For the purposes of
mathematical calculus it is indifferent which force we term negative,
and which positive, and consequently we appropriate the latter to
that, which happens to be the principal object in our thoughts. Thus
if a man's capital be ten and his debts eight, the subtraction will be
the same, whether we call the capital negative debt, or the debt
negative capital. But in as much as the latter stands practically in
reference to the former, we of course represent the sum as 10-8. It is
equally clear that two equal forces acting in opposite directions,
both being finite and each distinguished from the other by its
direction only, must neutralize or reduce each other to inaction. Now
the transcendental philosophy demands; first, that two forces should
be conceived which counteract each other by their essential nature;
not only not in consequence of the accidental direction of each, but
as prior to all direction, nay, as the primary forces from which the
conditions of all possible directions are derivative and deducible:
secondly, that these forces should be assumed to be both alike
infinite, both alike indestructible. The problem will then be to
discover the result or product of two such forces, as distinguished
from the result of those forces which are finite, and derive their
difference solely from the circumstance of their direction.
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