ἀγεωμέτρητος μὴ εἰσίτω
Without Geometry, Enter Not.Sign over the door of the Academy
John Philoponus, In Aristotelis De anima libros commentaria,
Commentaria in Aristotelem graeca, XV,
ed. M. Hayduck, Berlin, 1897, p.117,27 [note]
Ἐὰν μή, ἦν δ᾽ ἐγώ, ἢ οἱ φιλόσοφοι βασιλεύσωσιν ἐν ταῖς πόλεσιν ἢ οἱ βασιλεῖς τε νῦν λεγόμενοι καὶ δυνάσται φιλοσοφήσωσι γνησίως τε καὶ ἱκανῶς καὶ τοῦτο εἰς ταυτὸν ξυμπέσῃ, δυναμίς τε πολιτικὴ καὶ φιλοσοφία, τῶν δὲ νῦν πορευομένων χωρὶς ἐφ᾽ ἐκάτερον αἱ πολλαὶ φύσεις ἐξ ἀνάγκης ἀποκλεισθῶσιν, οὐκ ἔστι κακῶν παῦλα, ὦ φίλε Γλαύκων, ταῖς πόλεσι, δοκῶ δ᾽ οὐδὲ τῷ ἀνθρωπίνῳ γένει.
"Unless," said I, "either philosophers become kings in the cities or those now called kings and rulers love wisdom seriously and adequately, and there is a conjunction of these two things, political power and philosophy, while the motley horde of the natures who at repesent pursue either apart from the other are excluded by force, there will be no end of evils, dear Glaucon, for the cities, nor, I think, for the human race either."
Plato, Republic, 473c-d, Republic I, translated by Paul Shorey, Loeb Classical Library, Harvard University Press, 1930, 1969, p.509, color added, translation modified.
Τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν τὴν τοῦ ἀγαθοῦ ἰδέαν φάθι εἶναι, αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας ὡς γιγνωσκομένης μὲν διανοοῦ...
This reality, then, that gives their truth to the objects of knowledge and the power of knowing to the knower, you must say is the idea of the good, and you must conceive it as being the cause of knowledge [ἐπιστήμη] and of truth [ἀλήθεια] in so far as known.
Plato, Republic, 508e, Republic II, translated by Paul Shorey, Loeb Classical Library, Harvard University Press, 1930, 1969, pp.102-105, color added.
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| Scuola di Atene, School of Athens, 1511, by Raffaello Santi/Sanzio da Urbino (1483-1520), detail of Plato, Vatican Apartments, Rome; Raphael modeled the face of Plato on Leonardo da Vinci (1452-1519) |
When Socrates was executed in 399, Plato was 28 years-old. He even went into exile for a while, but then returned to found the Ἀκαδήμεια, the Academy, in a grove of trees just outside the walls of Athens (a short walk from the now excavated Dipylon Gate), purportedly named to commemorate an Olympic athlete.
This was in the period from 387 to 385, in an area that is now completely surrounded by modern Athens. In fact, there are a couple possible sites for the Academy, one of which, suggestively, is an old monastery, which may have inherited buildings when the Academy was closed in 529 AD -- if the Academy of that period was even on the same site as earlier.
Plato's later adventures in Sicily, his only known trips outside Athens, were the result of foolish ideas about educating a tyrant into philosophy, and of his disdain for democracy. Both tendencies we can detect in the Republic.
Plato usually wrote relatively short pieces, like the Euthyphro, Meno, etc. In all his writings there are only two book length works, the Republic and the Laws. The Laws was the last thing Plato wrote, at eighty, and it is a grim and terrifying culmination of the totalitarian tendencies in his earlier political thought. It is also pretty dull, since Plato had all but abandoned his earlier lively dialogue format. The Republic, however, is the supreme product of Plato's most mature years, thought, and style. It contains virtually the entire universe of Plato's philosophy.
The word "republic" is from Latin: Res publica means "public matters" or "the state." In Greek, the title of our book was the Πολιτεία, Politeía, which means the Constitution. In the Middle Ages, Greek Πολιτεία translated Respublica as the kind of government of the Roman Republic and Empire. See recent discussion in The Byzantine Republic. But Plato's Republic does not start out about politics. It is initially a familiar kind of Socratic dialogue about justice, just as the Euthyphro is about piety and the Meno is about virtue. The Republic is divided into ten Books. Each of these was originally what would fit onto one papyrus scroll. By late Roman times, the scrolls were cut up and sewn together into codices, or the kind of bound books that we continue to use.
The entire first Book of the Republic may originally have been one of the standard early dialogues that Plato wrote about Socrates. Later it was expanded. Unusual features of the dialogue, however, are (1) that Socrates [note well that Plato continues to use Socrates to speak Plato's ideas in all his mature works] actually narrates the entire thing, (2) that he speaks with a large number of people, not just one, (3) that these include two brothers of Plato himself (Glaucon and Adeimantus), and (4) that, after the dialogue about justice proceeds in the fashion that we expect of Socrates, things take an unexpected turn: One of the characters, the sophist Thrasymachus, begins to object that he knows quite well what justice is, and that the kinds of definitions the others have been giving are nonsense.
Thrasymachus says:
For I declare justice is nothing but the advantage of the stronger. [Republic 338c, note] Robbery and violence are normally called "injustice," but when they are practiced wholesale by rulers, they are justice, i.e. the interest of the stronger, the rulers. Thus, when we consider ordinary citizens, "the just man comes off worse than an unjust man everywhere" (343d). Since the rulers do not obey the principles they impose on the citizens, they are in those terms "unjust." So Thrasymachus says, "You will understand it most easily, if you come to the most perfect injustice, which makes the unjust man most happy, and makes those who are wronged and will not be unjust most miserable" (344a).
Thus to Thrasymachus the tyrant is happy and fortunate, and he is so precisely because he breaks the rules ("justice") that he imposes on the weak. What the weak call "justice" is really slavery, and no one truly strong would act that way. Such sentiments are familiar in modern philosophy from the still popular and influential German philosopher Friedrich Nietzsche (1844-1900).
