But this evidently is valid only with regard to unconditioned
probability which only at great intervals and transiently may influence
our practical work. For, however well I may know that according to
statistics every xth witness is punished for perjury, I will not be
frightened at the approach of my xth witness though he is likely,
according to statistics, to lie. In such cases we are not fooled, but
where events are confused we still are likely to forget that
probabilities may be counted only from great series of figures in which
the experiences of individuals are quite lost.
Nevertheless figures and the conditions of figures with regard to
probability exercise great influence upon everybody; so great indeed,
that we really must beware of going too far in the use of figures. Mill
cites a case of a wounded Frenchman. Suppose a regiment made up of 999
Englishmen and one Frenchman is attacked and one man is wounded. No one
would believe the account that this one Frenchman was the one wounded.
Kant says significantly: “If anybody sends his doctor 9 ducats by his
servant, the doctor certainly supposes that the servant has either lost
or otherwise disposed of one ducat.” These are merely probabilities
which depend upon habits. So, it may be supposed that a handkerchief has
been lost if only eleven are found, or people may wonder at the doctor’s
ordering a tablespoonful every five quarters of an hour, or if a job is
announced with $2487 a year as salary.
But just as we presuppose that wherever the human will played any part,
regular forms will come to light, so we begin to doubt that such forms
will occur where we find that accident, natural law, or the unplanned
coöperation of men were determining factors. If I permit anybody to
count up accidentally concurrent things and he announces that their
number is one hundred, I shall probably have him count over again. I
shall be surprised to hear that somebody’s collection contains exactly
1000 pieces, and when any one cites a distance of 300 steps I will
suppose that he had made an approximate estimation but had not counted
the steps. This fact is well known to people who do not care about
accuracy, or who want to give their statements the greatest possible
appearance of correctness; hence, in citing figures, they make use of
especially irregular numbers, e.g. 1739, 7/8, 3.25%, etc. I know a case
of a vote of jurymen in which even the proportion of votes had to be
rendered probable. The same jury had to pass that day on three small
cases. In the first case the proportion was 8 for, 4 against, the second
case showed the same proportion and the third case the same. But when
the foreman observed the proportion he announced that one juryman must
change his vote because the same proportion three times running would
appear too improbable! If we want to know the reason for our superior
trust in irregularity in such cases, it is to be found in the fact that
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