In the 5th century BCE a man in southern Italy argued that a fast runner can never overtake a slow one with a head start. Everyone knew this was false: runners overtake. The point was that the argument looked airtight, and so something in our ordinary picture of motion, space or number must be wrong. Finding out what took, by some counts, until the 19th century, and some philosophers think it is not over.
That is the spirit of the whole period. Ancient and medieval philosophy is not a museum of wrong physics. It is the invention of a method: state a claim, find the strongest objection, and follow the argument where it goes. The chain runs from Miletus and Athens through Alexandria, Baghdad, Córdoba and Cairo to Paris and Oxford, and it depends, at every link, on people reading, translating and arguing with those before them.
"Presocratic" lumps together thinkers of the 6th and 5th centuries BCE who asked what the world is made of. Thales of Miletus (in modern Turkey) was said by Aristotle to have answered "water". Anaximander said an unlimited something (apeiron). Heraclitus said all is change and held together by a pattern, the logos. Democritus said atoms and void. These are guesses, but they were the first guesses that came with reasons.
Parmenides of Elea, in southern Italy, pushed the other way: what is cannot come from what is not, so change is impossible and the senses deceive. His student Zeno devised arguments to defend that conclusion by showing that belief in motion leads to absurdity, as reported by Aristotle in the Physics. In "Achilles and the tortoise", Achilles must first reach where the tortoise started, by which time it has moved on, and so on without end. The tool below runs the race and adds up the stages.
Head start 100 m, Achilles 10 m/s; the tortoise's speed is 10r m/s. Infinitely many stages, finite distance and finite time: that is the modern answer. Philosophers still ask whether it explains how an infinite series is completed.
Without JavaScript: with r = 0.5 the stages are 100, 50, 25 … metres and sum to 200 m, reached after 20 s; with r = 0.9 they sum to 1000 m after 100 s.
The sum was not made rigorous until the 19th century. The Greeks themselves answered in different ways, and Aristotle distinguished a potential infinity of divisions from an actual one.
Socrates (470/469–399 BCE) wrote nothing. We know him from Plato, Xenophon and Aristophanes, whose portraits differ (the "Socratic problem"). In Plato's early dialogues he questions someone who claims to know what courage, piety or justice is, and shows, step by step, that the definitions contradict the person's other beliefs. This method, the elenchus, produces no final answer, only the discovery of ignorance. He was tried in Athens in 399 BCE for impiety and corrupting the young and executed by hemlock.
"The life which is unexamined is not worth living."Plato, Apology 38a, Benjamin Jowett's translation
The best-known case is the Euthyphro. Euthyphro defines piety as what the gods love. Socrates asks (10a): is the pious loved by the gods because it is pious, or is it pious because they love it? Try both horns.
Without JavaScript: if the gods love it because it is pious, piety exists independently of the gods' say-so; if it is pious because they love it, their love looks arbitrary. Philosophers of religion still discuss this.
Plato (c. 428/427–348/347 BCE), who founded the Academy in Athens, turned Socrates' search into a theory. We know many beautiful things, but never beauty itself; yet we recognise them as beautiful by something. That something, the Form of the Beautiful, is perfect, unchanging and grasped by reason, not by the senses. In the Republic (Book VII, 514a on) he pictured ordinary life as prisoners in a cave watching shadows; the one who climbs out sees the sun, the Form of the Good. (See 05/06 for the cave in full.)
Just before the cave (509d–511e) he draws a divided line. Cut a line into two unequal parts, visible and intelligible, then cut each in the same ratio. The four segments give four grades of cognition: images, things, mathematical reasoning and understanding of the Forms. A small result follows from the geometry, and you can check it.
Plato says only "unequal" and "in the same ratio"; the line's total length of 100 is arbitrary. The tradition makes the intelligible part longer.
Without JavaScript: for any ratio, the two middle segments come out equal. With a ratio of 2 they are each 22.2 on a line of 100.
The objections began at once. Aristotle asked where the Forms are and what they add. Plato himself, in the Parmenides, lays out the "third man" regress: if a Form makes many men alike, what makes the men and the Form alike? And the Republic is political philosophy as well: its guardians include women, an extraordinary idea for the time, though it also proposes strict state control of education and a ruling class. Readers have disagreed since about whether to call it utopia or warning.
Aristotle (384–322 BCE), Plato's student for twenty years and later tutor of Alexander of Macedon, reversed the direction. Forms are not elsewhere; they are in things. Study the world as it is. He wrote on logic (the first system of formal inference, the syllogism), biology (he studied and dissected animals, many of them marine), ethics, politics, poetry and what he called first philosophy.
"All men by nature desire to know."Aristotle, Metaphysics I.1, W. D. Ross's translation
To explain anything, he said, give four causes (Physics II.3): what it is made of (material), its form or structure (formal), what made it (efficient), and what it is for (final). Choose a thing.
Without JavaScript: for a bronze statue, the material cause is bronze, the formal cause is the shape of the figure, the efficient cause is the sculptor and the final cause is to honour the person shown.
Final causes, purposes in nature, were rejected by much of early modern science and are still disputed in biology, where some philosophers say natural selection brought them back. In ethics, Aristotle held that virtue is a habit that finds the mean between two excesses, relative to the person and the situation. His views on slavery and on women in the Politics are among the worst of his writing, and later thinkers, including Christine de Pizan, argued with them.
