Terminology
R
the runner
S
the starting point (=
Z
0
)
G
the end point
Z
1
the point halfway between
S
and
G
Z
2
the point halfway between
Z
1
and
G
Z
n
the point halfway between
Z
n
1
and
G
Z
run
a run that takes the runner from one
Z
point to the next
Z
point
Zeno’s Argument formulated
1.
In order to get from
S
to
G
,
R
must make infinitely many
Z
runs.
2.
It is impossible for
R
to make infinitely many
Z
runs.
3.
Therefore, it is impossible for
R
to reach
G
.
ø
Evaluating the argument
a.
Is it
valid
?
Yes
: the conclusion follows from the premises.
b.
Is it
sound
? I.e., is it a valid argument with
true premises
? This is what is at
issue.
c.
One might try to object to the first premise, (1), on the grounds that one can get from
S
to
G
by making one run, or two (from
S
to
Z
1
and from
Z
1
to
G
). But this is not an
adequate response. For according to the definitions above, the runner, if he passes
from
S
to
G
, will have passed through all the
Z
points. But to do that is to make all
the
Z
runs.
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 Summer '09
 MarkElwin
 Logic, Zeno, point halfway

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