the
privative is an independent thought, that a thought and its limitation
are two thoughts; whereas they are but the two aspects of the one
thought, like two sides to the one disc, and the absurdity of speaking
of them as separate thoughts is as great as to speak of a curve seen
from its concavity as a different thing from the same curve regarded
from its convexity. The privative can help us nowhere and to nothing;
the positive only can assist our reasoning.

This elevation of the privative into a contrary, or a contradictory, has
been the bane of metaphysical reasoning. From it has arisen the doctrine
of the synthesis of an affirmative and a negative into a higher
conception, reconciling them both. This is the maxim of the Hegelian
logic, which starts from the synthesis of Being and Not-being into the
Becoming, a very ancient doctrine, long since offered as an explanation
of certain phenomena, which I shall now touch upon.

A thought and its privative alone--that is, a quality and its
negative--cannot lead to a more comprehensive thought. It is devoid of
relation and barren. In pure logic this is always the case, and must be
so. In concrete thought it may be otherwise. There are certain
propositions in which the negative is a reciprocal quality, quite as
positive as that which it is set over against. The members of such a
proposition are what are called "true contraries." To whatever they
apply as qualities, they leave no middle ground. If a thing is not one
of them, it is the other. There is no third possibility. An object is
either red or not red; if not red, it may be one of many colors. But if
we say that all laws are either concrete or abstract, then we know that
a law not concrete has all the properties of one which is abstract. We
must examine, then, this third law of thought in its applied forms in
order to understand its correct use.

It will be observed that there is an assumption of space or time in many
propositions having the form of the excluded middle. They are only true
under given conditions. "All gold is fusible or not," means that some is
fusible at the time. If all gold be already fused, it does not hold
good. This distinction was noted by Kant in his discrimination between
_synthetic_ judgments, which assume other conditions; and _analytic_
judgments, which look only at the members of the proposition.

Only the latter satisfy the formal law, for the proposition must not
look outside of itself