100 Influential Philosophers - Sayed Badar Zaman Shah

7 The 100 Most Influential Philosophers of All Time 7
for each. For the first premise, he argued that that which,
added to or subtracted from something else, does not
increase or decrease the second unit is nothing. For the
second, he argued that a unit, being one, is homogeneous
and that therefore, if divisible, it cannot be divisible at one
point rather than another. His argument for the third
premise was that a unit, if divisible, is divisible either into
extended minima, which contradicts the second premise
or, because of the first premise, into nothing. He had in his
hands a very powerful complex argument in the form of a
dilemma, one horn of which supposed indivisibility, the
other infinite divisibility, both leading to a contradiction
of the original hypothesis. His method had great influence
and may be summarized as follows: he continued
Parmenides’ abstract, analytic manner but started from
his opponents’ theses and refuted them by reductio ad
absurdum. It was probably the two latter characteristics
which Aristotle had in mind when he called him the
inventor of dialectic.
That Zeno was arguing against actual opponents,
Pythagoreans who believed in a plurality composed of
numbers that were thought of as extended units, is a matter
of controversy. It is not likely that any mathematical
implications received attention in his lifetime. But in fact
the logical problems which his paradoxes raise about a
mathematical continuum are serious, fundamental, and
inadequately solved by Aristotle.
soCrates
(b. c. 470, Athens, Greece—d. 399 BCE, Athens)
Socrates was a Greek philosopher whose way of life,
character, and thought exerted a profound influence
on ancient and modern philosophy. Although Socrates
himself wrote nothing, he is portrayed in conversation in
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