Zeno

Zeno’s arguments about motion which provide trouble for those who try to resolve them are four in number. The first [the dichotomy argument] maintains that nothing moves because what is travelling must first reach the half-way point before it reaches the end…

The second is the so-called Achilles. This maintains that the slowest thing will never be caught when running by the fastest. For the pursuer must first reach the point from which the pursued set out, so that the slower must always be ahead of it. This is the same argument as the dichotomy, but it differs in that the additional magnitudes are not divided in half. Aristotle Physics VI:9, 239b15

Zeno’s Dichotomy Argument 1)In order for something to move, it would have to do an infinite number of things in a finite amount of time. 2)It’s impossible to do an infinite number of things in a finite amount of time. 3)Nothing moves.

© Paul Hornschemeier

Zeno’s Dichotomy Argument 1)In order for something to move, it would have to do an infinite number of things in a finite amount of time. 2)It’s impossible to do an infinite number of things in a finite amount of time. 3)Nothing moves.

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

Zeno’s Arrow Argument 1.Everything when it occupies the same space is at rest. 2.Everything is always occupying such a space at every moment. 3.[So] Everything is at rest at every moment. 4.If (3), then (4). 5.Nothing moves.

The fourth argument is that concerning equal bodies which move alongside equal bodies in the stadium from opposite directions—the ones from the end of the stadium, the others from the middle—at equal speeds, in which he thinks it follows that half the time is equal to its double…. Aristotle Physics, 239b33