Chapter 17

Zeno

The third and last important thinker of the Eleatic School
is Zeno who, like Parmenides, was a man of Elea. His birth
is placed about 489 B.C. He composed a prose treatise in
which he developed his philosophy. Zeno’s contribution to
Eleaticism is, in a sense, entirely negative. He did not add
anything positive to the teachings of Parmenides. He sup-
ports Parmenides in the doctrine of Being. But it is not
the conclusions of Zeno that are novel, it is rather the rea-
sons which he gave for them. In attempting to support the
Parmenidean doctrine from a new point of view he devel-
oped certain ideas about the ultimate character of space
and time which have since been of the utmost importance
in philosophy. Parmenides had taught that the world of
sense is illusory and false. The essentials of that world are
two— multiplicity and change. True Being is absolutely
one; there is in it no plurality or multiplicity. Being, more-
over, is absolutely static and unchangeable. There is in it
no motion. Multiplicity and motion are the two charac-

teristics of the false world of sense. Against multiplicity

and motion, therefore, Zeno directed his {53} arguments,

and attempted indirectly to support the conclusions of Par-

menides by showing that multiplicity and motion are im-

possible. He attempted to force multiplicity and motion to

refute themselves by showing that, if we assume them as

real, contradictory propositions follow from that assump-

tion. Two propositions which contradict each other can-

not both be true. Therefore the assumptions from which

both follow, namely, multiplicity and motion, cannot be

real things.

Zeno’s arguments against multiplicity.

(1) If the many is, it must be both infinitely small and in-

finitely large. The many must be infinitely small. For it is

composed of units. This is what we mean by saying that

it is many. It is many parts or units. These units must

be indivisible. For if they are further divisible, then they