The principle of induction, _prima facie_, is as follows: Let there be two kinds of events, A and B (_e.g._ lightning and thunder), and let many instances be known in which an event of the kind A has been quickly followed by one of the kind B, and no instances of the contrary. Then either a sufficient number of instances of this sequence, or instances of suitable kinds will make it increasingly probable that A is always followed by B, and in time the probability can be made to approach certainty without limit provided the right kind and number of instances can be found. This is the principle we have to examine. Scientific theories of induction generally try to substitute well-chosen instances for numerous instances, and represent number of instances as belonging to crude popular induction. But in fact popular induction depends upon the emotional interest of the instances, not upon their number. A child who has burnt its hand _once_ in a candle-flame establishes an induction, but words take longer, because at first they are not emotionally interesting. The principle used in primitive practice is: Whatever, on a given occasion, immediately precedes something very painful or pleasant, is a sign of that interesting event. Number plays a secondary part as compared with emotional interest. That is one reason why rational thought is so difficult. The logical problem of induction is to show that the proposition “A is always accompanied (or followed) by B” can be rendered probable by knowledge of instances in which this happens, provided the instances are suitably chosen or very numerous. Far the best examination of induction is contained in Mr. J. M. Keynes’s _Treatise on Probability_. There is a valuable doctor’s thesis by the late Jean Nicod, _Le Problème logique de l’induction_, which is very ably reviewed by R. B. Braithwaite in _Mind_, October 1925. A man who reads these three will know most of what is known about induction. The subject is technical and difficult, involving a good deal of mathematics, but I will attempt to give the gist of the results.