1. In the last chapter it was assumed that in some cases the probabilities of two arguments may be equal. It was also argued that there are other cases in which one probability is, in some sense, greater than another. But so far there has been nothing to show how we are to know when two probabilities are equal or unequal. The recognition of equality, when it exists, will be dealt with in this chapter, and the recognition of inequality in the next. An historical account of the various theories about this problem, which have been held from time to time, will be given in chapter 7.

2. The determination of equality between probabilities has received hitherto much more attention than the determination of inequality. This has been due to the stress which has been laid on the mathematical side of the subject. In order that numerical measurement may be possible, we must be given a number of equally probable alternatives. The discovery of a rule, by which equiprobability could be established, was, therefore, essential. A rule, adequate to the purpose, introduced by James Bernoulli, who was the real founder of mathematical probability, has been widely adopted, generally under the title of the principle of non-sufficient reason, down to the present time.