Ecclesia Ordinis Caelestis Templum Olympicus/Celestial Order and Temple of Olympus

Great Pagans in Science

ARYABHATA, also Aryabhatta (476-550? BCE), Hindu astronomer and mathematician, born in Pataliputra (modern Patna, India). He was known to the Arabs as Arjehir, and his writings had considerable influence on Arabic science. Aryabhata held that the earth rotates on its axis, and he gave the correct explanation of eclipses of the sun and the moon. In mathematics he solved the quadratic equation, although many of his geometric formulas were incorrect. His only extant work is the "Aryabhatiya," a series of astronomical and mathematical rules and propositions, written in Sanskrit verse.

ERASISTRATUS (c. 304-250 BCE), Greek anatomist, born in Iulis (now Kéa). As a young man he became physician at the court of Seleucus Nicator, king of Syria. Later, he founded a school of anatomy in Alexandria. He traced sensory and motor nerves to the brain, and veins and arteries to the heart. Erasistratus believed that the nerves carried "nervous spirit" from the brain and that the arteries carried "animal spirit" that the heart created out of air from the lungs. His remarkably modern concepts were replaced by those of Galen and were not revived until the Renaissance.

ERATOSTHENES (276?-196? BCE), Greek mathematician, astronomer, geographer, and poet, born in Cyrene (now Shahhat, Libya). Among his teachers was the Greek poet Callimachus. About 240 BCE, Eratosthenes became the head of the library at Alexandria, Egypt. He measured the obliquity of the ecliptic with an error of only 7 min of arc, drew up a catalog (now lost) of 675 fixed stars, and measured the circumference of the earth with extraordinary accuracy by determining astronomically the latitudes of Aswan and Alexandria, Egypt, and measuring the distance between them. His most important work was a systematic treatise on geography. After becoming blind, he died in Alexandria of voluntary starvation.

PTOLEMY (about ad 100-70), astronomer and mathematician, whose synthesis of the geocentric theory that the earth is the center of the universe dominated astronomical thought until the 17th century (see PTOLEMAIC SYSTEM). He is also remembered for his contributions to the fields of mathematics, optics, and geography. Ptolemy was probably born in Greece, but his actual name, Claudius Ptolemaeus, reflects all that is really known of him: "Ptolemaeus" indicates that he was a resident of Egypt, and "Claudius" signifies Roman citizenship. In fact, ancient sources report that he lived and worked in Alexandria, Egypt, for the greater part of his life. The Almagest. Ptolemy's earliest and most famous treatise, originally written in Greek, was translated into Arabic as al-Majisti (Great Work). In Europe, medieval Latin translations reproduced the title as Almagesti, and it has since become known simple as the Almagest. In this work, Ptolemy proposed a geometric theory to account mathematically for the apparent motions and positions of the planets, sun, and moon against the background of fixed stars. He began by accepting the generally held theory that the earth did not move but was at the center of the system. The planets and stars, moving eternally, were considered (for philosophical reasons) to move in perfectly circular orbits. He then elaborated on the theory in an attempt to account for such astronomical puzzles as the periodically retrograde (backward) motions of the planets and periodic variations in size or brightness of the moon and planets. Ptolemy's abilities as an observational astronomer have been questioned, but his complex system seemed to account for celestial motions. Anomalies in a planet's motion were accounted for by the use of the epicycle, a circle centered on the circumference of a larger circle called the deferent. The planets, sun, and moon were regarded as located on the rims of rotating epicycles, and the earth itself was placed eccentrically to the center of the deferent. By adjusting the radii of the circles and their speeds of rotation, Ptolemy made the system fit most of the observed facts.Ptolemy also had to introduce, however, another mathematical device known as the equant: an imaginary point halfway between the center of the deferent and the eccentric point representing the earth's position. Rather than maintain the constant, uniform motion of all circles in the system (deferents and epicycles), as had been required in all previous models of ancient astronomy, he assumed that the deferent moved uniformly with respect to the equant. (Thus the deferent's motion would not be uniform with respect to its own center.) This major departure from traditional assumptions was one reason the Polish astronomer Nicolaus Copernicus rejected Ptolemy's system in the 16th century and developed his own heliocentric world view of a sun-centered system (see COPERNICAN SYSTEM). Even so, Copernicus retained an elabor ate system of epicycles.Other Works. Ptolemy also contributed substantially to mathematics by advancing the study of trigonometry, and he applied his theories to the construction of astrolabes and sundials. In his Tetrabiblios, he applied astronomy to astrology and the casting of horoscopes. Of considerable historical importance, despite considerable factual inaccuracies, is Ptolemy's Geography, which charts the then-known world. This work, which employs a system of longitude and latitude, influenced mapmakers of the Renaissance, but it suffered from a lack of reliable information. Ptolemy also devoted a treatise, Harmonica, to music theory, and in Optics he explored the properties of light, especially refraction and reflection. This latter work, known only from an Arabic version, is of special interest for its combination of experiment and the construction of apparatus to promote the study of light and to develop a mathematical theory of its properties. J.W.D

APELLES (fl. 352-308 BCE), Greek painter, one of the most celebrated artists of the ancient world. Born in Colophon on the Ionian coast, he studied in Sicyon (now Sikion) under Pamphilus of Amphipolis. Apelles' works, characterized by a unique grace, are known only from literary descriptions, but they inspired Renaissance artists. The works include portraits of Philip of Macedon, his son Alexander the Great, and Alexander's generals, as well as mythological and allegorical scenes, such as Venus Anadyomene and Calumny, in which Ignorance, Suspicion, Envy, and other qualities are personified. According to a well-known anecdote, a cobbler detected a fault in the shoe of a figure painted by Apelles, who quickly rectified it. When the cobbler criticized the legs, however, Apelles exclaimed "Ne supra crepidam sutor judicaret," advice immortalized as "Let the cobbler stick to his last."

APOLLODORUS (fl. 5th cent. BCE), Athenian painter known as Skiagraphos (the "Shadow Painter"). By skillful use of light and shade he improved perspective and the modeling of figures in order to heighten the illusion of three-dimensional space. His innovations were further developed by Zeuxis. None of Apollodorus' works has survived.

EXEKIAS, also Execias (fl. about 550-525 BCE), Greek potter and vase painter, who excelled in the black-figure style of the 6th century BCE. His vases are noted for their refined and slender elegance and strong, incisive painting. Of nine extant vases, probably the most famous is the Vatican Museum vase depicting the mythological warriors Ajax and Achilles playing dice, which shows Exekias's characteristic qualities of balanced composition, precise drawing of figures, and their elegant disposition around the circumference of the vase. His painting has a grandeur and power that are derived from his talent for portraying the particular dramatic moment in a scene when the gestures of the participants reveal their inner thoughts.

AENESIDEMUS (fl. 1st cent. BCE), Greek skeptic philosopher, who attempted to demonstrate the relative character of all judgments and opinions. Born in Knossos, Crete, he taught at Alexandria. Ten well-known arguments (called tropoi) for skepticism (q.v.) are attributed to him. He held that judgment must be suspended in seeking knowledge and that nothing is certain either in itself or through anything else. This principle seemed evident to him, as objects appear differently to people according to the perspective taken, and proof of an assumption requires an infinite process of proof (that is, one assumption is based on another, and so on indefinitely).

