The views of Zeno of Elea (Zeno’s Paradoxes)

Zeno of Elea (c. 495 - 430 B.C.E.) was a Greek philosopher who lived in the Greek city state of Elea. Elea is now Velia, about 75 miles due south of Naples on the Amalfi coast of Italy. He was known for his "paradoxes" that have interested ancient and modern philosophers. Zeno conceived of these paradoxes not as logical amusement, but as support for the doctrine of his teacher, Parmenides, that all evidence of the senses is illusory and that reality is “being”. See this link to Joseph Mazur, author of “Zeno’s Paradox” (aka The Motion Paradox).

Zeno used the logic of his paradoxes to show how reason and logic (thinking) are fundamentally flawed. I can imagine Zeno as a young student in a modern day classroom where the math instructor is giving the definition of a line as consisting of an infinite set of points. Zeno would immediately interrupt by blowing a raspberry and say it was impossible to get anything real including a line from an assembly of non-dimensional points. At this point the math instructor would remind Zeno that “reality” is not a part of mathematics and that the definition of a line as an infinite set of points is an axiom and cannot be challenged. Zeno knew that mathematics was being used to describe physical reality and the wool was being pulled over his eyes.

Aristotle was quoted as saying that Zeno was a master of the dialectic. I believe this was a faulty translation from the Greek and what Aristotle really said was something like: “Zeno is a master of the  raspberry.”

Zeno’s reasoning on the impossibility of motion:  An object that moves has first to move through the point closest to it. Since that point is dimensionless there is no distance to it and thus since there is no distance to the closest point there can be no motion needed to get to it. No amount of calculus or transfinite number reasoning can remedy this.

Zeno’s logical assertion is correct, an object cannot move. And yet in the physical world that most of us acknowledge, objects can move despite Zeno’s logic. See section 12 for more about Zeno’s paradoxes.