ly probable,
and that our belief that it will hold in the future, or in unexamined
cases in the past, is itself based upon the very principle we are
examining.

The principle we are examining may be called the _principle of
induction_, and its two parts may be stated as follows:

(a) When a thing of a certain sort A has been found to be associated
with a thing of a certain other sort B, and has never been found
dissociated from a thing of the sort B, the greater the number of cases
in which A and B have been associated, the greater is the probability
that they will be associated in a fresh case in which one of them is
known to be present;

(b) Under the same circumstances, a sufficient number of cases of
association will make the probability of a fresh association nearly a
certainty, and will make it approach certainty without limit.

As just stated, the principle applies only to the verification of our
expectation in a single fresh instance. But we want also to know that
there is a probability in favour of the general law that things of the
sort A are _always_ associated with things of the sort B, provided a
sufficient number of cases of association are known, and no cases of
failure of association are known. The probability of the general law is
obviously less than the probability of the particular case, since if the
general law is true, the particular case must also be true, whereas
the particular case may be true without the general law being true.
Nevertheless the probability of the general law is increased by
repetitions, just as the probability of the particular case is. We may
therefore repeat the two parts of our principle as regards the general
law, thus:

(a) The greater the number of cases in which a thing of the sort A has
been found associated with a thing of the sort B, the more probable it
is (if no cases of failure of association are known) that A is always
associated with B;

b) Under the same circumstances, a sufficient number of cases of the
association of A with B will make it nearly certain that A is always
associated with B, and will make this general law approach certainty
without limit.

It should be noted that probability is always relative to certain data.
In our case, the data are merely the known cases of coexistence of A and
B. There may be other data, which _might_ be taken into account, which
would gravely alter the probability. For example, a man who had seen a
great many white