Athens Parthenon Acropolis, photo by Margareths1

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This article is reprinted from the Winter 2003 issue of FIDELIO Magazine. Plato's dialogues encompass an historical sweep of time, from Athens at its height in 450 B.C. to its defeat in the Peloponnesian War, to the death of Socrates in 399 B.C. and beyond. That more than half-century witnessed the self-destruction of Athens, as its imperial ambitions brought it into conflict with its neighboring city-states, especially Sparta, thus precipitating the Peloponnesian war in 432. A series of disasterous decisions led to Athens' ultimate defeat in 404.

Born in 427, Plato spent the first decades of his life amidst the catastrophes of war, defeat, tyranny, and its twin—mob-rule. Plato's close relatives, Critias and Charmides, who were leaders of the Spartan-imposed Thirty Tyrants that briefly ruled the city in 404, were killed in the overthrow of the Tyrants by the radical Democrats. They were victims of their own unexamined axioms.

Against this backdrop, Plato sketched the tragedy of Athens, peopling his dialogues with the very political and military leaders, and pseudo-philosophers, who, step-by-step, led Athens to its doom.

Were the dialogues no more than a history of Athens' tragedy, they would have their place in the important literature of our civilization. But what makes them a cornerstone of Western civilization, is Plato's discovery of a solution to the tragedy—a solution found in his examination of immortality, and of the concept of the Complex Domain.

1. The Rise of Sophistry: An Historical Overview

Homer's great poems, The Iliad and The Odyssey, describe the events of the Trojan War and its immediate aftermath, events which marked the descent of Greece into a dark age. Following the Trojan War, around 1190 B.C. the civilization of mainland Greece collapsed: population shrank, the written language was lost (and not deciphered until the 1950's!), cities disappeared. The Iliad and The Odyssey, written around 700 B.C. heralded the reversal of the collapse, and the beginnings of Classical Greek culture.

By 600, under the intellectual sponsorship of Egypt, with its millennia-long mastery of astronomy and mathematics, Athens and the city-states in Ionia began to flourish. Solon of Athens, Thales of Miletus (in Ionia), and Pythagoras in Italy, brought breakthroughs in statecraft, science, astronomy, music and geometry to Greek society. By the end of that Sixth century, Greece stood prepared to accomplish a task at which all others had failed: she defeated the Persian Empire, first at Marathon in 490, and then at Salamis in 480.

Greece, led by Athens but including Sparta, defeated the Persians through superior military strategy, better technology, and citizen soldiers. The Persians lost 6,000 men at Marathon; the Greeks, fewer than 200.

Those capabilities were but derivatives of a more important character given to Greece, and especially Athens, by the ideas of Solon, Thales, Heracleitus, and Pythagoras—the understanding that society must be governed on the basis of universal principles, principles knowable to the human mind. This gave Athens the technological and moral superiority to defeat the Persians.

It also gave Athens something else. As Persia swept through the Greek city-states, first Ionia and then northeastern Greece, many cities simply surrendered, because they had consulted the Oracle of the Pythian Apollo at Delphi, were told to surrender, and did. (Not unlike the American voters, who, in the early spring 2000 primaries, began voting for either Al Gore or George Bush, because they were told by that modern-day oracle—the Mass Nedia—that Gore and Bush had been decreed the winners.)

Athens did not consult the Oracle in the matter of fighting the Persians. Rather, it acted with the self-confidence of a society that bases itself on knowable principles.

But the Cult of Apollo and the Delphi Oracle, which were, in fact, the front-end of Persian intelligence and penetration operations into Greece, eventually succeeded where the Persian military had failed. Within 50 years, Athens was drawn into the suicidal Peloponnesian War, fighting against Sparta and her former Persian War allies, and sinking deeper into her own tragedy. By the time the Peloponnesian War broke out in 432, the Oracle of Delphi was able to manipulate all parties in the conflict, Athens included. Athens' leaders and citizens had lost their compass, and truth was rejected in favor of the god of opinion: Sophistry. The Sophists had taken over, with their argument that there is no truth, that each man is the measure of his own “truth.”

As will be developed below, Plato addresses the Sophist infection in many of his dialogues, including the Protagoras, Gorgias, and Symposium, all of which take place during the Peloponnesian War. One can imagine actually performing each of these dialogues, since Plato wrote them with stage directions, drama, conflict, and no little comedy.