ALCIBIADES (c. 450-404 BCE), ill-fated Athenian statesman and general, whose opportunistic acts and divisive influence contributed to the defeat of Athens in the Peloponnesian War (431-404 BCE). After the death of his father in 447 BCE, Alcibiades was raised in the house of his uncle, the Greek statesman Pericles. Alcibiades was influenced by Socrates, who was his personal friend. Alcibiades gained great wealth through his marriage, but he squandered his money and led a dissipated life. By expensive public displays, especially at the Olympian Games of 420, he won the favor of the common people. His only political rival was the Athenian statesman Nicias (d. 413 BCE), who had secured a treaty of peace for 50 years between the Athenians and the Spartans. In 415 Alcibiades made himself head of the army and induced the Athenians to undertake an expedition against Syracuse, for which he was elected one of the commanders. Before the departure of the expedition, all the statues of the god Hermes in Athens were mutilated in a single night; the blame for the sacrilege was laid in all likelihood falsely on Alcibiades, who was charged with impiety and recalled from the expedition. On his return he fled to Sparta, where he divulged the plans of the enterprise and helped the allied Spartans and Syracusans to defeat the Athenians. For this act of treason, a sentence of death was recorded against him at Athens, and his property was confiscated.In 414 Alcibiades went with the Spartan expedition to the island of Khios, where he incited an Ionian revolt against the Athenians. Difficulties with the Spartan leaders led to a plot to assassinate Alcibiades. On learning of the plot, Alcibiades fled to the Persian provincial governor Tissaphernes (fl. 413-395 BCE) and attempted without success to win him over to the Athenians on the ground that it was in the interest of Persia to prevent Sparta from gaining complete ascendancy over Athens. Alcibiades then offered to bring Persian support to the Athenians if they would revoke the decree making him an exile. His offer was accepted, but he wished to render some service to Athens before returning. He therefore remained abroad and won important victories for the Athenians, including the capture of the cities of Cyzicus, Chalcedon, and Byzantium.Alcibiades returned to Athens in 407 and was received with general enthusiasm. He was again sent to Asia with 100 ships, but the expedition was defeated at Notium in 406. As a result his enemies brought a new accusation against him, and he was relieved of his command. He thereupon again joined the Persians, taking refuge in Phrygia. At the request of the Athenian government, and with the approval of the Spartans, Alcibiades' residence was set on fire during the night, and, as he fled, he was killed by a volley of arrows.

ANAXAGORAS (500?-428 BCE), Greek philosopher who introduced the notion of nous (Gr., "mind" or "reason") into the philosophy of origins; previous philosophers had studied the elements (earth, air, fire, water) as ultimate reality.Born in Clazomenae (near modern $Izmir, Turkey), Anaxagoras was the first philosopher to settle (c. 480) in Athens, later a flourishing center of philosophy. His pupils included the Greek statesman Pericles, the Greek dramatist Euripides, and probably Socrates. Anaxagoras had taught in Athens for about 30 years when he was imprisoned for impiety for suggesting that the sun is a hot stone and the moon made of earth. Later he went to Ionia (in Asia Minor) and settled at Lampsacus, a colony of Miletus, where he died. Anaxagoras explained his philosophy in Peri Physeos (On Nature), but only fragments of the books have survived. He held that all matter had existed originally as atoms, or molecules; that these atoms, infinitely numerous and infinitesimally small, had existed from all eternity; and that order was first produced out of this infinite chaos of minute atoms through the influence and operation of an eternal intelligence (nous). He also believed that all bodies are simply aggregations of atoms, for example, that a bar of gold, iron, or copper is composed of inconceivably minute particles of the same material.Anaxagoras marks a great turning point in the history of Greek philosophy: His doctrine of the nous was adopted by Aristotle, and his doctrine of atoms prepared the way for the atomic theory of the philosopher Democritus.

ANAXIMANDER (c. 611-c. 547 BCE), Greek philosopher, mathematician, and astronomer, born in Miletus in what is now Turkey. He was a disciple and friend of the Greek philosopher Thales. Anaximander is said to have discovered the obliquity of the ecliptic, that is, the angle at which the plane of the ecliptic is inclined to the celestial equator. He is credited with introducing the sundial into Greece and with inventing cartography. Anaximander's outstanding contribution was his authorship of the earliest prose work concerning the cosmos and the origins of life. He conceived of the universe as a number of concentric cylinders, of which the outermost is the sun, the middle is the moon, and the innermost is the stars. Within these cylinders is the earth, unsupported and drum-shaped. Anaximander postulated the origin of the universe as the result of the separation of opposites from the primordial material. Hot moved outward, separating from cold, and then dry from wet. Further, Anaximander held that all things eventually return to the element from which they originated.

ANAXIMENES (c. 570-500 bc), Greek philosopher of nature, the last member of the Ionian school founded by the philosopher Thales. Born at Miletus, Ionia, in Asia Minor, he held that air is the primary element to which everything else can be reduced. To explain how solid objects are formed from air, he introduced the notions of condensation and rarefaction. These processes, he claimed, make air, in itself invisible, visible as water, fire, and solid matter. He thought that air becomes warmer and turns to fire when it is rarefied and that it becomes colder and turns solid when it is condensed. His importance lies not in his cosmology but in his attempt to discover the ultimate nature of reality.

ANTISTHENES (444?-after 371 BCE), Greek philosopher, founder of the school of philosophy called Cynicism. He was born in Athens and became a disciple of Socrates. Antisthenes taught in the gymnasium known as the Cynosarges outside Athens, and his followers were called Cynics. Antisthenes regarded happiness as attainable only through virtue. He denounced art and literature, condemned luxury and comfort, and extolled hard work. His most famous pupil was the Greek Cynic philosopher Diogenes.

