Everybody knows that, in the real world, Achilles would quickly run past the tortoise, but Zeno’s argument seemed to prove that Achilles could never catch up. The philosophers of his day were unable to refute the paradox. Even though they knew that the conclusion was wrong, they could never find a mistake in Zeno’s mathematical proof. The philosophers’ main weapon was logic, but logical deduction seemed useless against Zeno’s argument. Each step along the way seemed airtight, and if all the steps are correct, how could the conclusion be wrong?
