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(a) When a thing of a certain sort A has been found to be associated with a thing of a certain other sort B, and has never been found dissociated from a thing of the sort B, the greater the number of cases in which A and B have been associated, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present; (b) Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit.

This is a statement of the the principle of induction. Russell formulates it in two parts. He develops this principle from observing our expectations about the future. On this principle, the greatest degree of certainty about things that are unknown is that the more often it is the case that A signifies the occurrence of B, the more probable it is that the instance will also be the case in the future.

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