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Chapter XV
Of Probability
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.
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 doubt at all about
them; but assent to them as firmly, and act, according to that 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' experience. 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 nature 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.
The king of Siam. 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.
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