Abelard was a pupil of Roscelin, an 11c C.E. French monk of whom little is known apart from two outstanding students, Abelard and Anselm. Abelard and Anselm both attest that Abelard was a nominalist. Roscelin seems to have rejected nominalism, on the grounds that the whole cannot be equal to or greater than their parts. From this opservation Roscelin was apparently let to conclude that universals are not real. The whole, he held, is equal to or greater than its parts. This opinion inevitably led him to difficulties with Rome on the question of the nature of the trinity. He recanted under pressure in Rheims in 1092.
Having studied there, Abelard to Pairs in 1113 C.E.. It was in the years following his return to Paris that he commenced his famous affair with the nun Heloise. Their secret correspondence is one of the great love stories of western literature, despite (or perhaps because of) the reaction of Heloise's uncle Canon Fulbert, who arranged for Abelard's castration and the incarceration of Abelard and Eloise in isolated cells.
Abelard like his teacher was a nominalist. He held that universals arise from resemblances,, which are not themselves things or attributes ("characteristics") of things.
BASILEUS) he mounted further campaigns northward toward the Caspian Sea and present day Turkestan, and eastward to the Hindu Kush and the Punjab. In the course of all these conquests he founded many new cities, virtually all them on excellent sites near good trade routes. He turned back simply because his army refused to follow him further. For the return trip he divided his army for exploration. One half went by land and sea, turning southeast further into India (all the way to the Indus River) before a planned voyage through the Persian Gulf. Meanwhile, Alexander himself led the other half of the army on foot through the hostile terrain and deserts of Gedrosia to prepare the land support necessary for ancient voyages. This was not the highlight of his career, but he survived. Meanwhile, however, quarrels and rivalries back home in Greece and Macedonia and mistrust of Alexander's "Persianizing" ways (he adopted Persian dress and customs, and married a Persian wife, much as his ancestors had "Greekisized" Macedonia.) He added local troops at every point to his army. This did not sit well with his own men, and eventually even his loyal Macedonians expressed their unhappiness. He appears to have thought that mixing the army would build unity. Too often it increased tensions. Then in 324 he made an even bigger miscalculation. Either he allowed himself to be declared a god or, as is more likely, he made the declaration himself. This did not sit well with the Greeks, who, though they had no objection to new gods, were not accustomed to the deification of politicians and generals. He was by all accounts a charismatic leader on the battle field, a brilliant strategist, an accomplished horseman, and inventive in the field. He died of a fever in his third-third year.
Anaxagoras, together with Empedocles, took up the challenge laid down by Melissus, who said that if there is a many, it must be like Parmenides' one. According to Anaxagoras, the world from its beginnings has been a mixture of seeds (SPERMATA) of every qualitiatively distinct thing, both organic and inorganic. Things are infinitely divisible into parts that are like each other and like the whole. The elements of blood, for example, are infinitessimal blood-bits. (We might say that according to this theory, everything can be represented as a fractal: it will appear the same when viewed from any level or distance.) Aristotle called these elements HOMOEOMERIES to emphasize this striking feature of sameness. Seeds take their main feature from the dominant element in a thing, but all objects share elements of everything, except mind (Unmoved Mover?) According to his cosmology, NOUS introduces a spiral motion that grows outward. As it expands it "separates out" elements or seeds, the dense, moist, dark, and cold moving toward the center, their opposites toward the circumference. Anaxagoras explains growth and development by appeal to what was there already at a thing's origin. This is a theory of emergent properties. But Anaxagoras has difficulties of his own. The role of opposites is obscure, and both Plato anmd Aristotle criticized him for failing to invoke NOUS in teleological arguments.
GNOMON, a device that enabled a sun-dial to indicate season as well as time-of-day. Among other inventions attributed to him was map-making. For an on-line biography, visit this brief biography.