Before the ideas of Solon, Pythagoras, and Thales could be extinguished by the Sophistry that said there is no truth, the Eleatic philosophy had first to inject its idea, that truth was unknowable. Parmenides' poem, “The Way of Truth,” asserted that the One was indivisible, unchangeable, immovable—in short, unknowable in the discrete manifold of human sense perception. Rejecting, or more accurately, opposing the Pythagorean breakthroughs in music and geometry, which explored the tension between the world of sense perception and the geometry of invisible universal principles—the principles which produce the shadows of sense perception—Parmenides' philosophy leaves mankind trapped in the world of the senses, offering only the vague notion that the One can be grasped dimly through the irrationality of an initiate's mystical experience. (It is not surprising, therefore, that such modern fascists and existentialists as Friedrich Nietzsche, Martin Heidegger, Hannah Arendt, and Karl Popper, wrote extensively on, and were enamored of, the Eleatics.)

By placing the Parmenides dialogue in 450 B.C. the earliest of his historical settings, Plato signaled to his contemporaries and to future generations how the philosophical cancer took hold. Socrates' dialogue with Parmenides and his disciple Zeno, is perhaps the most intense examination of a set of axioms in all his dialogues.

Unlike the raucous atmosphere of the Protagoras, or the almost violent encounter with Gorgias, Socrates' examination of the axioms of Parmenides is sober and exhaustive. (Not to say, exhausting, if one is trapped in the world of sense perception). In this way, Plato's treatment of Parmenides is echoed by C.F. Gauss's handling of Euler and Lagrange in his treatise on the Fundamental Theorem of Algebra. Plato gave to his youth movement, as Gauss has given to the LaRouche Youth Movement today, a method for understanding and combatting enemy philosophies, coupled with the power to know and discover universal principles. By using the method of exhausting each of the paradoxes embedded in Parmenides's epistemology, Plato forces the reader to discover the solution, noetically, in “the suddenly” [to eksaiphnas] outside of Parmenides' dead world.

The fundamental importance of the Parmenides dialogue is dramatically intensified by its historical setting in 450 B.C. during the period when Athens abandoned its fight against the Persians.

In 454, Athens announced an end to oversees expeditions against the Persians, and then, Athens redirected the funds collected from other city-states for defense against the Persians, for use by Athens alone. Then, in 449, Athens signed a peace treaty with Persia. Athens was transformed, from a leader of the league of Greek city-states allied in common defense against the Persians, to an unwitting pawn of the Persians themselves.

As Helga Zepp LaRouche outlined in a speech in September 2002, Athens, as it adopted an imperial policy under Pericles (460-430), bears an eerie resemblance to the United States at the turn of the Twenty-first century.¹ Pericles' strategy for the coming war with Sparta involved fortifying the “Long Wall” around Athens, and allowing Athens to be supplied by its navy, from its port of Pireaus. This, however, meant that all those who lived outside the walls, had to abandon their farms and homes and crowd into Athens whenever the Spartans laid siege. The result was a horrible plague, which broke out as soon as the war began in 431, ravaging Athens. Pericles' oratorical skills, learned under the leading Sophists of the time, swayed the Athenians to support the war and his strategy. But Sophistry was no match for natural law: Pericles died of the plague in 430.

Alcibiades, Nicias, Critias, and Tragedy

From the Parmenides dialogue of 450, Plato jumped to the eve of the Peloponnesian War, and set three of his dialogues in 432, the year before the official outbreak of war. Other dialogues mark nodal points in the series of decisions which led Athens to its disasterous end in 404.

Let us first look at that sweep of history through the lives of three key figures who populate Plato's dialogues, and play crucial roles throughout the war—Nicias, Critias, and Alcibiades.

Alcibiades may appear in Plato's dialogues more than any other character, if one includes the dialogues Alcibiades I and Alcibiades II, which some scholars argue may not have been written by Plato. We know a great deal about Alcibiades, whose life mirrors the tragedy of Athens, from the works of Plato, Thucydides, and Plutarch.

Raised in Pericles' household, Alcibiades would have been in direct contact with Sophists such as Protagoras. Ambitious, well-connected, and handsome as Alcibiades was, Socrates nonetheless saw promise in him, and devoted no inconsiderable effort to his cognitive development. But, ultimately, Socrates lost the battle for Alcibiades' mind to Gorgias, one of the most prominent Sophists of the time, to whom Plato devotes a dialogue discussed below.

Alcibiades came into direct conflict with the second of our figures, Nicias, ten years into the war. In 421, Nicias negotiated a peace treaty with the Spartans (called the Peace of Nicias). After the plague, years of war, and disruption of the economy, the cessation of warfare could have put Athens back on course to sanity. But it was not to be so. Alcibiades, representing the war faction, convinced the Athenians to resume the war, setting the stage for the next major ratchet down in 416.

