13. The Milesians, Pythagoras, and Heraclitus: Matter, Form, and Change

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Lecture Notes

The Three Milesians and First Matter #

The Progression of Guesses #

The Milesians sought a single material cause underlying all things. Each successive guess moves from the thicker to the thinner:

• Thales: Water—observable in seeds and living things; limited in both quantity and quality
• Anaximander: The unlimited (τὸ ἄπειρον, apeiron)—qualityless matter, unlimited in both quantity and quality; more abstract than water
• Anaximenes: Air—more unlimited than water in quantity; more transparent and formless in quality

Why Air is a Better Guess Than Water #

Quantitative Sense: Air appears everywhere and extends indefinitely upward, while water is confined to lakes and seas.

Qualitative Sense: Air is more invisible and transparent than water. Water is distinctly wet and cool everywhere; air lacks such definite qualities.

Influenced by Anaximander: Air represents a middle ground between Anaximander’s abstract unlimited and sensible matter—more concrete than the apeiron but more formless than water.

The Principle: Thin Over Thick #

Central Argument: The first matter should be the thinnest and finest thing, because:

• Thick things are composed from thin things (a thick book is made from thin pages)
• You cannot make thin things from thick things
• Elementary particles make up atoms; atoms make up molecules—not vice versa
• Letters of the alphabet (στοιχεῖα, stoicheia) make words; words make sentences; sentences make paragraphs

Therefore, whatever is smallest and finest would be the best guess for first matter.

Pythagoras: The Introduction of Form as Cause #

Mathematics and Form Distinct from Matter #

Pythagoras approaches natural philosophy from mathematics, where there is no matter—only formal causes (order, ratio).

Example of Formal Causation: When straight lines intersect, opposite angles are equal. Why? Because the lines are straight. The form (straightness) is the cause, not the material composition.

The Discovery of Harmonic Ratios #

Pythagoras discovered that harmonious sounds follow simple numerical ratios:

• The octave (eight notes: do, re, mi, fa, sol, la, ti, do) is produced by objects in the ratio 2:1
• The higher note has twice the frequency of the lower; together they sound well together
• Other harmonious sounds similarly exhibit simple numerical ratios

The Pythagorean Overreach #

The Pythagoreans, seeing mathematical ratios underlying sensible harmony, supposed that all things—including virtues in ethics—could be explained by numbers:

• Justice as an even number (“getting even”)
• The soul as “a self-moving number”

Heraclitus: Change, Contradiction, and the Mover #

The Reality of Change #

The River Fragment: “It is not possible to step twice into the same river” because the waters are always different.

All things flow; nothing remains: Change is the fundamental feature of reality. Understanding change is foundational to understanding anything:

• “If you don’t understand change, you don’t understand changing things”
• “If you don’t understand changing things, you don’t understand unchanging things” (we know unchanging things by negation of change)
• Therefore: “If you don’t understand change, you don’t understand anything”

Apparent Contradictions in Change #

Heraclitus points out that change seems to involve contradiction:

• We step and do not step into the same river (same river, different waters)
• Something becomes what it was not (warm becomes cold; wet becomes dry; sleep becomes waking)
• The hard becomes soft; the opposite becomes itself

Change appears to involve something both being and not being simultaneously.

The Problem of Contradiction and Aristotle’s Response #

Parmenides’ Axiom: “Something cannot both be and not be at the same time in the same way.”

Apparent Conflict:

• Heraclitus affirms change but seems to admit contradictions
• Parmenides denies contradictions and therefore denies real change
• Aristotle accepts Parmenides’ axiom as more certain than the appearance of change

Aristotle’s Resolution: Apparent contradictions in change are not real contradictions. The same thing does not have opposite qualities simultaneously; rather, it successively has different qualities (changing at rest = the body is in motion while emotions come to rest—not a real contradiction).

The Third Kind of Cause: The Mover #

Heraclitus introduces a cause beyond matter: the mover or maker (ἄρχων, archon).

Key Fragment: “War is the father of all things, the king of all things.”

• Uses “father” (not “mother”) to indicate the mover/maker
• Matter is associated with mother (materia from mater)
• The mover is the maker, appropriately called “father”

“All things come to be by strife”: Change and becoming arise from the struggle of opposites.

Fire as First Matter #

Heraclitus proposes fire as the beginning of all things:

• Fire is the thinnest and most active of substances
• “All things are exchanged for fire and fire for all things” (economic analogy: goods exchange for gold; gold exchanges for goods)
• Fire represents the principle of change and transformation itself

Modern Parallel: Substitute “energy” for “fire” and you have modern physics (Heisenberg).

Listening to Reason #

“Listen not to me, but to reason” means:

• Listen to what is common to your reason and my reason
• “Those who speak with understanding must be strong in what is common to all”
• Reason naturally knows what is common; disagreements must be resolved by appeal to common ground

Key Methodological Principles #

The Natural Road of Knowledge #

We proceed from the senses (what is most known to us) through reason to what is less known to us but more fundamental:

• Matter is more known than the maker (we come from mother more obviously than father)
• Begin with material cause; if insufficient, proceed to formal cause and efficient cause

Why Matter Comes First #

We inquire about matter before the maker because matter is more known to us, even though the maker is more fundamental in reality.

Important Definitions #

Apeiron (τὸ ἄπειρον): The unlimited; qualityless matter, unlimited in both quantity and quality

Form (μορφή, morphē): Not merely shape, but order and ratio; the formal cause that explains why things are as they are

Stoicheia (στοιχεῖα): Elements; letters of the alphabet; the fundamental constituents from which all things are composed

Notable Quotes #

Heraclitus: “Nature loves to hide” (ἡ φύσις φιλεῖ κρύπτεσθαι)—what is fundamental is within, hidden from immediate perception.

Max Born (The Restless Universe): “Strange we have a name for what doesn’t exist, namely rest. There is no such thing."—Modern physics confirms Heraclitus’s doctrine of universal flux.

Examples & Illustrations #

The Book and Pages: A thick book is composed from thin pages; you cannot make thin pages from a thick book. Therefore, the finest particles are the best candidates for first matter.

Geometric Causation: Straight lines intersecting produce equal opposite angles because of the form (straightness) of the lines, not their material composition.

Harmonic Ratios: The octave produced by a 2:1 ratio of frequencies demonstrates that mathematical form underlies sensible phenomena.

The Room Full of Air: A room with all furniture removed appears empty, yet it is filled with air—showing that air is less known and less sensible than solid objects.

Movement and Attention: Things in motion catch the eye more readily than things at rest (Troilus and Cressida). Police and ambulance lights blink to capture attention. This reflects how change is what first enters our knowledge.

The River and the Foot: Cratylus (a student of Heraclitus) pushed the doctrine further: “It is not possible to step once into the same river,” because as the foot breaks the surface, the water at the surface is already different.

Ostracism in Athens: A man famous for justice was voted into exile simply because someone was tired of hearing him called “the just”—people cast out what they perceive as superior to themselves, a form of irrationality Heraclitus criticized in the Ephesians.