ARISTOTLE (384-322 BCE), Greek philosopher and scientist, who shares with Plato the distinction of being the most famous of ancient philosophers.Aristotle was born at Stagira, in Macedonia, the son of a physician to the royal court. At the age of 17, he went to Athens to study at Plato's Academy. He remained there for about 20 years, as a student and then as a teacher.When Plato died in 347 BCE, Aristotle moved to Assos, a city in Asia Minor, where a friend of his, Hermias (d. 345 BCE), was ruler. There he counseled Hermias and married his niece and adopted daughter, Pythias. After Hermias was captured and executed by the Persians, Aristotle went to Pella, the Macedonian capital, where he became the tutor of the king's young son Alexander, later known as Alexander the Great. In 335, when Alexander became king, Aristotle returned to Athens and established his own school, the Lyceum. Because much of the discussion in his school took place while teachers and students were walking about the Lyceum grounds, Aristotle's school came to be known as the Peripatetic ("walking" or "strolling") school. Upon the death of Alexander in 323 BCE, strong anti-Macedonian feeling developed in Athens, and Aristotle retired to a family estate in Euboea. He died there the following year.Works. Aristotle, like Plato, made regular use of the dialogue in his earliest years at the Academy, but lacking Plato's imaginative gifts, he probably never found the form congenial. Apart from a few fragments in the works of later writers, his dialogues have been wholly lost. Aristotle also wrote some short technical notes, such as a dictionary of philosophic terms and a summary of the doctrines of Pythagoras. Of these, only a few brief excerpts have survived. Still extant, however, are Aristotle's lecture notes for carefully outlined courses treating almost every branch of knowledge and art. The texts on which Aristotle's reputation rests are largely based on these lecture notes, which were collected and arranged by later editors.Among the texts are treatises on logic, called Organon ("instrument"), because they provide the means by which positive knowledge is to be attained. His works on natural science include Physics, which gives a vast amount of information on astronomy, meteorology, plants, and animals. His writings on the nature, scope, and properties of being, which Aristotle called First Philosophy (Prot- philosophia), were given the title Metaphysics in the first published edition of his works (c. 60 BCE), because in that edition they followed Physics. His treatment of the Prime Mover, or first cause, as pure intellect, perfect in unity, immutable, and, as he said, "the thought of thought," is given in the Metaphysics. To his son Nicomachus he dedicated his work on ethics, called the Nicomachean Ethics. Other essential works include his Rhetoric, his Poetics (which survives in incomplete form), and his Politics (also incomplete).Methods. Perhaps because of the influence of his father's medical profession, Aristotle's philosophy laid its principal stress on biology, in contrast to Plato's emphasis on mathematics. Aristotle regarded the world as made up of individuals (substances) occurring in fixed natural kinds (species). Each individual has its built-in specific pattern of development and grows toward proper self-realization as a specimen of its type. Growth, purpose, and direction are thus built into nature. Although science studies general kinds, according to Aristotle, these kinds find their existence in particular individuals. Science and philosophy must therefore balance, not simply choose between, the claims of empiricism (observation and sense experience) and formalism (rational deduction).One of the most distinctive of Aristotle's philosophic contributions was a new notion of causality. Each thing or event, he thought, has more than one "reason" that helps to explain what, why, and where it is. Earlier Greek thinkers had tended to assume that only one sort of cause can be really explanatory; Aristotle proposed four. (The word Aristotle uses, aition, "a responsible, explanatory factor" is not synonymous with the word cause in its modern sense.)These four causes are the material cause, the matter out of which a thing is made; the efficient cause, the source of motion, generation, or change; the formal cause, which is the species, kind, or type; and the final cause, the goal, or full development, of an individual, or the intended function of a construction or invention. Thus, a young lion is made up of tissues and organs, its material cause; the efficient cause is its parents, who generated it; the formal cause is its species, lion; and its final cause is its built-in drive toward maturity. In different contexts, the same four causes apply analogically. Thus, the material cause of a statue is the marble from which it was carved; the efficient cause is the sculptor; the formal cause is the shape the sculptor realized--- Hermes, perhaps; and the final cause is its function, to be a work of fine art. In each context, Aristotle insists that something can be better understood when its causes can be stated in specific terms rather than in general terms. Thus, it is more informative to know that a "sculptor" made the statue than to know that an "artist" made it; and even more informative to know that "Polycleitus" chiseled it rather than simply that a "sculptor" did so.Aristotle thought his causal pattern was the ideal key for organizing knowledge. His lecture notes present impressive evidence of the power of this scheme.Doctrines. Some of the principal aspects of Aristotle's thought can be seen in the following summary of his doctrines, or theories.Physics, or natural philosophy. In astronomy, Aristotle proposed a finite, spherical universe, with the earth at its center. The central region is made up of four elements: earth, air, fire, and water. In Aristotle's physics, each of these four elements has a proper place, determined by its relative heaviness, its "specific gravity." Each moves naturally in a straight line¾earth down, fire up¾toward its proper place, where it will be at rest. Thus, terrestrial motion is always linear and always comes to a halt. The heavens, however, move naturally and endlessly in a complex circular motion. The heavens, therefore, must be made of a fifth, and different element, which he called aither. A superior element, aither is incapable of any change other than change of place in a circular movement. Aristotle's theory that linear motion always takes place through a resisting medium is in fact valid for all observable terrestrial motions. Aristotle also held that heavier bodies of a given material fall faster than lighter ones when their shapes are the same; this mistaken view was accepted as fact until Galileo proved otherwise.Biology. In zoology, Aristotle proposed a fixed set of natural kinds ("species"), each reproducing true to type. An exception occurs, Aristotle thought, when some "very low" worms and flies come from rotting fruit or manure by "spontaneous generation." The typical life cycles are epicycles: The same pattern repeats, but through a linear succession of individuals. These processes are therefore intermediate between the changeless circles of the heavens and the simple linear movements of the terrestrial elements. The species form a scale from simple (worms and flies at the bottom) to complex (human beings at the top), but evolution is not possible.Aristotelian psychology. For Aristotle, psychology was a study of the soul. Insisting that form (the essence, or unchanging characteristic element in an object) and matter (the common undifferentiated substratum of things) always exist together, Aristotle defined a soul as a "kind of functioning of a body organized so that it can support vital functions." In considering the soul as essentially associated with the body, he challenged the Pythagorean doctrine that the soul is a spiritual entity imprisoned in the body. Aristotle's doctrine is a synthesis of the earlier notion that the soul does not exist apart from the body and of the Platonic notion of a soul as a separate, nonphysical entity. Whether any part of the human soul is immortal, and, if so, whether its immortality is personal, are not entirely clear in his treatise On the Soul.Through the functioning of the soul, the moral and intellectual aspects of humanity are developed. Aristotle argued that human insight in its highest form (nous poetikos, "active mind") is not reducible to a mechanical physical process. Such insight, however, presupposes an individual "passive mind" that does not appear to transcend physical nature. Aristotle clearly stated the relationship between human insight and the senses in what has become a slogan of empiricism¾the view that knowledge is grounded in sense experience. "There is nothing in the intellect," he wrote, "that was not first in the senses."Ethics. It seemed to Aristotle that the individual's freedom of choice made an absolutely accurate analysis of human affairs impossible. "Practical science," then, such as politics or ethics, was called science only by courtesy and analogy. The inherent limitations on practical science are made clear in Aristotle's concepts of human nature and self- realization. Human nature certainly involves, for everyone, a capacity for forming habits; but the habits that a particular individual forms depend on that individual's culture and repeated personal choices. All human beings want "happiness," an active, engaged realization of their innate capacities, but this goal can be achieved in a multiplicity of ways.Aristotle's Nicomachean Ethics is an analysis of character and intelligence as they relate to happiness. Aristotle distinguished two kinds of "virtue," or human excellence: moral and intellectual. Moral virtue is an expression of character, formed by habits reflecting repeated choices. A moral virtue is always a mean between two less desirable extremes. Courage, for example, is a mean between cowardice and thoughtless rashness; generosity, between extravagance and parsimony. Intellectual virtues are not subject to this doctrine of the mean. Aristotle argued for an elitist ethics: Full excellence can be realized only by the mature male adult of the upper class, not by women, or children, or barbarians (non-Greeks), or salaried "mechanics" (manual workers) from whom, indeed, Aristotle proposed to take away voting rights. In politics, many forms of human association can obviously be found; which one is suitable depends on circumstances, such as the natural resources, cultural traditions, industry, and literacy of each community. Aristotle did not regard politics as a study of ideal states in some abstract form, but rather as an examination of the way in which ideals, laws, customs, and property interrelate in actual cases. He thus approved the contemporary institution of slavery but tempered his acceptance by insisting that masters should not abuse their authority, inasmuch as the interests of master and slave are the same. The Lyceum library contained a collection of 158 constitutions of the Greek and other states. Aristotle himself wrote the Constitution of Athens as part of the collection, and after being lost, this description was rediscovered in a papyrus copy in 1890. Historians have found the work of great value in reconstructing many phases of the history of Athens.Logic. In logic, Aristotle developed rules for chains of reasoning that would, if followed, never lead from true premises to false conclusions (validity rules). In reasoning, the basic links are syllogisms: pairs of propositions that, taken together, give a new conclusion. For example, "All humans are mortal" and "All Greeks are humans" yield the valid conclusion "All Greeks are mortal." Science results from constructing more complex systems of reasoning. In his logic, Aristotle distinguished between dialectic and analytic. Dialectic, he held, only tests opinions for their logical consistency; analytic works deductively from principles resting on experience and precise observation. This is clearly an intended break with Plato's Academy, where dialectic was supposed to be the only proper method for science and philosophy alike. Metaphysics. In his metaphysics, Aristotle argued for the existence of a divine being, described as the Prime Mover, who is responsible for the unity and purposefulness of nature. God is perfect and therefore the aspiration of all things in the world, because all things desire to share perfection. Other movers exist as well the intelligent movers of the planets and stars (Aristotle suggested that the number of these is "either 55 or 47"). The Prime Mover, or God, described by Aristotle is not very suitable for religious purposes, as many later philosophers and theologians have observed. Aristotle limited his "theology," however, to what he believed science requires and can establish.Influence. Aristotle's works were lost in the West after the decline of Rome. During the 9th century CE, Arab scholars introduced Aristotle, in Arabic translation, to the Islamic world. The 12th-century Spanish-Arab philosopher Averroës is the best known of the Arabic scholars who studied and commented on Aristotle. In the 13th century, the Latin West renewed its interest in Aristotle's work, and St. Thomas Aquinas found in it a philosophical foundation for Christian thought. Church officials at first questioned Aquinas's use of Aristotle; in the early stages of its rediscovery, Aristotle's philosophy was regarded with some suspicion, largely because his teachings were thought to lead to a materialistic view of the world. Never-the-less, the work of Aquinas was accepted, and the later philosophy of scholasticism (q.v.) continued the philosophical tradition based on Aquinas's adaptation of Aristotelian thought.The influence of Aristotle's philosophy has been pervasive; it has even helped to shape modern language and common sense. His doctrine of the Prime Mover as final cause played an important role in theology. Until the 20th century, logic meant Aristotle's logic. Until the Renaissance, and even later, astronomers and poets alike admired his concept of the universe. Zoology rested on Aristotle's work until Charles Darwin modified the doctrine of the changelessness of species in the 19th century. In the 20th century a new appreciation has developed of Aristotle's method and its relevance to education, literary criticism, the analysis of human action, and political analysis.Not only the discipline of zoology, but the world of learning as a whole, seems to amply justify Darwin's remark that the intellectual heroes of his own time "were mere schoolboys compared to old Aristotle."