In Book I Socrates proceeds to refute Thrasymachus and does so. If the weak, after all, can prevent the strong from taking what they want or can prevent someone from becoming a tyrant, then they are the strong! Thrasymachus is finally quieted. At the beginning of Book II however, Socrates is told by Glaucon and the others that this was all too easy. They argue that anyone would be unjust, given the opportunity, just as Gyges seduced and murdered his way to the throne of Lydia, once he had found a ring that made him invisible, because everyone believes that injustice leads to happiness, if only one can get away with it [note]. They want Socrates to prove that it is better to be just than to be unjust even if the unjust man is praised, celebrated, and rewarded and the just man is reviled, punished, and rejected. Socrates must prove that such a just man is actually happy and such an unjust man (a tyrant perhaps) is unhappy.
As I have examined elsewhere, the Greek virtue of being "just," δίκαιος, díkaios, is often more what in English we would call "right" or "righteous." In Greek, "right, correct, straight" is ὀρθός, orthós, which is really not used in this moral sense. In Latin, δίκαιος would be jus, "right," which gives us justitia, i.e. "justice," while ὀρθός would be rectus, "straight," which is itself a cognate of "right." Thus, the question of the Republic might be better put as "Why be righteous [Biblical δικαιοσύνη]?" rather than "Why be just?" We will then not be surprised when there is nothing in the Republic about lawcourts or even law, which we now associate the most directly with justice -- and which are even used by the judicial positivists to define "justice."
The rest of the Republic answers Glaucon's challenge. It does so by way of an analogy. Socrates says that it is difficult to distinguish what is going on in the soul, but it is easier to see what is going on in the state. Thus the state will be examined by analogy to the soul. Now we would say -- Plato doesn't use this terminology -- that the state is the macrocosm (μακρός, makros, "large," κόσμος, kosmos, "universe"), the large scale analogue, and the soul is the microcosm (μικρός, mikros, "small"), the small scale analogue. When matters are sorted out for the state, then the soul can be understood in its own right.
As it happens, Plato ends up using the theory of the soul that he also proposes in the Phaedrus. The soul, on this view, has three parts, which correspond to three different kinds of interests, three kinds of virtues, three kinds of personalities -- depending on which part of the soul is dominant -- and so, properly, to three kinds of social classes that should be based on the three personalities, interests, and virtues.
"Spirit," θυμός, is in the sense of a "spirited" horse. Plato thinks that this is the energy that drives the soul and may be used to reason to keep desire in line. Temperance, or moderation, σωφροσύνη, will mean the limitation of desires. The word "temperance" is now a little archaic, and it tends to suggest "temperance" as it came to mean abstention from alcohol, as was advocated in the early days of this century by Cary Nation and the Women's Christian Temperance Union, who brought about Prohibition. The three parts of the soul also correspond to places in the body: reason to the head, spirit to the heart, and desire to the organs of desire, mostly in the abdomen. Plato simply made a good guess that reason had something to do with the brain. There wasn't a lot of evidence about this; and many people, including the Egyptians and Aristotle, thought that intelligence was centered in the heart. When the Egyptians mummified bodies, they actually used to throw the brain away, while the heart was carefully prepared and replaced in the body. Remember later in the course to compare Plato's parts of the soul and social classes with the doctrine of the gunas and the varnas later in Indian philosophy.
Now, Plato was originally looking for justice, but justice does not appear in the list of virtues. The answer is that justice applies to them all in the sense of their organization. Reason (and the philosophers) should be in control, with the help of spirit (and the warriors). The philosophers and the warriors are thus the "Guardians," φύλακες (singular φύλαξ), of Plato's ideal state. This does not seem like a familiar sort of definition for justice, but the result, Plato says, is that each interest is satisfied to the proper extent, or, in society, everyone has what is theirs. The philosophers have the knowledge they want; the warriors have the honors they want; and the commoners have the goods and pleasures they want, in the proper moderation maintained by the philosophers and warriors. The root of all trouble, as far as Plato is concerned, is always unlimited desire [note].
John E.E.D. Acton, or Lord Acton (1834-1902) famously said, "Power tends to corrupt, and absolute power corrupts absolutely." Even Plato was aware of this and that commoners might be envious of the power of the Guardians, desiring it for themselves so as to obtain greater goods and pleasures. Thus Plato proposes a set of rules for his Guardians that would render their position undesirable to the commoners:
When I used to live in Honolulu, occasionally I liked to visit the State Legislature when it was in session. The Hawaii State Capitol is unique, with an open central courtyard instead of the traditional dome and rotunda. On each side of the courtyard, you can look through windows down into sunken chambers for the two houses of the legislature. When the legislature is in session, you can enter a visitors balcony through doors in the windows. You sit in the balcony, however, on hard wooden benches, like church pews, while the legislators below sit on huge, stuffed, reclining, leather chairs that look good enough to sleep in -- and you will often see the lawmakers, indeed, sleeping in them. This has always struck me as just the opposite of what Plato would have required. It is the visitors, the commoners, who should have the comfort and the "servants of the people," the politicians who should have the Spartan conditions -- but what we see now suits the comfort and status of the ruling class.
With these views about nudity, the Greeks were all the more impressed with India when Alexander the Great arrived there and found naked holy men. These were Jain monks, and others, who had renounced the world even to the extent of renouncing clothing also. The Greeks called them the Γυμνοσοφισταί, gymnosophistai "naked philosophers" (well, "sophists"); and Greek philosophers like Pyrrho of Elis, who was with Alexander's army, reportedly spent a great deal of time talking with them. Pyrrho, at least, seems to have actually picked up some ideas from Indian philosophy thereby. Naked monks still exist in India. They are called Of all the serious criticisms that can be made against Plato's ideal state, I think that a couple of the most telling are that his theory involves two serious internal contradictions:
Taking Plato's theory at face value, however, does not answer the whole challenge originally posed by Thrasymachus. This might give us a definition of justice, after a fashion, but it does not show why it is better to be just or why the just person is happier. Plato does that in Book VIII of the Republic by examining "imperfect" states. He imagines what would happen if his ideal state decays.
Recent economists in the area of Public Choice theory [e.g. James M. Buchanan and the Virginia School of Public Choice], have described how the politicization of economic goods inevitably creates increased public conflict as the sense grows that wealth is something to be seized and distributed through state action. As everyone comes to believe that their prosperity depends on political success and consequent government largess, such a dynamic will tend to destabilize democracy, since in politics there are always losers and they begin to think that they are victims of the regime and have no stake in it.