As Thucydides describes it in the famous Melian dialogue in his History of the Peloponnesian War, the treatment of the Melians in 416 underscored the degeneration of Athens. Under attack, the leaders of Melos argued for justice, but the Athenians simply asserted, as Plato's Thrasymachus does, that justice is determined by whomever has power. Melos was conquered, all the males put to death, and the females taken into slavery.²

This brutality abroad was mirrored by political insanity at home. That same year, 416, Alcibiades and his faction convinced the Athenians to embark upon their greatest imperial adventure—the invasion of Syracuse on the island of Sicily, one of the richest independent Greek cities in the world. Although Nicias opposed the invasion, he was chosen, along with Alcibiades and one other commander, to lead the invasion.

Before the expedition could be launched, a bizarre event took place in Athens—the night of the Hermae. In one night, sacred statues throughout Athens (phallic symbols known as Hermae, or Herms) were desecrated throughout the city. This was used to launch a witch-hunt, accusing various leading Athenians of the crime. Among those accused were Alcibiades and Plato's relative Critias. Alcibiades insisted upon being tried, before he was sent on the Sicilian expedition, but he was ordered to undertake the campaign with the charges still hanging over his head.

The Sicilian expedition was a disaster almost beyond description, although Thucydides does it justice. Alcibiades' opponents in Athens found him guilty in absentia and called him back to Athens. Rather than returning to his fate in Athens, Alcibiades escaped en route, fled to Sparta, and joined the enemy cause! Left in command, Nicias conducted an ineffectual campaign, calling upon Athens to provide massive reinforcements. In response to Nicias's plan for a final assault in 412, Athens depleted itself of men and materiel. The attack was ready to proceed when Nicias called it off because he interpreted a lunar eclipse as a bad omen! The Syracusans had time to discover the planned attack, and counterdeployed. Athens suffered a devastating defeat, and the capture and slaughter of most of its army. Nicias was among those killed.

Alcibiades, who was often ruled by erotic emotions despite Socrates' attempts to educate them in service of reason, was forced to flee Sparta after an affair with the Spartan king's wife left her pregnant. He fled to the court of the Persian satrap Tessepharnes in Asia Minor.

The twists and turns in Alcibiades' life were mirrored by the political chaos of Athens. The defeat at Sicily dealt a devastating blow. In 411, Aristophanes wrote the play Lysistrata, in which the women of Athens withhold sex from their husbands in an attempt to stop the insanity of the war. That same year, a faction representing the oligarchy, briefly overthrew the Democrats who had been ruling Athens since the war began.

In the fickle, shifting political winds of Athens, Alcibiades was invited to return, and he and other Athenian commanders managed to win several significant battles. But the people and leaders of Athens, drunk with Sophistry and easily manipulated, turned on their successful commanders! Alcibiades was unjustly blamed for a military defeat, forced again into exile, and assassinated in 404.

Other generals, who won a significant naval battle in 405, were brought up on charges of failing to rescue wounded sailors in the midst of a storm, which, if attempted, would have destroyed the entire fleet. Socrates, serving as a public official at the time, was alone among his peers in opposing their conviction. They were all executed, including Pericles' own son.

A year later, Athens, depleted and deranged, surrendered. Sparta's allies, Corinth and Thebes, called for Athens to be treated as Athens had treated Melos: slaughter all the males and take the women into slavery. This slaughter would have included Plato! Sparta, largely for geopolitical reasons, rejected that punishment, instead placing the city under a Sparta-approved Athenian leadership known as the Thirty Tyrants. Plato's second cousin, Critias, was the leader of the Tyrants, and his uncle, Charmides, was part of the ruling faction. Both Critias and Charmides were members of Plato's immediate family on his mother's side, an intensely political family that could trace its lineage back to Solon!

Recall the section of the Republic which describes the transition of mob democracy into tyranny. Plato was not engaged in a sociological exercise there—he was reliving a history which claimed the lives of his close relatives.

Reacting to the insanity of the war years, the Thirty Tyrants were, in their turn, brutal—executing opponents, seizing property, and ruling with an iron hand. But the pendulum of political madness quickly swung back to the Democrats, who overthrew the Tyrants in 403. Critias and Charmides were killed.

It was that Democratic government, and explicitly the Democratic leaders who had overthrown the Tyrants, which executed Socrates in 399 B.C. Plato was then 28 years old.

The Dialogues against the Backdrop of History

Now, let us look at the dialogues which Plato set during the period of the Peloponnesian War. After placing the Parmenides in 450, when the philosophical cancer first appeared, Plato jumped to the year before the war began—432 B.C. By this time, the Eleatic disease had metastasized into Sophistry, and the Sophists, and their victims, populate the dialogues set between 432 and 404. Among the Sophists we meet are Protagoras, Prodicus, Gorgias, Thrasymachus, and Pausanias. Among their victims are Critias and Alcibiades.

