er of the class without taking account of
his education, interest in the case, prejudice, or general capacity.
Still, the numerical illustration of the rapid deterioration of hearsay
evidence, when less than quite veracious, puts us on our guard against
rumour. To retail rumour may be as bad as to invent an original lie.

(4) If an event may coincide with two or more other independent events,
the probability that they will together be a sign of it, is found by
multiplying together the fractions representing the improbability that
each is a sign of it, and subtracting the product from unity.

This is the rule for estimating the cogency of circumstantial evidence
and analogical evidence; or, generally, for combining approximate
generalisations "self-corroboratively." If, for example, each of two
independent circumstances, A and B, indicates a probability of 6 to 1 in
favour of a certain event; taking 1 to represent certainty, 1-6/7 is the
improbability of the event, notwithstanding each circumstance. Then 1/7
x 1/7 = 1/49, the improbability of both proving it. Therefore the
probability of the event is 48 to 1. The matter may be plainer if put
thus: A's indication is right 6 times in 7, or 42 in 49; in the
remaining 7 times in 49, B's indication will be right 6 times.
Therefore, together they will be right 48 times in 49. If each of two
witnesses is truthful 6 times in 7, one or the other will be truthful 48
times in 49. But they will not be believed unless they agree; and in
the 42 cases of A being right, B will contradict him 6 times; so that
they only concur in being right 36 times. In the remaining 7 times in
which A is wrong, B will contradict him 6 times, and once they will both
be wrong. It does not follow that when both are wrong they will concur;
for they may tell very different stories and still contradict one
another.

If in an analogical argument there were 8 points of comparison, 5 for
and 3 against a certain inference, and the probability raised by each
point could be quantified, the total value of the evidence might be
estimated by doing similar sums for and against, and subtracting the
unfavourable from the favourable total.

When approximate generalisations that have not been precisely quantified
combine their evidence, the cogency of the argument increases in the
same way, though it cannot be made so definite. If it be true that most
poets are irritable, and also that most invalids are irritable, a sti