APEIRON---boundless, unlimited
ARCHEAITIAI (Physics, 194b16-195a3, tr. R. Hardie " R. Gaye), including:
These definitions sustained a long influence, extending to St. Thomas Aquinas' four ways to demonstrate the existence of God.
ARETEARETE is traditionally translated as "virtue," but it has in Greek both a broader and a more specific meaning. Things as well as people have their own special ARETE. The ARETE of a chimney, for example, consists in the reliability of its draw in various climatological conditions and in the efficiency of its shape, which reflects heat into the room and conducts smoke through the roof. ARETE is excellence within a kind. The ARETE of a spinter is speed, of a long-distance runner endurance, of a knight, horsemanship, of a foot-soldier courage, etc. An instance of a type that posseses, exhibits, or exemplifies the particular ARETE of that type is AGATHOS ("good.") (Recall Dustin Hoffman's character in Rainman: " I am an excellent driver." In ancient Greek this would be rendered as: " I am an AGATHOS driver," meaning " I possess and exhibit the ARETE of driving.") For introducing Greek concepts such as ARETE to what the British once dismissively referred to as "Greek-less readers" there is still no greater nor more imaginative guide than A. W. H. Adkins.
BOULE-- Council of Five Hundred
ARCHE
COSMOS or ordered world. In Greek traditions the cosmos represents a triumph of order over prevailing CHAOS that pre-existed it and that, in many accounts, poses a continual threat. Things might just "fall apart, the center (might) not hold" Yeats' imagery would have been immediately understandable to the ancient Greeks. (Cp. the account in Genesis of the creation of the world, "and God moved upon the face the deep" which implies a preexisting, disordered background.) Order, of course, is formal. Hence the seeds of the Greek philosophical fascination with form are embedded in the ancient stories. Chaos is dis-order, hence bad, pernicious, dark, even black (yes, our color imagery plays its role in racism) and ugly. (Nothing ugly could be good. When Odysseus justifies beating up on the hapless Thersites Iliad, 2.212ff he tops off his list of offences with the observation that Thersites is ugly. Socrates went out of his way to emphasize his lack of physical beauty, his pugnosed ugliness, which he turned in his characteristic way to ironic advantage. "Cosmo" means beautiful, as Helen Gurley Brown knows.)
ELENCHUS--Refutation
EKKLESIA-- Assembly
EUDAIMONIA
PANTALOS ON, PANTELOS GNOSTON.) From the Pythagoreans, he took to heart the lesson that mathematics gives us privileged access to perfect, intelligiblt, immaterial "objects." In mathematics we make use of physical representations (we name them in Greek "diagrams") which we treatv as approximations to the real objects of our inquiries. In Plato's phrase in the Phaedo Plato says that instantiations of a form are "trying to be like" the pure form itself. This idea merges with the concept of ARETE. Every kind or species has its on specific excellence, and each of its instances, exemplars instantiations is striving to exemplify that specific excellence.
LOGOSLOGOS signified in Greek both speech and reason, and as Greek thinkers became increasingly fascinated with the magic and mystery of language's ability to connect with the world, LOGOS assumed ever more technical and metaphysical characteristics. This process can be traced to Heraclitus, although there remains considerable doubt as to what precisely he meant by LOGOS. In some contexts Heraclitus seems to suggest that the LOGOS is the underlying, intelligible law of the universe, the common, unifying principle in all things. Certainly this is how the later Stoics interpreted Heraclitus. (It was convenient from their point of view that Heraclitus was fascinated both by fire and the LOGOS, but some considerable element in their interpretation must be discounted as anachronistic projection.) Still, from the dawn of an idea as abstract as the very concept of speech and reason, one tendency in Western philosophy developed the notion of an underlying law or rationality of the universe and of its connection with the reason, understanding, and linguistic abilities of human beings. LOGOS to identify divine Wisdom. The term came to play a central role in the philosophy of Philo, a Jewish philosopher and Platonist of the turn of the common era. In Philo's thought, LOGOS plays multiple roles. It is the divine "template" of which the visible world is a copy; it is the divine power of manifestation, process, and unfolding in that world; and it is the agent of creation, an intermediary or DEMIOURGOS, following Plato's Timaeus, that realizes God's plan. (Without being glib or disrespectful, I would suggest that it is useful to think of the DEMIOURGOS as a sort of Cosmic General Contractor.)In the beginning was theLOGOSand theLOGOSwas with God and theLOGOSwas God. All things were made by Him and without Him was not anything made that was Made. In Him was life and the life was the light of the world. (John, 1.1-3)And the
LOGOSbecame flesh and dwelt among us. (John 1.14)