His great fame in philosophy stems from his talent for abstraction, since sources agree that he held that the source (ARCHE) of all things (the original stuff of our questions) must be the APEIRON ("boundless" or "unlimited" sometimes translated as the "infinite.") He also argued that this APEIRON must be eternal and ageless and therefore, according to Greek thought, divine. Aristotle speculated that Anaximander recognized that none of the four elements (nor any other thing in the world) could serve as an answer to the question, "What is the original stuff?" since none of the extant things could be the principle of its own explanation. This would be particularly true in a world characterized, as Anaxminader and the Greeks in general believed that ours is, by opposites. If Thales believed that water is the fundamental principle of all things, then the appearance of water in the world would be without explanation, since it would not be capable of providing an explanation of its own appearance. By the logic of this line of reconstructed argument, the best translation of APEIRON might be "undifferentiated." On the other hand, if the original principle is literally without differentiation or characteristic, then no appeal to that original stuff will ever explain how one state of what was later called matter could change or be transformed into any other. Anaximines may have grasped this implication, which could explain why he turned his back on what otherwise was the unanswerable objection of Anaximander to the choice of any determinate thing in our world as the original stuff of everything.
Tradition holds that a more or less genuine fragment of Anaximander's thought has made its way down the ages to us (R. McKirahan translation, Simplicius, Comm. on Aris. Phys., 24.18-21=DK 12B1 + A9) :
The things that are perish into the things out of which they come to be, <">according to necessity, for they pay penalty and make restitution to each other for their injustice in accordance with the ordering of time,<"> as he says in rather poetical language.It is commonly assumed that the language embedded in added quotation marks '<">' above represents something close to direct quotation. The first phrase is more problematic. Is it paraphrase or interpolation? On the assumption that it paraphrases an authentic component of Anaximander's thought, McKirahan (1996, 43) summarizes the cosmology embedded in this fragment as follows:
We have a picture of a world full of change--things coming to be and in turn being destroyed. These changes are ordered in two ways: (1) when a thing (A) is destroyed, A turns into something definite--the same sort of thing that perished when A came to be; (2) each thing has a determinate time span. In addition, comings-to-be and destructions are acts of injustice that one thing (A) commits against another (B) and for which A is compelled to make restitution to B.The A's and B's of McKirahan's gloss suggest paired opposites (wet/dry, hold/cold, that sort of thing) which we have Aristotle's authority in attributing to Anaximander's basic framework of thought. (Physics, 3.3 204b22-29=DK 12A16.) Anaximander seems to have felt that opposites require explanation. In this he anticipated another long line of greek philosophical analysis, eventually culminating inPlato's wrestlings with the concept of relational terms (how can "shortness" and "tallness" both be characteristics of Socrates?) and Aristotle's solution to these connundrums. According to Anaxminader, opposites must somehow have "separated off" from the
APEIRON. (Note once again the similarities to late 20c C.E. cosmologies. A cataclysmic explosion of the original super-dense matter set off a nuclear chain reaction that theoretically should lead to an account of the distribution of matter and energy in the world as we know it today. What's more, the "threat " of CHAOS still exists. Some regions of this far-flung and expanding universe or COSMOS run the risk of building up such densities that they could implode on themselves, trapping even light in their gargantuan gravitational forces. Could the universe itself, shrapnelled outward in a world-creating explosion, eventually generate its own "recycling " implosion?)
Once the original separation occured, the world order (COSMOS) takes over, according to Anaximander, and the cosmic enforcers, philosophical analogs of the EUMENIDES of Greek myth and chief among them, significantly, time, were called upon to mete out punishment to elements that have the audacity (hybris to usurp more than their just (DIKAIOS) share or portion.
