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in which A is true will be turn out to be a
case in which B is true also. But in order
to obtain a way of expressing that
sort of conditional proposition, we must begin by
getting a way of expressing a simpler
kind, which does not often occur in
ordinary speech but which has great
importance in logic. The sort of conditional
proposition I mean is
one in which no range of possibilities
is contemplated, which speaks only
of the actual state of things. “If A is true
then B is true,” in this sense is called a conditional
proposition de inesse. In case A is not
true, it makes no assertion at all and
therefore involves no falsity. And since
every proposition is either true or false,
if the antecedent, A, is not true, the conditional de inesse
is true, no matter how it may be with B.
In case the consequent, B, is true, all that the conditional