In order to clear up this difficulty, we shall suppose a person to take
a dye, formed after such a manner as that four of its sides are marked
with one figure, or one number of spots, and two with another; and to
put this dye into the box with an intention of throwing it: It is plain,
he must conclude the one figure to be more probable than the other, and
give the preference to that which is inscribed on the greatest number
of sides. He in a manner believes, that this will lie uppermost; though
still with hesitation and doubt, in proportion to the number of chances,
which are contrary: And according as these contrary chances diminish,
and the superiority encreases on the other side, his belief acquires new
degrees of stability and assurance. This belief arises from an operation
of the mind upon the simple and limited object before us; and therefore
its nature will be the more easily discovered and explained. We have
nothing but one single dye to contemplate, in order to comprehend one of
the most curious operations of the understanding.
This dye, formed as above, contains three circumstances worthy of our
attention. First, Certain causes, such as gravity, solidity, a cubical
figure, &c. which determine it to fall, to preserve its form in its
fall, and to turn up one of its sides. Secondly, A certain number
of sides, which are supposed indifferent. Thirdly, A certain figure
inscribed on each side. These three particulars form the whole nature of
the dye, so far as relates to our present purpose; and consequently are
the only circumstances regarded by the mind in its forming a judgment
concerning the result of such a throw. Let us, therefore, consider
gradually and carefully what must be the influence of these
circumstances on the thought and imagination.
First, We have already observed, that the mind is determined by custom
to pass from any cause to its effect, and that upon the appearance
of the one, it is almost impossible for it not to form an idea of the
other. Their constant conjunction in past instances has produced such
a habit in the mind, that it always conjoins them in its thought, and
infers the existence of the one from that of its usual attendant. When
it considers the dye as no longer supported by the box, it can not
without violence regard it as suspended in the air; but naturally places
it on the table, and views it as turning up one of its sides. This
is the effect of the intermingled causes, which are requisite to our
forming any calculation concerning chances.