1. Probability is the appearance of agreement upon fallible proofs.
As demonstration is the showing the agreement
or disagreement of two ideas by the intervention of one or more proofs, which have a constant, immutable, and
visible connexion one with another; so probability is nothing but the appearance of such an agreement or
disagreement by the intervention of proofs, whose connexion is not constant and immutable, or at least is not
perceived to be so, but is, or appears for the most part to be so, and is enough to induce the mind to judge the
proposition to be true or false, rather than the contrary. For example: in the demonstration of it a man perceives
the certain, immutable connexion there is of equality between the three angles of a triangle, and those
intermediate ones which are made use of to show their equality to two right ones; and so, by an intuitive
knowledge of the agreement or disagreement of the intermediate ideas in each step of the progress, the whole
series is continued with an evidence, which clearly shows the agreement or disagreement of those three angles in
equality to two right ones: and thus he has certain knowledge that it is so. But another man, who never took the
pains to observe the demonstration, hearing a mathematician, a man of credit, affirm the three angles of a triangle
to be equal to two right ones, assents to it, i.e., receives it for true: in which case the foundation of his assent is the
probability of the thing; the proof being such as for the most part carries truth with it: the man on whose testimony
he receives it, not being wont to affirm anything contrary to or besides his knowledge, especially in matters of this
kind: so that that which causes his assent to this proposition, that the three angles of a triangle are equal to two
right ones, that which makes him take these ideas to agree, without knowing them to do so, is the wonted veracity
of the speaker in other cases, or his supposed veracity in this.