Capitalism is often disparaged as a system with "winners and losers," but the losers in capitalism are just the unsuccessful businesses, while the winners do win by providing what is most agreeable to consumers. In politics, the "winners and losers" are both consumers, and the losers are those who are then legally robbed to pay off the winners, who have the power of the state to take what they want (if you rob Peter to pay Paul, you can at least get Paul to vote for you).
One would think that the United States Constitution shuts off any drift towards a regime of seizure and redistribution because of the "Takings" clause of the Fifth Amendment: "Nor shall private property be taken for public use, without just compensation." The Takings clause, however, was an early casualty of enthusiasm over the New Deal and has steadily eroded ever since. It is only now that a movement has developed, and received some attention from the Supreme Court, to enforce it -- though the recent Kelo v. City of New London decision represents a setback.
For Plato's argument, the tyrannical state is the final refutation of Thrasymachus. It is clearly the most unhappy kind of state. Thrasymachus, of course, can argue that he doesn't care. It is Plato's analogy, not his. All that matters is whether the tyrant himself is happy or unhappy. Plato's answer to that is to identify the nature of the "tyrannical personality": since the tyrant is subject to completely unlimited desire, he can never be satisfied with anything he has. He will always want more. That is also the answer in a famous scene in the 1948 movie Key Largo, with Humphrey Bogart and Edward G. Robinson. Robinson is a gangster holding a hotel full of people, including Bogart, hostage. Bogart at one point asks him what he really wants out of all this. Robinson can't say, so Bogart, like Socrates, makes a suggestion: is it that what he really wants is just more? Robinson says, yes, yes, he wants more, more! That is the tyrannical personality.
In our century, it is not hard to find tyrannical personalities to fit Plato's description. Both Hitler and Mussolini were undone by their inability to be satisfied with their successes. When Hitler had conquered France, there was only one country left in the world at war with him, Britain. Stalin's Soviet Union was busy mollifying Hitler by supplying him anything he needed. If Hitler had been content to absorb his conquests and develop Germany's potential, there is no doubt that he would have been in little danger for some time to come. He destroyed himself because he just had to invade Russia. Similarly, Mussolini was cautious enough that Italy remained neutral when Britain and France declared war on Germany for invading Poland. He lost his caution when he saw France defeated and decided to jump on Hitler's bandwagon. It meant, literally, his death. Otherwise Mussolini might have ridden out the war and died peacefully in bed, like his colleague the dictator of Spain, Francisco Franco.
Franco, however, is one of the people who spoils Plato's argument. Hitler really wanted Franco in the war. And he knew that Franco, and Spaniards in generally, really wanted to recover Gibraltar, after over two hundred years, from Britain -- Gibraltar was captured by Britain in 1704 during the War of the Spanish Succession and ceded to Britain by the Treaty of Utrecht in 1713 -- one of the British admirals leading the capture had the extraordinary name of "Clowdisley Shovell." Since Gibraltar was a thorn in the side of German and Italian operations in the Mediterranean, Hitler told Franco that if Spain entered the war, German troops would take Gibraltar and then give it to Spain. It was the kind of offer Franco couldn't refuse, but he did.
Franco knew how to limit his desire, but that didn't prevent him from being a serious tyrant -- and now we know that Hitler's own envoy to Franco, Admiral Wilhelm Canaris, was actually advising him against accepting Hilter's offer! -- eventually, in 1944, Hiltler learned that Canaris had been working against him and had him executed. Worse is the case of Josef Stalin, who had an uncanny ability to bide his time and to take advantage of every opportunity.
To the embarrassment of Western leftists, World War II itself began with Hitler and Stalin actually partitioning Poland between them. When Stalin subsequently invaded Finland, there was a moment when it looked like the Soviet Union might join Germany as the common totalitarian enemy of the Western democracies. When Stalin became an ally of the West instead (when Hitler invaded Russia), he could cash in his position with a post-war empire than would have been the envy of the Tsars.
Poor Poland, whose fate called Britain and France to war in 1939, and whose exiled citizens fought bravely in many of the major actions of World War II, including many Polish pilots in the Royal Air Force during the Battle of Britain, was at Yalta left to Stalin without argument by Franklin Roosevelt and remained a vassal state of the Soviet Union until 1989.
Although Plato didn't know about such a variety of tyrannical personalities, he seems to have felt that his ultimate argument about the unhappiness of the tyrant was not strong enough. To seal the argument, he ended the Republic with a myth: the Myth of Er. Er was supposed to have been a soldier who was struck down and left for dead in a battle. When the bodies were collected after ten days for burning, Er revived and said that he had seen the reward of the good and the punishment of the wicked in the hereafter. After the judgment of the gods, the souls of the dead went to a place of reward in heaven or a place of punishment in the underworld. Since Plato believed in reincarnation there were no eternal rewards or punishments -- except for an evil few who were not allowed out of Hades (as in Buddhism). All the others had to face the prospect of their next life, and they were given the opportunity to choose the character of their next life from a variety of alternatives.
The Republic thus ends rather lamely with the argument that we better be good or the gods will punish us. We hardly needed to go through the whole book just to be told that. But in the midst of this there comes a very striking moment. Er describes the souls choosing their next life. The first one he sees doing this chooses badly (as in Indiana Jones and the Last Crusade, 1989) -- the life of a tyrant who is fated "to eat his children and suffer other horrors" [Republic 619b-c, Rouse p.420]. Plato's comment about this reveals an important principle of his thought: This was a person who had lived a good life and had just returned from a reward for it in heaven. But, says Plato, he had "some share of virtue which came by habit without philosophy." That is how Rouse puts it, p.420. Lee's translation is, "having owed his goodness to habit and custom and not to knowledge," p.399. The terms in Greek are ἀρετή, aretê, "virtue"; ἔθος, ethos, "custom," "habit" (only one word in Greek); and φιλοσοφία, philosophia. So Rouse's translation is more literal.
This was a prescient critique of Plato's own student Aristotle, who later believed that virtue actually was a matter of habit and that the good had no independent nature to know, as Socrates and Plato had thought. Plato, of course, can allow for Aristotle's kind of virtue, but he regards it, as at the end of the Meno, as a matter of correct opinion only, not knowledge. The shortcoming of that kind of virtue is that, being habitual, it is effective only in habitual circumstances.