432 B.C.

Plato set three dialogues in 432—Alcibiades, Charmides, and Protagoras. Protagoras, a frequent guest of Pericles, was the most influential Sophist of the time, and the Protagoras dialogue is filled with some of the most significant figures of the age.

As we shall see again later in the Gorgias, there is a characteristic of those of Plato's dialogues in which the Sophists are the principals: they are richly staged and exceedingly dramatic. Plato sets one particular scene in the Protagoras with great humor: A group of sycophants follow Protagoras, back and forth across a courtyard, parting like a flock of birds at each end, to allowing Protagoras to parade back through them. While Protagoras is the main subject, the presence of Critias, Alcibiades, Prodicus, and Hippias among the characters, underscores the political weight of the dialogue.

Set in the same year, Plato's Alcibiades dialogues show us Alcibiades at the age of 18, eager to assume political leadership. With great affection, Socrates asks Alcibiades to consider what principles he holds that would qualify him for political leadership. Plato composes the dialogue to foreshadow Alcibiades future, and concludes with the following:

Alcibiades: Well, that is the position, and I shall begin here and now to take pains over justice.
Socrates: I should like to think you will continue to do so; yet I am apprehensive, not from any distrust of your nature, but in view of the might of the states, lest it overcome both me and you. (135e)³

Plato treats Critias similarly in the Charmides, a dialogue named for a younger relation of Critias. While Socrates begins by questioning the young Charmides, the dialogue quickly turns to Critias and his wholly unexamined axioms. Again, Plato foreshadows Critias' future as one of the Thirty Tyrants (supported by Charmides) in the concluding exchange of the dialogue. While what precedes this has been somewhat light in tone, the undercurrent of future events is unmistakable:

Socrates: What are you two plotting to do?
Charmides: Nothing, we have made our plot.
Socrates: So you will use force, before even allowing me to make my affidavit?
Charmides: You must expect me to use force, since he [Critias] gives me the command: take counsel; therefore, on your side, as to what you will do.
Socrates: But that leaves no room for counsel; for if once you set about doing anything, and use force, no man alive will be able to withstand you.
Charmides: Then do not you withstand me.
Socrates: Then I will not withstand you. (176c-d)⁴

That Alcibiades died in 404, Critias and Charmides in 403, was fresh in the minds of Plato's audience.

421 B.C.

From this prelude to the war in 432, Plato jumped to 421, and the opportunity to end the fighting with the Peace of Nicias. And so, Nicias appears in the Laches dialogue, set in 421. Socrates engages in a discussion with several Athenians, over methods of education, in which it is clear that Nicias and others hold certain traditional, decent axioms, but, because they are unexamined in their underlying hypothesis, are vulnerable to manipulation. One is reminded of the World War II generation, which fought fascism, rebuilt the nation, and launched the space age, but lost its footing in the 1950's and 1960's. Nicias's unrigorous approach to knowledge has horrible consequences, ten years later, when he postpones the crucial battle in Sicily, because of his superstitious response to the eclipse.

416 B.C.

From the collapse of the Peace of Nicias, Plato takes us, with the Symposium dialogue, to 416—the year of the attack on Melos, the night of the Herms, and the decision to launch the Sicilian expedition. Again, Plato weaves a tapestry of characters, Socrates, Aristophanes, the poet Agathon, and the Sophist Pausanias. With dramatic flourish, Plato has Alcibiades burst into the dialogue—late, and drunk. Given the accusation that Alcibiades not only defaced the Herms, but also engaged in wild revelries and defamations of the gods, one is left to wonder if he had just come from such a bacchanal, or, even, if the Symposium took place on the night of the Herms. That Alcibiades was about to lead Athens into the disaster of the Sicilian expedition, and that Aristophanes was to write the Lysistrata in reaction to the war, intensifies the drama of the dialogue.

411 B.C.

Plato's great trilogy—The Republic, Timaeus, and Critias—set over a three-day period, is most likely set in 411. While it can be argued that it was set before the Sicilian expedition, the presence in Athens of Cephalus, and, especially of his son Polemarchus, argue for the 411 date, since the sons of Cephalus were expelled from Sicily during the Sicilian campaign, on account of alleged Athenian sympathies.

