131

G73

A yet fourth theory of induction received by implication the assent of Mill. All the ordinary treatises on the doctrine of chances teach that if from an infinitely numerous collection of object any number, m, of them be drawn at random and they are found to possess any common character, then the mathematical probability that the next one drawn will have the same character is (m+1)/(m+2). If this be true, it is easy to see that the facts observed of the instance on which an ordinary induction is founded render the predicate the induction probably true for as many new instances; and a theory of the validity