In unfamiliar circumstances, where novel cases of good and evil must be recognized, the person does not possess the knowledge that would make that recognition possible. Socrates had asked Eurthyphro for a definition of piety so that he would "look upon it" and "use it as a model [παράδειγμα]" [Euthyphro 6d] to recognize novel cases of piety and impiety. The soul that picks the terrible life of a tyrant obviously has no model and doesn't know what it is doing. This is why Meno actually makes a good observation at Meno 97c, when he says, "he who has knowledge will always succeed, while he who has right opinion will sometimes succeed, sometimes not." Although Socrates oddly disagrees with this, the point is to be well taken that right opinion will only work for a limited sphere of possibilities, the familiar ones, while knowledge will always work.
In the end, probably the most enduring image of the entire Republic, as an expression of Plato's view of life and the world, is the Allegory (or Simile) of the Cave. This occurs in Book VII (at 514), following his discussion of the Divided Line (in Book VI), Plato says that we are all like prisoners chained up on the floor of a cave. We are so restricted that we can only look in one direction, and there we see shadows on the wall that seem to talk and move around. We and our fellow prisoners observe, discuss, and remember what these shadows do or say.
But, what happens if we happen to be released from our chains? We stand up and look around, and we see a fire burning at the back of the cave. In front of the fire is a low wall, and on the wall puppets are manipulated, which cast the shadows that are all we have ever seen. So suddenly we realize that all the things we have ever known all our lives were not the true reality at all, but just shadows [σκιαί, skiai] -- significantly the same word that occurs at the end of the Meno, when Plato says that the statesman who can teach his virtue and make another into a statesman will be like "the only true reality compared with shadows," ὥσπερ παρὰ σκιὰς ἀληθὲς ἂν πρᾶγμα εἴη [100a, Plato: Laches, Protagoras, Meno, Euthydemus, translated by W.R.M. Lamb, Loeb Classical Library, Harvard University Press, 1924, 1962, p.370; "Meno," Plato, Five Dialgoues, translated by G.M.A. Grube, Hackett Publishing, 1981, p.88].
But there is more. There is an exit from the cave, which leads up to the surface. There we are at first blinded, but then begin to see trees, animals, etc. which in the cave were only represented by puppets. Eventually we notice that all those things exist and are knowable because of the sun. Returning to the cave, we would at first be blinded by the darkness, and our fellow prisoners would have no idea what we were doing or saying -- they would probably regard us as insane -- but we could not, of course, take them seriously for an instant.
In modern terms, Plato's description of the cave bears an uncanny resemblance to a movie theater. There we do indeed sit in the dark with our fellow movie goers, not looking at them but at the screen. Instead of a fire and puppets, we have a projector light and film. Instead of shadows, we have focused images -- much more compelling than shadows, but something about whose possibility Plato did not have a clue. But what we see on the movie screen, in turn, usually bears no more resemblance to reality than what Plato expected from the shadows on the cave wall.
The freed prisoner is, of course, the philosopher. The cave itself represents the world of Becoming and its fire the physical sun in the sky. The world on the surface outside of the cave represents the world of Being, where the individual objects are the Forms -- eídê, εἴδη (singular eîdos, εἶδος) or idéai, ἰδέαι (singular idéa, ἰδέα). Two peculiarities of the Allegory of the Cave, however, are the status of the shadows, as opposed to the puppets, and the nature of the sun. If the puppets are the actual objects in the world of Becoming, then the shadows must be people's opinions. We do mostly go through life paying attention to people's opinions rather than to the things themselves, so that is suitable. Plato, of course, thinks that even the things themselves are like shadows of the Forms. The sun, in turn, is a unique kind of Form: the Form of the Good, ἡ τοῦ ἀγαθοῦ ἰδέα [508e].
This is a unique moment in Plato's writings, since he does not elsewhere single out any Form as different in kind from the others, and he does not elsewhere pay any sustained attention to the good as such. He has already said in the Republic (at 506) that he cannot really give a definition of the good. He will only give us an analogy, that the good is to knowledge and truth what the sun is to light and sight.
The Good therefore may be said to be the source not only of the intelligibility of the objects of knowledge, but also of their existence and reality; yet it is not itself identical with reality, but is beyond reality, and superior to it in dignity and power. [508e-509b, Lee translation, p.273.] This is suggestive and intriguing, and Plato's own students wanted to hear more. Once Plato even promised to give a lecture on the good. But when the day came, all he did was do a geometry proof. So we are left at a kind of incomplete pinnacle of Plato's thought, with a sense of how important in reality the good is, but with mostly metaphorical statements about it. That was either the best Plato thought he could do or, like the Pythagoreans, he thought that his most serious views should not be spoken in public. Later the Neoplatonists would simply conclude that the Form of the Good was God, but there is no hint of that in Plato. He goes so far and then, like Parmenides, leaves us to continue the quest.
Plato's actual argument for why we should be just suffers from a fundamental misconception. He is always recommending justice from prudential considerations, i.e. we should be just because of our own best interest, either to be happy (the main argument) or to avoid the punishment of the gods (in the Myth of Er). If there is a difference between moral and merely prudent action, however, Plato has misdirected us. Instead, morality may require actions that are not in our self-interest. This is agreed upon by Immanuel Kant, Confucius, and even the Bhagavad Gita. Thus, Confucius holds that righteouness,
The famous sign about geometry at the Academy is surprisingly attested only in very late sources. First of all is John Philoponus, who of course did not live until the remarkable Age of Justinian in the 6th Century AD. He tells us that it said ἀγεωμέτρητος μὴ εἰστίω, "Without geometry, enter not." We get a slightly different version from another commentator on Aristotle, Elias, a younger contemporary of Philoponus, who reports it as ἀγεωμέτρητος μὴδεὶς εἰστίω, "Without geometry, no one enter" [In Porphyrii Isagogen et Aristotelis Categorias commentaria, Commentaria in Aristotelem graeca, XVIII, ed. Adolfus Busse, Berlin, 1900, p.118,18-19]. Either of these is commonly translated in such terms as, "Let no one ignorant of geometry enter."
