he rationality of it depends on the
objective condition of the facts, and is the same for all men, however
much their actual degree of confidence may vary with individual
temperament. That black will be drawn seven times out of every ten
on an average if we go on drawing to infinity, is as certain as any
empirical law: it is the probability of a single draw that we measure
by the fraction 7/10.

When we build expectations of single events on statistics of observed
proportions of events of that kind, it is ultimately on the same
principle that rational expectation rests. That the proportion will
obtain on the average we regard as certain: the ratio of favourable
cases to the whole number of possible alternatives is the measure
of rational expectation or probability in regard to a particular
occurrence. If every year five per cent. of the children of a town
stray from their guardians, the probability of this or that child's
going astray is 1/20. The ratio is a correct measure only on the
assumption that the average is maintained from year to year.

Without going into the combination of probabilities, we are now in a
position to see the practical value of such a calculus as applied to
particular cases. There has been some misunderstanding among logicians
on the point. Mr. Jevons rebuked Mill for speaking disrespectfully
of the calculus, eulogised it as one of the noblest creations of the
human intellect, and quoted Butler's saying that "Probability is the
guide of life". But when Butler uttered this famous saying he was
probably not thinking of the mathematical calculus of probabilities
as applied to particular cases, and it was this special application to
which Mill attached comparatively little value.

The truth is that we seldom calculate or have any occasion to
calculate individual chances except as a matter of curiosity. It is
true that insurance offices calculate probabilities, but it is not the
probability of this or that man dying at a particular age. The precise
shade of probability for the individual, in so far as this depends on
vital statistics, is a matter of indifference to the company as long
as the average is maintained. Our expectations about any individual
life cannot be measured by a calculation of the chances because a
variety of other elements affect those expectations. We form beliefs
about individual cases, but we try to get surer grounds for them than
the chances as calculable from statistical da