Zeno’s Paradoxes

Can I move?

Zeno

The Arrow Paradox

You cannot even move. If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.

(Aristotle Physics VI:9, 239b5)

The Arrow Paradox

Time is composed of instants, which have no extension.

Time is continuous in the sense that, between any two times, there is another.

The Arrow Paradox

1) At no instant during the flight is the arrow in motion.

2) If (1), then the arrow is not in motion during the flight.

3) [So] The arrow is not in motion during the flight.

Achilles and the Tortoise

You can never catch up. In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

(Aristotle Physics VI:9, 239b15)

Achilles and the Tortoise

Space is composed of points, which have no extension.

Space is continuous in the sense that, between any two points, there is a third.

Space is infinitely divisible in the sense that a line can be “cut” in half and then into quarters and then into eighths and...

Achilles and the Tortoise

1) In order to catch the Tortoise, Achilles would have to complete an infinite number of tasks in a finite amount of time.

2) Achilles cannot complete an infinite number of tasks in a finite amount of time.

3) [So] Achilles cannot catch the Tortoise.