BOETHIUS (c. 480-524), Roman philosopher and statesman. He gained the esteem and confidence of Theodoric, king of the Ostrogoths, then the ruler of Rome, and in 510 was made a consul. Later Boethius was accused by his enemies of plotting treason, and, although innocent, was imprisoned in Pavia and executed. During his imprisonment he wrote De Consolatione Philosophiae (The Consolation of Philosophy, c. 523), a philosophic work that, although written by a non-Christian, contained so many elements of profound ethics that it was highly regarded in Europe during medieval times. Many translations of the work were made, notably (in England) by King Alfred the Great and by the poet Geoffrey Chaucer. Boethius also wrote treatises on logic that profoundly influenced the terminology of medieval logic; translations and commentaries on the works of Aristotle, from which medieval scholars largely derived their knowledge of the Greek philosopher; and works on music, arithmetic, and theology.

CLEANTHES (c. 331-232 BCE), Stoic philosopher and poet of ancient Greece, born in Asia Minor. While supporting himself by manual labor, he attended the lectures of the Stoic philosopher Zeno and became Zeno's successor as leader of the Stoic school after about 263 BCE. Of the more than 50 works he is said to have written, only fragments are extant; the most important of these is called the "Hymn to Zeus."

CONFUCIUS, in Chinese K'UNG FU-TZU (c. 551-479 BCE), Chinese philosopher, one of the most influential figures in Chinese history.According to tradition, Confucius was born in the state of Lu (present-day Shandong [Shantung] Province) of the noble K'ung clan. His original name was K'ung Ch'iu. His father, commander of a district in Lu, died three years after Confucius was born, leaving the family in poverty; but Confucius nevertheless received a fine education. He was married at the age of 19 and had one son and two daughters. During the four years immediately after his marriage, poverty compelled him to perform menial labors for the chief of the district in which he lived. His mother died in 527 BCE, and after a period of mourning he began his career as a teacher, usually traveling about and instructing the small body of disciples that had gathered around him. His fame as a man of learning and character and his reverence for Chinese ideals and customs soon spread through the principality of Lu. Living as he did in the second half of the Chou dynasty (c. 1027-256 BCE), when feudalism degenerated in China and intrigue and vice were rampant, Confucius deplored the contemporary disorder and lack of moral standards. He came to believe that the only remedy was to convert people once more to the principles and precepts of the sages of antiquity. He therefore lectured to his pupils on the ancient classics. He taught the great value of the power of example. Rulers, he said, can be great only if they themselves lead exemplary lives, and were they willing to be guided by moral principles, their states would inevitably become prosperous and happy. Confucius had, however, no opportunity to put his theories to a public test until, at the age of 50, he was appointed magistrate of Chung-tu, and the next year minister of crime of the state of Lu. His administration was successful; reforms were introduced, justice was fairly dispensed, and crime was almost eliminated. So powerful did Lu become that the ruler of a neighboring state maneuvered to secure the minister's dismissal. Confucius left his office in 496 BCE, traveling about and teaching, vainly hoping that some other prince would allow him to undertake measures of reform. In 484 BCE, after a fruitless search for an ideal ruler, he returned for the last time to Lu. He spent the remaining years of his life in retirement, writing commentaries on the classics. He died in Lu and was buried in a tomb at Ch'-fu, Shandong. Confucius did not put into writing the principles of his philosophy; these were handed down only through his disciples. The Lun Y (Analects), a work compiled by some of his disciples, is considered the most reliable source of information about his life and teachings. One of the historical works that he is said to have compiled and edited, the Ch'un Ch'iu (Spring and Autumn Annals), is an annalistic account of Chinese history in the state of Lu from 722 to 481 BCE. In learning he wished to be known as a transmitter rather than as a creator, and he therefore revived the study of the ancient books. His own teachings, together with those of his main disciples, are found in the Shih Shu (Four Books) of Confucian literature, which became the textbooks of later Chinese generations. Confucius was greatly venerated during his lifetime and in succeeding ages. Although he himself had little belief in the supernatural, he has been revered almost as a spiritual being by millions. The entire teaching of Confucius was practical and ethical, rather than religious. He claimed to be a restorer of ancient morality and held that proper outward acts based on the five virtues of kindness, uprightness, decorum, wisdom, and faithfulness constitute the whole of human duty. Reverence for parents, living and dead, was one of his key concepts. His view of government was paternalistic, and he enjoined all individuals to observe carefully their duties toward the state. In subsequent centuries his teachings exerted a powerful influence on the Chinese nation. See also CONFUCIANISM. W.C.L. For further information on this person, see ~BIBLIO. EASTERN RELIGIONS.

DAMON AND PHINTIAS (often incorrectly Pythias) (4th cent. BCE), philosophers of the Pythagorean school noted for their faithful friendship to each other. They lived in Syracuse, in Sicily, a city then under the rule of Dionysius the Younger. Dionysius condemned Phintias to death for plotting against his rule. Phintias requested permission to go home to arrange his private affairs, and Dionysius consented when Damon offered to remain as a hostage. Phintias was delayed and returned just as Damon was about to die in his place. Dionysius was so impressed by this example of fidelity that he pardoned Phintias and asked to share their friendship. The story has been retold in several literary works, notably in a ballad by the German poet Friedrich von Schiller and in a drama by the English playwright Richard Edwards (1523?- 66).

