Greek Philosophy
Socrates & Plato

Philosophic Directions
Refinement and Conversion

1 Philosophy is the love of wisdom. To love wisdom is to pursue wisdom, and the two approaches to wisdom are notable. If you are on the right road, your approach depends on continuing in an effective way. But if you are not on the right road, or if you mistake your road for the right road, then you need to change directions. Much useful philosophy results from refining assumptions, from modifying views. But Socrates and Plato focused intently on conversions, beginning with destabilizing tradition, convention and common sense. WHAT we see depends on HOW we see. Socrates and Plato focus energies on changing HOW we see.

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Socrates

Ethical Appeals

Aristotle divides persuasive appeals into three categories ethical, rational and emotional. Ethical appeals, according to Aristotle, are not the mere attention to good and bad attitudes and actions. Judging ethical appeals depends on the perceived character of the speaker. Pre-eminent among philosophers as a credible speaker is Socrates. Socrates invites reconsideration and conversion. Like Aeschylus’ practice of recognition, Socrates questioning initially leads to disorientation, a motion away from appearances, sensations, conventions, to an indeterminate openness to discovery. Socrates’ character and reputation draws attention to this interest and focus, sometimes positively, sometimes critically.

What makes Socrates an engaging voice? A combination of irony and conviction. Socratic irony plays variations on the weak foundations underlying conspicuous authority. The Delphic Oracle identified Socrates as the wisest of mortals. Puzzled, since he was painfully aware of his ignorance, because his mind gravitated to questions, not to answers, because his years of questioning and his innumerable discussions with a range of Athenian and foreign participants had raised more questions, Socrates eventually concluded  that his distinction was to be aware of his ignorance. Without doubt, the discovery of a fresh approach necessary to approach true knowledge would be impossible.

Socrates’ character and personality generated controversy. Eventually an Athenian jury would sentence him to exile or to death, and an Athenian to the last, he drank the hemlock which ended his mortal life. Charges against him included disrespect for religion, an inappropriate reliance on natural science, and a disrespect for tradition. Moreover, his appeal to young Athenians in formative periods of life, threatened Athenian tradition and traditional Athenians. He took Athens as the rare city which allowed such critical activities, choosing death as a loyal Athenian to life elsewhere. :He could not and would not stop questioning, stop his quest. His interest in questioning all belief (as an approach to discovering beauty and truth) appeared as an attack on prominent Athenians and as an attack on Athens.

Socrates’ influence depended as much on his character as on his philosophical approaches. His disinterest in material possessions and in status combined with his attention to the mind and spirit. Among his most memorable activities was an event during the retreat from Persian forces after heavy casualties at Potidaea. A leader in organizing dispirited soldiers for retreat, Socrates, before joining the retreat, paused, lost in thought, his attention elsewhere. Plato’s Appolodorus recalls this memorable scene when guests assembled at a symposium learn that the absent Socrates appeared once more lost in thought as one of the guests passed him on the way to the party.

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Pericles
Rational Appeals

Pericles considered Athens as a distinctive city, a city in which characters and activities like those of Socrates drives Athenians to defend their way of life at all costs. Athenians, leading the defense of Greece when Persians invaded (in 490bc and in 480bc) could not imagine living under restrictions of traditional cities (including Sparta), where acting in accordance with how people previously acted, living with institutions like previous institutions, took precedence over the discovery of new character and new institutions, as well as a new sense of history inviting adaptations to changing circumstances. Pericles’ invitation to love Athens, rather than idolize the bravery of the greatest of soldiers, parallels Socrates love not just of philosophical beauty and truth, but more of the practices necessary to discovery, the character necessary for conversion. Pericles’ funeral oration invites audiences not merely to support democracy, but more to practice philosophical approaches to history.

If mourners at a funeral, threatened with invasion, death and slavery, are to survive, they must appreciate the way of life defended by deceased soldiers. They must think, as well as act, as Athenians.

View events historically. How do funeral practices arise? How do traditions relate to circumstances? In new circumstances, how may new traditions arise? If plague threatens Athenians, how does it arise? What courses does it follow? What peculiarities are discernable worth the consideration of others, present or future? Pericles argues that Athenians, falling in love with Athens will distinguish themselves from traditional citizens including Spartens: they love not just their city, but the character and practices that make Athens a new world

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Plato’s Cave
Emotional Appeals

Plato’s Parable of the Cave still offers participants a surprising experience. Imagine yourself in the most compelling of times, places, company and activities Plato suggests. Your circumstances, person, and company appear real in large part through sense perceptions. But consider an alternative. Observe another person, chained in immobility, looking at the polished walls of a cave. Images move, grow, diminish, approach and depart. In this projection, not unlike a movie screen, mere projections attract involvement, arouse passions. What appears most engaging and convincing to us may be no more than superficial appearances. Plato’s projection lamp is a flickering fire behind his audience. His images are objects on a ledge. As the fire flickers and the objects arrange and rearrange, their projections on the cave walls in front of us are the only images we have ever reacted to. We are immobile, but our immobility never appears to us, since flickering images provide action. We are immobile, so we never have an alternative perspective to reveal the originating activities which create our sensational world.

