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consists of oppositions of sign, or, if we prefer, diametrical oppositions. Although these last are
often confused with the preceding in the language of mathematics, in which plus and minus symbolize
increase and diminution as well as positive and negative directions, it is nevertheless true that the
alternate increase and decrease of a force acting always in the same direction constitutes a very
different sort of opposition from that of two forces, one of which acts from A toward B, and the other
from B toward A, both along the same straight line. Similarly, the contrast between the increase and
decrease of a credit balance must not be confused with the contrast between such a credit and an
equal debt; and the growth or diminution of the tendency to theft or crime, in a given society, is quite a
different thing from the antithesis between this tendency and the tendency to charity and philanthropy.
In order to give at once a psychological explanation of these and many other social contrasts, we may
observe that an increase followed by a diminution of our affirmative belief in a notion, whether
religious or scientific, legal or political, is quite a different matter from our affirmation followed by
our rejection of this same idea, and that an increase followed by a diminution of our desire for
something, for instance our love for a woman, is quite a different matter from a desire followed by a
repugnance to the same object, such as our love toward this woman and then our hatred of her. It is
certainly interesting to note that each of these subjective quantities, belief and desire, possesses two
opposite signs, the positive and negative, and that in this respect they admit of comparison with
objective quantities, such as mechanical forces which act in opposite directions along the same
straight line. Space is so constituted as to admit of an infinity of couples whose members are opposed
to each other in direction, and our consciousness is so constituted as to admit of an infinity of
affirmations opposed to negations, or an infinity of desires opposed to repugnances, each having
precisely the same object. Except for these two unique instances, whose coincidence is remarkable,
the universe would know neither war nor discord, and all the tragic side of life would be both
impossible and inconceivable.
One observation is necessary, however. The oppositions of every sort—of series, degrees, or signs
—may take place between terms that find expression either in one and the same being (whether
molecule, organism, or self), or in two different beings (molecules, masses, organisms, or human
consciousnesses). But we must distinguish carefully between these two cases. This is of primary
importance for the sake of another distinction that is no less essential, namely, the distinction between
the case where the terms are simultaneous and the case where they are successive. In the former there
is a collision, strife, and then equilibrium; in the latter there is alternation and rhythm. In the former
there is always destruction and loss of energy; in the latter there is neither. Now when any
oppositions whatsoever, whether of series, degrees, or signs, occur in two different beings, they may
be either simultaneous or successive—either strife or rhythm. But when both of their terms belong to
one and the same being, body, or self, they can only be both simultaneous and successive if they are
oppositions of signs. As for the oppositions of series and degrees under this hypothesis, they admit
only of a succession or alternation of terms. For instance, it is impossible for the velocity of a body
moving in a given direction to increase and diminish at the same time; it can only do so successively.
But it may well happen that it is impelled at the same time by two distinct forces to move in two
opposite directions; this is the case of equilibrium, which is often characterized by a symmetry of
opposite forms, notably in the case of crystals. Similarly, it is impossible for the love of a man for a
woman to increase and diminish at the same time: such a thing can only occur alternately; but it may
easily occur for him to love and hate the same woman at the same time—an antinomy of the heart that
finds illustration in many crimes of passion. Again, it is impossible for the religious faith of a man to
increase and diminish at the same time: this can only occur successively; but it may easily happen that