stop to inquire whether the distinctions which he makes are shadowy and
fallacious, but 'whither the argument blows' he follows.

III. The negative series of propositions contains the first conception of
the negation of a negation. Two minus signs in arithmetic or algebra make
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