for its completion. Most analytic propositions
cannot extend our knowledge beyond their immediate statement. If A is
either B or not B, and it is shown not to be B, it is left uncertain
what A may be. The class of propositions referred to do more than this,
inasmuch as they present alternative conceptions, mutually exhaustive,
each the privative of the other. Of these two contraries, the one always
evokes the other; neither can be thought except in relation to the
other. They do not arise from the dichotomic process of classification,
but from the polar relations of things. Their relation is not in the
mind but in themselves, a real externality. The distinction between such
as spring from the former and the latter is the most important question
in philosophy.

To illustrate by examples, we familiarly speak of heat and cold, and to
say a body is not hot is as much as to say it is cold. But every
physicist knows that cold is merely a diminution of heat, not a distinct
form of force. The absolute zero may be reached by the abstraction of
all heat, and then the cold cannot increase. So, life and death are not
true contraries, for the latter is not anything real but a mere
privative, a quantitative diminution of the former, growing less to an
absolute zero where it is wholly lost.

Thus it is easy to see that the Unconditioned exists only as a part of
the idea of the Conditioned, the Unknowable as the foil of the Knowable;
and the erecting of these mere privatives, these negatives, these
shadows, into substances and realities, and then setting them up as
impassable barriers to human thought, is one of the worst pieces of work
that metaphysics has been guilty of.

The like does not hold in true contrasts. Each of them has an existence
as a positive,and[TN-3] is never lost in a zero of the other. The one is
always thought in relation to the other. Examples of these are subject
and object, absolute and relative, mind and matter, person and
consciousness, time and space. When any one of these is thought, the
other is assumed. It is vain to attempt their separation. Thus those
philosophers who assert that all knowledge is relative, are forced to
maintain this assertion, to wit, All knowledge is relative, is
nevertheless absolute, and thus they falsify their own position. So
also, those others who say all mind is a property of matter, assume in
this sentence the reality of an idea apart from matter. Some have argued
that space