Zeno's paradoxes
A set of arguments attributed to Zeno of Elea that use apparent contradictions to challenge motion, plurality, and assumptions about space and time.
Dichotomy paradox: An argument that reaching a destination requires first crossing infinitely many successive halfway points. Its infinite sequence of required journeys makes ordinary travel appear impossible.
Zeno of Elea: An ancient Greek philosopher associated with arguments defending the ideas of Parmenides. Ancient reports attribute the paradoxes to him as defenses of Parmenides.
Eleatic school: A group of ancient Greek philosophers associated with Elea and arguments about the unity of reality. Zeno's arguments emerged within this philosophical tradition.
Aristotle's solution to Zeno's paradoxes: Aristotle's response that an infinite number of divisions need not be traversed as separately completed tasks. It treats potential division and finite completed motion as compatible.
Motion (physics): A change in an object's position relative to a reference frame over time. The paradoxes ask how motion is possible, not merely how it is measured.
Achilles and the tortoise: An argument that a faster runner cannot overtake a slower one who has a head start, because each lead must first be reached. It turns infinitely many shrinking gaps into an apparent barrier to overtaking.
Parmenides: A pre-Socratic Greek philosopher who argued that reality is fundamentally one and unchanging. Zeno's arguments are traditionally understood as supporting Parmenides' rejection of change and plurality.
Aristotle: An ancient Greek philosopher whose writings shaped later accounts of logic, nature, and metaphysics. His Physics preserves and analyzes several of the best-known motion paradoxes.
Calculus: The branch of mathematics concerned with limits, derivatives, integrals, and continuous change. Limits provide a precise way to handle quantities approached through infinitely many subdivisions.
Philosophy of space and time: The philosophical study of space, time, motion, and their relation to physical reality. Zeno's arguments remain a foundational test of theories about spatial and temporal structure.