After Alexander's conquests (d. 323 BCE) the Greek world was larger and less secure, and philosophy turned to a practical question: how do I live well when I cannot control events? Four schools answered. The Epicureans (Epicurus, 341–270 BCE, taught in a Garden) said pleasure is the good, mainly the quiet of having few fears and few needs; death is nothing to us. The Stoics (Zeno of Citium, c. 334–262 BCE; later Epictetus, c. 50–135 CE, born a slave; and the emperor Marcus Aurelius, 121–180) said virtue is the only good and we should accept what is outside our control. The Pyrrhonian sceptics (Pyrrho, c. 360–270 BCE; Sextus Empiricus, around 200 CE) suspended judgment on everything and reported that calm followed. The Cynics (Diogenes) lived by nature in public, ignoring convention.
"Of things some are in our power, and others are not."Epictetus, Enchiridion 1, George Long's translation
Without JavaScript: for the Stoics, judgments and efforts are up to us; the result, other people's opinions, and our bodies are not wholly so.
Stoicism was no passive creed: Marcus governed an empire, and Stoic ideas of a common human reason fed into later law and ethics. Critics from Aristotle's side say that making virtue everything undervalues the goods a life needs. See Stoicism for Real Life (05/02) for practice.
When Roman power wavered, philosophy did not stop. In Alexandria, Plotinus's Neoplatonism (Enneads, c. 3rd century) held that everything flows from an ineffable One. Hypatia (born between about 350 and 370, murdered in March 415) taught philosophy and mathematics there; she edited a book of Ptolemy's Almagest, and some scholars credit her with material in an Arabic version of Diophantus, but no philosophical writing of hers survives. The quote "Reserve your right to think" often credited to her was written in 1908 by Elbert Hubbard, who made it up. In North Africa, Augustine (354–430) joined Christian faith to Platonism and asked about time.
"What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not."Augustine, Confessions XI.14, E. B. Pusey's translation
Boethius (c. 477–524), writing in prison awaiting execution under Theodoric, finished The Consolation of Philosophy and had already translated Aristotle's logic into Latin, which kept it alive in the West. Meanwhile, from the 8th century in Baghdad, translators turned Greek into Arabic. Al-Kindī, al-Fārābī and then Ibn Sīnā (Avicenna, 980–1037) built systems on them. Avicenna's "floating man", suspended in air with no sensation, still knows he exists, an argument that the self is not the body. His distinction between what a thing is and that it is, with a Necessary Existent whose essence is existence, drove the next three centuries. Al-Ghazālī (1058–1111) attacked the philosophers' claim that causes necessitate effects; Ibn Rushd (Averroes, 1126–1198) answered him and wrote the commentaries on Aristotle that Latin Europe read. Moses Maimonides (1138–1204), writing in Judeo-Arabic in Cairo, held that we can say only what God is not (Guide of the Perplexed). More on this world in 36/11.
Dates are conventional and many early ones are approximate (c.). Hypatia's birth year is uncertain (350–370). Confucius, Mencius and Nāgārjuna are added from other traditions (36/10).
Without JavaScript: in 400 BCE Democritus, Socrates and Plato were alive, and in 1100 CE Anselm and al-Ghazālī were; try the year slider with JavaScript on.
In the Latin West, Anselm (1033–1109) argued in the Proslogion that God is "that than which nothing greater can be conceived", and so must exist in reality; his contemporary Gaunilo replied that the same move would prove a perfect island. Peter Abelard (1079–1142) worked on universals. By the 13th century the new universities of Paris and Oxford were reading Aristotle in translation, partly through Ibn Rushd, and Thomas Aquinas (1225–1274) built the largest synthesis, in the Summa Theologiae. His "Five Ways" (I, q.2, a.3) are short arguments from features of the world to a first cause. The first, reconstructed:
Critics deny 2 (after Newton, steady motion needs no cause), deny 3, or deny that the conclusion is God. Defenders reply that Aquinas means a chain of simultaneous dependence, not a series of past events, which is a different matter. The 1277 condemnation by the bishop of Paris of more than 200 propositions, many of them Aristotelian, shows that this was no calm synthesis. Many believers and non-believers still find the argument worth testing.
Christine de Pizan (1364–c. 1430), born in Venice and writing in France, supported her family by writing after being widowed. In The Book of the City of Ladies (1405) she answered the misogyny of the Romance of the Rose and of authorities including Aristotle, and built an allegorical city from the examples of learned women. Her case that women's apparent inferiority comes from lack of education is an early entry in a long argument we meet again in 36/09.
Ancient and medieval philosophy invented the method of following an argument to its end. Its big structures (Plato's Forms, Aristotle's causes, the Stoic line between what we can and cannot control, Avicenna's essence and existence, Aquinas's synthesis) are still the ones modern debates are built on or against, and they were shaped by a chain of readers from Athens to Cairo to Paris, including women whose voices were often lost.
Try this: take a belief you hold firmly and ask Socrates' question, "what exactly do I mean by it?", until your definition contradicts something else you believe.
Sources. Plato, Apology, Euthyphro and Republic (Jowett); Aristotle, Physics II.3 and VI.9, Metaphysics I.1 (Ross), Nicomachean Ethics II.6; Epictetus, Enchiridion (Long); Augustine, Confessions (Pusey); Anselm, Proslogion; Aquinas, Summa Theologiae I q.2 a.3; Maimonides, Guide of the Perplexed; Christine de Pizan, Le Livre de la Cité des Dames (1405); Stanford Encyclopedia of Philosophy entries on Zeno's paradoxes, Hypatia, Avicenna, Boethius, Christine de Pizan and Aquinas; Wikipedia's Hypatia entry on Hubbard's 1908 invention of the "right to think" quote.