Of the three, the Republic is the most historically gripping. The counterposition of the Sophist Thrasymachus, with his assertion that justice is defined by those in power, to Socrates, who will be executed by the Democratic spawn of the Sophists, is one point of tension. Another, is the role of Plato's own brothers, Glaucon and Adeimantus, as the principal subjects of Socrates' examination in the dialogue. While little is known about their personal participation in the political events of the time, they, at least, are representatives of a family which was beset by political tragedy. And, finally, the character Polemarchus, who would become one of the victims of the Thirty Tyrants—murdered, in part, so that his land and fortune could be seized.

Again, Plato's examination of the degeneration of society from timocracy (rule by the traditional values of honor [timos]), to oligarchy (rule of the few [oligos], usually in pursuit of money or pleasure), to democracy (rule of the many or common people [demos], in pursuit of the same), to tyranny, is no idle exercise.

The Critias of the incomplete Critias dialogue is Plato's second cousin, one of the Thirty Tyrants, who was himself dead by 404. One wonders how Plato would have completed this dialogue, whose subject was to have been the political organization of a state, given his relative's tragedy.

The third of the dialogues, the Timaeus, stands by itself. More of a monologue, it is delivered by a Pythagorean, Timaeus, who may have been Timaeus of Locri. Addressing the question of the composition of the universe, Plato presents a first approximation of the idea of the Complex Domain, which will be discussed in Part 2.

404 B.C.

As if to book-end the Peloponnesian War with dialogues devoted to the Sophists, the Protagoras dialogue of 432, is matched by the Gorgias dialogue of 404, at the conclusion of the war. Here, the thuggery of Sophistry is presented at its most naked. Gorgias claims that nothing exists, and if it did, we couldn't know it anyway. Gorgias and his cohort, Callicles, bluntly assert their fascist doctrines and openly threaten Socrates for his refusal to succumb.⁵ While Socrates deals with Protagoras's arguments rigorously, the tone of the earlier dialogue is, at times, comic. No such levity colors the Gorgias—after 27 year of the political degeneration of Athens, which will lead to the death of Socrates, the mood of the Gorgias is confrontational and threatening.

402 B.C.

The final dialogue set before those dealing with the death of Socrates in 399 is the Meno, placed in 402. This dialogue contains all the elements of Plato's repertory: history, method, an introduction to the Complex Domain in the discussion of powers in the doubling of the square, and the seed crystal for the political solution for society. Meno, for whom the dialogue is named, and who never grasps the concept which Socrates develops, is a Democrat, and the “hereditary guest-host” for the ambassador of the Persian king when he visits Meno's Thessaly. Hence, the shadow of Persian manipulation looms just off stage. Anytus, who bursts in toward the end of the dialogue to bluster and to threaten Socrates personally, was one of the two main Democratic leaders who overthrew the Thirty Tyrants the year before, and who became the main prosecutor of Socrates. Anytus, it should be noted, managed to escape the fate of the other generals in the naval affair of 405, which resulted in their execution.

It is a powerful irony that Plato counterposes these two major political figures, who never grasp Socrates' ideas, to the slave boy, who, with Socrates' help, makes a discovery of the concept of power and incommensurability. In this dialogue, Plato shines the first light on the shadow of slavery, a shadow which is not fully dissipated until 2,500 years later. Plato's demonstration that a slave boy has the innate capacity to discover universal principles, was the first gleam of light on an idea that was not to achieve political standing until the intention of the American Revolution was finally fulfilled by Abraham Lincoln and the Civil War.

2. The Complex Domain and the Sublime

The dialogues dealing with the death of Socrates in 399 B.C. the Apology, Crito, and Phaedo, mark the final chapter in the destruction of Athens by her own hand, through mob democracy and tyranny. However, if one reaches back to the time of Solon, the great lawgiver of Athens, and his poem on the constitutional principle, written around 590, one can find a forewarning of what was to engulf Athens nearly 200 years later:

Never will our city be destroyed by Zeus' decree,
Nor by the will of the bless'd immortal gods, ...
But, by money seduced, the Athenians themselves
Seek mindlessly to corrupt the great city,
Joined by the iniquitous schemes of their leaders,
Who from arrogance great woes shall suffer:
For they understand not how to restrain gluttony,
Nor best to order their feating in quiet. ...
Sparing neither sacred ground nor public goods,
Greedily they steal from the one place or the other.
They fail to protect the rev'rend temples of Justice,
She who notes silently the “what is and what has been,”
Who in time shall come exacting retribution.
Behold, an inex'rable harm visits all Athens:
To vile slavery is she swiftly progressed,
Which rouses up from slumber civil strife and war—
War that wipes out for many their cherished youth;
Now our much-loved city is soon worn down by faction,
While the wicked stir them to confrontations. ...
Thus does the public evil come to each of us ...⁶