We have no notion where Philoponus or Elias got their information on Plato's Academy, although there were certainly sources available in their day, and which were still available for centuries (as we know from Photius), that are now lost. There is also the curious dynamic that even later authors have more elaborate versions of the sign.
In the 12th century, John Tzetzes in the Chiliades reported the sign as, μὴδεὶς ἀγεωμέτρητος εἰστίω μου τὴν στέγην, "Let no one ignorant of geometry enter [under] my roof." I originally found this on a webpage, which transcribed the quote with anomalous accents. For all I knew, John himself used the anomalous accents.
Now I have consulted the original text (which is available in a print-on-demand photocopy from the University of Michigan Library), and the accents are as shown here, which are not anomalous [Ioannis Tzetzae, Historiarum Variarum Chiliades, Leipzig, 1826, VIII, 973, p.322]. John knew his Greek, apparently better than the author of the webpage (transcribing Greek without mangling it seems to be a general challenge). It is unlikely that Tzetzes had better sources than Philoponus and Elias, but we don't know what they were either.
In any case, the sentiment seems characteristic of Plato, as I discuss in relation to the Euthyphro. It is consistent with his provision that philosophy should not be taught to just anyone, while he has himself withdrawn his instruction from the streets of Athens to the removed campus of the Academy. Far from the spirit of Socrates, who, of course, never asked people about geometry.
The Greek text here is from the Loeb Classical Library Republic I, translated by Paul Shorey [Harvard University Press, 1930, 1969, p.46]. The translation given is that of W.H.D. Rouse in his Great Dialogues of Plato [Mentor Books, 1956, p.137]. The following two citations in the text above are Rouse's translation also.
However, Rouse seems to have taken some liberties with the Greek here. A more literal translation would be, φημὶ γὰρ ἐγώ, "For I say," εἶναι τὸ δίκαιον, "the just to be," οὐκ ἄλλο τι, "nothing other," ἢ, "than," τὸ ξυμφέρον, "the advantage," τοῦ κρείττονος, "of the stronger." We see κρείττονος, "stronger" (in the genitive), in the description of Constantinople as κρείττων (in the nominative) by Michael Psellus, in the neuter as κρεῖττον in the physics of John Philoponus, and (the same way) in a statement by Aristotle about male & female.
A key word here, naturally, is ξυμφέρον, "advantage." This is an adjective, a participle from the verb συμφέρω (infinitive συμφέρειν) -- the word in Plato begins with a ξ, ksi, rather than a sigma, because that is the Attic dialect of Athens. The verb is defined by Liddell & Scott as, "to confer a benefit, be useful or profitable, is of use, is profitable, expedient" [Intermediate Greek-English Lexicon, Oxford, 1889, 1964, p.764]. For the participle (not in Attic) -- συμφέρων (masculine), συμφέρουσα (feminine), and συμφέρον (neuter) -- Liddell & Scott say, "useful, expedient, fitting." These are all suitable to translate what Thrasymachus says.
The interest of the verb increases when we realize that it figures in the famous statement of the High Priest Caiaphas at John 11:47-50:
Here we get the third person singular use of συμφέρω. The moral issues involved, which are very different from the argument of Thrasymachus, are discussed under the treatment of Niccolò Machiavelli. While the verb in the Bible is generally translated "expedient," which gives it a sense of unprincipled opportunism, the meaning, as we see, is more general, although still amenable to such an interpretation. Thrasymachus, of course, uses his prinicple to justify any crime, for the benefit of the "stronger," while both Caiaphas and Machiavelli appeal to the principle of necessity (Italian necessitato) for the benefit, not of the "stronger," but of the people, ὁ λαός, the nation, τὸ ἔθνος, or the state, ἡ πόλις. Also, while Thrasymachus is willing to redefine justice, Machiavelli is clear that, in the dilemma of statecraft, injustice must sometimes be practiced.
The Tempest, William Shakespeare, Act 5, Scene 1:42-57 The "Ring of Gyges," which confers invisibility, is used in Plato's Republic as a thought experiment to argue that a person with such a ring, whether previously just or unjust, would use it to commit as many crimes as necessary to get what they want [Book II, 359d]. Plato does not agree with this. The argument of the rest of the Republic, consequently, is that the just man would not be tempted by invisibility to commit crimes, because he would know that crime itself makes one unhappy and that he is better off to remain just.
The issue of the ring has recently emerged in popular culture, with the Paul Verhoeven movie Hollow Man [Columbia Pictures, 2000]. In publicity and documentary interviews, Verhoeven explicitly invokes Plato to explain the theme of the movie. However, the moral of the film appears to be quite the opposite of what Plato intended. When actor Kevin Bacon becomes invisible, he very soon begins committing rape and murder. It may be that this was the result of flaws in his character, but such a question is unanswered by the story, since there is no comparison with anyone who resists the temptations of the power conferred by invisibility. One is left to suppose that anyone would act this way, and Verhoeven appears to see that as, indeed, the point. We would not know from Verhoeven's statements that Plato had something different in mind.
A fictional character who displays Platonic virtue is Prospero, the deposed Duke of Milan in Shakespeare's The Tempest. In the epigraph above, Prospero provides a rather chilling catalogue of his powers, which apparently extend to raising the dead, and which in the play have called forth the storm that delivers his enemies to his island of exile. Prepared for a terrible revenge, Prospero instead forgives:
Act 5, Scene 1: 27-30 Having merely righted the wrongs done, regained his Dukedom, and arranged the marriage of his daughter Miranda to Ferdinand, son of the King of Naples, Prospero surrenders his power. Although certainly "the rarer action" in history, this does happen, from the retirement of Diocletian to the refusal of a Third Term by George Washington.
The Tempest, by William Shakespeare
Plato's theory of the three parts of the soul in effect produces a typology of personalities, such as has become popular in modern psychology. Instead of any emphasis on this, Plato's system mostly gets compared to the Caste System of India, with which it shares some features and where Georges Dumézil speculated that the notion of a triple social division, found in Plato, Greek mythology, Ireland, Iran, and India (in terms of the Twice Born), goes back to an original common Indo-European ideology. In these terms, it is noteworthy that the theory of the Chinese social classes works rather differently,
φημὶ γὰρ ἐγὼ εἶναι τὸ δίκαιον οὐκ ἄλλο τι ἢ τὸ τοῦ κρείττονος ξυμφέρον.
