Zeno lived in the 5th century BC and, like his friend and mentor Parmenides, was part of the Eleatic school of philosophy.

Zeno was to radically change the course of philosophical history by making argument the central tool of the philosopher.

The Eleatics were “monists”: they believed that the One is the ultimate reality.
Zeno was notorious for his paradoxes.

These are ingenious arguments which aim to show that our ordinary or common-sense view of the world is riddled with contradiction and so must be rejected as false.

Zeno’s aim was to show that two particular common-sense beliefs are false: the belief in plurality (that there are many things) and the belief in motion (that there are things that move).

These are almost universally accepted beliefs, but Zeno thought they could not possibly be true.

In attempting to prove the unreality of plurality and motion, Zeno employed various intricate arguments.

For this reason, Aristotle called him “the inventor of dialectic”.

Previous philosophers (such as the Milesians and Heraclitus) offered little or no philosophical argument.

Zeno was to radically change the course of philosophical history by making argument the central tool of the philosopher.

One of Zeno’s arguments against motion is called “The Stadium”.

Suppose someone tries to move across a soccer stadium within a certain amount of time.

In order to cover this distance it is necessary first to cover half the distance, then half the remainder, and so on without limit.

But it is impossible to cover an unlimited number of half-way points in a limited amount of time.

Conclusion: it is impossible to move across the stadium. In other words, there is no such thing as motion.

Closely related to The Stadium is Zeno’s most famous puzzle, that of Achilles and the tortoise.

Achilles decides to race a tortoise, and gives it a head start. But he can never reach the tortoise. This is because each time Achilles sets off to catch up with the tortoise it will turn out that, by the time Achilles arrives at where the tortoise originally was, the tortoise has already moved on a bit further.

The end result is that the faster runner (Achilles) cannot overtake the slower runner (the tortoise)!

Some have found Zeno’s arguments to be persuasive.

But most have thought that his arguments must contain some mistake or fallacy, since the world obviously does contain a plurality of things in motion.

But it is still hotly debated as to where exactly Zeno’s arguments go wrong.

Dr Nick Trakakis teaches Philosophy and Religious Studies at Monash and Deakin Universities. His most recent book is The End of Philosophy of Religion, published by Continuum in London.