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 knowings them to do so, is the
wonted veracity of the speaker in other cases, or his supposed veracity
in this.
2. It is to supply our Want of Knowledge.
Our knowledge, as has been shown, being very narrow, and we not happy
enough to find certain truth in everything which we have occasion to
consider; most of the propositions we think, reason, discourse--nay, act
upon, are such as we cannot have undoubted knowledge of their truth:
yet some of them border so near upon certainty, that we make no act,
according to the assent, as resolutely as if they were infallibly
demonstrated, and that our knowledge of them was perfect and certain.
But there being degrees herein, from the very neighbourhood of certainty
and demonstration, quite down to improbability and unlikeness, even to
the confines of impossibility; and also degrees of assent from full
assurance and confidence, quite down to conjecture, doubt, and distrust:
I shall come now, (having, as I think, found out THE BOUNDS OF HUMAN
KNOWLEDGE AND CERTAINTY,) in the next place, to consider THE SEVERAL
DEGREES AND GROUNDS OF PROBABILITY, AND ASSENT OR FAITH.
3. Being that which makes us presume Things to be true, before we know
them to be so.
Probability is likeliness to be true, the very notation of the word
signifying such a proposition, for which there be arguments or proofs to
make it pass, or be received for true. The entertainment the mind gives
this sort of propositions is called BELIEF, ASSENT, or OPINION, which is
the admitting or receiving any proposition for true, upon arguments or
proofs that are found to persuade us to receive it as true, without
certain knowledge that it is so. And herein lies the difference between
PROBABILITY and CERTAINTY, FAITH, and KNOWLEDGE, that in all the parts
of knowledge there is intuition; each immediate idea, each step has its
visible and certain connexion: in belief, not so. That which makes me
believe, is something extraneous to the thing I believe; something not
evidently joined on both sides to, and so not manifestly showing the
agreement or disagreement of those ideas that are under consideration.
4. The Grounds of Probability are two: Conformity with our own
Experience, or the Testimony of others.
Probability then, being to supply the defect of our knowledge, and to
guide us where that fails, is always conversant about propositions
whereof we have no certainty, but only some inducements to receive them
for true. The grounds of it are, in short, these two following:--
First, The conformity of anything with our own knowledge, observation,
and experience.
Secondly, The testimony of others, vouching their observation and
experience. In the testimony of others is to be considered: 1. The
number. 2. The integrity. 3. The skill of the witnesses. 4. The design
of the author, where it is a testimony out of a book cited. 5. The
consistency of the parts, and circumstances of the relation. 6. Contrary
testimonies.
5. In this, all the Arguments pro and con ought to be examined, before
we come to a Judgment.
Probability wanting that intuitive evidence which, infallibly determines
the understanding and produces certain knowledge, the mind, if it WILL
PROCEED RATIONALLY, ought to examine all the grounds of probability, and
see how they make more or less for or against any proposition, before
it assents to or dissents from it; and, upon a due balancing the whole,
reject or receive it, with a more or less firm assent, proportionably to
the preponderancy of the greater grounds of probability on one side or
the other. For example:--
If I myself see a man walk on the ice, it is past probability; it is
knowledge. But if another tells me he saw a man in England, in the midst
of a sharp winter, walk upon water hardened with cold, this has so great
conformity with what is usually observed to happen, that I am disposed
by the natures of the thing itself to assent to it; unless some manifest
suspicion attend the relation of that matter of fact. But if the same
thing be told to one born between the tropics, who never saw nor
heard of any such thing before, there the whole probability relies on
testimony: and as the relators are more in number, and of more credit,
and have no interest to speak contrary to the truth, so that matter
of fact is like to find more or less belief. Though to a man whose
experience has always been quite contrary, and who has never heard of
anything like it, the most untainted credit of a witness will scarce
be able to find belief. As it happened to a Dutch ambassador, who
entertaining the king of Siam with the particularities of Holland, which
he was inquisitive after, amongst other things told him, that the water
in his country would sometimes, in cold weather, be so hard, that men
walked upon it, and that it would bear an elephant, if he were there. To
which the king replied, HITHERTO _I_ HAVE BELIEVED THE STRANGE THINGS
YOU HAVE TOLD ME, BECAUSE _I_ LOOK UPON YOU AS A SOBER FAIR MAN, BUT NOW
_I_ AM SURE YOU LIE.
6. Probable arguments capable of great Variety.
Upon these grounds depends the probability of any proposition: and as
the conformity of our knowledge, as the certainty of observations,
as the frequency and constancy of experience, and the number and
credibility of testimonies do more or less agree or disagree with it, so
is any proposition in itself more or less probable. There is another, I
confess, which, though by itself it be no true ground of probability,
yet is often made use of for one, by which men most commonly regulate
their assent, and upon which they pin their faith more than anything
else, and that is, THE OPINION OF OTHERS; though there cannot be a more
dangerous thing to rely on, nor more likely to mislead one; since there
is much more falsehood and error among men, than truth and knowledge.
And if the opinions and persuasions of others, whom we know and think
well of, be a ground of assent, men have reason to be Heathens in Japan,
Mahometans in Turkey, Papists in Spain, Protestants in England, and
Lutherans in Sweden. But of this wrong ground of assent I shall have
occasion to speak more at large in another place.