...Tyranny is not a matter of minor theft and violence, but of wholesale plunder, sacred and profane, private or public. If you are caught committing such crimes in detail you are punished and disgraced; sacrilege, kidnapping, burglary, fraud, theft are the names we give to such petty forms of wrongdoing. But when a man succeeds in robbing the whole body of citizens and reducing them to slavery, they forget these ugly names and call him happy and fortunate, as do all others who hear of his unmitigated wrongdoing. [Republic 344a-c, H.D.P. Lee translation, Penguin Books, 1955, p.73.]
SOUL INTEREST CLASS METAL VIRTUE 
reason
knowledge
guardians
philosophers
gold
wisdom
justice
spirit
honor
auxiliaries,
warriors
silver
courage
desire
pleasurescommoners, farmers 
iron
temperance
craftsmen
copper
, digambara or "sky-clad," since the sky is their only covering.
, a doctoral graduate or "presented scholar" of the Chinese examination system] at fifty is still comparatively young." The Chinese system is in traditional societies perhaps the institution closest to what Plato imagined for the Guardians -- with some of the negative effects, such as the dynamics of bureaucracy, that we might anticipate from Plato's vision.
The warriors will take over. They have the monopoly of force anyway, so they decide to use it. The kind of state they will establish Plato's calls a "timocracy," τιμοκρατία, timokratía, or "timarchy," τιμαρχία, timarkhía (from τιμή, timê, "honor" and ἀρχή, archê, "beginning," "power" "sovereignty"), the rule of honor. The principle of this state is the spirit of the warriors. We may say that this kind of state has actually existed, not only with Sparta in Plato's day, as Plato says himself, but in mediaeval Europe or Japan, or among the Kshatriya caste in India, with the kind of feudal military society that they all had. European or Japanese nobility felt themselves superior to the desire for wealth (although they didn't always live in poverty) and tended to fight each other over issues of honor. This kind of state will decay, however, when the children of the warriors fall to the temptation to use their military power to obtain wealth.
which illustrated the levels of knowledge and reality in the discussion of the nature of philosophy and the good. (At right, the Divided Line is in black and the elements of the Allegory of the Cave are in red.)
Then what gives the objects of knowledge their truth and the mind the power of knowing is the Form of the Good. It is the cause of knowledge and truth, and you will be right to think of it as being itself known, and yet as being something other than, and even higher than, knowledge and truth. And just as it was right to think of light and sight as being like the sun, but wrong to think of them as being the sun itself, so here again it is right to think of knowledge and truth as being like the Good, but wrong to think of either of them as being the Good, which must be given a still higher place of honor.... [note]
, is to do what is right, regardless of the consequences. That is how Kant defined the "categorical imperative," the moral command (the imperative) that is to no ulterior purpose (i.e. it is categorical). Similarly, the Gita says, "Set thy heart upon thy work, but never on its reward. Work not for a reward; but never cease to do thy work" [2:47]. This might not satisfy Thrasymachus; but then, with someone of that sort, while we may argue the issues, the ultimate point is not alone to persuade him, but to stop him. That is the surest way to prevent the tyrant from being happy.
Copyright (c) 1996, 1997, 1998, 2000, 2002, 2005, 2011, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2023, 2024 Kelley L. Ross, Ph.D. All Rights Reserved
Plato's Republic, Note 1
Plato's Republic, Note 2
"You know nothing at all," ὑμεῖς οὐκ οἴδατε οὐδεν, "nor do you stop to consider that it is expedient for you," οὐδε λογίζεσθε ὅτι συμφέρει ὑμῖν, "that one man should die," ἵνα εἷς ἄνθρωπος ἀποθάνῃ, "for the people [λαός]," ὑπὲρ τοῦ λαοῦ, "that the whole nation [ἔθνος] should not perish," καὶ μὴ ὅλον τὸ ἔθνος ἀπόληται.
Plato's Republic, Note 3
The Ring of Gyges, Hollow Man, and The Tempest
Prospero I have bedimmed
The noontide sun, called forth the mutinous winds,
And 'twixt the green sea and the azured vault
Set soaring war. To the dread rattling thunder
Have I given fire, and rifted Jove's stout oak
With his own bolt. The strong-based promontory
Have I made shake, and by the spurs plucked up
The pine, and cedar. Graves at my command
Have waked their sleepers, op'd, and let 'em forth
By my so potent art. But this rough magic
I here abjure. And when I have required
Some heavenly music (which even now I do)
To work mine end upon their senses, that
This airy charm is for, I'll break my staff,
Bury it certain fathoms in the earth,
And deeper than did ever plummet sound
I'll drown my book.Prospero The rarer action is
In virtue than in vengeance. They, being penitent,
The sole drift of my purpose doth extend
Not a frown further.
Copyright (c) 2001, 2012 Kelley L. Ross, Ph.D. All Rights Reserved
Plato's Republic, Note 4;
Plato's Typology
| SOUL | INTEREST | CLASS | CASTE |
|---|---|---|---|
| reason | knowledge | philosophers | Brahmins,  |
| spirit | honor | warriors | Ks.atriyas,  |
| desire | pleasures | commoners | Vaishyas,  |
What has become a significant matter in the interpretation of Plato is the notion that Plato's typology abridges or compromises the previous principle of Socratic philosophy that "virtue is knowledge," or that to know the good is to do the good. If we stipulate that Plato's theory is not about the intelligence of individuals, but about their interest, then we could imagine that warriors or commoners would be smart enough to know the good but then would not do it because this would conflict with their interest. Thus, Plato may be said to have added a necessary condition to the Socratic priniciple, namely that one must know the good and also possess the requisite psychological interest. So Professor Moriarty has no difficulty knowing what is right, but he just doesn't want to do it. In Plato's political theory, a tyrant, dominated by desire, may be an evil genius but will have no desire ever to do the good. Some may comfort themselves that, for instance, the Nazis were just stupid; but intelligence tests given after World War II to high value Nazi prisoners revealed that many were of unusual intelligence. This is a frightening circumstance in itself, but especially when the modern Left, containing many evil geniuses, flatters itself about its own brilliance and has come to dominate American education.
