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