NOMOS/PHYSIS DebateNOMOS and PHYSIS. The debate was vigorous. It appeared as a theme in political discourse, in historical writings, in philosophy, and in dramatic literature.NOMOS originally referred to an allotment, custom, or practice, and by extension to enacted (so-called "positive") law. A pasture was NOMOS, a parcel of land acknowledged by custom and tradition as belonging to a particular family. NOMOS is prescriptive: customs not only prevail, they are right. Violations of NOMOS are not only contrary to custom, they are enjoined and proscribed. But from relatively early in Greek experience, NOMOS was also associated with variability. The so-called "logographers," early prose writers who specialized in travelogs and anthropology, related tales of quaint and exotic customs (NOMOI) practiced by non-Greek peoples. (Herodotus offers many examples.) From these writers Greeks became aware that customs NOMOI were not necessarily universal.PHYSIS was a word related to growth, birth, and development. It came to mean "nature," which, after all, has similar etymological roots in Latin. By the time of Aristotle "On Nature" (PERI PHSYEOS) had become the standard, interchangeable title of the surviving works of the Presocratic philosophers. PHYSIS referred to the essential nature of a thing, as opposed to its acquired characteristics. As such, PHYSIS took on connotations of permanence and inviolability, and by extension came to refer to how things really are, as opposed to how they may appear. (Parmenides' poem PERI PHSYEOS is an example.)NOMOI) expanded, the question arose whether what given custom regards as dishonorable or abhorrent is so merely by convention, or whether certain practices or even customs themselves actually are unnatural (contrary to PHYSIS.) This debate continues to be vigorous and contentious in our own day.NOMOS were Protagoras, Critias, and the so-called Iamblicus. The champions of the view that NOMOI are conventions designed to keep us in our place include Antiphon, Callicles (represented in Plato's Gorgias, and Thrasymachus (made famous from Plato's Republic, Bk 1.) (Richard McKirahan numbers Thucydides among this group. McKirahan's account (pp. 390-413) of all these issues is nuanced and very useful.)
NOUS
OUSIA
POLIS
An aura of mystery surrounds their life and origins. Pythagoras of Samos was their leader, but legend had already clouded accounts of his life by the time of Aristotle just a century and a half later. It is now generally agreed that Pythagoras left Samos, an island off the coast of Ionia, and moved west to establish a colony at Croton, on the extreme southeastern coast of mainland Italy. The colony prospered under the laws Pythagoras is said to have provided. (See comment on Lawgivers above.) The Pythagoreans lived a structured, religious life. They took their vegetarian meals in common, worked and studied together, and observed strict rituals of purity and diligence. They regarded wisdom as something rare, appropriate only for the initiates. Idle talk about their beliefs was forbidden, as were written accounts. Although some of their views were widely known and influential, the prohibition against written accounts of their philosophy probably went unchallenged for more than 150 years, until the impoverished Philolaus succumbed to Plato's urging that he write a book, which Plato persuaded his patron, Dion, the tyrant of Syracuse, to buy.
Pythagoreanism had the following important elements. Purity and communitarianism were encouraged. Women, as well as men, were welcome. A ritualistic regimen and dietetic laws were observed (no meat was the most striking rule.) The soul was thought to be the principle of life that goes through cycles "trapped" in physical bodies. The body was sometimes called a tomb. (Plato's Phaedo provides an important and sympathetic summary of this outlook.) In this respect Pythagoreanism may represent the most ancient Greek ascetic philosophy. The doctrine of the transmigration of the soul (metempsychosis) implies a concept of reincarnation that has much in common with Indian traditions. Whether the influence actually extended that far is doubtful, but recurrent if unsubstantiated ancient traditions held that Pythagoras travelled widely, and may have visited Egypt and perhaps even Babylon. The ordered world or COSMOS depended, on the Pythagorean view, on HARMONIA. The soul is a kind of harmony or fine tuning of the body, as is so poignantly explained in the Phaedo. Where discord or dissonance prevail, there CHAOS overwhelms the COSMOS.
Our sources all broadly agree that musical discoveries were crucial to the development of the Pythagorean philosophy. Pythagoras or some other early member of his society either discovered or learned from some non-Greek source that the relationships among pitches which we call "octaves," "fifths, " "fourths," etc. obtain for all tunings of taut strings, independent of their length, thickness, or composition. They correlate simply and directly with ratios of length (respectively, 2:1 for the octave, 3:2 for the fifth, 4:3 for the fourth.) This means that any wire, if fretted at the exact half-way point on its length, will subdivide into two sub-sections of wire each of will sound when plucked exactly one octave higher than the full length of wire. This may well represent the first completely abstract, general, and universal mathematical law in the Western tradition of natural science. It is a law or rule that invokes measurement but does not logically depend upon it. Any string (A) twice the length of a given string (B) resonates when plucked at one octave lower than does A when it is plucked. It would be difficult to overstate the importance of this discovery. When Newton more than twenty centuries later isolated the general laws of gravity and thermodynamics, he was invoking a Pythagorean example. Oblivious to the obvious differences among physical objects, Newton realized that any two bodies in space exercise a pull on each other proportionate to their mass and inversely proportionate to the square of the distance between them. I know of no similarly universal discovery in Western thought that predates the Pythagorean discovery of the constancy of the relationship between the length of a fixed wire (irrespective of its length, cross-section, or material composition) and the pitches that it sounds when plucked. At more or less the same time one of the Pythagoreans may well have discovered the so-called Pythagorean Theorem, although it is unlikely that they discovered anything like Euclid's proof of this famous theorem.
