests, his espousal of the atomic theory accounts for his renown and also for the disappearance of the treatises which won him that renown.
Democritus did not originate the atomic theory; he learned it from its founder, Leucippus, the author of the Big Cosmology. While this work too has vanished, some conception of its contents may be obtained from Aristotle. He opposed the atomic theory, but in doing so he summarized its principal doctrines. Thus he attributed to Leucippus the ideas that the atoms are “infinite in number and imperceptible because of the minuteness of their size. They move about in empty space (for there is empty space) and by joining together they produce perceptible objects, which are destroyed when the atoms separate.” The point at which Leucippus’s elaboration of the atomic theory stopped and Democritus’s contributions to it began can no longer be identified. In antiquity the theory’s major features were sometimes ascribed to Leucippus and Democritus jointly and sometimes to Democritus alone.
Perhaps according to both of them and certainly according to Democritus, the atom was the irreducibly minimal quantity of matter. The concept of the infinite divisibility of matter was flatly contradicted by the atomic theory, since within the interior of the atom there could be no physical parts or unoccupied space. Every atom was exactly like every other atom as a piece of corporeal stuff. But the atoms differed in shape, and since their contours showed an infinite variety and could be oriented in any direction and arranged in any order, the atoms could enter into countless combinations. In their solid interior there was no motion, while they themselves could move about in empty space. Thus, for the atomic theory, the physical universe had two basic ingredients: impenetrable atoms and penetrable space. For Democritus, space was infinite in extent, and the atoms were infinite in number.
By their very nature the atoms were endowed with a motion that was eternal and not initiated by any outside force. Since the atoms were not created at any time in the past and would never disintegrate at any time in the future, the total quantity of matter in the universe remained constant: this fundamental principle of Democritus’s atomic theory implies the conservation of matter, the sum total of which in the universe neither increases nor diminishes. Though Democritus’s conception of the atom has been modified in several essential respects in modern times, his atomic theory remains the foundation of modern science.
For Democritus, “time was uncreated.” His atomic universe was temporally everlasting and spatially boundless, without beginning and without end in either space or time. Just as no special act of creation brought Democritus’s universe into being, so the operations of his cosmos did not serve any particular purpose. Consequently, Democritus’s atomic theory was irreconcilable with the teleological view, which regarded the world as having been planned to fulfill some inscrutable destiny. As the founder of the atomic theory declared in his only surviving statement, “Nothing occurs at random, but everything happens for a reason and by necessity.”
Just as Democritus’s cosmogony invoked no creator-god, so his moral teachings appealed to no supernatural judge of human conduct. He attributed the popular belief in Zeus and other deities to primitive man’s incomprehension of meteorological and astronomical phenomena. To support his theory about the origin of worship of the various divinities, Democritus assailed the widespread notion that rewards for righteous actions and punishments for wrongdoing were administered in an afterlife. In the long history of Greek speculation Democritus was the first thinker to deny that every human being has an individual soul which survives the death of the body.
Democritus sought to diminish pain during life, of which “the goal is cheerfulness.” Cheerfulness is identical not with pleasure, as he was misinterpreted by some people, but “with a calm and steady mind, undisturbed by any fear or superstition or other irrational feeling.” Yet Democritus did not advocate a quiet life of repose. His was not the outlook of the retired citizen, drowsing in his rocking chair on the front porch and idly watching the world go by. Democritus taught a naturalistic morality, avoiding ascetic renunciation as well as excessive indulgence, and urging energetic participation in beneficial activities. In particular, “Democritus recommends mastering the art of politics as most important, and undertaking its tasks, from which significant and magnificent benefits are obtained for the people.” Perhaps from his governmental experience in Abdera, Democritus learned that “good conduct seems to be procured better by the use of encouraging and convincing words than by statute and coercion. For he who is restrained by law from wrongdoing is likely to commit crime covertly. On the other hand, he who is attracted to uprightness by persuasion is unlikely to transgress either secretly or openly.”
Probing the Infinitesimal
Archimedes, the most brilliant mathematician of antiquity, gave Democritus credit for the discovery that the volume of a cone is one-third that of a cylinder having the same base and altitude. Archimedes added, however, that this theorem was enunciated by Democritus “without proof.” In Democritus’s time Greek geometry had not yet reached the stage at which it demanded rigorous proofs of its theorems. Democritus stated: “If a cone is cut by a plane parallel to its base, shall we regard the surfaces forming the sections as equal or unequal? If unequal, they make the cone uneven, having numerous indentations and protrusions, like a flight of stairs. But if the surfaces are equal, the sections will be equal and the cone comes to look like a cylinder, consisting of equal circles.” Democritus’s conception of the cylinder as being made up of an indefinite number of minutely thin circular layers shows him beginning to probe the momentous question of the infinitesimal, the starting point of a most valuable branch of modern mathematics.