Greek Dualities. From our retrospect, Greek philos-
ophy was little affected by symmetries and asym-
metries, but, from the first, had dualities in its thought
patterns, perhaps even to a fault. Book 13 of Euclid's
Elements is a splendid essay on the existence, con-
struction, and uniqueness of regular solids in space, and
as such it is a triumphant exercise in mathematical
symmetry in our present-day sense. It is even a hall-
mark and acme of Greek originality. And yet it is an
isolated achievement of Greek rationality, exclusive,
and compartmentalized.
However, almost every great Greek philosopher had
a thematic duality in his thinking. In Anaximander it
was injustice and retribution; in Heraclitus it was
change and constancy in the cosmos; in Parmenides
it was the ontological contrast between Being and
Appearance; in Empedocles it was, quite primitively,
and insensitively, Love and Strife; in Anaxagoras it was
mind versus the senses; in Democritus it was the work-
ing physicist's contrast between the material and the
void, or between the full and the empty, or between
the particle and the field; in Plato it was the
epistemologist's difference between opinion and
knowledge and the idealist's dualism between body and
soul, either or both of which Plato may have inherited
from Socrates; and in Aristotle it was the hardiest
duality of all, the gigantic contrariety between the
Potential and the Actual.
Lesser Greek philosophers dwelt on lesser dualisms,
unimaginative ones. Aristotle reports (Metaphysica
986a 23-986b 4) that a school of Pythagoreans drew
up a list of ten opposites, viz., Limit-Unlimited, Odd-
Even, Unity-Plurality, Right-Left, Male-Female, Rest-
Motion, Straight-Crooked, Light-Darkness, Good-Evil,
Square-Oblong. Aristotle is apparently not impressed
with the particular selection of pairs in this list, because
he adds that Alcmaeon of Croton (of whom Aristotle
does not know whether he inspired the Pythagoreans
or they him) held similar views, but stated that there
is nothing fixed about pairs of contraries and that they
can be made up as the context demands it. And
Aristotle firmly adds that the real outcome of such
reflections is only this that “contraries are first princi-
ples of things.” If “contraries” are meant to be polari-
ties and dualities then this finding of Aristotle is just
as much a leitmotif in the natural philosophy of our
century as it was in classical Greece.
In addition to dualities from nature and knowledge
as listed above, there was also an all-Greek antithesis
of nomos (“human law,” or “norm”) and physis (“natu-
ral law”), and it was a dominant trait in statements
of Sophists on moral, social, and political issues
(Guthrie, III, 55-134). As a curiosity we note that an
anonymous Sophist (cf. Iamblichus, Protrepticus, Ch.
20) dwells on the contrast between lawlessness
(anomia) and order (eunomia) in such a manner as to
make him very like a champion of “law (nomos) and
order (
eunomia)” in our sense today (Guthrie, III, 71).