What are we to make of these references to injustice and penalties? The underlying metaphor is what we would call "legal." "Law" is, of course, a homonym in our vocabulary. We think of the laws of nature, or physical laws, as expressions of very general principles and uniformities (e.g., the law of gravity) and we contrast these laws with legislation (or human law) that enjoins (pre- or pro-scribes) certain behavior. (So-called "natural law" in ethical and religious arguments occupies a middle ground between these two. The Sophists debated many of these issues in the so-called NOMOS/PHYSIS debate.) The entire point of human legislation is that violation of the law is all-too-possible. We do not establish laws against attempting to levitate of the Pentagon (which is impossible) but we do make it illegal to trespass of private or posted property. Sanctions against possible violations must be established to deter acts that otherwise might be perpetrated, but not against actions that are in simple cannot be performed, i.e., that are impossible. To our post-Newtonian way of thinking, violations of physical laws are by definition impossible. Evidence of any apparent violations is either explained away as error (illusory) or taken as evidence that a supposed law is not (was not) really a law. (To see what this would mean in the realm of legislation, imagine that a murder could only be regarded as either not having occurred or as invalidating laws against murder!) But for the early Greeks, violations of what we think of as physical laws were real and present threats. Laws in this sense described and governed the COSMOS, or "ordered world. " Order exists against the constant threat of disorder, or CHAOS. One of the key characteristics of world-order, as Anaximander seems to have recognized, is balance. When things get out of balance, chaos follows. The world order (or cosmos) must be ever vigilant and prepared to punish the violators whose HYBRIS leads them to take a bigger portion than is their due. (It would be hard to overstate the importance of this pattern of thought among the Greeks. One of its implications can be seen in Plato's definition of justice as "giving everyone their due.")
Anaximander developed an elaborate and sophisticated cosmology that did not appeal in any obious way to his most abstract and abstruse idea, the APEIRON. According to Anaximander, the world is a cylindrical disk, with a height to breadth ratio of 3:1. We live on one of its flat surfaces. Rings of fire and mist surround this disk (the heavens and the clouds?), their winds perhaps explaining how the earth maintains its celestial position. The stars (closest), moon, and sun (the same size as the earth) circle the earth in diurnal, circular orbits, the diameter of the moon's orbit 18 or 19 times the width of the earth's cylinder, that of the sun 27 times its width. Many of the specific features of his account echoed Thales' observations of the fundamental and life-giving properties of water. Others anticipated (influenced?) the views of Anaximines, who emphasized air and its transformations by condensation and rarefaction.
(For a balanced and thorough summary, see McKirahan, 1996, 32-47; for an extended scholarly account, see Kahn, 1960.)
Little is known of his life, except that a tradition well back into the ancient world attests that he came from Miletus and was the pupil and younger contemporary of Anaximander. He is reported to have written simple, direct Ionic prose, and to have asserted that the COSMOS perpetually comes into being and passes out of existence in an endless cycle. He is said to have believed that the COSMOS consists in, and is surrounded and sustained by, the eternally moving and infinite (therefore divine) air (AER.) He seems to have relied heavily on observations of the transformations of air from one state to another, as in rarefaction & condensation. Rarified air warms and eventually ignites in fire (think of hot, parched, dry climates, or poorly venitlated grain silos that burst into combustion under the unrelenting pressure of rising temperatures.) Condensed air generates, progressively, wind (we would say from gradients in air pressure associated with relative humidity), cloud, water, earth and, by extension, rock. From these "derived" elements everything else is generated. He held that the earth is thin and flat (the familiar disk) and that it floats on air. (In this he provided an explanation for the stability of the earth's position.) The earth is surrounded by the sun, moon, and stars, which he ssems to have thought of as "leaves" of fire.
Already in antiquity Anaximines was regarded as in some ways an unworthy successor to Anaximander, but his accounts of evaporation ("rarefaction") and condensation, although perhaps derived from those aspects of Anaximander's thought that do not refer directly to the indefinable APEIRON, may well signal the first proofs by appeal to controlled observation in the history of Western physical science.
R. G. Collingwood argued (1945) that Anaximines saw that what we might call the program of Milesian philosophy was beyond reach. The defensible answer (Anaximander's) to the first question (What is the utimate stuff?) rendered the second question (How does this stuff change?) unanswerable. By this line of reasoning, Anaximines chose to advance scientific understanding on the subject of transformations, depsite the fact that this required him to turn his back on the most general metaphysical questions.