If such dangers were understood more than a century and a half earlier, what was missing in Athenian society which caused it to succumb nonetheless? Or, more importantly, what did Plato discover as the solution to this degeneration? As he develops most thoroughly in The Republic, Plato shows that society must be governed by those who are committed to discovery of the Good, which must be sought for in the examination of universal principles. In his “Visualizing the Complex Domain,”⁷ Lyndon LaRouche asserts that the Preamble of the U.S. Constitution is of the same character:

“The unexcelled genius so embedded in that Preamble, is that it obliges the Federal government to return to the standpoint of true universality, to rescue the nation from the follies of recurring, errant and petty currents of popular opinion. Thus, when we adhere to that Constitution, in that mode, our republic has a certain genius for immortality, if we use it, not achieved by others to date.”

The failure to adhere to universal principles is captured in the tragedy of those Athenians who people Plato's dialogues, and it becomes a concluding theme in last Book of The Republic. Socrates recounts a tale of the afterlife, in which the souls of the dead have the opportunity to come back, by choosing new lives. One man immediately seized the lot of the greatest tyrant, and, as a result, suffered a horrible fate. “He was ... a man who had lived in a well-ordered polity in his former existence, participating in virtue by habit and not by philosophy.” (Book X, 619c)⁸ [Emphasis added] This is especially poignant, given that it is Glaucon, a member of Plato's family, whom Socrates is immediately addressing.

Plato, like LaRouche in the above-mentioned work, devotes the body of The Republic to the question of how man can know these universal principles—by philosophy, not habit. Therefore, these are principles which can only be found in eternal existences, or “that which is, eternally” [to an aei]

However, Plato sets up that discussion by taking what he later calls a short cut. In Books III-V, in a series of exchanges with Plato's brothers Glaucon and Adeimantus, Socrates examines exhaustively the question of producing guardians of the state, through an education based on training in music and gymnastics. These books come to jarring conclusions, which include the banning of Homer and many forms of music and drama, and the sharing of wives and children in common. When read aloud in a group, these books necessarily provoke much agitation and discussion. This entire hypothesis reaches its stretto, later, in the “Nuptial (or Marriage) Number,” in which Socrates asserts that guardians can only be produced by men and women who marry, conceive and bear children in accordance with a complex set of calculations involving rational, irrational, geometric and cubic numbers, means, and incommensurables. (Book VIII, 546b-c) By this time, readers are usually bouncing off of walls.

That Nuptial Number is a singularity in The Republic, as it encapsulates the transition from one hypothesis, to the next. One can only look at the Nuptial Number from the vantage point of the noetic study of arithmetic, geometry, solid geometry, and astronomy which has just proceeded. Rather than a eugenics prescription, it poses a complex exercise in Pythagorean mathematics, a kind of compression of the new hypothesis Plato has developed. Because, as Socrates has drawn out of Glaucon, the form of education discussed in the earlier chapters was insufficient, because it “educated the guardians through habits, imparting by the melody a certain harmony of spirit that is not science, and by the rhythm, measure and grace, and also qualities akin to these in the words of tales that are fables and those that are more nearly true. But it included no study that tended to any such good as you are now seeking.” (Book VII, 522a) [Emphasis added] Socrates has already established that the study of the Good is the “longer way around,” and that it is only through the study of “the idea of good” that any understanding of justice, temperance, bravery and other virtues becomes useful or beneficial. Presaging 1 Corinthians 13, Socrates declares that any other knowledge “would avail us nothing, just as no possession either is of any avail without the possession of the good.” (Book VI, 505b)

The great task of The Republic, then, is to discover the knowledge of the Good, and here Plato provides us with a preface to LaRouche's concept of the Complex Domain. Let us first look at LaRouche, as he takes on Plato's philosophical opponents:

The sophist (reductionist) method denies the existence of knowable truth, as the ancient Aristotelean hoaxsters denied such knowledge ... . The reductionist insists that we actually know only that which is presented to our senses. Contrary to the sophists, the measured characteristics of the compared planetary orbits of Earth and Mars, sufficed to exemplify the proof that we do not know physical reality from our senses ... our sense-apparatus is merely part of our organism. What our senses report to us, is at best, the effect of action by the world outside on those sense organs, not the image of the efficient action itself. The sense show us, at best, shadows cast by a universe which exists beyond the direct observation of the senses. The domain of sense-perception presents us the mere shadows of the real principles which operate in a universe outside the domain of direct sense perception.⁹

