imness of vision, upon his inability to grapple with his own
idea. It was Plato who built upon the light of Parmenides.

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 supports Parmenides in the doctrine of Being. But it is
not the conclusions of Zeno that are novel, it is rather the reasons
which he gave for them. In attempting to support the Parmenidean
doctrine from a new point of view he developed 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, moreover, is absolutely static
and unchangeable. There is in it no motion. Multiplicity and motion
are the two characteristics of the false world of sense. Against
multiplicity and motion, therefore, Zeno directed his {53} arguments,
and attempted indirectly to support the conclusions of Parmenides by
showing that multiplicity and motion are impossible. He attempted to
force multiplicity and motion to refute themselves by showing that, if
we assume them as real, contradictory propositions follow from that
assumption. Two propositions which contradict each other cannot 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 infinitely
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 are not units. Since they are indivisible they
can have no magnitude, for that which has magnitude is divisible. The
many, therefore, is composed of units which have no magnitude. But if
none of the parts of the many have magnitude, the many as a whole has
none. Therefore, the many is infinitely small. But the many must also
be infinitely large. For the many has magnitu