Were we to turn back, however, the projection lamp, too bright for our unaccustomed eyes, would blind us, would painfully burn our eyes. Leaving the cave, of course, we would not see and appreciate a world far more real than that projected world we had taken as our only experienced world. We would be even more disabled. Only with time might we accustom our senses to new inputs, might we “see” not merely new objects, but the way in which sunlight makes possible not only the appearance of objects, but also the ways in which they move, grow, relate, diminish.

Outside the cave, of course, engaged in real sunlight, with illuminated objects, with an awareness not just of things, but also of relationships, of originating principles, we note with pity the inhuman restrictions limiting, chaining, enslaving the residents of the cave. But those within the cave, knowing nothing else, have no such thoughts and feelings. Their world, the only world they experience, appears neither more nor less real than our own. But we, Plato suggests, are not observers of cave-dweller, ourselves perfectly situated in our won real world. Our world itself is the cave. And we, like the cave-dwellers we have imagined, will find discovering our superficialities a painful experience.

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Plato’s Line

Rational Appeals

To leave our cave we must discover a new world. How are we to do so? By distinguishing between belief and knowledge, by moving from the sensible to the intelligible. Could we once have the experience of true relationship Plato believes, we would be unlikely to find satisfaction in the objects, company, activities and assumptions we previously experienced, assumed, used and valued. How are we to experience such a key to conversion? For Plato mathematics offers just such a conversion. Through a geometrical demonstration, we may discover the light bulb turns on.

Among the most distinctive of all Athenian activities is the systematic discovery of geometry. Egyptians, among others, had extensive knowledge of shapes, knowledge sufficient to engineer architecture as memorable as any ever produced. Knowledge sufficient to justify boundaries yearly erased by the flooding Nile, returning chartered land to productive use. But consider the pentangle associated with Pythagorean communities. Take a pentagon. Inscribe a five-pointed star. Note the inscribed pentagon. Now inscribe once more the star. Take the original pentagon. Extend the sides, noting your circumscribed star. Joining the points, form the circumscribed pentagon. Your figure has no outermost or innermost limit. The shape grows and diminishes according to a generating principle. Christian Platonists will later explore Pythagorus’ active emblem through Solomon’s knot, a reincarnation of the Pythagorean pentangle which appears, for example, on Gawain’s shield in medieval romance.

Plato’s Meno offers a preliminary approach to his divided line. Return for the moment to the Nile valley. You have a square plot of land. You wish to sell a square of your plot half the size of your total square. Of course you can approximate such a plot. Divide the square into quarters. One quarter isn’t enough. Divide each quarter into quarters. 9/16ths is too much. Divide each sixteenth into quarters. 1/4, 5/8, 7/16, 31/64 . . . Every step approaches closer to the desired plot. But every step alternatively will be just too small, or just too big. (You probably “know” that the square root of 2 is irrational, that it can never be measured in perfect fractions of 2. But Greek geometers “see” such limitation through demonstration, and what they see they know as an experience, not merely as an alleged “fact”). Now mark the midpoints of each side of our original square. Joint these points to form an inscribed square. See how each quarter-square encloses two equal triangles (fold square to see how each triangle covers the other). Your inscribed square encloses four equal squares, leaving four additional equal squares to form the circumscribed square. We can see our inner square as exactly half the area of our original square. Unlike the square which “looks” close to half the original square, a sensible half-square, this square is we “see” as half the original square is an intelligible square.

Plato’s divided line invites us to a more surprising experience: the discovery of a division which has most unlikely generative properties, properties including those which unravel Solomon’s knot. Take a line and divide it unequally. Assume the longer side to be to the left of the division, and consider this segment to represent the sensible experience. Assume the shorter side to be to the right of the division, and consider this segment to represent intelligible experience. Now divide the longer segment unequally, such that the lengths of the two segments are proportional to the lengths of the original line segments. How are we to make such divisions?

