Xenocrates

• 1. Introduction

  ›

  Xenocrates of Chalcedon lived for roughly 82 years, from around 396/5 BC to 314/3 BC, and in that span he helped shape the direction of Western philosophy. He studied under Plato, led the Platonic Academy for more than two decades, advised Athenian ambassadors, and wrote on topics ranging from arithmetic to royalty. Yet he died in one of the most undignified ways imaginable: he tripped over a bronze pot in his own house and struck his head, and that was the end of him. What kind of person leads one of the ancient world's great intellectual institutions, debates the nature of the soul and the structure of the cosmos, and then meets his end stumbling in the dark at home? And what did Xenocrates actually believe? His ideas were strange, intricate, and deeply original. He thought the soul was a self-moving number. He counted unity and duality among the gods. He tried to calculate the total number of syllables the alphabet could produce. This documentary follows the arc of his life, his arguments, and the world he moved through.

• 2. The Man from Chalcedon

  ›

  Chalcedon, the city across the water from Byzantium, gave the ancient world Xenocrates. His father was named Agathon or, in some accounts, Agathanor. As a young man Xenocrates made his way to Athens, where he first attached himself to Aeschines Socraticus before crossing over to Plato's circle. He accompanied Plato to Sicily in 361 BC, a journey that was also made by other ambitious members of the Academy. After Plato died, Xenocrates and Aristotle together visited Hermias of Atarneus, the ruler of a small territory in Asia Minor who had himself studied at the Academy.

  In 339/8 BC, the school needed a new head. Speusippus had led it after Plato, and when Speusippus stepped aside, a competitive vote followed. Xenocrates defeated two rivals, Menedemus of Pyrrha and Heraclides Ponticus, by a narrow margin. He would hold that position for the rest of his life, until his death in 314/3 BC. His tenure lasted roughly a quarter century.

  Those who knew him described a man without natural social ease. He did not charm a room. What he had instead was a reputation for thoroughness, for steady application, and above all for integrity. People trusted him with public business precisely because his personal character seemed beyond question. On three separate occasions he served as a member of Athenian diplomatic missions: once to Philip of Macedon, and twice to Antipater, the Macedonian regent who held enormous power over Athens in the years after Alexander's campaigns.

• 3. Politics and Principle

  ›

  Xenocrates deeply resented the Macedonian dominance that pressed on Athens during his lifetime. That resentment was not merely an opinion he kept to himself. Soon after the death of Demosthenes, around 322 BC, Athens had attempted an unsuccessful rebellion against Macedonian control and lost. Xenocrates had played a role in negotiating the resulting peace with Antipater. As a reward for that service, the Athenian statesman Phocion moved that Xenocrates be granted Athenian citizenship.

  Xenocrates refused. His refusal was not a modest gesture. The peace settlement had come at a concrete cost: thousands of poor Athenians were stripped of their voting rights as part of the constitutional change imposed on the city. Xenocrates said plainly that he did not want to become a citizen within a constitution he had worked to prevent. The integrity that Athenians admired in him was not ceremonial. It cost him something.

  It also cost him financially. As a resident alien without citizenship, Xenocrates was liable for a tax on foreigners living in Athens. He apparently could not pay it. Ancient accounts differ on what saved him: one version credits the orator Lycurgus with stepping in; another says he was purchased by Demetrius Phalereus and then freed. Either way, his legal and financial situation was precarious for much of his later life, despite the prestige of running the Academy. Among those who attended his lectures were figures who would go on to mark very different paths: Polemon, his eventual successor, whom Xenocrates had reportedly rescued from a dissolute life; Phocion, the statesman; Chaeron, who became tyrant of Pellene; the philosopher Crantor; and, by some accounts, both Zeno the Stoic and Epicurus.

• 4. Three Grades of Knowing

  ›

  Xenocrates organized his epistemology around a tripartite structure that mapped different faculties onto different regions of reality. Knowledge, or episteme, corresponded to pure thought and the objects accessible only to the intellect, those essences that stand apart from the phenomenal world. Sensation, or aisthesis, corresponded to what passes into the world of phenomena. Opinion, or doxa, occupied the middle ground: the essences that are at once objects of sensuous perception and, mathematically, of pure reason.

  This third category, doxa, was the interesting one. Where common usage applied the word to mere conjecture or belief, Xenocrates used it in a higher sense. He identified its domain with the heavens and the stars, and he saw mathematics as the mediating discipline between sensory experience and pure thought. In this he went further than Plato in trying to carve out a precise role for mathematical objects in the structure of knowledge.

