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Figure 1.13 The School of Athens
(Rapheal)
Agora, Academy, and Lyceum
The most famous intellectual lineage in the history of philosophy spans the length of three personalities and the depth of intellect with which Athens was awash during its heydey. The lineage-- Socrates, Plato, and Aristotle-- spans across the decades (407-323 BCE) during which the glory of Athenian democracy and culture reigned throughout the Aegean and eastern Mediterranean world, then slid from its zenith in Aristotle's time as the Macedonian polity swooped down from the north toward its era of world conquest. This is not to say that Socrates lived in a happier time but rather, by the time Plato processed all he had learned from Socrates then advanced his thoughts beyond; and, by the time Aristotle did the same with what he'd learned from Plato, geopolitical events had conspired to disrupt this particular progression of thought. Something of the thoughts of all three became more or less codified, revered, studied, imitated, and criticized in the centuries after their deaths but no person was able to carry their work forward. In the open-air market (agora) of Athens, Socrates questioned the wisdom of his fellow citizens with such impressive style that Plato as a youth became devoted to him. An erudite Plato in his prime founded the Academy to provide a complete education for the brightest minds and a model for future universities. Plato's Academy attracted from Macedonia the young Aristotle who, in turn, became a serious student and went on to found another great institution of learning at Athens, the Lyceum. Each of this triad presented a unique philosophy, albeit influenced by their predecessors, but of these three only Aristotle devoted much thought to the nature of material substance.
Figure 1.14 |
Socrates
Born to a family of modest means circa 470 BCE, Socrates thrived in the bustling culture of Athens as his native city matured to become-- at least for several decades-- the beacon for creative thought and commerce in the ancient world. According to Theophrastus, the young Socrates studied at the school of Archelaus, a man best remembered as the successor to Anaxagoras. As the young Socrates grappled with the various theories of the cosmos, he may have been appalled by theorists who proclaimed blind mechanistic forces, and he may have rather favored Anaxagoras' claim that Mind was the motive force of the cosmos. Yet Socrates seems to have become dissatisfied with Anaxagoras' failure to articulate anything more of Mind after it had set the vortex into motion. |
From the mature Socratic perspective, nothing is fully explained or understood until its goodness-- whether judged in terms of human or divine utility but preferably both-- was made clear. So the youthful Socrates may have reasoned that, if Mind is truly a principle of cosmological import, then the principle of Mind should be used to explain how each and every thing in the cosmos is for the best. Perhaps he wondered how human thought judges 'best' and whether knowledge of that procedure might offer clues about manifestations of goodness in the cosmos. In search of somesuch explanation, the youthful Socrates seems to have turned his attention away from Nature at large to human nature as particular. Consternation with cosmological speculation was common at the time. Any speculation which doesn't yield earthly dividends is useless, afterall.The bustling commercial and political leaders of the Athens into which Socrates matured were particularly concerned with the enigma of human nature-- what makes some men worthy and others not?-- and its advantageous solution. Socrates sagely opened the market for speculation on that enigma. The market was very complicated at the time. Scepticism about political and moral issues prevailed as a result of cultural stresses which permeated Greek society in the 5th century BCE. Perhaps the Greeks were still haunted by ripples from the Minoan culture they'd overrun in the second millenium. More to the point, commerce and war had over recent centuries brought the Greeks familiarity with advanced civilizations to the south in Egypt and west in Mesopotamia-- Assyria, Babylonia, and Persia, with a taste of India. The Greeks also confronted the more primitive peoples known as Illyrians, Thracians, and Scythians to the north, as well as the Etruscans, Italics, Sicnas, and Sicels to the east along the Italian paeninsula. Each of these cultures had their own persistent mythos and way of doing business. Closer to home, the ancient Achaean tribal mode of political organization had slowly dissolved into a myriad of monarchs, oligarchs, despots, and landed aristrocrats among the Greek towns and city-states. A rising class of trade and craft folk was gaining influence in the cities. To underline the extremes in Socrates' time, Sparta had established a tightly regulated military regime while, in stark contrast, Athens bore a fragile democracy on the backs of slaves and to the exclusion of women. Within this arena of personal turmoil, a genera of philosopher arose in Greece which came to be known as sophist, after Sophia, the Goddess of Wisdom, since the sophists professed to impart wisdom to men engaged in practical affairs. The sophists taught grammar, the insight of the poets, the lessons of prevailing myth, religion, and politics, ethics, rhetoric, and eristic (the art of winning disputation). In exchange for a fee, the sophistical teacher promised to improve the student's ability to achieve success in the public arena through skillful conduct, and personal happiness through living well.
For some, that meant gaining wealth and power. The best sophists, among them Protagoras, provided something like a finishing school for aristocratic youth. Yet the well-honed mind might take even the best of teachings and use it without scruple as, for example, with the famous aphorism of Protagoras: "Man is the measure of all things, of those that are that they are, of those that are not that they are not." On one side of the agora, a civic-minded student might argue that we-- in and of the polis-- are the measure of our own morality, but proclamations attributed to divinity or despot are not. On the other side, a mean-spirited student might argue that an individual alone is the measure, in opposition to other individuals: To push the point, might makes right. We may further imagine each, after becoming a teacher, competing with the other teachers for paying pupils. The worst of the sophists perfected the arts of persuasion, and their more skillful graduates, whether practicing in the commercial, political, judicial, or philosophical arena, could project even the most pernicious premise as if it were a noble cause worthy of support. Brilliant manipulations of sentiment, both public and private, fostered greater scepticism. Into such intellectual melee, Socrates stepped forth to forge a path toward some higher truth. Exhuding charm from an unlovely face, this squat hearty fellow charged no fee, wrote no treatise, nor established any school. Rather, Socrates engaged stalwart minds wherever he chanced upon them in the marketplace, courtyard, or banquet hall.