DEMOCRITUS (c. 460-c. 370 bc), Greek philosopher, who developed the atomic theory of the universe, which had been originated by his mentor, the philosopher Leucippus.Democritus was born in Abdera, Thrace. He wrote extensively, but only fragments of his works remain. According to his exposition of the atomic theory of matter, all things are composed of minute, invisible, indestructible particles of pure matter (atoma, "indivisibles"), which move about eternally in infinite empty space (kenon, "the void"). Although atoms are made up of precisely the same matter, they differ in shape, size, weight, sequence, and position. Qualitative differences in what the senses perceive and the birth, decay, and disappearance of things are the results not of characteristics inherent in atoms but of quantitative arrangements of atoms. Democritus viewed the creation of worlds as the natural consequence of the ceaseless whirling motion of atoms in space. Atoms collide and spin, forming larger aggregations of matter. Democritus also wrote on ethics, proposing happiness, or "cheerfulness," as the highest good, a condition to be achieved through moderation, tranquility, and freedom from fear. In later histories, Democritus was known as the Laughing Philosopher, in contrast to the more somber and pessimistic Heraclitus, the Weeping Philosopher. His atomic theory anticipated the modern principles of the conservation of energy and the irreducibility of matter. R.S.B.

EMPEDOCLES (c. 493-433 BCE), Greek philosopher, statesman, and poet, born in Agrigentum (now Agrigento), Sicily. He was a disciple of the Greek philosophers Pythagoras and Parmenides. According to tradition, he refused the crown offered to him by the people of Agrigentum after he had aided in overthrowing the ruling oligarchy. Instead he instituted a democracy.Modern knowledge of his philosophy is based on the extant fragments of his poems on nature and purification. He asserted that all things are composed of four primal elements: earth, air, fire, and water. Two active and opposing forces, love and hate, or affinity and antipathy, act upon these elements, combining and separating them into infinitely varied forms. According to Empedocles, reality is cyclical. At the beginning of a cycle, the four elements are bound together by the principle of love. When hate penetrates the cycle, the elements begin to separate. Love reunites everything; then hate begins the process once again. The world as we know it is halfway between the primary sphere and the stage of total separation of the elements. Empedocles believed also that no change involving the creation of new matter is possible; only changes in the combinations of the four existing elements may occur. He also formulated a primitive theory of evolution in which he declared that humans and animals evolved from antecedent forms.

EPICTETUS (c. 55-135), name given to a Greek philosopher whose real name is unknown, and who was probably born at Hierapolis, Phrygia (now in Turkey). Although a slave, as a youth he studied the philosophy of Stoicism. His master subsequently granted him his freedom, and until 90 he taught philosophy at Rome. In that year the emperor Domitian, fearful of the dangers engendered by the teachings of the Stoics, exiled Epictetus and several other philosophers. Epictetus settled at Nicopolis, in southern Epirus, where he died. His doctrines have been preserved in two works compiled by his pupil, the Greek historian and philosopher Arrian: the Encheiridion (Handbook), the whole of which is extant, and Discourses of Epictetus, of which four of eight books survive. According to these works, Epictetus was concerned chiefly with the problem of morality, that is, of defining the good life. He asserted that humans are basically limited and irrational beings, but that the universe, ruled by God through pure reason, is perfect. Because human beings can neither know nor control their destiny, they must cease striving for the attainment of worldly ends and instead calmly accept the fact of their own powerlessness before fate. As a corollary of this doctrine, Epictetus held that a person must, because of his or her own weakness, be tolerant of the faults of others.

EUCLID OF MEGARA (fl. about 300 BCE), Greek philosopher and founder of the Megarian school of philosophy, born in Megara. One of the chief disciples of Socrates, Euclid combined the Socratic philosophy that virtue is knowledge with the Eleatic concept of the universe as a changeless unity that can be understood only by philosophic reflection.

GORGIAS (c. 485-c. 380 BCE), Greek rhetorician and Sophistic philosopher (see SOPHISTS). Gorgias was born in Leontini, Sicily. He served as an ambassador to Athens in 427 BCE and later settled in Athens to practice and teach the art of rhetoric (q.v.). As a rhetorician, Gorgias was among the first to introduce cadence into prose and to utilize commonplaces in arguments. He is the title character of Plato's dialogue Gorgias, in which Socrates discusses true and false rhetoric and rhetoric as the art of flattery. Gorgias's philosophy is a nihilistic one, expressed in three propositions: Nothing exists; if anything does exist, it cannot be known; if anything exists and can be known, it cannot be communicated. The extant works by Gorgias are The Encomium on Helen and The Apology of Palamedes. He died in Thessaly at the age of 105.

HERACLITUS (c. 540-c. 475 BCE), Greek philosopher, born in Ephesus in Asia Minor. Because of the loneliness of his life and the obscurity and misanthropy of his philosophy, he was called the dark philosopher or weeping philosopher. Heraclitus was in a sense one of the founders of Greek metaphysics, although his ideas stem from those of the Ionian school of Greek philosophy. He postulated fire as the primal substance or principle that, through condensation and rarefaction, creates the phenomena of the sensible world. Heraclitus added to the "being" of his predecessors the concept of "becoming," or flux, which he took to be a basic reality underlying all things, even the most apparently stable. In ethics, he introduced a new social emphasis, holding virtue to consist in a subordination of the individual to the laws of a universal, reasonable harmony. Although his thought was strongly tinged with elements of popular theology, he attacked the concepts and ceremonies of the popular religion of his day. Only one work, On Nature, is definitely attributable to Heraclitus. Numerous fragments of this work were preserved by later writers, and collected editions of all his surviving fragments may be found in several modern editions.

IAMBLICHUS (c. 250-c. 330), Syrian philosopher, a major figure and exponent of Neoplatonism (q.v.). He was born in Chalcis, Coele-Syria. A student of the philosopher Porphyry (c. 232- c. 304) in Rome, Iamblichus came under the influence of the Greek Neoplatonist philosopher Plotinus. In Syria he established his own school, which attempted to fuse Plato's ideas, those of the Greek mathematician and philosopher Pythagoras, and certain mystic and even magical elements of Oriental religion into a single coherent system. Iamblichus succeeded in transforming the intellectual and purely spiritual Neoplatonism of Plotinus into an even more intricate form of pagan religious philosophy that included myths, rites, and magical formulas. Among his works are On the Egyptian Mysteries (trans. 1821) and On the Pythagorean Life (trans. 1937).

MENCIUS (c. 371-c. 288 BCE), Chinese philosopher, who is also known as Mengtse. He was born in Chao (now in Shandong Province). After studying the philosophy of Confucius, he traveled for years expounding Confucianism and lecturing rulers on their duties toward their subjects. He believed that the power to govern comes from God and should be exercised in the interests of the common people. He opposed warfare except for purposes of defense. According to tradition, Mencius spent the latter part of his life in seclusion with his disciples. In his teachings he stressed the belief that people are by nature good, but that this goodness becomes manifest only when they experience peace of mind, which in turn depends on material security. If rulers, therefore, reduce their subjects to poverty and selfishness, they should be deposed. Since the 11th century Mencius has been recognized as one of China's greatest philosophers; the Mencius (Book of Mencius) is regarded as a basic Confucian text.

NAGARJUNA (fl. about CE 200), Indian Buddhist philosopher, founder of the Madhyamika (Middle Path) school of Mahayana Buddhism (see BUDDHISM). Various dates are given for his life, but it is likely that he flourished in the mid 2d or the 3d century CE. Tibetan tradition identifies him with an 8th-century magician-alchemist. Nagarjuna was born probably in southern India of Brahman (priestly) stock. He studied both the secular and religious branches of Hindu knowledge before converting to Buddhism. He spent most of his life in the great Mahayana centers of learning in southeast India. Two texts most clearly present his views: the Mula-Madhyamika Karikas (Fundamentals of the Middle Way) and the Vigrahavyavartani (Treatise on Averting the Arguments).Madhyamika is characterized by its logical refutation of other systems, Buddhist and non-Buddhist alike, while claiming no thesis of its own. It takes a middle path, affirming neither existence nor nonexistence, permanence nor impermanence, identity nor difference. Nagarjuna stressed the concept of emptiness (sunyata) as a way of showing the relativity of all conceptions. Even the basic elements of existence (dharmas) are taken to be void of ultimate reality. Together with the Vijnanavada school (Consciousness Only), Madhyamika forms the keystone of Mahayana Buddhist philosophical thought. J.P.M.

