First, We may observe, that there is no probability so great as not to
allow of a contrary possibility; because otherwise it would cease to be
a probability, and would become a certainty. That probability of causes,
which is most extensive, and which we at present examine, depends on a
contrariety of experiments: and it is evident an experiment in the past
proves at least a possibility for the future.
Secondly, The component parts of this possibility and probability are of
the same nature, and differ in number only, but not in kind. It has been
observed, that all single chances are entirely equal, and that the
only circumstance, which can give any event, that is contingent, a
superiority over another is a superior number of chances. In like
manner, as the uncertainty of causes is discovery by experience, which
presents us with a view of contrary events, it is plain, that when we
transfer the past to the future, the known to the unknown, every past
experiment has the same weight, and that it is only a superior number
of them, which can throw the ballance on any side. The possibility,
therefore, which enters into every reasoning of this kind, is composed
of parts, which are of the same nature both among themselves, and with
those, that compose the opposite probability.
Thirdly, We may establish it as a certain maxim, that in all moral as
well as natural phaenomena, wherever any cause consists of a number
of parts, and the effect encreases or diminishes, according to the
variation of that number, the effects properly speaking, is a compounded
one, and arises from the union of the several effects, that proceed from
each part of the cause. Thus, because the gravity of a body encreases or
diminishes by the encrease or diminution of its parts, we conclude that
each part contains this quality and contributes to the gravity of the
whole. The absence or presence of a part of the cause is attended with
that of a proportionable part of the effect. This connexion or constant
conjunction sufficiently proves the one part to be the cause of the
other. As the belief which we have of any event, encreases or diminishes
according to the number of chances or past experiments, it is to be
considered as a compounded effect, of which each part arises from a
proportionable number of chances or experiments.