132

G74

of induction has been based on this result. Mill in his first edition had a brilliant chapter (Bk. III, Chap. xviii,) attacking the doctrine, and rightly putting his finger upon the point at which falsity is introduced into it. But before his second edition was prepared some mathematician had so expounded the procedure of the mathematicians to Mill, that he was led to rewrite the chapter and withdraw from his position, and so virtually to admit that a correct theory of induction could be based on the doctrine of chances.