We will begin with the condition in which the problem had been left by J. S. Mill. He had four canons of induction, by means of which, given suitable examples, it could be demonstrated that A and B were causally connected, if the law of causation could be assumed. That is to say, given the law of causation, the scientific use of induction could be reduced to deduction. Roughly the method is this: We know that B must have a cause; the cause cannot be C or D or E, etc., because we find by experiment or observation that these may be present without producing B. On the other hand, we never succeed in finding A without its being accompanied (or followed) by B. If A and B are both capable of quantity, we may find further that the more there is of A the more there is of B. By such methods we eliminate all possible causes except A; therefore, since B must have a cause, that cause must be A. All this is not really induction at all; true induction only comes in in proving the law of causation. This law Mill regards as proved by mere enumeration of instances: we know vast numbers of events which have causes, and no events which can be shown to be uncaused; therefore, it is highly probable that all events have causes. Leaving out of account the fact that the law of causality cannot have quite the form that Mill supposed, we are left with the problem: Does mere number of instances afford a basis for induction? If not, is there any other basis? This is the problem to which Mr. Keynes addresses himself. Mr. Keynes holds that an induction may be rendered more probable by number of instances, not because of their mere number, but because of the probability, if the instances are very numerous, that they will have nothing in common except the characteristics in question. We want, let us suppose, to find out whether some quality A is always associated with some quality B. We find instances in which this is the case; but it may happen that in all our instances some quality C is also present, and that it is C that is associated with B. If we can so choose our instances that they have nothing in common except the qualities A and B, then we have better grounds for holding that A is always associated with B. If our instances are very numerous, then, even if we do not _know_ that they have no other common quality, it may become quite likely that this is the case. This, according to Mr. Keynes, is the sole value of many instances.