Having served with distinction for bravery in the Athenian military, Socrates did not shy away from direct confrontation. He rather seemed to welcome it. On frequent occasion he'd bump into a politician who professed the value of a certain form of government, or a jurist who claimed some particular sense of justice, or a teacher who exalted the value of expertise in a special intellectual art, e.g., rhetoric. After hearing an other crow, Socrates smoothed his way into the conversation by praising the speaker's esteemed knowledge of the topic, e.g., a just verdict in a public trial. Then Socrates would declare his own ignorance of the subject, e.g. the law or justice, and with all due respect to the speaker endeavor to elicit more detail from the 'knowledgable' person, followed by further honest questions. Soon enough an unwary braggart or self-proclaimed authority would find himself trapped in self-contradiction. |
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At the start of his career, few of his fellow citizens were exempt from Socrates' engaging style of conversation. With a bit of luck and much skill, the conversation might lead to a deeper insight on the topic or a better grasp on the human need to define-- for example, justice-- more completely. We can only imagine Socrates' ability to foment exciting discussions as we read Plato's "dialogues" which aimed to portray something of his master's art. And we may imagine that, while his first forays in the agora may have attracted a small audience, over the years Socrates developed a troop of devoted fans with youthful spirit who not only traded stories of Socrates' latest performance but also learned something from the experience.PlatoAny concept of importance to intelligent life was susceptible to Socrates' approach. Whether one should profit from another's loss, whether we should obey our elders and the gods, whether one form of government was able to function better than another-- Socrates' profession of ignorance empowered some of his listener's to think for themselves on each of many topics. Yet the Socratic style of investigation offended some who regarded their own opinions as above reproach and beyond questioning. Others were offended by the way in which Socrates beguiled innocent youth away from traditional values. After decades of publicly practicing his trade in ideas, Socrates was indicted by several outraged citizens of Athens and brought to trial by democratically elected officials in 399 BCE. Plato wrote this of the official charge: "[I]t states that Socrates is a wrongdoer because he corrupts the youth and does not believe in the gods the state believes in, but in other new spiritual beings."
The details of the trial and surrounding events have long been forgotten although several accounts have continued to fuel imagination over the millenia. I.F. Stonestates the case most completely in The Trial of Socrates (1989, Doubleday/Anchor, NY). While describing many fascinating details, Stone makes two points-- one philosophical and one political--, both of which interweave. Philosophically, it must be said that the main contribution made by Socrates to the art of clear thought was the elevation of the need for proper definition of important concepts. For example, what is the Public Good? But what happens, politically, when mere definition empowers men to act? Stone (pps. 68 and 71) refers to a later statement by Aristotle to underline the historical problem: "Socrates ... was busying himself about ethical matters and neglecting the world of nature as a whole but seeking the universal in these ethical matters, and fixed thought for the first time on definitions; Plato accepted his teaching, but held that the problem applied not to sensible things but to entities of another kind [which] he called Ideas..." (Metaphysics I.6)
How do we define 'civic virtue' or 'justice,' for example? If Socrates' listener believes that, by pursuing the definition vigorously, an absolute definition or grasp on the concept can be had, then the listener may be corrupted as that perfect conception is reified into a thing-- an Ideal-- which somehow exists beyond this confusing world of the senses. A tradesman or even a statesman may be elected to office based on his practical knowledge of justice gained from sensible experience. But if such person does not grasp the true ideal of civic virtue or justice, can he be trusted not to err in the making or application of law?
Perhaps Socrates wisely refrained from the reification of political concepts into absolute ideals. Or perhaps not. But we know that his star pupil, Plato, did advocate the Good and the Just as ideals with absolute import. In his works published long after the death of Socrates, Plato strongly delineates an ideal form of Justice and an ideal State, ruled by a philosopher king.
Presumably, Plato advocated his ideal notions prior to the trial, whether or not Socrates fully concured. Stone argues that in pursuit of a philosophical ideal both Plato and Socrates politically promoted a non-democratic faction of government over Athens twice, in 411 BCE and again-- through a band of oligarchs known as 'the Thirty'-- in 404 BCE. The sage and his protege, according to Stone, perceived a particular oligarchy to be closer to the ideal form of governance than democracy. Yet the Athenian democrats perceived that very same faction as tyranical and, after reestablishing a democratic regime in 403 BCE, eventually sought a modicum of 'just' retribution: They brought Socrates to lawful trial for crimes against the city-state. Apparently, Socrates was condemned to death by the poison of hemlock and, although offered the option of exile, willfully drank the cup. He swallowed the potion perhaps to prove the point, or so Plato's account in the Apology would have it, that for the sake of an ideal civic virtue he did obey the law.
Figure 1.16
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Born to Athenian aristocrats
circa 427 BCE, Plato was raised to value the finer things in life. While
still a boy, he may have imagined himself becoming a poet or playwright.
As a young man he showed some talent for leadership and considered a career
in politics. Perhaps he sought a sophist teacher to improve his knowledge
of human nature, the law, and the art of rhetoric. Perhaps not. But we
can safely suppose that Plato was keen to experience the full excitement
of the agora. One way or another, at the age of twenty Plato's path
crossed that of the mature Socrates.
