Filosofia
The Presocratics: A Clear Summary with Chart and 5 Solved Exercises
Who the Presocratic philosophers were and what they argued: the archē, the Milesian school, Pythagoras, Heraclitus, Parmenides, Empedocles, Anaxagoras and Democritus, with a summary chart, 5 solved exercises and 3 FAQs.
Recommended for: Grade 11 · Grade 12
The Presocratics are the first Greek philosophers, active between the sixth and fifth centuries BC, who explained the world with rational arguments instead of myths. One question unites them: what is the archē, the principle everything comes from, is made of, and returns to?
Why that name
The label “Presocratic” is not ancient. It took hold in the twentieth century with the collection of fragments edited by Hermann Diels. It does not mark chronology alone, since Democritus is younger than Socrates, but a way of doing philosophy: the object of enquiry is physis, nature, and not yet human conduct and morality.
Aristotle calls them physiologoi, “students of nature”. The break with myth lies in the kind of question asked. Myth tells us who made the world; the Presocratics ask what it is made of, and expect the answer to survive an objection.
One warning before you study them: none of their works has reached us whole. We know them through fragments (literal quotations) and testimonia (summaries by later authors), gathered in the Diels-Kranz edition, which is where codes like “DK 22 B 91” come from.
The Milesian school: water, apeiron, air
It all begins at Miletus, a wealthy trading city on the coast of Asia Minor, in the sixth century BC.
Thales (c. 624-546 BC) names water as the principle. The choice is not arbitrary: water is the one element we see as solid, liquid and vapour, and it is present in every living thing. Herodotus reports that Thales predicted the solar eclipse of 585 BC.
Anaximander (c. 610-546 BC) objects to his teacher: if the principle coincided with one of the elements, that element would overwhelm and absorb the rest. He therefore calls it the apeiron, the boundless and indeterminate, a reality without limits or fixed qualities, out of which the opposites (hot and cold, dry and wet) separate.
Anaximenes (c. 586-528 BC) goes back to a visible element, air, but supplies the missing piece: a mechanism of transformation. Rarefied, air becomes fire; condensed, it becomes wind, cloud, water, earth and stone. For the first time a qualitative difference between things is explained by a quantitative difference in density.
Pythagoras: substance is number
Pythagoras of Samos (c. 570-495 BC) founded at Croton a community that was at once a philosophical school, a religious brotherhood and a political group. His principle is not material: it is number.
The evidence that convinced the Pythagoreans came from music. Dividing a string according to simple ratios produces the consonant intervals: 2:1 gives the octave, 3:2 the fifth, 4:3 the fourth. If the harmony the ear recognises is a numerical ratio, then number is the structure of reality.
The school hit a crisis with the discovery of incommensurable magnitudes: the side and the diagonal of a square share no common unit, because √2 cannot be written as a ratio of whole numbers. “All is number” could not survive in its original form.
Heraclitus: everything flows
Heraclitus of Ephesus (c. 535-475 BC), nicknamed the Obscure for his aphoristic style, puts becoming at the centre. His principle is fire, the only element that exists solely while it is transforming.
Watch out for a common inaccuracy: the famous panta rhei (“everything flows”) is not a literal sentence of Heraclitus but Plato’s summary of him. The authentic fragment says that into the same river we step and do not step, because the waters flowing over us are always new.
Becoming is not chaos, though. It is governed by the logos, the rational law common to all things, and it arises from conflict: “polemos is father of all things” (DK 22 B 53). Opposites do not cancel out, they call each other into being: without illness we would not recognise health.
Parmenides: being is, non-being is not
Parmenides of Elea (c. 515-450 BC) turns the picture upside down, and does so in a poem in verse. There are two ways: the way of truth (aletheia), which follows reasoning alone, and the way of opinion (doxa), which trusts the senses.
The way of truth starts from an elementary principle: being is, non-being is not and cannot even be thought. From this Parmenides deduces that being is ungenerated (it would have to arise from non-being), imperishable, one, motionless and complete. Change becomes an illusion of the senses.
His pupil Zeno defends the thesis by reductio ad absurdum, through the paradoxes: the dichotomy, Achilles and the tortoise, the arrow. He does not claim to prove directly that being is motionless, only that admitting motion and plurality leads to contradictions. This is why Aristotle regards him as the inventor of dialectic.