One can have no better metaphor for this concept, than Plato's description of the Cave, at the beginning of The Republic's Book VII: men held in place all their lives, looking only at the back wall of a cave, seeing only the shadows cast by unseen light and unseen objects behind them—this is what our senses show us.
Ah, but where is the knowable truth? Return to LaRouche, as he presents Kepler's discovery of the principle of gravitation and Leibniz's defining of a universal physical principle of least action as

discoveries of universal physical principle, [which] show us principles by means of which we can increase our willful, and also visible control over the universe; but, they also show us the nature of that universal principle of physical hypothesis, the faculty of noesis, by means of which we are able to adduce the existence of, and effect the practical mastery of those specific physical principles. The acquisition of such efficiently practical knowledge of principles beyond the powers of sense perception, enables us to define the efficient function of sense perception within that real universe which lies within nothing less than the complex domain, a universe beyond the shadow-world of sense perception as such.¹⁰

In both The Republic, and his great masterwork, Timaeus, Plato addresses these concepts, of the shadow of sense perception versus the substance of universal physical principles, with the elegance of the Greek language. Objects which are knowable to the eye are “oratos” (a participle of the verb “to see”), and objects which are knowable to the mind are “noetos” (a participle of the verb, “to know with the mind, to cognize”). The Greek word for mind is “noos” or “nous”; readers of the writings of Lyndon LaRouche are familiar with the term “noösphere,” coined by the scientist Vladimir Vernadsky, which comes from the same root.

As Socrates puts it, “Conceive (or “use your mind,” since the verb is noeo) then, as we were saying that there are these two entities, and that one of them is sovereign over the intelligible order and region, and the other over the world of the eyeball ... . You surely apprehend the two types, the visible [oratos] and the intelligible [noetos].” (Book VI, 509d) [Emphasis added] Plato then enters into an examination of these two types, oratos and noetos, dividing each of them in turn between actual objects and images of such objects. The distinction is obvious in the visible domain, e.g., an object and its reflection in water. It is not so obvious in the intelligible, and, it is here that Plato, unfolds a concept of hypothesis, and higher hypothesis, which can only be conceived of in the Complex Domain: “By the distinction that there is one section of it which the soul is compelled to investigate by treating as images the things imitated in the former division (the visible), and by means of assumptions from which it proceeds not up to a first principle but down to a conclusion, while there is another section in which it advances from its assumption to a beginning or principle that transcends assumption, and which it makes not use of the images employed by the other section, relying on ideas only and progressing systematically through ideas.” (510b)

Since Glaucon, and most readers at first, do not quite grasp the idea, Socrates elaborates. In the first section of the intelligible, for example, he places geometrical figures and arithmetical concepts (such as odd and even), “but first, with the reservation that the soul is compelled to employ assumptions in the investigation of it, not proceeding to a first principle because of its inability to extricate itself from and rise above its assumptions, and, second, that it uses as images or likenesses the very objects [i.e., geometrical objects-N-SK] that are themselves copied and adumbrated by the class below them.” (511a) [Emphasis added] Think of Euclidean, post-Pythagorean geometry, which begins with a set of “self-evident,” unexamined axioms; or of Euler's assumption of linearity-in-the-small, as part of this section.

The other section of the intelligible is composed of the following: “That which reason itself lays hold of by the power of dialectics, treating its assumptions not as absolute beginnings, but literally as hypotheses, underpinnings, footings, and springboards so to speak to enable it to rise to that which requires no assumption and is the starting-point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense [oratos] but only of pure ideas moving an through ideas to ideas and ending with ideas.” (511b-c) [Emphasis added]

Having defined these two geometries, that of the shadow world of sense perception, and that of discoverable universal principles, both LaRouche and Plato address the interaction between the two, an interaction which produces paradoxes, or “provocatives” [parakalounta]. Again, in “Visualizing the Complex Domain,” LaRouche says, it “is the unperceived universe of these actual principles which produce those paradoxical sensory effects which prompt the recognition of the existence of the unperceived, but efficiently existing universal physical principles.”¹¹

Socrates describes the difference between those perceptions which do not provoke thoughts of reconsideration, and those that do: There are those for whom “the judgment of them by sensation seems adequate, while others always invite the intellect to reflection because the sensation yields nothing that can be trusted. ... The experiences that do not provoke thought are those that do not at the same time issue in a contradictory perception. Those that do, have that effect that I set down as provocatives.” (523b-c)

Indeed, one might look back at the experience of reading Books III-V of The Republic as a series of “provocatives,” which force a new hypothesis of education, one not based on training or habit. (A careful reader of those earlier books will notice Socrates, on numerous occasions, slyly referring to dog training.) The characteristic of the new hypothesis of education introduced in Book VI, is the unique ability of the human mind, provoked by paradoxes, to use its noetic powers to seek truth, that is, universal principles, culminating in the Good.