But Plato's typology may not compromise or contradict the Socratic principle at all. The first and most important point, of which people are now becoming more sensible, is that intelligence is not one undifferentiated thing, for which all kinds of knowledge are equal. This is the most conspicuous in individuals called "idiot savants," but also in those with various degrees of autism, who may have extraordinary abilities is certain areas, especially with memory or calculation but also sometimes even in art, but who may be lacking social skills or common sense at the most elementary levels. More specifically, the kind of knowledge relevant to Socratic inquiry, namely what would contribute to wisdom as the "human and political kind of virtue," is not something for everyone, not even to the very brilliant people one may find in philosophy departments or in the history of philosophy (e.g. Bertrand Russell, a brilliant fool if there ever was one).
Thus, we must consider that Plato's typology of interest is itself also a typology of intelligence, with intelligence itself differentiated by its own objects of interest. The intelligent warrior or commoner may seek knowledge in their own ways, but they are not going to be looking for wisdom the way Socrates was. They will be impatient and uninterested in the kinds of questions he asked, or even contemptuous of his preoccupations. People with any philosophical interests, for epistemology or metaphysics as well as ethics, may find other very intelligent people, lawyers or scientists, who dismiss the whole business as pointless or ridiculous. We have no reason to doubt the brilliance of Richard Feynman, but we have his own testimony that nothing that was ever said in any of his philosophy classes, when he was a student, ever made the slightest sense to him. He then avoided any such classes that were not requirements, where he was lucky to have passing grades.
Consequently, it is not like the evil genius, the brilliant tyrant, or the even the sharp lawyer or great physicist is going to be seeking or knowing the same things as Plato's philosophers. Socrates allowed for this himself, in that he found that the "craftsmen" knew what they were doing and to that extent "were wiser than I" [Apology, 22c-d]. But they were not wise about the right things, which we are left to infer means the "human and political kind of virtue." This can be generalized far beyond the craftsmen. Russell or Feynman, despite great brilliance is certain matters, could not be said by Socrates to be any wiser about the right things.
Of course, this is all ex hypothese. We do not need to worry about counterexamples of the wise tyrant, not only because there has never been such a thing, but because on Socratic principles there has never been anyone wise whatsoever. So it is not like all sorts of intelligent people have known the good and not done it, but that no one at all has known it. This is not difficult to believe when the elite of American intellectuals and academics is dominated by socialists, whose cognitive achievements are often expressed in the form of pronouncements that are little more than mindless slogans. The academy is not ruled by wisdom, but by many of the most painfully evident forms of folly and even of evil -- a combination of what Schopenhauer described as the "absurd and perverse" [Absurde und Verkehrte] and the "wicked and fraudulent" [Böse und Hinterlistige].
In The Republic we can even detect a particular form of folly that is still popular, namely that the problem of politics consists of not having the right people in charge. Plato thought that these people should be the philosophers, because they are the ones distinguished by wisdom, even though the very Socratic definition of the philosopher is the person who recognizes his own ignorance and his lack of wisdom. In the recent experience of history, some of the most educated political leaders have turned out to be the worst rulers. The shambles of the Obama Presidency is obvious at the moment, but we have the even more chilling examples of the French educated Pol Pot in Cambodia, who thought that killing a large percentage of his own people would produce the desirable workers' paradise. It is not difficult to gather where Pol Pot got these ideas, when it was the common currency of the post-War world that Communism had failed in Spain and Greece because not enough people were killed.
Of course, Schopenhauer, not unlike Socrates, would have thought real wisdom impossible in the practical affairs of this world. Even the most intelligent, in any area of knowledge, are perverted by interests, especially self-interest, that warps their judgment. Socrates said that only the gods are wise, and we are left to soberly reflect on the possible wisdom of this viewpoint.
Plato's description (at left) is really a thought experiment of how his ideal state, the Aristocracy of philosophers, would decay. His description is generational, that unworthy children fail to perpetuate the virtues of their parents. Thus, the Timarchy is produced by children who value themselves just for their honor and ability to use force, the Oligarchy is produced by children who decide to use their force to become wealthy, the Democracy is produced by children who think they have a right to that wealth just by being citizens, and the Tyranny is produced by children whose total lack of discipline and restraint produces a chaos that is only ended by one of their number seizing personal power. True to his generation, the tyrant uses his power to take whatever he wants. Plato's description is often psychologically true of many specific events and persons in history.
Machiavelli's description is also generational, but it also introduces another principle, and it results in a kind of conclusion foreign to Plato's thinking. The principle that Machiavelli uses is simply that of a classification by the distribution to power, i.e. power is exercised by one, by a few, or by the many. This is a useful device, and is used here in the theory of Liberties in Three Dimensions. Upon the scheme, Machiavelli imposes his generational thought experiment, beginning with a "state of nature" origin for Monarchy of a sort that we still find later in Thomas Hobbes or John Locke. The good monarch, however, is succeeded by corrupt rulers who begin to use their power for their own gain, becoming tyrants. The tyrant is then overthrown, and the rebels decide to retain power among themselves collectively, producing an Aristocracy. The aristocrats are succeeded by a generation that again begins to use its power to oppress the people, producing the Oligarchy, and so they end up getting overthrown like the tyrant. Now political power passes to the people, making for Democracy. Unlike Plato, Machiavelli, does not view democracy per se as worse than the other "good" forms of government. Indeed, Machiavelli includes a chapter in the Discourses (Book II Chapter LVIII) on how "The Multitude is Wiser and More Constant than a Prince." The propensity of Democracy to decay into Anarchy, which Machiavelli describes in much the same terms as Plato, is therefore no more a failing of Democracy than the similar propensities were of Monarchy and Aristocracy. The only difference might be in the next step: Plato sees a tyrant benefiting from the Anarchy produced by Democracy, while Machiavelli brings his thought experiment full circle by having Anarchy, which mimics the "state of nature," followed once again by Monarchy. As a matter of historical fact, we have no difficulty finding chaotic conditions that led to both tyrants (Hitler) and virtuous monarchs (Diocletian).
Machiavelli's thought experiment, like Plato's, would seem to be entirely pessimistic. Plato's only hope would be his government of philosophers where precautions are taken to prevent the principle of hereditary succession from beginning. Machiavelli also sees hereditary succession as a source of evil; but, as a realist and a historian, he does not imagine that it can be long prevented, especially when people are inherently bad. His solution for the corruption of the "good" governments must therefore come from a different direction.