  He also went further in one other direction. He gave his three grades of cognition a mythological anchor. He connected knowledge, sensation, and opinion to the three Fates: Atropos, Clotho, and Lachesis. Whether this was a didactic device, a genuine metaphysical commitment, or something in between, it reflected a broader tendency in his thinking: a preference, as ancient sources noted, for symbolic and sensualizing modes of expressing abstract ideas. He was not content to leave philosophy as pure abstraction. He wanted it legible, grounded in images that could be held in the mind.

• 5. Gods, Daemons, and the Soul

  ›

  Plutarch recorded that Xenocrates described the soul as a self-moving number. That phrase sounds cryptic until you follow the argument. Xenocrates called unity and duality - monas and duas - divine principles. Unity he characterized as male, ruling in heaven, as father and Zeus, as the uneven number and spirit. Duality he characterized as female, the mother of the gods, the soul of the universe presiding over the mutable world beneath the heavens.

  Below the level of these supreme principles, Xenocrates filled the cosmos with what he called daemonical powers, intermediate beings that stand between gods and ordinary mortals. He offered a geometric analogy: these daemons are related to gods and humans as the isosceles triangle is related to the equilateral and the scalene. The divine world-soul expressed itself differently in different spheres. In the purer zones it animated the planets, the sun, and the moon as Olympic gods. In the sublunary elements it appeared as figures like Hera, Poseidon, and Demeter, daemonical rather than fully divine.

  At the level of these sublunary daemons, the opposition between good and evil first becomes real. A good daemon makes happy those in whom it takes up residence; a bad one ruins them. Xenocrates derived the word eudaimonia, commonly translated as happiness or flourishing, from the idea of a good daemon dwelling within a person. The entire structure rested on a single underlying principle: divine power pervades all grades of existence, but it grows less energetic the further it descends toward the perishable and the individual. Even irrational animals, Xenocrates held, partake of some intuition of that ruling divine power.

• 6. Mathematics at the Foundation

  ›

  Aristotle, in his Metaphysics, sorted the Platonists of his day into three camps based on how they handled the relationship between ideal numbers and mathematical numbers. Plato distinguished the two. Speusippus accepted mathematical numbers alone. Xenocrates identified them: ideal numbers and mathematical numbers were, for him, the same thing. Aristotle objected sharply to this position. If ideal numbers are made of ordinary arithmetic units, he argued, they can no longer function as first principles, because they become subject to ordinary arithmetic operations.

  Xenocrates also embraced the concept of indivisible lines. Zeno of Elea had constructed famous paradoxes around the infinite divisibility of space and time. Xenocrates countered by positing minimal magnitudes, lines that cannot be further divided, which he called first or original lines. He extended this to original plane figures and bodies. The principia of existing things, he insisted, must be sought not in the material, not in what is infinitely divisible, but in the ideal definiteness of form.

  Pluarch records a remarkable calculation. Xenocrates tried to find the total number of syllables that could be formed from the letters of the Greek alphabet. His result was 1,002,000,000,000. Whether his method was correct is a separate question, but the attempt itself may represent the first recorded effort to solve a combinatorial problem involving permutations. A man who believed number lay at the foundation of all reality and consciousness was naturally drawn to the question of how many arrangements were possible from a finite set of symbols.

• 7. Living Well, Living Rightly

  ›

  On ethics, Xenocrates drew from the tradition of the older Academy while pressing it toward greater practical definition. He sorted everything into three categories: the good, the bad, and a middle zone that is neither. Health, beauty, fame, and good fortune fell into that middle zone. They were not intrinsically valuable, but they were not worthless either. Their value depended on whether they served as means toward the good or toward the bad, and how they were used.

  Virtue alone, he maintained, has unconditional value. Everything else is conditional. Happiness, properly understood, coincides with the consciousness of virtue. But he was not indifferent to circumstances. Human happiness requires that a person be able to enjoy the good things originally suited to human life by nature. Sensuous gratification, however, did not belong on that list.

  His moral seriousness came through in particular examples. He declared that casting longing eyes on the property of another amounts to the same thing as actually setting one's feet upon it. Intention and act were morally equivalent in his view. He also warned that the ears of children should be protected from the poison of immoral speech. This was not a man who separated intellectual virtue from personal conduct. The lectures attended by Polemon, whom Xenocrates reportedly drew back from a dissolute life, were also attended by Zeno of Citium, who would go on to found the Stoic school. What Zeno absorbed from Xenocrates about the relationship between virtue and happiness left traceable marks on the Stoic tradition that followed.