As the LaRouche Youth Movement of today begins its education in the geometrical and mathematical work of C.F. Gauss and Bernhard Riemann, so Plato, through the voice of Socrates, likewise enjoins his future guardians of the state. The paradoxes one encounters in the study of numbers, he explains, “would compel the soul to be at a loss and to inquire, by arousing thought in itself, and to ask, whatever is the one as such, and thus the study of unity will be one of the studies that guide and convert the soul to the contemplation of true being” (Book VII, 525a). Socrates continues in Gaussian terms: “The study of reckoning ... is useful for our purpose in many ways, provided it is pursued for the sake of knowledge and not for huckstering. ... [I]t strongly directs the soul upward and compels it to discourse about pure numbers [numbers-in-themselves], never acquiescing if anyone proffers to it in the discussion of number attached to visible and tangible bodies” (525d-e).

Socrates leads Glaucon through a similar examination of geometry and solid geometry, ending with astronomy: “These sparks that bespangle the sky, since they are decorations on a visible surface, we must regard, to be sure, as the fairest and most exact of material things; but we must recognize that they fall far short of the truth, the movements, namely of real speed and real slowness in true number and all true figures both in relation to one another, and as vehicles of the things they carry and contain. These can be comprehended only by reason [logos] and thought [dianoia], but not by sight.” (529c-d) (Compare this to the section “The Case of the Night-Time Sky,” in LaRouche's “Visualizing the Complex Domain.” Then look at Plato's comparison of the sun to the Good, with the section on “Our Creative Sun,” in the same piece.)

It is after this exploration of the complex domain in Books VI and VII, and thus, of an education which turns the soul to the Good, that Plato returns to the question of statecraft. And it is only now that Plato introduces the Nuptial Number, in Book VIII, to launch his discussion of a state governed by the best, an aristocracy (aristos, meaning “the best”).¹²

If society is not based on the commitment to discover and know the complex domain, and, hence, to make decisions based on universal principles, and a commitment to the Good, it will begin to degenerate, as Plato's Athens did. Once one substitutes any other quality or virtue for this, the devolution begins. Socrates traces the downward spiral from timocracy, to oligarchy, to democracy, to the final reaction and descent into tyranny.

Look again at Critias, Nicias, and Alcibiades. To varying degrees, and at various points in their lives, each was committed to “traditional values.” None consciously started out to destroy Athens. Yet, none of the three would walk Socrates' path—the unswerving path toward universal principles in service of the Good. And so, each, succumbing to honor, or money, or pleasure, or ignorance, lead himself and Athens to their mutual tragedies.

Socrates did walk that path, and walked it happily, even though it would lead to his execution. However, Socrates' death was not a tragedy, as he himself addressed in the concluding scene of the Phaedo, where he chastises his friends for wailing and grieving as he is about to drink the hemlock. Have I not, he says, just proven to you the immortality of the soul? Socrates' death was sublime, and it was his passion which turned Plato's soul to be “able to endure the contemplation of essence and the brightest region of being ... the Good.” (The Republic, Book VII, 518d)

The failed characters of Plato's dialogues located their identities in their mortal existences. Socrates located his in his immortality. Plato's dialogues are, at once, tragedies of the former, and great spiritual exercises toward development of the knowledge of the latter. Or, one might simply call them, exercises in the pursuit of happiness.


1. Excerpted in Helga Zepp LaRouche, “Thucydides' 'Melian Dialogue': Beware of the Athenians, Mr. Bush!,” Fidelio, Summer/Fall 2002, Vol. XI, No. 3-4.

2. See footnote 1.

3. Alcibiades I, in Plato XII, Loeb Classical Library, trans. by W.R.M. Lamb (Cambridge, Mass.: Harvard University Press).

4. Charmides, in ibid.

5. See accompanying article, “Sophistry:” by Michael Liebig, page XX.

6. Solon of Athens, “The Constitutional Order,” trans. by David Shavin, assisted by Kenneth Kronberg, Fidelio, Summer 1993 (Vol. II, No. 2).

7. Lyndon H. LaRouche, Jr., “Science for Teachers: Visualizing the Complex Domain,” Executive Intelligence Review, July 11, 2003 (Vol. 30, No. 27).

8. All quotations from The Republic are taken from Plato: The Republic, Loeb Classical Library, trans. by Paul Shorey (Cambridge, Mass.: Harvard University Press).

9. LaRouche, op. cit.

10. Ibid.

11. Ibid.

12. The word "aristocracy" obviously has a different meaning today, involving class or hereditary distinctions.