Zeno of Elea (ca. 490–425
B
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C
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E
.) Greek Philosophy
Born in Elea, Luciana (now southern Italy), Greek
philosopher Zeno is remembered for his invention of a
number of
PARADOX
es that significantly influenced, and
challenged, the Greek perception of magnitude,
motion, and continuity. The question of whether or not
matter and time are composed of fundamental indivisi-
ble parts (“atoms”) was of great interest to philoso-
phers at the time. Zeno managed to devise a variety of
convincing arguments that seem to prove that any view
one wishes to adopt cannot be correct. Four of his
paradoxes in particular garnered certain notoriety.
They remained unresolved for over two millennia.
Essentially nothing is known of Zeno’s life, except
for what can be gleaned from the writings of P
LATO
in
his dialogue Parmenides. There we learn that Zeno
studied at the Eleatic School of Philosophy under the
guidance of the founder Parmenides. This sect analyzed
the concept of monism, the idea that “all is one” and
that change and motion are simply illusions and are
not part of an eternal reality. It is believed that Zeno
wrote just one text, his collection of 40 paradoxes on
the nature of time, space, and motion. The text, unfor-
tunately, has not survived, and we learn of its content
through the writings of others. A
RISTOTLE
describes the
four famous paradoxes in his work Physics.
See also Z
ENO
’
S PARADOXES
.
Zeno’s paradoxes In his studies, Greek philosopher
Z
ENO OF
E
LEA
proposed 40
PARADOX
es that challenge
our understanding of time, space, and motion. Four of
his paradoxes have garnered considerable attention for
being particularly troublesome.
With regard to time and space, there are two pos-
sibilities: either such magnitudes can be divided into
smaller and smaller parts an unlimited number of
times (that is, space and time each form a continuum),
or there is some fundamental indecomposable unit of
each that can no longer be divided (akin to the notion
that matter is composed of indivisible particles). The
first two of Zeno’s famous paradoxes argue that
motion is impossible if the first point of view is
adopted, while the last two argue that motion is again
impossible if the latter perspective is taken. His para-
doxes are the following:
1. Dichotomy: Assume that time and space
each are infinitely divisible.
In order to walk across the room, one must first reach
the midway point. But to do that, one must reach the
point one-quarter of the way along. But to get this far,
one must pass through the point one-eighth of the way
across, and before that, the point 1/16th the way along.
As this division can be done indefinitely, it seems then
we can never start our walk across the room—we can
never reach a first point of our journey. Motion is
therefore impossible.
2. Achilles and the Tortoise: Assume that time
and space each are infinitely divisible.
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