“You can never reach another physical location: to get there, you have to cross half the intervening distance; next, you have to cross half the distance that remains; next, half again—no matter how far you go, half the remaining distance remains.”
That’s Zeno’s dichotomy paradox, and it’s easy to disagree with. It’s much harder to refute.1
It’s what’s called sophistry: “the use of reasoning or arguments that sound correct but are actually false,”2 or at least misleadingly strong.
But sophistry hasn’t always meant something bad, and the sophists—teacher-scholars who flourished first in Greece and later in Rome—are absolutely worth knowing.
- They made some key contributions to early Western thought.
- They provided the counterarguments against which Plato and Aristotle, pushing for objective truth and virtue, defined philosophy itself.
- They can help you learn to recognize misleading arguments, which, unfortunately, aren’t just an ancient phenomenon.
- Aristotle countered Zeno’s paradox by arguing that as distance decreases, the time needed to cover it decreases correspondingly. Archimedes, and modern calculus, found a way to calculate the sum of infinitely many terms as they get progressively smaller. Diogenes the Cynic simply stood up and walked. [↩]
- From Merriam-Webster. [↩]