PARMENIDES (b. about 515 bc), Greek philosopher, considered by many scholars the greatest member of the Eleatic school. He is said to have visited Athens at the age of 65, and on that occasion Socrates, then a young man, heard him speak. Parmenides expounded his philosophy in verse form, his only surviving work being large fragments of a didactic poem, On Nature. This work demonstrated the reality of Absolute Being, the nonexistence of which Parmenides declared to be inconceivable, but the nature of which, on the other hand, he admitted to be equally inconceivable, inasmuch as it is dissociated from every limitation under which human beings think. Parmenides held that the phenomena of nature are only apparent and due to human error; they seem to exist, but have no real existence. He also held that reality, True Being, is not known to the senses but is to be found only in reason. This belief makes him a precursor of the idealism of Plato. Parmenides' theory that Being cannot arise from Nonbeing, and that Being neither arises nor passes away, was applied to matter by his successors Empedocles and Democritus, who made it the foundation of their materialistic explanations of the universe.

PLATO (c. 428-c. 347 BCE), Greek philosopher, one of the most creative and influential thinkers in Western philosophy. Life. Plato was born to an aristocratic family in Athens. His father, Ariston, was believed to have descended from the early kings of Athens. Perictione, his mother, was distantly related to the 6th-century BCE lawmaker Solon. When Plato was a child, his father died, and his mother married Pyrilampes, who was an associate of the statesman Pericles. As a young man Plato had political ambitions, but he became disillusioned by the political leadership in Athens. He eventually became a disciple of Socrates, accepting his basic philosophy and dialectical style of debate: the pursuit of truth through questions, answers, and additional questions. Plato witnessed the death of Socrates at the hands of the Athenian democracy in 399 BCE. Perhaps fearing for his own safety, he left Athens temporarily and traveled to Italy, Sicily, and Egypt. In 387 Plato founded the Academy in Athens, the institution often described as the first European university. It provided a comprehensive curriculum, including such subjects as astronomy, biology, mathematics, political theory, and philosophy. Aristotle was the Academy's most prominent student. Pursuing an opportunity to combine philosophy and practical politics, Plato went to Sicily in 367 to tutor the new ruler of Syracuse, Dionysius the Younger, in the art of philosophical rule. The experiment failed. Plato made another trip to Syracuse in 361, but again his engagement in Sicilian affairs met with little success. The concluding years of his life were spent lecturing at the Academy and writing. He died at about the age of 80 in Athens in 348 or 347 BCE. Works. Plato's writings were in dialogue form; philosophical ideas were advanced, discussed, and criticized in the context of a conversation or debate involving two or more persons. The earliest collection of Plato's work includes 35 dialogues and 13 letters. The authenticity of a few of the dialogues and most of the letters has been disputed. Early dialogues. The dialogues may be divided into early, middle, and later periods of composition. The earliest represent Plato's attempt to communicate the philosophy and dialectical style of Socrates. Several of these dialogues take the same form. Socrates, encountering someone who claims to know much, professes to be ignorant and seeks assistance from the one who knows. As Socrates begins to raise questions, however, it becomes clear that the one reputed to be wise really does not know what he claims to know, and Socrates emerges as the wiser one because he at least knows that he does not know. Such knowledge, of course, is the beginning of wisdom. Included in this group of dialogues are Charmides (an attempt to define temperance), Lysis (a discussion of friendship), Laches (a pursuit of the meaning of courage), Protagor as (a defense of the thesis that virtue is knowledge and can be taught), Euthyphro (a consideration of the nature of piety), and Book I of the Republic (a discussion of justice). Middle and late dialogues. The dialogues of the middle and later periods of Plato's life reflect his own philosophical development. The ideas in these works are attributed by most scholars to Plato himself, although Socrates continues to be the main character in many of the dialogues. The writings of the middle period include Gorgias (a consideration of several ethical questions), Meno (a discussion of the nature of knowledge), the Apology (Socrates' defense of himself at his trial against the charges of atheism and corrupting Athenian youth), Crito (Socrates' defense of obedience to the laws of the state), Phaedo (the death scene of Socrates, in which he discusses the theory of Forms, the nature of the soul, and the question of immortality), the Symposium (Plato's outstanding dramatic achievement, which contains several speeches on beauty and love), the Republic (Plato's supreme philosophical achievement, which is a detailed discussion of the nature of justice).The works of the later period include the Theaetetus (a denial that knowledge is to be identified with sense perception), Parmenides (a critical evaluation of the theory of Forms), Sophist (further consideration of the theory of Ideas, or Forms), Philebus (a discussion of the relationship between pleasure and the good), Timaeus (Plato's views on natural science and cosmology), and the Laws (a more practical analysis of political and social issues). Theory of Forms. At the heart of Plato's philosophy is his theory of Forms, or Ideas. Ultimately, his view of knowledge, his ethical theory, his psychology, his concept of the state, and his perspective on art must be understood in terms of this theory. Theory of knowledge. Plato's theory of Forms and his theory of knowledge are so interrelated that they must be discussed together. Influenced by Socrates, Plato was convinced that knowledge is attainable. He was also convinced of two essential characteristics of knowledge. First, knowledge must be certain and infallible. Second, knowledge must have as its object that which is genuinely real as contrasted with that which is an appearance only. Because that which is fully real must, for Plato, be fixed, permanent, and unchanging, he identified the real with the ideal realm of being as opposed to the physical world of becoming. One consequence of this view was Plato's rejection of empiricism (q.v.), the claim that knowledge is derived from sense experience. He thought that propositions derived from sense experience have, at most, a degree of probability. They are not certain. Furthermore, the objects of sense experience are changeable phenomena of the physical world. Hence, objects of sense experience are not proper objects of knowledge. Plato's own theory of knowledge is found in the Republic, particularly in his discussion of the image of the divided line and the myth of the cave. In the former, Plato distinguishes between two levels of awareness: opinion and knowledge. Claims or assertions about the physical or visible world, including both commonsense observations and the propositions of science, are opinions only. Some of these opinions are well founded; some are not; but none of them counts as genuine knowledge. The higher level of awareness is knowledge, because there reason, rather than sense experience, is involved. Reason, properly used, results in intellectual insights that are certain, and the objects of these rational insights are the abiding universals, the eternal Forms or substances that constitute the real world. The myth of the cave describes individuals chained deep within the recesses of a cave. Bound so that vision is restricted, they cannot see one another. The only thing visible is the wall of the cave upon which appear shadows cast by models or statues of animals and objects that are passed before a brightly burning fire. Breaking free, one of the individuals escapes from the cave into the light of day. With the aid of the sun, that person sees for the first time the real world and returns to the cave with the message that the only things they have seen heretofore are shadows and appearances and that the real world awaits them if they are willing to struggle free of their bonds. The shadowy environment of the cave symbolizes for Plato the physical world of appearances. Escape into the sun-filled setting outside the cave symbolizes the transition to the real world, the world of full and perfect being, the world of Forms, which is the proper object of knowledge. Nature of Forms. The theory of Forms may best be understood in terms of mathematical entities. A circle, for instance, is defined as a plane figure composed of a series of points, all of which are equidistant from a given point. No one has ever actually seen such a figure, however. What people have actually seen are drawn figures that are more or less close approximations of the ideal circle. In fact, when mathematicians define a circle, the points referred to are not spatial points at all; they are logical points. They do not occupy space. Nevertheless, although the Form of a circle has never been seen, indeed, could never be seen, mathematicians and others do in fact know what a circle is. That they can define a circle is evidence that they know what it is. For Plato, therefore, the Form "circularity" exists, but not in the physical world of space and time. It exists as a changeless object in the world of Forms or Ideas, which can be known only by reason. Forms have greater reality than objects in the physical world both because of their perfection and stability and because they are models, resemblance to which gives ordinary physical objects whatever reality they have. Circularity, squareness, and triangularity are excellent examples, then, of what Plato meant by Forms. An object existing in the physical world may be called a circle or a square or a triangle only to the extent that it resembles ("participates in" is Plato's phrase) the Form "circularity" or "squareness" or "triangularity." Plato extended his theory beyond the realm of mathematics. Indeed, he was most interested in its application in the field of social ethics. The theory was his way of explaining how the same universal term can refer to so many particular things or events. The word justice, for example, can be applied to hundreds of particular acts because these acts have something in common, namely, their resemblance to, or participation in, the Form "justice." An individual is human to the extent that he or she resembles or participates in the Form "humanness." If "humanness" is defined in terms of being a rational animal, then an individual is human to the extent that he or she is rational. A particular act is courageous or cowardly to the extent that it participates in its Form. An object is beautiful to the extent that it participates in the Idea, or Form, of beauty. Everything in the world of space and time is what it is by virtue of its resemblance to, or participation in, its universal Form. The ability to define the universal term is evidence that one has grasped the Form to which that universal refers. Plato conceived the Forms as arranged hierarchically; the supreme Form is the Form of the Good, which, like the sun in the myth of the cave, illuminates all the other Ideas. There is a sense in which the Form of the Good represents Plato's movement in the direction of an ultimate principle of explanation. Ultimately, the theory of Forms is intended to explain how one comes to know and also how things have come to be as they are. In philosophical language, Plato's theory of Forms is both an epistemological (theory of knowledge) and an ontological (theory of being) thesis. Political Theory. The Republic, Plato's major political work, is concerned with the question of justice and therefore with the questions "what is a just state" and "who is a just individual?" The ideal state, according to Plato, is composed of three classes. The economic structure of the state is maintained by the merchant class. Security needs are met by the military class, and political leadership is provided by the philosopher-kings. A particular person's class is determined by an educational process that begins at birth and proceeds until that person has reached the maximum level of education compatible with interest and ability. Those who complete the entire educational process become philosopher-kings. They are the ones whose minds have been so developed that they are able to grasp the Forms and, therefore, to make the wisest decisions. Indeed, Plato's ideal educational system is primarily structured so as to produce philosopher-kings. Plato associates the traditional Greek virtues with the class structure of the ideal state. Temperance is the unique virtue of the artisan class; courage is the virtue peculiar to the military class; and wisdom characterizes the rulers. Justice, the fourth virtue, characterizes society as a whole. The just state is one in which each class performs its own function well without infringing on the activities of the other classes. Plato divides the human soul into three parts: the rational part, the will, and the appetites. The just person is the one in whom the rational element, supported by the will, controls the appetites. An obvious analogy exists here with the threefold class structure of the state, in which the enlightened philosopher-kings, supported by the soldiers, govern the rest of society. Ethics. Plato's ethical theory rests on the assumption that virtue is knowledge and can be taught, which has to be understood in terms of his theory of Forms. As indicated previously, the ultimate Form for Plato is the Form of the Good, and knowledge of this Form is the source of guidance in moral decision making. Plato also argued that to know the good is to do the good. The corollary of this is that anyone who behaves immorally does so out of ignorance. This conclusion follows from Plato's conviction that the moral person is the truly happy person, and because individuals always desire their own happiness, they always desire to do that which is moral. Art. Plato had an essentially antagonistic view of art and the artist, although he approved of certain religious and moralistic kinds of art. Again, his approach is related to his theory of Forms. A beautiful flower, for example, is a copy or imitation of the universal Forms "flowerness" and "beauty." The physical flower is one step removed from reality, that is, the Forms. A picture of the flower is, therefore, two steps removed from reality. This also meant that the artist is two steps removed from knowledge, and, indeed, Plato's frequent criticism of the artists is that they lack genuine knowledge of what they are doing. Artistic creation, Plato observed, seems to be rooted in a kind of inspired madness. Influence. Plato's influence throughout the history of philosophy has been monumental. When he died, Speusippus (407?-339BCE) became head of the Academy. The school continued in existence until CE 529, when it was closed by the Byzantine emperor Justinian I, who objected to its pagan teachings. Plato's impact on Jewish thought is apparent in the work of the 1st-century Alexandrian philosopher Philo Judaeus. Neoplatonism (q.v.), founded by the 3d-century philosopher Plotinus, was an important later development of Platonism. The theologians Clement of Alexandria, Origen, and St. Augustine were early Christian exponents of a Platonic perspective. Platonic ideas have had a crucial role in the development of Christian theology and also in medieval Islamic thought (see ISLAM). During the Renaissance (q.v.), the primary focus of Platonic influence was the Florentine Academy, founded in the 15th century near Florence. Under the leadership of Marsilio Ficino, members of the Academy studied Plato in the original Greek. In England, Platonism was revived in the 17th century by Ralph Cudworth and others who became known as the Cambridge Platonists (q.v.). Plato's influence has been extended into the 20th century by such thinkers as Alfred North Whitehead, who once paid him tribute by describing the history of philosophy as simply "a series of footnotes to Plato." See also GREEK PHILOSOPHY; IDEALISM; METAPHYSICS; PHILOSOPHY. R.M.B. For further information on this topic, see ~BIBLIO. GREEK PHILOSOPHY.

