Read another response by Stephen Maitzen

What makes Xeno's paradox paradoxical?
It sounds more like a trick question than a bona fide paradox.
Achilles and the tortoise are going to have a half-mile race, and Achilles gives the tortoise a 1/4 mile head start.
Suppose Achilles runs as fast as a decent male high school track athlete, and he can cover 1/2 mile in 2-1/2 minutes.
He gives the tortoise a head start of 1/4 mile. According to a quick internet search, the average turtle moves at 3 to 4 mph. Let's say our tortoise is particularly fast, and moves at 5 mph. It thereby takes the tortoise 3 minutes to cover 1/4 mile.
Achilles finishes 30 seconds ahead of the tortoise. Where's the paradox?

### The reasoning you gave

The reasoning you gave illustrates why Zeno's example has a chance of counting as a paradox at all. As you show, *of course* Achilles will overtake the tortoise. But Zeno claimed to have equally good reasoning showing that Achilles never overtakes the tortoise. That's the paradox: apparently good reasoning in favor of each of two incompatible claims.

For Zeno's reasoning and a critique thereof, see sections 3.1 and 3.2 of this SEP entry.

- Log in to post comments