Interpretation: A Journal of Political Philosophy

168
"Limit"
Interpretation
in the Philebus can also be named the "One."
calls the "elements"
What Aristotle
can be called the ultimate sources of everything, that
which has the first rank both as beginnings and as ruling
powers. That is
what is meant by dpxr), in common parlance as well as in most thoughtful
speech. We should not assume, I think, that Plato had a definitely fixed
name for each of these dpxat. The terms the Good, the One, the Precise
itself, the Same, the Limit, and perhaps the Whole are aU suited to one
of the dpxai, depending on the context in which they
names of the second ao/i], the "indeterminate dyad,"
as the less,"
are used. As to the
"the more as well
and the Other (which also implies a duality 38) seem aU of them
no less suitable. In the Philebus Socrates, in putting a seal on the tribe of
the cbiEipov, makes its intrinsic character perfectly clear. But the character
of the jtspag, the "limit,"
remains obscured.
Now let us take up the third tribe,
of the "Limit."
dpxai, the "Limitless,"
"One,"
What does "mixing"
"mixture"
the of the "Limitless"
the "indeterminate dyad,"
and
here mean? It means that the two
and the "Limit,"
exert their power on each other. What happens then may be
described as follows. The "indeterminate dyad"
duplicates the "One,"
is to say, produces two entities, two i8r|, duplicates each of these
ei8t| we may also say "divides"
the
that
each of these i8r| and keeps on du
plicating we have to assume up to a certain point. In Aristotle's reports
the "indeterminate dyad"
is explicitiy characterized as a "doubling
power"
(8uojtoiog). 39 It is the ultimate source of definite manyness, of
"numbers,"
in the realm of the Ei8n as weU as in our world. In the earlier
passage, when Socrates first introduced the Promethean gift of "infinitude"
and of "limit"
and urged that in every case a definite number of tibr\ had
to be found (the alphabet helping him to clarify this point), there was
hardly
a discernible hint that the "Limitless"
with its doubling power is
responsible for the multiplicity of the ei8i> You wiU remember that in
this context the "limitless,"
the infinite, was ultimately dismissed. Not so
in the world in which we live. What happens here is this: the "Limit,"
the "One,"
transforms the "indeterminate dyad"
into a determinate one,
that is to say, transforms the two constantly and indeterminately changing
terms of the dyad into two stationary and determinate ones and keeps
doing this, produces, in other words, a multitude of ratios. That's why
Socrates can call the manyness of ratios "the offspring of the limit." 40
We understand now what confused Protarchus and us when Socrates
substituted "that which has limit,"
The "limited,"
the "limited,"
for the "limit"
itself.
the assemblage of ratios, is already a part of the mixture,
of the third tribe. But it represents a mixture, or rather mixtures,
of a
special kind, mathematical partnerships that can give to parts of the
world we live in a certain Tightness, remove the excess and indefiniteness,
ss Cf. Soph. 255 D and 256 E-257 A.
so Met. XIII, 7, 1082 a 15 and 8, 1083 b 36.
25 D.