The Timpson Lyceum · History of Philosophy (2024)

Anaximander, Anaximenes, and Xenophanes – Lecture 3 (History of Philosophy)

Overview

This lecture continues the Milesian school — the first natural philosophers, all asking what is the arche, the single underlying principle of everything — and adds a sharp critic of Greek religion. Anaximander and Anaximenes are successors of Thales in Miletus; Xenophanes of Colophon is a wandering poet-philosopher who turns the same rational spirit against anthropomorphic myth.

The through-line is a maturing method: Thales named a substance (water); Anaximander abstracts to something beyond any element; Anaximenes supplies a mechanism for how one substance becomes the many; and Xenophanes applies critical reason to the gods themselves.

Key Concepts

• Anaximander of Miletus (~610–546 BC) — Successor of Thales; among the first to write philosophy in prose and to draw a map of the world.
• The apeiron (τὸ ἄπειρον, "the boundless") — Anaximander's arche: not water or any single element, but an indefinite, unlimited, eternal source from which all things separate out and into which they return. Reasoning: no specific element could be the origin, since it would overpower its opposites; the source must be neutral and inexhaustible.
• Cosmic justice — Things come to be and pass away "according to necessity, paying penalty to one another for their injustice according to the ordering of time" — opposites (hot/cold, wet/dry) encroach and are balanced over time.
• Earth in equilibrium — The earth floats unsupported at the center of the cosmos, held by symmetry rather than resting on water — an early appeal to sufficient reason.
• Proto-evolution — Life arose from moisture; humans descended from fish-like creatures, since a helpless human infant could not have survived unaided in an earlier world.
• Anaximenes of Miletus (~585–528 BC) — Successor of Anaximander; his arche is air (aēr).
• Rarefaction and condensation — Anaximenes' key advance: a single quantitative mechanism for change. Air rarefied becomes fire; condensed it becomes wind → cloud → water → earth → stone. Change is a matter of density (a "more/less" of one stuff), not mysterious transformation.
• Xenophanes of Colophon (~570–478 BC) — Critic of anthropomorphic religion: "if oxen and horses could draw, they would draw the gods like oxen and horses"; Ethiopians' gods are dark, Thracians' are blue-eyed. He proposes one greatest god, not like mortals in body or mind (a step toward monotheism).
• Xenophanes' epistemology — Early fallibilism: certain truth is unattainable by us; "opinion is allotted to all." He also reasoned naturally — fossils of sea creatures inland show the earth was once covered by sea.

Worked Example

Anaximander's equilibrium argument (why the unsupported earth does not fall) — an early use of the principle of sufficient reason.

1. Suppose the earth sits at the exact center of a spherical cosmos, equidistant from every point on the outer boundary.
2. For the earth to move, it must move in some particular direction (up, down, sideways).
3. But every direction from the center is perfectly symmetric to every other — nothing distinguishes "down" from "up" or from any lateral direction.
4. So there is no sufficient reason for the earth to move one way rather than another.
5. Absent any reason to move in a particular direction, it moves in none.
6. Therefore the earth stays put at the center with no physical support — held in place by symmetry alone. $\blacksquare$

Summary

• The Milesian program refines itself: Thales (water) → Anaximander (the apeiron, an indefinite boundless source) → Anaximenes (air, with a real mechanism — rarefaction and condensation).
• Anaximander contributes striking ideas: cosmic justice among opposites, the earth held by symmetry, and a proto-evolutionary origin of humans.
• Anaximenes' lasting move is methodological — explaining qualitative change by a single quantitative variable (density).
• Xenophanes turns reason on religion, rejecting man-made gods for one non-anthropomorphic god, and voices an early skepticism about the limits of human knowledge.
• Across all three, the founding question — what underlies the many? — is pursued with ever more abstraction and rigor.