 Form a pentagon and then extend sides to form the circumscribed star. Each arm of our star, together with a side of our pentagon forms a divided line. Now consider the remaining arm of our star. It forms a segment of the line also containing our original two segments. We could explore a procedure to produce these segments clearly with an intelligible procedure, but such would require following Euclid at some length. For the moment assume the ratio of segments to be (the square root of 5 + 1)/2. You can take a square; divide in half horizontally; form the diagonal of the upper square; rotate the diagonal to form a vertical line. Now the lower half segment of the original square plus the rotated segment forms the longer unit and the bottom of the original square forms the shorter segment of our divided line. But “seeing” such relationships will take energy and time.

Perhaps, like our half-square procedure, we can approximate such a division. Consider the numbers generated by adding successive numbers such that each addition sums the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 35, 56 . . . Some two millennia after Pythagoras Fibonacci initiated consideration of peculiar features of this sequence, features which include convergence on Plato’s divided line, as well as modeling of stock fluctuations under particular conditions.

Why does Plato remind all who seek his guidance to study mathematics? First, because mathematics is intelligible: it discovers not facts, but the principles through which significant facts manifest themselves. Mathematics is systematic, is structural, is intelligible. Next, because astonishing regularities far from expected  may reveal generating principles for appearances. Consider the infinite sequence of integers. In 1742 Goldbach conjectured that every even number greater than 4 is the sum of two primes. Every number can be generated from the multiplication of two primes (with the addition of 1 for odd numbers). To date no proof for this conjecture has appeared, but no exceptions have been found. Reconsider such numbers as generated by prime numbers (numbers not divisible by other numbers. Generating small numbers from primes may not appeal ( since many primes appear among small integers), but as integers grow larger, primes grow increasingly scarce. For large numbers, a relatively tiny number of primes will suffice to create all such numbers.

Geometry, like geography, seeks to make the earth intelligible. Geography maps the  world, and maps require principles. Geometry enables participants to make intelligible (as well as practical) their world. As head of the great library of Alexandria. Eratosthenes noted, filed and considered the widest range of views available in his time. Hearing that  a well existed in Cyrene (modern Aswan) where light reached the bottom on one day of the year (the longest day, the summer solstice), Eratosthenes made intelligible the size of the earth. In Cyrene the sun was directly overhead (we might consider the overhead sun to indicate that Cyrene lies on the earth’s equator, but Eratosthenes lacked both globe abd encylopoedia). On the longest day, Eratosthenes placed a stick in the ground pointing directly upward. When the shadow cast by the stick was shortest (indicating the sun was highest), he marked the length of shadow. The angle at the top of his triangle was about 7 degrees. He understood that the circumference of the earth was about fifty times the3 distance between Alexandria and Cyrene. Allowing for  uncertainty as to the precise length of the stadia he used as a unit in his recorded distance, his intelligible circle was remarkably close to 25,000 miles. Galileo will later “see” the circumference of the moon, and the distance of the moon from the earth.

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Philosophical Skepticism
Plato and Gorgias

Plato’s intellectual competitors (notably Gorgias) were sophists who shared with him the skeptical character which precedes fresh discovery, without which conversion could not arise. Sophists believed that man is the measure of all things. Man is the measure not because man is omniscient, certainly not due to omnipotence. In the absence of perfect inspiration human truths will be partial, will be relative. Open debate, in the mind, in the market place, in the courts, will not reveal truth. But debate can shape more productive attitudes and actions than rigid tradition or unreflective common sense. Choices among beliefs may be decided not by habit, and not by objectivity, but rather by consideration of plausible consequences of competing approaches. Aware of fools and knaves, the former imagining they alone possessed true knowledge, the later manipulating subjects with the pretence of certainty, Gorgias sought to educate his followers in fruitful rhetoric, a skill crucial to political as well as personal advancement.

Plato shared with Gorgias a distaste for tradition, convention or common sense as sufficient evidence of truth, but believed true directions towards wisdom were intelligible, however demanding travel would be. Plato further believed that the consequences of taking rhetoric as the guide for actualizing desires, personal and social and political, would be disastrous.

Philosophy for Plato is the pursuit of Wisdom. Serious practitioners of philosophy develop powers of skepticism to limit the appeal of tradition, of convention, of common sense. But serious philosophers also must keep in mind credible experiences where the approach to objective truth, where the experience of attending true beauty, not mere theorizing, are actual, personal experiences. Plato shares with Gorgias a sceptical a scepticism towards traditional understandings of truth. But he invites followers to experience through geometric demonstrations experiences which reinforce approaches to systematic truth.

Leaving Plato's Cave: The Divided Line

We will join Socrates at Plato’s Symposium to share in the pleasures of instruction and the instruction of pleasures.

Plato’s Art of Love: The Symposium