We do not know how close they became, but after seven years had passed in the circle of Socrates the young man faced the death of his revered elder. Dismayed at the trail and punishment of Socrates by the Athenian democracy, Plato retreated across the bay of Eleusis to the city of Megara (see map below). He may have returned within the year or he may have traveled to Cyrene, Italy, and Egypt-- the record is unclear. At the start of Athen's conflict with Corinth (395-394), Plato is said to have served his native city militarily. Near the age of forty, Plato is known to have traveled to Italy and Sicily where he presumably studied with the Pythagoreans. There he became familiar with the family of Dionysius I, Tyrant of Syracuse, through which he may have suffered some misadventure. By 387 BCE Plato had returned to Athens and established an institution, according to Frederick Copleston "near the sanctuary of the hero Academus." It became known as the Academy and quickly grew in reputation. The dignity of the school is further described by Copleston: "The Academy may rightly be called the first European university, for the studies are not confined to philosophy proper, but extended over a wide range of auxiliary sciences, like mathematics, astronomy and the physical sciences, the members of the School joining in the common worship of the Muses. Youths came to the Academy, not only from Athens itself, but also from abroad; and it is a tribute to the scientific spirit of the Academy and a proof that it was not simply a 'philosophical-mystery' society, that the celebrated mathematician Eudoxus transferred himself and his School from Cyzicus to the Academy." (Copleston, p129-130) |
We may suppose Plato wrote a few philosophical dialogues prior to taking on the responsibilities of school administration and the presentation of regular lectures. Over his lifetime he published some two dozen dialogues, the earlier of which portrayed Socrates as the interlocutor in substance and style. The later dialogues use the dramatic figure of Socrates to argue towards philosophical positions which are more likely Plato's than his mentor's. Perhaps beginning with the Apology, Crito, and Euthyphron-- the early dialogues which feature Socrates discussing his trial and issues surrounding it-- Plato discovered his own literary strength in the attempt to capture something of Socrate's vivacity in the written word.As literature, those earlier dialogues have worked everafter to project Socrates as a hero in the minds of youth who are prone to thought. Yet the later dialogues appear increasingly populated by strawmen, dummies cast as adversaries in the dialogue; they too readily succumb to the fictional Socrates as he mouths the brilliance of Plato's ideation. Regardless of our judgments on their literary merits, the later dialogues have offered food for thought to subsequent generations on a variety of topics including politics (The Republic and The Laws), virtue, beauty, and the nature of knowledge and being-- all of which are anchored by Plato's doctrine on the ideal forms.
Perhaps the most widely known manifestation of Plato's thought, his theory of Ideas (i.e., ideal forms, Forms) is anchored in the Socratic quest for definition and heavily influenced, as we'll soon see, by the doctrines of Parmenides and Pythagoras. Plato seems to have accepted the Heraclitean notion that all sensible things are in a state of flux and concluded that study of such things could only provide an ephemeral familiarity but not true knowledge. Plato's notion is outlined by Aristotle:
"[I]f knowledge or thought is to have an object, there must be some other and permanent entities, apart from those which are sensible." The path to such permanence was pioneered by Socrates who "became the first to raise the problem of universal definition." Yet in seeking to know the ultimate definition-- the essence --of a thing, "Socrates did not make the universals or the definitions exist apart [from objects and human activities in the sensible world]." Plato and his cohort, however, "gave them separate existence, and this was the kind of thing they called Ideas." (Metaphysics, XIII.4)Of course, the greatest idea is singular. With Parmenides and the Pythagoreans, Plato insisted that the Cosmos is One, Unchanging and Eternal, which cannot be known through the imperfect senses but only through reason. (By reason of its virtue, the One is the Good.) With Pythogoras, Plato insisted that true reality is best approached through mathematics and emphasized the teaching of geometry and number at his Academy. The ideal forms are akin to number, abstract and empty of sensible content, manifest hierarchically from the One true Being to the Many ephemeral manifestations. Yet the ideal is not number but a level of being beyond, the very source from which number is generated as an intermediary between the ideal and the sensible. There are many '3' numerals, for example, but only a single Idea of Triplicity. Likewise for men, or cows, or stars, or goodness, or justice. The Ideal Man and Ideal Cow were no doubt a manifestation of the Ideal Good in Ideal Justice. And all of these flowed hierarchically from the One of Pure Being. Or so we suppose, not being ourselves initiates.The Platonic logic begins with the assumption that the universal (the general 'essence') is more real than the particulars (the many) in a class of objects, then procedes with the assumption (in a Platonist's mind, the reasoned necessity) that the particulars only become manifest as they partake of the universal. As Aristotle explained:
"[T]he many existed by participation in the Ideas that have the same name as they. Only the name 'participation' was new: for the Pythagoreans say that things exist by 'imitation' of numbers and Plato says they exist by participation, changing the name. But what the participation or the imitation of the Forms could be they left an open question. Further, besides sensible things and Forms [Plato] says there are the objects of mathematics, which occupy an intermediate position, differing from sensible things in being eternal and unchangeable, from Forms in that there are many alike, while the Form itself is in each case unique. Since the Forms were the causes of all other things, [Plato] thought their elements were the elements of all things. As matter, the great and the small were principles; as essential reality, the One; for from the great and the small, by participation in the One, come the Numbers." (Metaphysics, I.6)The theory of Ideas was never fully explained in any of Plato's dialogues. Some contain hints, allusions, and bits of doctrine (e.g. Meno, Symposium, and Phaedo). Other dialogues articulate one aspect or another of the doctrine more explicitly (e.g. Theaetetus, Parmenides, and Sophistes). Yet these exoteric publications merely whet the appetite for the whole truth-- the esoteric doctrine reserved for the worthy, admitted to private lectures. Only devotees at the Academy were blessed with the true knowledge, presumably after they had mastered the prerequisite teachings. "We are told [by Aristoxenus, a disciple of Aristotle] that Aristotle used to relate how those who came to hear Plato's lecture on the Good were often astonished to hear of nothing but arithmetic and astronomy, and of the limit and the One." (Copleston p130-1)Given the heady import of his Ideas, Plato seldom publicly focused on the nature of materiality (i.e., the sensible world) in any detail. But around the age of seventy he published the Timaeus, a dialogue which may represent his views on how, why, and of what the physical world is made. Or it may not, since this creation story is arguably Plato's fable for the masses about matters only comprehensible to trained acolytes. In his previous dialogues, Plato always portrayed Socrates as the primary speaker but the Timaeus takes a different approach. Here, the story of creation is not told by Socrates but rather by Timaeus, a philosophical acquaintance of Socrates with some knowledge of the cosmos. Socrates only speaks at the beginning of the dialogue to launch the Timaean monologue as a story, an 'entertainment' among friends. Early in his oration it is obvious that Timaeus is speaking for Plato with these words:
"We must in my opinion begin by distinguishing between that which always is and never becomes from that which is always becoming but never is. The one is apprehensible by intelligence with the aid of reasoning, being eternally the same, the other is the object of opinion and irrational sensation, coming to be and ceasing to be, but never fully real. In addition, everything that becomes or changes must do so owing to some cause; for nothing can come to be without a cause." (Timaeus, p40)After this simple brilliant core of Platonic doctrine, the teleological cause is given by Timaeus a godly face-- but whether cartoon or devotional, the reader must decide. As Timaeus goes on to explain, this cosmos we inhabit was caused by a being called variously a craftsman, a framer, a god. Furthermore, "this world came to be in very truth, through god's providence, a living being with soul and intelligence."Although modeled on the eternal, this world of change is necessarily "corporeal, visible and tangible: but nothing can be visible without fire [i.e., light], nor tangible without solidity, and nothing can be solid without earth. So god, when he began to put together the body of the universe, made it of fire and earth. But it is not possible to combine two things properly without a third to act as a bond to hold them together." For geometrical reasons, "god placed water and air between fire and earth, and made them so far as possible proportional to one another, so that air is to water as water is to earth..." (Timaeus, p41)
The creative being was not an Absolute God but rather a demiurge, since he worked within the limits of necessity and began with a preexisting matrix:
"[T]his world came into being from a mixture [of] necessity and intelligence. Intelligence controlled necessity by persuading it for the most part to bring about the best result..." Moreover, the demiurge began with a primordial set of givens in a state of chaos. "There were, before the world came into existence, being, space, and becoming, three distinct realities. The nurse of becoming was characterized by the qualities of water and fire, or earth and air, and by others that go with them, and its visual appearance was therefore varied; but as there was no homogeneity or balance in the forces that filled it, no part of it was in equilibrium, but it swayed unevenly under the impact of their motion... And its contents were in constant process of movement and separation, rather like the contents of a winnowing basket..." (Timaeus, p66 and p72)That passage suggests a deviation from the Parmenidean doctrine. Being (the One) is modified into the Many (becoming) in space thanks to the force of motion. While this might suggest a nod of respect to the atomist theory which insisted upon the reality of motion in space, Plato's schema is more peculiar. The atomists held that chance collisions brought their indivisible particles into contact during the assembly of material bodies, but Plato believed that intelligence with necessity motivated the 'winnowing basket' to generate things in their becoming on the model of pure being. The Platonic 'space' through which motion occurs is no mere void but rather a receptable which Timeaus likens to a womb. Never empty, this space is "a kind of neutral plastic material on which changing impressions are stamped by the things which enter it, making it appear different at different times. And the things which pass in and out of it are copies of the eternal realities, whose form they take in a wonderful way that is hard to describe..." (Timaeus, p69) Furthermore, while the indivisible atoms of Democritus had an infinite variety of shapes, some of which just happened to be geometric, Plato advocated tiny solids of just four geometric types, each composed entirely of indivisible triangles-- themselves but manifestations of a Form, the ideal right triangle."In the first place," Timaeus explains, "it is clear to everyone that fire, earth, water and air are bodies, and all bodies are solids. All solids again are bounded by surfaces, and all rectilinear surfaces are composed of triangles. There are two basic types of triangle, each having one right angle and two acute angles: in one of them these two angles are both half right angles, being subtended by equal sides [i.e., isosceles], in the other they are unequal, being subtended by unequal sides [i.e., scalene]. ... Of [these two], the isosceles has only one variety, the scalene an infinite number. We must therefore choose, if we are to start according to our own principles, the most perfect of this infinite number [of scalene types]. [W]e propose to pass over all the rest and pick on a single type, that of which a pair compose an equilateral triangle." (Timaeus, p73-4)
Figure 1.17 |
Obviously, two such isosceles
triangles of identical size can be arranged to form a square. And conversely,
a square cut along its diagonal will form two such isosceles triangles.
We may further note, more esoterically, that using a pair of scalene triangles
to compose an equilateral triangle requires each right angled component
triangle to have an hypotenuse of two units, a short side of one unit,
and a long side equal to the square root of three units. The isosceles
triangle, of course, has an hypotenuse equal to the square root of two
and two equal sides each of one unit. The Pythagorean Theorem states why
these particular square roots manifest in just these two types of triangle.
But while the Pythagoreans found the roots of 2 and 3 troubling because
'irrational', Plato seems to have exalted them.
From these triangles-- the isosceles and the most perfect scalene, as just described-- "the four most perfect possible bodies" are constructed on an atomic scale. The constructions begin with two plane figures, a perfect square and a perfect equilateral triangle. But the square and the equilateral triangle are not simply formed from isosceles and perfect scalene triangles as shown in Figure 1.17(b). For some odd reason, Plato specifies the combination as shown in Figure 1.17(c). It makes no obvious geometric difference whether schema (b) or (c) is used since the only size requirement for the triangles is that they be invisibly tiny. We can only suppose it makes an esoteric difference (for conjectural details, see footnote). Thus using the schema of Figure 1.17(c), Plato's square is formed by using a combination of four very tiny isosceles triangles. Plato's equilateral triangle is formed by using a combination of six very tiny 'perfect' scalene triangles. Given his unit square and unit equilateral triangle, the most perfect three-dimensional bodies are formed by fitting many such units along their sides to enclose spaces. |
The miniscule equilateral triangles are variously combined in 'right proportion' to construct what the uninitiated call 'the four elements.' From those triangles are born the invisibly tiny (1) pyramids we sense as fire, (2) octahedrons we sense as water, and (3) icosahedrons we sense as air. The pyramid, octahedron, and icosahedron require the conjoining of, respectively, four, eight, and twenty equilateral triangles along their sides to enclose a space. More uniquely, the miniscule squares combine six at a time to form invisibly tiny (4) cubes that we sense in large amounts as earth.