His inspiration turns out to be a historical one, the Roman Republic, which, although followed by the Empire, nevertheless endured for several centuries and accomplished great things. Following the original argument of Polybius, the strength of the Republic, according to Machiavelli, depended on its combination of the devices of the "good" forms of government:
I say, therefore, that all these kinds of government are harmful in consequence of the short life of the three good ones and the viciousness of the three bad ones. Having noted these failings, prudent lawgivers rejected each of these forms individually and chose instead to combine them into one that would be firmer and more stable than any, since each form would serve as a check upon the others in a state having monarchy, aristocracy, and democracy at one and the same time. [The Prince by Niccolo Machiavelli, With selections from THE DISCOURSES, translated by Daniel Donno, Bantam, 1981, p. 94, boldface added] The Roman Republic thus had monarchical authority in the Consuls, aristocratic authority in the Senate, and popular authority in the Tribunes. In Machiavelli's phrase, "...since each form would serve as a check upon the others," we see the idea of checks and balances as means to prevent the corruption and oppression of government. If people cannot be good, then we must have a government where the interests and power of some work to secure the conscientiousness and honesty of others. This idea is later expanded by 17th and 18th century thinkers, until we have the great system of the Executive, Legislative, and Judiciary, and the States and the Federal Governments, designed as checks upon each other in the United States Constitution.
That this system has now failed to actually protect freedom and virtue is a consequence of historical circumstances, failure in the original design, and changing, fallacious, unsympathetic ideology. Nevertheless, it is clear that the principle is sound and is able to secure responsible government for extended periods. The fallacy in Plato is exposed: the problem is not who is in power, since none is wise.
Over time, of course, what we see is that the ingenuity of those in power never ceases to undermine the limitations of their power, and the cupidity of some citizens never tires in the hope of extracting the substance of their less politically powerful fellows. Our challenge, then, is simply to perfect the design and prepare the ground so that, when the next Franklin, Washington, Jefferson, and Madison come along, it may be put to the test -- hopefully to even more enduring results.
Machiavelli and the Moral Dilemma of Statecraft
The Byzantine Republic, by Anthony Kaldellis
With Plato's reference to the Form of the Good, ἡ τοῦ ἀγαθοῦ ἰδέα, we get something similar in another word. Where Plato says, "it is right [ὀρθός] to think [νομίζειν] of knowledge [ἐπιστήμη] and truth [ἀλήθεια] as being like-the-Good [ἀγαθοειδής, hyphens added to Loeb translation], but to think [νομίζειν] that either of them is the good is not right [οὐκ ὀρθός]."
The Loeb translator, Paul Shorey, says, "ἀγαθοειδῆ [the accusative of ἀγαθοειδής] occurs only here in classical Greek literature. Plato quite probably coined it for this purpose" [Volume II, p.105 note d]. The Unabridged Liddell & Scott Lexicon, which gives full citations for references, only gives this passage in the Republic, "509a"; so that is consistent with Shorey's statement. Their definition is "like good, seeming good, opp. ἀγαθός" [Liddell & Scott, p.4]. Plato has just used another word, ἥλιοειδής, with the same form, meaning, with respect to light [φῶς] and vision [ὄψις], being "like the sun" [509a] -- "sun" being ἥλιος.
While ἀγαθοειδής looks like a combination of ἀγαθός and εἶδος, and could mean "Form of the Good," the word is actually a third declension adjective (ἀγαθοειδής in masculine and feminine, ἀγαθοειδές in the neuter), and, as we see, Plato uses it to deny that knowledge and truth are the same thing as the Good, but only "like" the Good. So εἶδος means more like "image" than the Platonic metaphysical entity of the "Form." In this passage, ἰδέα does the work of the latter.
See discussion of ὀρθός here. The word ὄψις can mean "face" or "countenance," besides "vision," and is related to ὤψ, "eye, face," one of whose forms we see in the name of the Muse Καλλιόπη, Calliope, "Beautiful Face." Both words come from one of the roots used for "see" in Greek, which turns up in the future form ὄψομαι, "I will see." Otherwise, we get ὁράω in the present, "I see," and εἶδον in the past, "I saw." The latter, of course, has the same root as Plato's term εἶδος.
Meanwhile, the verb νομίζειν (the infinitive of νομίζω), "to deem, hold, believe," is an issue in the trial of Socrates, where Socrates is accused of not believing in the gods. Attempts to misrepresent Socrates are examined here.
Plato's Republic, Note 5;
Machiavelli's View of GovernmentIn his Discourses Upon the First Ten Books of Titus Livy, Niccolò Machiavelli, more famous for The Prince, describes the "various kinds of states" in a fashion similar, but in some important ways different, from Plato. Machiavelli repeats in detail the analysis of government, formulated to explain the success of the Roman Republic, intiated by the Greek historian Polybius of Megalopolis (c.200-120 BC) in Book VI of his Histories. After the Roman defeat of the Achaean League in 167 BC, Polybius was held by the Romans as a hostage; but this allowed him direct familiarity with Roman institutions, practices, and the events of the age. Machiavelli, following Cicero and Livy, continues the form of analysis begun by Polybius.
Thus, power exercised by one is a Monarchy, by a few, an Aristocarcy, and by the many, a Democracy. However, Machiavelli (with Polybius) allows that there are good and bad versions of each of these, reserves these terms for the good forms, and introduces "Tyranny," "Oligarchy," and "Anarchy" for the bad versions of rule by one, the few, and the many, respectively. These terms are conveniently schematic and descriptive and ignore a utopian possibility like Plato's government of philosophers.
Dico adunque che tutti i detti modi sono pestiferi, per la brevità della vita che è ne' tre buoni e per la malignità che è ne' tre rei. Talché, avendo quelli che prudentemente ordinano leggi conosciuto questo difetto, fuggendo ciascuno di questi modi per se stesso, ne elessero uno che participasse di tutti, giudicandolo più fermo e più stabile, perché l'uno guarda l'altro,
sendo in una medesima città il Principato, gli Ottimai e il Governo Popolare.
Copyright (c) 1999, 2003, 2004, 2015, 2024 Kelley L. Ross, Ph.D. All Rights Reserved
Plato's Republic, Note 6