1. It has often been thought that the essence of inductive argument lies in the multiplication of instances. ‘Where is that process of reasoning,’ Hume inquired, ‘which from one instance draws a conclusion, so different from that which it infers from a hundred instances, that are no way different from that single instance?’ I repeat that by emphasising the number of the instances Hume obscured the real object of the method. If it were strictly true that the hundred instances are no way different from the single instance, Hume would be right to wonder in what manner they can strengthen the argument. The object of increasing the number of instances arises out of the fact that we are nearly always aware of some difference between the instances, and that even where the known difference is insignificant we may suspect, especially when our knowledge of the instances is very incomplete, that there may be more. Every new instance may diminish the unessential resemblances between the instances and by introducing a new difference increase the negative analogy. For this reason, and for this reason only, new instances are valuable.

If our premisses comprise the body of memory and tradition which has been originally derived from direct experience, and the conclusion which we seek to establish is the Newtonian theory of the solar system, our argument is one of pure induction, in so far as we support the Newtonian theory by pointing to the great number of consequences which it has in common with the facts of experience.