After Parmenides: pluralists and atomists
The philosophers who follow accept the Parmenidean constraint (nothing comes from nothing) while wanting to save our experience of change. The solution is the same for all of them: multiply being.
Empedocles of Acragas (c. 490-430 BC) posits four eternal roots, earth, water, air and fire, moved by two opposing forces: Love, which unites, and Strife, which separates. Birth and death are nothing but mixture and separation.
Anaxagoras of Clazomenae (c. 496-428 BC) admits infinitely many qualitatively different seeds, holding that there is a portion of everything in everything. The initial mixture is set in order by the Nous, the Intelligence.
Leucippus and Democritus (c. 460-370 BC) arrive at atomism: all that exists are atoms, full, eternal and indivisible particles, and the void through which they move. Atoms differ in shape, arrangement and position; colours and flavours depend instead on how their configuration appears to us.
Summary chart
| Philosopher | School or city | Principle | Key idea |
|---|---|---|---|
| Thales | Miletus | water | first natural explanation of the world |
| Anaximander | Miletus | apeiron | the principle cannot be a determinate thing |
| Anaximenes | Miletus | air | rarefaction and condensation |
| Pythagoras | Croton | number | reality has a mathematical structure |
| Heraclitus | Ephesus | fire | becoming, logos, unity of opposites |
| Parmenides | Elea | being | being is, becoming is illusion |
| Empedocles | Acragas | four roots | Love unites, Strife separates |
| Anaxagoras | Clazomenae | seeds | the Nous orders the mixture |
| Democritus | Abdera | atoms and void | materialism and mechanism |
The exercises below give you a philosopher-to-principle matching task, a true or false, the attribution of four claims, the calculation that dissolves the Achilles paradox, and a synthesis question on the generation after Parmenides.
Solved exercises
1. Match each philosopher with the first principle (archē) he proposed: Thales, Anaximander, Anaximenes, Pythagoras, Heraclitus, Democritus. Available principles: air, number, water, atoms and void, apeiron, fire. base
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- Thales, the first Milesian, chooses water: it is the only element we see as solid, liquid and vapour, and it is present in every living thing.
- Anaximander rejects any already-determined element and picks the apeiron, the boundless: if the principle were one of the elements, it would overwhelm the others.
- Anaximenes returns to a visible element, air, but adds the missing piece, a mechanism: rarefied it becomes fire, condensed it becomes wind, cloud, water, earth and stone.
- Pythagoras moves the principle from matter to form: the substance of things is number, that is, measurable ratio.
- Heraclitus chooses fire, the only element that exists only while it is transforming: it is becoming made visible.
- Democritus closes the enquiry with atoms and void: full, indivisible particles moving through empty space.
Answer: Thales → water; Anaximander → apeiron; Anaximenes → air; Pythagoras → number; Heraclitus → fire; Democritus → atoms and void
2. True or false? Correct the false statements. a) They are called Presocratics only because they all lived before Socrates. b) We possess their complete works. c) For Parmenides, non-being can be neither thought nor spoken. d) For Anaxagoras the order of the cosmos is produced by an intelligence, the Nous. base
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- a) False: Democritus was born after Socrates. The label mainly marks a way of doing philosophy, focused on nature rather than on human conduct.
- b) False: no Presocratic work survives whole. We have fragments (literal quotations) and testimonia (summaries by later authors).
- c) True: this is the core of the way of truth. To think non-being would be to think nothing at all, which is not thinking.
- d) True: the original mixture of seeds would stay undifferentiated without the Nous, the Intelligence that starts the ordering motion.
Answer: a) False (Democritus is later than Socrates); b) False (only fragments and testimonia); c) True; d) True
3. Attribute each claim to the right philosopher and justify your choice in one line. 1) 'Into the same river we step and do not step.' 2) 'Being is ungenerated and imperishable, for it would have to come from non-being.' 3) 'Things arise from the union of four roots driven by Love and Strife.' 4) 'Before reaching the goal you must cover half the distance, and before that half of that half: so motion can never begin.' intermedio
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- 1) Heraclitus: the river is his image of becoming. It stays the same in form while the matter that composes it changes without pause.
