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A Treatise of Human Nature

PART I.4: Of The Sceptical And Other Systems Of Philosophy
In all demonstrative sciences the rules are certain and infallible; but when we apply them,
our fallible said uncertain faculties are very apt to depart from them, and fall into error.
We must, therefore, in every reasoning form a new judgment, as a check or controul on
our first judgment or belief; and must enlarge our view to comprehend a kind of history
of all the instances, wherein our understanding has deceived us, compared with those,
wherein its testimony was just and true. Our reason must be considered as a kind of
cause, of which truth is the natural effect; but such-a-one as by the irruption of other
causes, and by the inconstancy of our mental powers, may frequently be prevented. By
this means all knowledge degenerates into probability; and this probability is greater or
less, according to our experience of the veracity or deceitfulness of our understanding,
and according to the simplicity or intricacy of the question.
There is no Algebraist nor Mathematician so expert in his science, as to place entire
confidence in any truth immediately upon his discovery of it, or regard it as any thing, but
a were probability. Every time he runs over his proofs, his confidence encreases; but still
more by the approbation of his friends; and is raised to its utmost perfection by the
universal assent and applauses of the, learned world. Now it is evident, that this gradual
encrease of assurance is nothing but the addition of new probabilities, and is derived from
the constant union of causes and effects, according to past experience and observation.
In accompts of any length or importance, Merchants seldom trust to the, infallible
certainty of numbers for their security; but by the artificial structure of the accompts,
produce a probability beyond what is derived from the skill and experience of the
accomptant. 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 accompt. 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 it is 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 shew 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.