Importantly, since the scalene triangles are of the same type, the elements of fire, air, and water are, according to Timaeus, all subject to decomposition and recomposition as their 'perfect' scalene subunits are aligned or sundered, thus enabling the transformation of one element into the other as the component triangles are rearranged. Being isoscelean, earth alone is the element not transformed into the other elements. As Timaeus explains: Although the earthly cube is readily decomposed and even though its isosceles triangles readily mix with the scalene triangles in the raw, the isosceles half-squares cannot align properly with any shape other than half-squares for reassembly. And of course, through assembly and disassembly of these four elemental bodies, and their various combinations, all the many things we sense becoming and perishing in our cosmos are given material appearance. (Timaeus, p73-8)While we might assume that Plato was building on notions first developed by Empedocles (the four elements), the devout Platonist must insist that the four manifestations of geometric form were considered to be 'qualities', not substance.
"For it is difficult to say with complete certainty which of the elements we really ought to call water rather than fire, or indeed which we ought to call by any name rather than by another or even by all four. ... We see [water, for example,] solidifying into stones and earth, and again dissolving and evaporating into wind and air, air by combustion becomes fire, and fire in turn when extinguished and condensed takes the form of air again, air contracts and condenses into cloud and mist, and these when still more closely compacted become running water, which again turns into earth and stones. There is in fact a process of cyclical transformation. Since therefore none of them ever appears constantly under the same form, it would be embarrassing to maintain that any of them is certainly one rather than another.... Whenever we see anything in process of change, for example fire, we sould speak of it not as being a thing but as having a quality." (Timaeus, p67-8)The dynamic of transformation is a function of the triangles as their composite elements are subject to motion and rest:"When earth meets fire, [the cube] will be dissolved by [the pyramid's] sharpness, and, whether dissolution takes place in fire itself or in a mass of air or water, will drift about until its parts meet, fit together and become earth again, for they can never be transformed into another figure. But when water is broken up by fire or again by air, its parts can combine to make one of fire and two of air, and the fragments of a single particle of air can make two of fire. Again, when a little fire is enveloped in a large mass of air or water or earth and continues its motion in the moving mass, its resistance is overcome and it is broken up, and two particles of fire combine to make a single figure of air; and when air is forcibly broken up two and a half of its figures will unite to make up a single figure of water." (Timaeus, p79-80)Varying manifestations of the 'elements' or 'qualities' are further explained as their component triangles have longer or shorter sides (but always in the isosceles and scalene divine proportions based on the unit, two, and the square roots of two and three). The causes of motion include the after-effects of the winnowing force supplemented by a space-filling dynamic:"The circuit of the whole [the celestial sphere?], within which the constituents [i.e., the elements] are comprised, being spherical and therefore naturally inclined to return on itself, hems them in and allows no space to remain empty. ... So the contraction involved in process of compression [like atmospheric pressure?] forces the small particles into the gaps left between the large ones. You thus have a process in which small particles are juxtaposed with large ones, and the smaller disintegrate the larger while the larger cause the smaller to combine, and all are carried, up or down, to their own region; for a change in size involves a change in the position of their region. In this way a constant disequilibrium is maintained which ensures that the perpetual motion of the constituents shall continue unceasingly." (Timaeus, p81-2)Besides a few more thoughts on physics, Timaeus explains how the senses interface with this materiality. Then he goes on to explain the mortal basis of the soul, the functioning of bodily organs, and disease. A smattering of comment on animals and plants completes the survey and allows him to conclude: "We can now claim our account of the universe is complete."(Timaeus, p124)The 'entertainment' offered by Timaeus is only peripheral to Plato's theory of Ideas and thus is not considered by scholars today as vital to his philosophical legacy. But in its day, the Timaeus offered something material to any student who might be subject to the competing temptations of the atomist legacy. And although Plato's idealist approach overall might be said to supercede if not synthesize the thoughts of Empedocles, Parmenides, and Pythagoras, its ultimate impact on the history of thought was to confuse the difference between being (ontos) and knowing (episteme) while forcing a complete separation of sense from reason for the sake of that confusion. While giving Heraclitus his due, Plato was the first to advocate that the pursuit of knowledge is necessarily divided into two loci, the object known (i.e., that which has being) and the means of knowing (i.e., intelligence). As Plato drew the line, the particular within any class of objects is perishable, always changing, and initially known imperfectly through the senses. Such is true opinion (common knowledge). But the universal-- as an object with an independent being rather than, as we nowadays postulate, simply that which all examples of a class have in common-- is only known through Platonic reason (i.e., intelligence). And once known (according to Plato), the universal of a class enables a complete knowledge of all particulars in that class. By pursuing the universal for any class of particular objects as the essence within each, and then the Universal of universals, Plato claimed knowledge of True Being.