PROTAGORAS (480?-411? BCE), Greek philosopher, born in Abdera, Thrace. About 445 BCE he went to Athens, where he befriended the statesman Pericles and won great fame as a teacher and philosopher. Protagor as was the first thinker to call himself a Sophist and to teach for pay, receiving large sums from his pupils. He gave instruction in grammar, rhetoric, and the interpretation of poetry. His chief works, of which only a few fragments have survived, were entitled Truth and On the Gods. The basis of his speculation was the doctrine that nothing is absolutely good or bad, true or false, and that each individual is his or her own final authority; this belief is summed up in his saying: "Man is the measure of all things." Charged with impiety, he fled into exile; he drowned on his way to Sicily. Two dialogues by Plato, the Theaetetus and the Protagor as, refuted the doctrines of Protagor as. G.E.D.

PYRRHO (c. 360-c. 272 bc), ancient Greek philosopher, who introduced pure skepticism (q.v.) into Greek philosophy, founding the school known as Pyrrhonism, and who is thus considered the founder of philsophical skepticism. He was born in Elis and studied with the Greek philosopher Anaxarchus (fl. about 350 BCE), a disciple of the Greek philosopher Democritus. Pyrrho accompanied Alexander the Great on his expedition to the East, and became acquainted with the teachings of the Persian magi (q.v.) and the Indian Brahmans (see BRAHMAN). Much of Pyrrho's long life was spent in seclusion. He did not put his doctrines into writing, and they are known chiefly from the works of his follower Timon of Phlius (fl. about 280 BCE), a philosopher and writer of satires. Pyrrho taught that the real nature of things can never be truly comprehended, and hence objective knowledge is impossible to attain. He held that the correct attitude for the philosopher is imperturbability and complete suspension of judgment, and that in this attitude lies freedom from passion, calmness of mind, and tranquility of soul, which constitute the highest human qualities.

