a plus. Two negatives destroy each other. This abstruse notion is
the foundation of the Hegelian logic. The mind must not only admit
that determination is negation, but must get through negation into
affirmation. Whether this process is real, or in any way an assistance
to thought, or, like some other logical forms, a mere figure of speech
transferred from the sphere of mathematics, may be doubted. That Plato
and the most subtle philosopher of the nineteenth century should have
lighted upon the same notion, is a singular coincidence of ancient and
modern thought.

IV. The one and the many or others are reduced to their strictest
arithmetical meaning. That one is three or three one, is a proposition
which has, perhaps, given rise to more controversy in the world than
any other. But no one has ever meant to say that three and one are to be
taken in the same sense. Whereas the one and many of the Parmenides have
precisely the same meaning; there is no notion of one personality or
substance having many attributes or qualities. The truth seems to
be rather the opposite of that which Socrates implies: There is no
contradiction in the concrete, but in the abstract; and the more
abstract the idea, the more palpable will be the contradiction. For just
as nothing can persuade us that the number one is the number three, so
neither can we be persuaded that any abstract idea is identical with
its opposite, although they may both inhere together in some external
object, or some more comprehensive conception. Ideas, persons, things
may be one in one sense and many in another, and may have various
degrees of unity and plurality. But in whatever sense and in whatever
degree they are one they cease to be many; and in whatever degree or
sense they are many they cease to be one.

Two points remain to be considered: 1st, the connexion between the first
and second parts of the dialogue; 2ndly, the relation of the Parmenides
to the other dialogues.

I. In both divisions of the dialogue the principal speaker is the same,
and the method pursued by him is also the same, being a criticism on
received opinions: first, on the doctrine of Ideas; secondly, of Being.
From the Platonic Ideas we naturally proceed to the Eleatic One or Being
which is the foundation of them. They are the same philosophy in two
forms, and the simpler form is the truer and deeper. For the Platonic
Ideas are mere numerical differences, and the moment we attempt to
distin