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# Zeno’s Paradoxes - PowerPoint PPT Presentation

Zeno’s Paradoxes. Can I move?. Zeno. The Arrow Paradox. Y ou 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.

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Presentation Transcript

Can I move?

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)

• Time is composed of instants, which have no extension.
• Time is continuous in the sense that, between any two times, there is another.
• At no instant during the flight is the arrow in motion.
• If (1), then the arrow is not in motion during the flight.
• [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
• In order to catch the Tortoise, Achilles would have to complete an infinite number of tasks in a finite amount of time.
• Achilles cannot complete an infinite number of tasks in a finite amount of time.
• [So] Achilles cannot catch the Tortoise.