Zeno of Elea

Zeno of Elea was a fifth-century BCE Greek philosopher whose paradoxes used regress and division to challenge the possibility of motion and plurality.

Parmenides: Parmenides was a pre-Socratic Greek philosopher who argued that reality is one, unchanging, and distinct from appearance. Zeno defended Parmenides’ account of reality by exposing difficulties in its alternatives.
Dichotomy paradox: The dichotomy paradox argues that reaching a destination requires completing infinitely many successive halfway distances. It presents the regress of subdivisions that makes motion seem impossible to begin or finish.
Infinite divisibility: Infinite divisibility is the property of a quantity that can be divided into smaller parts without reaching a smallest part. Zeno’s motion arguments rely on distances admitting endlessly many subdivisions.
Aristotle's Physics: Aristotle's Physics is a work examining nature, change, place, time, and motion. Aristotle preserves and answers several of Zeno’s arguments in his discussion of motion.
Eleatic school: The Eleatic school was an ancient Greek philosophical tradition associated with the unity and changelessness of being. Zeno’s arguments grew from this tradition’s rejection of ordinary accounts of change.
Achilles and the tortoise: Achilles and the tortoise is a paradox in which a faster runner must reach a slower runner’s successive former positions. This race gives the infinite-subdivision challenge a vivid form.
Actual infinity: Actual infinity is the conception of an infinite collection treated as complete rather than merely indefinitely extendable. The paradoxes raise the question of whether infinitely many required stages can be treated as a completed task.
Aristotle: Aristotle was an ancient Greek philosopher whose writings shaped logic, natural philosophy, and many other fields. His surviving discussion is a major ancient source for Zeno’s paradoxes and their early replies.
Reductio ad absurdum: Reductio ad absurdum is a form of argument that derives a contradiction from an assumption to reject it. Zeno often assumes motion or plurality, then draws out consequences meant to be impossible.
Arrow paradox: The arrow paradox argues that an arrow at each instant occupies a space equal to itself and is therefore at rest. It challenges motion by examining what can be said about an object at a single instant.

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Zeno's paradoxesRelated: Ancient reports attribute the paradoxes to him as defenses of Parmenides.