Eleatic School

The claim

You cannot think or speak of what is not. Therefore nothing can come to be, since it would have to come from what is not; and nothing can change, since change requires it to become what it is not.

What it held

Parmenides wrote a poem in which a goddess sets out two roads: that it is, and that it is not. The second is unthinkable, because to think of nothing is not to think. Everything else follows with alarming speed. What is cannot have come into being, since there was nothing for it to come from. It cannot perish, cannot move, cannot be more here and less there, and cannot be many, since dividing it would require gaps of what is not.

The conclusion contradicts everything anyone sees, and Parmenides knows it. He offers a second part of the poem describing the world of appearances, and it has been argued about ever since whether that is a concession, an account of how error arises, or the best that can be said of a false way of speaking.

Zeno's paradoxes are usually read as support: not proof that motion is impossible so much as a demonstration that assuming plurality and divisibility leads to results just as absurd as anything Parmenides is accused of. Achilles and the tortoise, the arrow, the stadium — each takes an obvious fact and makes it look untenable.

How it argued

Deduction from a single premise, driven without regard for how unwelcome the conclusion is. This is the first sustained piece of purely a priori argument anywhere.

What it was arguing against

The Milesians and Heraclitus, and with them the entire assumption that a world of many changing things can be coherently described.

Where it disagreed with itself

What the second part of Parmenides' poem is for. Whether Melissus, who made being infinite where Parmenides made it complete, is improving the argument or misunderstanding it.

Common misconceptions

That Zeno was trying to prove motion impossible. He was showing that the alternatives to Parmenides generate paradoxes of their own — an argument by embarrassment rather than by demonstration. And Parmenides is not denying that we experience change, only that the experience can be coherently described.

How it began

Elea was a Phocaean colony in Italy, and Parmenides is said to have written laws for it. The setting matters: this is not Ionian natural science but something colder and more geometrical.

What became of it

The school ended with Melissus, but the problem it set did not. Almost everything in the next century is an attempt to allow change back in without conceding the argument.

Lasting influence

The atomists, Empedocles and Anaxagoras are all answers to it: each keeps something unchanging and lets it rearrange. Plato's Sophist is a direct assault on the premise about what is not. Modern debates about whether time passes still work in its terms.

Why it still matters

It remains the strongest case ever made that an argument can be valid, its premises plausible, and its conclusion impossible to believe — which is a permanent problem in method rather than a historical curiosity.

Put another way

A proof on a blackboard that shows the room you are standing in cannot exist.

Where to start

The Way of Truth itself, in any decent translation. It is short, and its strangeness is the point rather than an obstacle.

The surprising bit

Plato names a dialogue after Parmenides and has the young Socrates comprehensively out-argued in it — the one place he lets his teacher lose.

In their own words

Connections

Answers

Milesian School

Opposed by

Heraclitean School

Influenced

Atomism, Megarian School

The verdict

An argument nobody has ever accepted and nobody has ever cleanly refuted.

Sources

• Stanford Encyclopedia of Philosophy