Athenian Science and Politics

The Presocratics

The Principles of Nature

Principle: arche (ἀρχή)

Material Principles

Everything comes from material principles either by

  1. Condensation and Rarefaction (Thales, Heraclitus. Xenophanes, Anaxemines)

  2. Separation and Mixture (Empedocles, Anaxagoras)

Sometimes "Efficient Principles" (Empedocles' Love and Strife, Anaxagoras' Mind, Heraclitus' Logos) explain change.


To explain the world, in terms of what it's made of.

Example: Xenophanes on clouds.

The sea is the source of water and of wind, For without the great sea, there would be no wind nor streams of rivers, nor rainwater from on high. But the great sea is the begetter of clouds, winds, and rivers.

The sort of fires that appear on ships---whom some call the Dioscuri [St. Elmo's fire]---are tiny clouds glimmering in virtue of the sort of motion they have.

Systematic Understanding

As Heraclitus puts it:

Those who would speak with understanding must ground themselves firmly in that which is common to all, just as a city does in its law, and even more firmly! For all human laws are nourished by one law, the divine; for it rules as far at it wishes and suffices for all, and is still more than enough.

Suspicion of the Senses


Eyes and ears are bad witnesses to those with barbarian souls.


By convention sweet and by convention bitter... In reality, atoms and void.


  1. Democritus and the Cone

  2. Zeno and the Arrow

  3. Zeno and the Millet

The Melian Dialogue vs. The Funeral Oration

The Funeral Oration

Note the context. A speech given in praise of the war dead.

Before: Cypress coffins are borne in cars... Among those is carried one empty bier decked for the missing.

After: Such was the funeral... In the first days of summer, the Lacedaemonians ... laid waste to the country. Not many days after ... the plague first began to show itself ... a pestilence of such extent and mortality was nowhere remembered.

Democratic values:

Our constitution does not copy the laws of neighboring states; we are rather a pattern to others than imitators ourselves... If we look to the laws, they afford equal justice to all in their private differences

Military conduct.

If we turn to our military policy, there also we differ from antagonists. We throw open our city to the world, and never by alien acts exclude foreigners from any opportunity of learning or observing, although the eyes of an enemy may occasionally profit by our liberality

it is only the Athenians who, fearless of consequences, confer their benefits not from calculations of expediency, but in the confidence of liberality.

The Melian Dialogue

Cut-throat Political Realism.

we both alike know that into the discussion of human affairs, justice only enters where there is equal power to enforce it, and that the powerful exact what then can, and that the weak suffer what they must.

This is elevated to a kind of moral rule:

of Gods we believe, and of men we know, that by a law of their nature, wherever they can rule they will

Greek Geometry

The Elements

  1. Written by Euclid, Greek mathematician, around 300 BC; likely a student at Plato's Academy.
  2. Said to summarize work of Plato's students.
  3. Until the 20th century, a basic part of university education.

Basic structure

  1. Definitions
  1. Postulates
  1. Common Notions


Statement, Construction, Verification.

Later Propositions Build on Earlier.

A Model of Knowledge

  1. Builds on basic principles
    • Starts from definitions
    • Hierarchical
  2. Outstrips any possible observation
    • Common notions (equality)
    • Postulates (parallels)
    • Definitions (points)


  1. Navigational techniques (Thales)
  2. Explain retrograde motions of planets (Aristarchus of Samos)
  3. Calculate circumference of earth (Eratosthenes)
  4. Elements culminates in proof that these are the only five regular convex polyhedra.

Possible Inference

There are principles.

But not of this world


Elements, up to proposition 3

Meno Excerpts p265-335