PYTHAGORAS (582?-500? BCE), Greek philosopher and mathematician, whose doctrines strongly influenced Plato. Born on the island of Sámos, Pythagor as was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes. He is said to have been driven from Sámos by his disgust for the tyranny of Polycrates (r. about 533-522 BCE). About 530 BCE he settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. The philosophy of Pythagor as is known only through the work of his disciples. Basic Doctrines. The Pythagoreans adhered to certain mysteries, similar in many respects to the Orphic mysteries (see MYSTERIES; ORPHISM). Obedience and silence, abstinence from food, simplicity in dress and possessions, and the habit of frequent self-examination were prescribed. The Pythagoreans believed in immortality and in the transmigration of souls. Pythagoras himself was said to have claimed that he had been Euphorbus, a warrior in the Trojan War, and that he had been permitted to bring into his earthly life the memory of all his previous existences. Theory of Numbers. Among the extensive mathematical investigations carried on by the Pythagoreans were their studies of odd and even numbers and of prime and square numbers. From this arithmetical standpoint they cultivated the concept of number, which became for them the ultimate principle of all proportion, order, and harmony in the universe. Through such studies they established a scientific foundation for mathematics. In geometry the great discovery of the school was the hypotenuse theorem, or Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides; Pythagorean numbers are numbers so related, for instance, 5, 4, and 3 (52 = 42 + 32). Astronomy. The astronomy of the Pythagoreans marked an important advance in ancient scientific thought, for they were the first to consider the earth as a globe revolving with the other planets, including the sun, around a central fire. They explained the harmonious arrangement of things as that of bodies in a single, all-inclusive sphere of reality, moving according to a numerical scheme. Because the Pythagoreans thought that the heavenly bodies are separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound, the "harmony of the spheres."

SOCRATES (c. 470-399 BCE), Greek philosopher, who profoundly affected Western philosophy through his influence on Plato. Born in Athens, the son of Sophroniscus, a sculptor, and of Phaenarete, a midwife, he received the regular elementary education in literature, music, and gymnastics. Later he familiarized himself with the rhetoric and dialectics of the Sophists, the speculations of the Ionian philosophers, and the general culture of Periclean Athens. Initially, Socrates followed the craft of his father; according to a former tradition, he executed a statue group of the three Graces, which stood at the entrance to the Acropolis until the 2d century CE. In the Peloponnesian War with Sparta he served as an infantryman with conspicuous bravery at the battles of Potidaea in 432-430 BCE, Delium in 424 BCE, and Amphipolis in 422 BCE. Socrates believed in the superiority of argument over writing and therefore spent the greater part of his mature life in the marketplace and public resorts of Athens in dialogue and argument with anyone who would listen or who would submit to interrogation. Socrates was unattractive in appearance and short of stature but was also extremely hardy and self-controlled. He enjoyed life immensely and achieved social popularity because of his ready wit and a keen sense of humor that was completely devoid of satire or cynicism. Attitude Toward Politics. Socrates was obedient to the laws of Athens, but he generally held aloof from politics, restrained by what he believed to be divine warning. He considered that he had received a call to the pursuit of philosophy and could serve his country best by devoting himself to teaching and by persuading the Athenians to engage in self-examination and in tending to their souls. He wrote no books and established no regular school of philosophy. All that is known with certainty about his personality and his way of thinking is derived from the works of two of his distinguished scholars: Plato, who at times ascribed his own views to his master, and the historian Xenophon, a prosaic writer, who probably failed to understand many of Socrates' doctrines. Plato represents Socrates as hiding behind an ironical profession of ignorance, known as Socratic irony, and possessing a mental acuity and resourcefulness that enabled him to penetrate arguments with great facility. Teachings. Socrates' contribution to philosophy was essentially ethical in character. Belief in a purely objective understanding of such concepts as justice, love, and virtue, and the self-knowledge that he inculcated, were the basis of his teachings. He believed that all vice is the result of ignorance, and that no person is willingly bad; correspondingly, virtue is knowledge, and those who know the right will act rightly. His logic placed particular emphasis on rational argument and the quest for general definitions, as evidenced in the writings of his younger contemporary and pupil Plato and of Plato's pupil Aristotle. Through the writings of these philosophers Socrates had a profound effect on the entire subsequent course of Western speculative thought. Another thinker befriended and influenced by Socrates was Antisthenes, the founder of the Cynic school of philosophy. Socrates was also the teacher of Aristippus, who founded the Cyrenaic philosophy of experience and pleasure, from which developed the more lofty philosophy of Epicurus. The ideal Socrates, depicted in Plato's Apology, Crito, Gorgias, and Phaedo, became, as the influence of the ancient Greek and Roman divinities waned, the chief religious type of the ancient world. To such Stoics as the Greek philosopher Epictetus, the Roman philosopher Marcus (or Lucius) Annaeus Seneca the Elder (c. 55 BCE-c. CE 39), and the Roman emperor Marcus Aurelius, he appeared as the very embodiment and guide of the higher life. The Trial. Although a patriot and a man of deep religious conviction, Socrates was nonetheless regarded with suspicion by many of his contemporaries, who disliked his attitude toward the Athenian state and the established religion. He was charged in 399 BCE with neglecting the gods of the state and introducing new divinities, a reference to the daemonion, or mystical inner voice, to which Socrates often referred. He was also charged with corrupting the morals of the young, leading them away from the principles of democracy; and he was wrongly identified with the Sophists, possibly because he had been ridiculed by the comic poet Aristophanes in the Clouds as the master of a "thinking-shop" where young men were taught to make the worse reason appear the better reason. Plato's Apology gives the substance of the defense made by Socrates at his trial; it was a bold vindication of his whole life. He was condemned to die, although the vote was carried by only a small majority. When, according to Athenian legal practice, Socrates made an ironic counterproposition to the court's death sentence, proposing only to pay a small fine because of his value to the state as a man with a philosophic mission, this offer so angered the jury that it voted by an increased majority for the death penalty. Socrates' friends planned his escape from prison, but he preferred to obey the law and die for his cause. His last day was spent with his friends and admirers, as described in Plato's Phaedo, and in the evening he calmly fulfilled his sentence by drinking a cup of hemlock according to a customary procedure of execution. He was married to Xanthippe, a reputedly shrewish woman, and had three children.

THALES (c. 625-546 BCE), Greek philosopher, born in Miletus, Asia Minor. He was the founder of Greek philosophy, and was considered one of the Seven Wise Men of Greece. Thales became famed for his knowledge of astronomy after predicting the eclipse of the sun that occurred on May 28, 585 BCE. He is also said to have introduced geometry in Greece. According to Thales, the original principle of all things is water, from which everything proceeds and into which everything is again resolved. Before Thales, explanations of the universe were mythological, and his concentration on the basic physical substance of the world marks the birth of scientific thought. Thales left no writings; knowledge of his teachings is derived from an account in Aristotle's Metaphysics.

ZENO OF CITIUM (fl. late 4th and early 3d cent. BCE), Greek philosopher, founder of Stoicism (q.v.). He was born in Citium, Cyprus. Little is known of his early life except that his contemporaries referred to him as a Phoenician. He was a student of the 4th century BCE Cynic philosopher Crates of Thebes (365?-285 BCE) and of the Platonist Xenocrates. About 300 BCE, Zeno founded his own school of philosophy, known as Stoicism. The name of the school was derived from Stoa Poikil- ("painted porch"), the name given to the public portico where the master taught his disciples. Moral obligation, self-control, and living in harmony with nature were some of the principles of practical ethics with which Zeno was chiefly concerned. He taught in Athens for more than 50 years and was publicly honored for his upright manner of living. It is said, however, that he refused the offer of Athenian citizenship out of loyalty to his native Cyprus. Zeno left no written accounts of his teachings, but they were transmitted by his many disciples.