Upon an encounter with such fine ideas, a youthful mind might wonder unceasingly and, thus in disequilibrium, find it difficult to separate fact from fantasy without a mentor. But under the winnowing wing of a loving guide, Plato's world as materially manifest ideality might then appear as eminently reasonable. Especially when the youth is reminded of the key to such doctrine: "[T]rue opinion is a faculty shared, it must be admitted, by all men, intelligence by the gods and only a small number of men." (Timaeus, p71)
Aristotle |
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Figure 1.19 |
At the age of seventeen Aristotle walked into Plato's Academy and decided to develop his intelligence with a small number of men. Over the next twenty years, Aristotle gained there a broad education in philosophy and mathematics as well as an intimate knowledge of the Platonic doctrine. There is no doubt that as a young man he fully studied the works of every major thinker in the Greek lineage prior to Plato, intially in the shadow of the latter's Ideas. At the age of eighty, Plato died of natural causes in 347 BCE. |
Perhaps because he was dissatisfied with Plato's successor as head of the Academy, Aristotle traveled to the eastern Aegean. He settled for a while on the coast of Asia Minor at Atarneus where he may have attempted to establish a branch of the Academy. Aristotle definitely married there and after three years the couple moved to Mytilene on the island of Lesbos, where he befriended the native Theophrastus who became his student and eventual academic successor. During this four year period, Aristotle exercised his curiosity of marine biology, collecting many samples and deepening his sense of classification by genus and species. Indeed, form and function as manifest in animal and plant may have been a life-long passion.In 343 BCE, after a brief stay in Stagira, Aristotle was called to the court of Macedonia by Phillip II who had ascended the throne and desired a tutor for his thirteen year old son, Alexander. While the boy may not have been too scholarly, Aristotle did his best to imbue Alexander with a reverence for knowledge and scientific investigation.
Seven years passed, during which time a daughter and son were born to Aristotle and his wife. Then Phillip's untimely death brought Alexander to the Macedonian throne. As his student thus graduated into statecraft and the arts of war, Aristotle may have relocated briefly to Stagira before returning in 335/4 to Athens. As his family resettled, Aristotle founded a school in a region of the city known as the precinct of Apollo Lyceus. Although the school was formally named the Lyceum, its members became known as peripatetics due to their ambulatory style of discourse and discussion, modeled after Aristotle's technique. The Great Peripatetic always lectured while walking around, his listeners following closely. Far to the north, Alexander meanwhile busied himself with the political and military resources organized by his father to launch the Macedonian conquest of the known world.
The Lyceum soon became a gathering place for scholars and researchers, offering a substantial library as well as lectures on a variety of topics but without the idealistic agenda of the Academy (which continued to thrive under Plato's successors). Aristotle's lectures, as reflected in his propadeutic manuscripts (see below), covered every domain of intellectual inquiry-- logic, mathematics, astronomy, meteorology, cosmology, biology, physics, metaphysics, ethics, psychology, politics, rhetoric, and poetics. Judging from the breadth of his interests, the apparent structure in his presentation of a given topic, and his occasional statements which address the nature of science, we suppose he was above all dedicated to the enterprize of human knowledge pursued systematically. Each branch of knowledge, as Aristotle envisioned it, could be rooted in a few axioms or statements of self-evident principle particular to that domain of human inquiry, from which theorems or universal statements could be derived and proofs or particular examples could be presented to demonstrate the truth of the matter. He held the same view of artful enterprize in general, respecting the masters of a craft, the orderly sequence of actions required for its daily practice, and the practical steps required for passing the art from master to apprentice.
In most of his treatises, Aristotle uses the first few paragraphs systematically to define the domain of his exposition. Let's take the science of clear reasoning, for example:
"We must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science. We must next define a premiss, a term, and a syllogism, and the nature of a perfect and of an imperfect syllogism; and after that, the inclusion or non-inclusion of one term in another as in a whole, and what we mean by predicating one term of all, or none, of another." (Prior Analytics, I.1.24a10-15)Applying such clarity to the art of poetry, he begins a treatise thus:"Our subject being Poetry, I propose to speak not only of the art in general but also of its species and their respective capacities; of the structure of plot required for a good poem; of the number and nature of the constituent parts of a poem; and likewise of any other matters in the same line of inquiry. Let us follow the natural order and begin with the primary facts. "Epic poetry and Tragedy, as also Comedy, Dithyrambic poetry, and most flute-playing and lyre-playing, are all, viewed as a whole, modes of imitation. But at the same time they differ from one another in three ways, either by a difference of kind in their means, or by differences in the objects, or in the manner of their imitations." (Poetics, I.1.1447a7-18)One of Aristotle's several treatises on ethics begins with a statement that illustrates a primary principle which informs all of his efforts:"Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. But a certain difference is found among ends; some are activities, others are products apart from the activities that produce them. Where there are ends apart from the actions, it is the nature of the products to be better than the activities. Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity-- as bridle-making and the other arts concerned with the equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others-- in all of these the ends of the master arts are to be preferred to all the subordinate ends..." (Nichomacean Ethics, I.1.1094a1-10)Some five pages of means and ends later, we are ready for consideration of the universal good which will lead us to understand the master art of being good human beings. The spirit of Socrates shines through this exposition.While it is good that Aristotle pursued each of his topics systematically, even the most orderly introduction tends to unravel when the domain of inquiry is not neatly bounded by established practice, common sense, and syllogistic reasoning. Or at least an auditor unfamiliar with the state of the art in natural sciences -- in the fourth century BCE unmoored from an anchor of empirical evidence-- might feel lost in Aristotle's presentation of physics or biology. What we might call in retrospect the 'unfinished sciences' were in Aristotle's era muddled at best. Besides all that, Aristotle's method for any given topic was to present all the conflicting points of view. His approach to any given topic has been characterized by a modern scholar of Aristotle's teachings:
"You set out 'what seems to be the case'-- which includes all the 'reputable opinions' on the matter; you then survey the puzzles which this material engenders; you try to resolve the difficulties without disturbing too many of the reputable opinions. And then? Then nothing: your philosophical task is over." (Barnes, p24)Indeed, that task was Herculean and Aristotle's resolution of certain difficulties, e.g. on being and becoming (for which, see the following section), was inventive to say the least. Yet Aristotle did not blaze any new trails in philosophical thought but instead sorted through, organized, and in some cases advanced and/or synthesized the prolific ideations of those who'd come before-- from Thales to Plato. His most unique achievements were in logic, ethics, and ontology (regretably for the latter and admirably for the former two). No doubt Aristotle was always working on one unresolved difficulty or another and encouraged his associates and students to do the same.A dozen years of lecturing and writing passed productively for Aristotle at the head of his Lyceum. Meanwhile, the Macedonian conquest of territory so brilliantly led by Alexander included subjugation of the Greek city-states, including Athens, along with the rest of the civilized world. Athenians resented their loss of sovereignty but dared not trouble Aristotle about his Macedonian past until after Alexander's untimely death in 323 BCE. Subsequently, the Athenians' vehement reaction against all things Macedonian caused Aristotle to leave the Lyceum in the hands of Theophrastus and retreat north to Chalcis on the island of Euboea. There the estates of his deceased mother's family provided Aristotle nearly a year's refuge before a natural illness caused his death.