- 2) Parmenides: this is the central deduction of the way of truth. If non-being is not, being has nowhere to come from and nowhere to end.
- 3) Empedocles: the four roots (earth, water, air, fire) are eternal, and the two cosmic forces of Love and Strife explain their combining and separating.
- 4) Zeno of Elea: this is the dichotomy paradox, built by reductio ad absurdum in defence of Parmenides against those who admit motion.
Answer: 1 → Heraclitus; 2 → Parmenides; 3 → Empedocles; 4 → Zeno of Elea
4. Zeno's Achilles paradox claims the runner will never catch the tortoise, because every time he reaches where the tortoise was, it has moved further ahead. Suppose Achilles runs at 10 m/s, the tortoise at 1 m/s, and the tortoise starts 90 m ahead. After how long, and how far from Achilles' starting point, does he overtake it? What does the calculation tell us about the paradox? intermedio
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- Write the positions as functions of time: Achilles x = 10t, tortoise x = 90 + t.
- The overtake happens when the positions coincide: 10t = 90 + t, so 9t = 90 and t = 10 s.
- Compute the distance: Achilles covers 10 · 10 = 100 m. Check on the tortoise: 90 + 10 = 100 m. The positions match, so the result holds.
- Now redo the journey 'Zeno's way': Achilles covers the 90 m in 9 s, but meanwhile the tortoise has gained 9 m; he covers those 9 m in 0.9 s, but the tortoise has gained 0.9 m; and so on without end.
- Add up the times: 9 + 0.9 + 0.09 + … is a geometric series with ratio 0.1, whose sum is 9 / (1 − 0.1) = 9 / 0.9 = 10 s. Exactly the value found above.
- Conclusion: Zeno is right that the steps are infinite, but wrong to infer that the time must be infinite. Infinitely many intervals can add up to a finite total.
Answer: Achilles catches the tortoise after 10 s, 100 m from his own starting point. The infinite chases Zeno describes have a finite sum (9 + 0.9 + 0.09 + … = 10 s), so the paradox does not prove that motion is impossible.
5. Parmenides argues that nothing can come from nothing and that being is unchanging, which seems to make change an illusion. Explain how Empedocles, Anaxagoras and Democritus each manage to respect that principle while still saving our experience of change. avanzato
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- Fix the constraint: if non-being is not, nothing comes from nothing. Any account of change must give up creation and destruction.
- The shared move is the same in all three: multiply being. What is remains unchanging, but it is no longer one: many eternal items mix and separate.
- Empedocles posits four eternal roots (earth, water, air, fire) moved by Love and Strife, so that birth and death become nothing but mixture and separation.
- Anaxagoras pushes the division further: infinitely many qualitatively different seeds, with a portion of everything in everything. To change is to change the proportions of the mixture, not to produce something new.
- Democritus reduces everything to full, eternal, indivisible atoms, which carry the properties of Parmenidean being. He does admit the void, which Parmenides would call non-being, precisely because without it motion would be impossible.
- Conclusion: becoming is no longer creation but rearrangement of what has always existed. It is the same logical structure as the conservation principles of modern physics.
Answer: All three accept that nothing comes from nothing and reduce becoming to the aggregation and separation of eternal items: the four roots moved by Love and Strife in Empedocles, the infinite seeds ordered by the Nous in Anaxagoras, and the atoms moving through the void in Democritus.
FAQ
Why are they called Presocratics?
The label spread in the twentieth century through the collection of fragments edited by Hermann Diels in 1903. It is not purely chronological: Democritus was born after Socrates, yet he counts as a Presocratic because he investigates nature rather than, as Socrates did, human conduct and the good.
What does archē mean?
It is the first principle of things in three senses at once: what everything comes from, what everything is made of, and what everything dissolves back into. Looking for the archē means looking for a single, permanent explanation beneath the shifting variety of appearances.
How do we know their thought if their books are lost?
Through two channels: fragments, the literal quotations preserved by later authors, and testimonia, the summaries given by Plato, Aristotle and the doxographers. Modern editions cite them with the DK code (Diels-Kranz), for example 'Heraclitus, DK 22 B 91'.