Having discovered the clue to what is ONE or Common amongst the MANY, the Pythagoreans seem to have leaped by a staggering act of induction to the generalization that ratios are the clue to everything. They lent particular value to the so-called TECTRACTYS, a pattern familiar to us from ten-pin bowling. This diagram combines the first four numbers, graphically represented, as components of the perfect number ten. (As we would say, with our more algebraic imagination,
n + (n+1) + (n+2) + (n+3) = 10, where n = 1.The Pythagoreans are credited with a stunning series of mathematical discoveries. It may not be too great an exaggeration to say that they invented number theory. They were the first to distinguish and define odd and even numbers, prime numbers, squares, and cubes. The even and the odd they identified as the fundamental principles of all things (even associating them with gender differences.) Ancient as the patronymic of the "Pythagorean Theorem" is, it is natural to conclude that someone in Pythagorean society must have stumbled across the existence of irrational numbers by applying the well known formula to an equilateral right triangle with equal sides set at one unit. The hypotenuse of such a triangle must have the value of the square root of 2, which cannot be expressed as the ratio of two integers. (One legend, no doubt considerably exaggerated, holds that upon discovery of this shocking secret the Pythagoreans swore themselves to secrecy, and that when this vow of silence was violated, they put out a Sycilian-style contract against the disloyal member.)
It was one thing for the Pythagoreans to explain consonant musical intervals and geometric patterns by appeal to ratios of integers, but how were they to ever going to apply this theory to produce a cosmology? How from this account of numbers and ratios could they explain the variety and multiplicity of the world? That they took this challenge seriously we have on good authority. Diogenes Laertius cites the following gloss from Alexander Polyhistor, DK 58B1a, McKirahan, following Hicks, translator):
From the unit and the indefinite dyad spring numbers; from numbers, points, from points, lines, from lines, plane figures; from plane figures solid figures; from solid figures, sensible bodies, the elements of which are four: fire, water, earth, and air; these elements interchange and turn into one another completely, and combine to produce a universe [COSMOS] animate, intelligent, spherical, with the earth at its center, the earth itself being spherical, and inhabited round about.
This theory no doubt functioned reasonably well in explaining how lines can be generated from points, planes from lines, and solids from planes, as well as in explaining the numerical relationships among the simple, regular solids (pyramid, cube, octahedron, icosahedron, etc.), but the Pythagoreans were determined to extend this insight far beyond geometry, and when we come to assertions that what we think of as abstract concepts like "justice" are expressions of their own number (the number is given as twelve) most modern, and even ancient, commentators have admitted that they have come to the limits of their ability to think like Pythagoreans. Perhaps we can glimpse the intermediate ground in the metaphor of the soul as the harmony of the body. A body out of tune and out of balance is in risk of disease and eventual death. Life and strength reside not in some organ but in the integrity of the organism, in its harmonious, well-tuned functioning. This insight of Pythagoreanism has informed the outlook Western medical practice since Hippocrates and Galen. The theory of the "four humours" is profoundly Pythagorean as are the recurrent medieval and renaissance efforts to grasp the music of the spheres. These examples testify to the power and resiliency of Pythagorean modes of thought.
Pythagoreanism disappeared as mysteriously as it began. By 400 B.C.E. all record and evidence of the Pythagoreans has vanished, although Simias and Cebes in Plato's Phaedo are represented as having been present on the day Socrates died (404.) In its later years Pythagoreanism had already splintered into two schisms. The MATHEMATIKOI held that inquiry was the heart of Pythagoras' legacy. The AKOUSMATIKOI or "auditors" held in opposition that purification cam e from hearing and repeating lessons of the past.
SOPHISTES. Originally a term for a man of wisdom and skill, it quickly came to be particularly identified with a group of people who practiced a new trade or profession: the tutors or teachers who moved from city to city, practicing their trade for a fee. The Sophists were the first professional lecturers and seminar consultants. Their lessons, although ranging over a wide set of topics, tended to have a practical focus. They claimed to be able to teach useful skills to their clients, usually including rhetorical and oratorical skills. The most famous of them, like Protagoras claimed to be able to teach ARETE, excellence within a kind. Hippias developed a system of mnenomnics, to improve people's skill in memory and recall. Gorgias earned famed as a tutor in giving speeches--including set speeches. He famously defended Helen of Troy against a hostile, if imaginary, Greek jury. Public speaking was an important skill in Classical Athens. Many issues were debated before large assemblies, and the Greeks, particularly the Athenians, cultivated an appetite, which they shared with 20c C.E. Americans, for litigation. However, in their system plaintiffs and defendents both spoke for themselves and cross-examined clients in court, as Socrates and his prosecutors do in Plato's account of the Apology. (For background on Greek legal proceedings, see Freeman) There is a certain parallel between the reputation of the Sophists in ancient Greece and lawyers in our own time. That they would take on clients and causes for a fee was a source of concern and misgiving to their countrymen. Aristophanes lampooned Socrates as one of the Sophists in The Clouds.
STRATEGOS