In accounts of any length or importance, merchants seldom trust to the infallible certainty of numbers for their security; but by the artificial structure of the accounts, produce a probability beyond what is derived from the skill and experience of the accountant. For that is plainly of itself some degree of probability; though uncertain and variable, according to the degrees of his experience and length of the account. Now as none will maintain, that our assurance in a long numeration exceeds probability, I may safely affirm, that there scarce is any proposition concerning numbers, of which we can have a fuller security. For 'tis easily possible, by gradually diminishing the numbers, to reduce the longest series of addition to the most simple question which can be formed, to an addition of two single numbers; and upon this supposition we shall find it impracticable to show the precise limits of knowledge and of probability, or discover that particular number at which the one ends and the other begins. But knowledge and probability are of such contrary and disagreeing natures, that they cannot well run insensibly into each other, and that because they will not divide, but must be either entirely present, or entirely absent. Besides, if any single addition were certain, every one would be so, and consequently the whole or total sum; unless the whole can be different from all its parts. I had almost said, that this was certain; but I reflect that it must reduce _itself_, as well as every other reasoning, and from knowledge degenerate into probability. Since, therefore, all knowledge resolves itself into probability, and becomes at last of the same nature with that evidence which we employ in common life, we must now examine this latter species of reasoning, and see on what foundation it stands. In every judgment which we can form concerning probability, as well as concerning knowledge, we ought always to correct the first judgment, derived from the nature of the object, by another judgment, derived from the nature of the understanding. 'Tis certain a man of solid sense and long experience ought to have, and usually has, a greater assurance in his opinions, than one that is foolish and ignorant, and that our sentiments have different degrees of authority, even with ourselves, in proportion to the degrees of our reason and experience. In the man of the best sense and longest experience, this authority is never entire; since even such a one must be conscious of many errors in the past, and must still dread the like for the future. Here then arises a new species of probability to correct and regulate the first, and fix its just standard and proportion. As demonstration is subject to the control of probability, so is probability liable to a new correction by a reflex act of the mind, wherein the nature of our understanding, and our reasoning from the first probability, become our objects.