Writing in the third century CE, Diogenes Laertius listed over 150 titles in a catalogue of Aristotle's works, itself a copy of an earlier list passed down through the generations in lieu of the works themselves. Jonathan Barnes has estimated the listed works contained some 6,000 pages of text of which less than 2,000 have survived in thirty works. (Barnes, p9) What we today have intact of Aristotle was handed down through the Lyceum as each Scholarch (chief scholar and administrator of the Lyceum) did his best to preserve and pass forward the Great Peripatetic's writings. From Aristotle's immediate successor, Theophrastus, to Adronicus of Rhodes, who headed the Lyceum circa 70-50 BCE, there were ten Scholarchs. (Copleston, p426) Over the intervening two and one-half centuries, the Lyceum had waxed and waned while two-thirds of Aristotle's written works disappeared. Perhaps the best was lost. While it is known that he wrote substantially during his years with Plato and his wanderings away from Athens, only a few fragments of those early works have survived the ravages of time. Evidence suggests that those works were well composed in a refined literary style, including artful dialogues in which Aristotle's own voice was primary-- in contrast to Plato's use of the surrogate Socrates.
Compared to those early literary works, the surviving Lyceum collection was more pedagogical, consisting mostly of compilations from unadorned treatises, working drafts, and lectures which were aimed at the small circle of peripatetics. While the thoughts therein may once have been enlivened by Aristotle's animations during lecture, these texts as bare literature seem very dull to read and those on the natural sciences oft confusing. Nonetheless, a scholar of honest thought must find them provocative, and Andronicus did his best to organize what he had into a coherent body of works, some thirty in all. The Adronicus edition of the collection survived down to our time, and we have of Aristotle little more than that. Except for a few of those texts which read smoothly, many bear the marks of works in progress and/or cut-and-paste editing. All too often, lines of thought tend to trail off uncompleted, abrupt abridgements interrupt the development of important themes, and lacunae abound. Some, like the Physics, contain major segments which were written at different periods of Aristotle's life and intellectual development. Some, like his two major works on ethics, contain identical passages, a section from one work obviously copied from the other by an errant editor. One (at the least) may have chapters woefully misplaced. For example, On the Soul appears to contain two final chapters (III.12 and III.13) which belong much earlier in the treatise (between II.4 and II.5, according to Everson, p180, footnote 17).
The most extreme case of editorial doctoring is unfortunately the very work we seek to understand. As Jonathan Barnes has declared,
"The Metaphysics is a farrago, a hotch-potch. [A]s soon as we ask the most elementary question, namely 'What is Aristotelian metaphysics? what study does Aristotle suppose himself to be undertaking in these essays?', we find ourselves in a perplexity. For the texts appear to offer us three or even four answers: the answers are certainly different one from another, and it looks at first glance as if they are actually incompatible with one another." (Barnes p68)The themes of the essays (or, were they scripts for lectural addresses?), sketches, and notes (lecture notes?) hotched together in the Metaphysics include Aristotle's thoughts on a science of first principles, the nature of 'being', the nature of 'substance', the question of theology as 'first science' (which is mentioned only in passing and not pursued), and the ultimate source of causality (i.e., the Unmoved Mover). Throw in a sketch of outstanding problems in philosophy, a philosophical lexicon, excerpts from the Physics, and a few references to Divinity-- viola! melange.If we imagine the task which Andronicus faced, we can hardly blame him for the solution he bequeathed us. All of the surviving Aristotlean corpus existed as a collection of separate scrolls, each containing 5-10 thousand words (15-30 pages) at most, grouped together as 'books' of larger treatises kept on one or another of the many shelves in the library. Just keeping them organized during constant use over the centuries must have been challenging. While the same was true of any manuscript collection in ancient times, few authors had been as prolific as Aristotle and none was so redundant. For example, a consideration of motion in the Physics reads quite similar to that in On the Heavens and On Generation and Corruption. For many of Aristotle's writings, there was neither an obvious story-line nor cast of characters such as the librarian might expect from Plato while working to refile misplaced scrolls. And aside from Aristotle's works on logic, ethics, rhetoric, and poetics, most every paragraph he wrote is peripatetic-- a rambling walk around some subject or another which soon digresses into yet another.
By the time Adronicus was given responsibility for the collection, there were a number of scrolls which had lost their rightful places on the shelves and ended in a heap which had come to be called "ta meta ta phusika" (what comes after the scrolls on physics) on the shelves. Aside from an occasional scroll's mention of "a science of Wisdom" (or "a science of first principles and causes"), little more than the vagaries of time had brought these particular scrolls together-- some fourteen 'books' in all. Not knowing what else to do with them, Adronicus organized them as a single treatise which became serendipitously entitled the Metaphysics. By the same token, as subsequent generations of men pondered the farrago as if it were a meaningful whole, the treatments of similar topics-- first principles, being, substance, essence, formal cause (including the question of Ideas as actualizing), final cause (teleology)-- by other authors were termed 'metaphysical.' The term did not exist before the Scholarchs' neologism took root in the minds of men and its meaning became subsequently as diffuse as its applications.
