Q&A: Zeno’s Paradoxes
Originally published:
This is an English translation (via GPT-5.4). Read the original Hebrew version.
Zeno’s Paradoxes
Question
Hello Rabbi
Is there a way to solve Zeno’s paradoxes logically? By “logically” I mean through purely logical analysis, without calculus.
Answer
I didn’t understand the question. What about calculus is not purely logical? The fact that it is written in formal form? Beyond that, you don’t need any calculus at all to solve them. Achilles and the tortoise is an infinite series. You don’t need derivatives or integrals (you do need limits, but only for the formalism). And regarding the arrow in flight, see my article on that.
Discussion on Answer
What does wording have to do with it? Pure logic can be described in words or in a formula. Beyond that, you can also present the infinity without words.
A lot of calculus is full of verbal definitions, like the definition of a set, element, relation, and so on.
It’s not just pure notation.