The initial six pages of the Metaphysics is something of a prologue for "a science of first principles" which soon draws the reader into scroll after scroll of preambulatory consideration-- but nowhere near the science which was apparently promised. We'll examine that promise in Chapter 6, but here we must note that, aside from this prologue, every topic in the Metaphysics had been addressed by Aristotle elsewhere in his corpus-- logical principles in the Analytics; lexical considerations in the Categories; and questions of first principles, substance, causality, and being in the Physics, On the Heavens, and On Generation and Corruption. Are we then to judge that Aristotle's contribution to philosophy is in general metaphysical? Or shall we judge that by weight of complicated thought his Metaphysics is relatively more metaphysical than the rest of his work? Either alternative is confused by the cachet of the neologism grown encrusted over the aeons.
Examples of fanciful thoughts abound in Aristotle's writings not included in his Metaphysics and, if we wanted to begin a list of them on a frivolous note, we might turn to On the Soul (e.g., III.4.429a20-429b5, III.5.430a22-25, III.8.432a1-2) or Prophesying By Dreams (e.g., 2.463b12-20, 2.464a21). At the heavy end of the scale, if we suppose the notion of an Unmoved Mover in Book XII of the Metaphysics to be the most 'metaphysical' of topics, we may find it in the Physics as the 'unmoved movent' which "causes a motion that is eternal and does cause it during an infinite time. It is clear, therefore, that the first movent is indivisible and is without parts and without magnitude." (Physics, the closing sentences.) This God also plays a major role in On Generation and Corruption (II.10.336b24-35). While it may be said that Aristotle paints more of a face on this ultimate being in the Metaphysics (at XII.7) than elsewhere in his writing, his doctrine of four causes-- which serves as a foundation throughout his works on natural science-- at every employment logically demands the Unmoved Mover as the final cause (i.e., the first movent). Having then cause for a second heavy example, we must note that his doctrine of four causes is frequently employed and several times described, although not fully explicated, in the Metaphysics (e.g. I.3.983a24-33, I.7) and yet the reader is therein referred to the Physics (II.3 and II.7) for a complete statement, and the doctrine finally finds its most gainful employment in On Generation and Corruption (II.9 and II.10, especially at 336b24-35).
Let's take the notion of actuality and potentiality, the very foundation of Aristotle's understanding of substance, as a final example of his treatment of 'metaphysical' topics outside the Metaphysics. This thread of Aristotle's writing is perhaps the most 'metaphysical' (in the worst sense of the word) since it promises to explain how materiality is manifest from the immaterial. Yet actuality and potentiality are only discussed over several pages in the Metaphysics (XI.9.1065b-1066b). And this discussion only regards the phenomenon of movement and that only as a restatement (arguably not even written by Aristotle: see Barnes, p67) of the Physics (III.200b25-202a35). As we shall see in the following section, movement for Aristotle is only fully explained as the cosmos is explained and he does not offer such explanation in the Metaphysics, although referring to it. From the Physics, On the Heavens, and On Generation and Corruption, we learn that Aristotle's cosmos consists of a celestial realm which is pure actuality-- nothing comes to be or passes away, the celestial beings (stars and sun) are permanent eternally-- rotating around a center which contains the realm of potentiality, the sublunary world of materiality in which we live. The potentially is actualized from a substratum-- a reservoir of 'prime matter' --from which the perishable material things of our sublunary realm arise and to which they eventually return as they decompose. The nature of the reservoir and its actualization is barely addressed in the Metaphysics (V.7.1017a35-1017b5, IX.8) and mentioned only en passant in the Physics with reference to "the principle that everything either is or is not" which the Parmenideans used to deny motion and change. Aristotle there explains one way out of difficulty with that principle "can be explained in terms of potentiality and actuality. But this has been done with greater precision elsewhere." (Physics, I.8.191b26-28) We are not told where, but presumably it's where we find potentiality and actuality most completely explicated in On Generation and Corruption (II.7-II.10), to which we turn in the next section.
Summary
If neither topic nor treatment in the Metaphysics (aside from the initial six pages on principle) is there treated uniquely in comparison to Aristotle's other works about the cosmos, how are we to specify a metaphysical topic or mark the concept of metaphysics? The question becomes more vexing when we note that any topic which we might deem metaphysical was first raised in one guise or another by one or more of Aristotle's predecessors. Their claims to have explained the true nature of this or that aspect of the cosmos prompted Aristotle to search for the most sound arguments before the rules of, or even need for, empirical evidence had been established.In other words, Aristotle and all of his most important predecessors were engaged in an enterprize of generating far-flung explanations with little regard for evidence. So if the word 'metaphysics' is used to suggest the presentation of fanciful explanations of cosmic proportions while skating on thin evidentiary ice, they were all doing it more often than not. If on the other hand we take the venerable term to mean a science of first principles-- as yet unrealized, including a principle of evidence-- then with Aristotle we may wonder how a principle is constituted, what virtue gives a principle priority, and what is the worth of the principle employed by this or that theorist in explaining any particular-- or every-- phenomenon. We'll further explore metaphysics along principled lines in Chapter 6, leaving the topic now with two observations:
- in the generations after Aristotle few men felt the need to weave with yarns of fresh gossamer because the market was already glutted by the looms of the Greek sages, and would remain so for nearly two millenia; and,
- the principles of natural science invoked by Aristotle to explain the cosmos were over the centuries demonstrated to be fallacious.
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