If you ignore the generalizing nature of intelligence, as the empiricist logician does, you are impaled on the horns of a dilemma: you must justify induction either by way of a complete enumeration or by way of formulating rules for jumping from some particulars to the general. However, complete enumeration is neither an induction nor a generalization. Complete enumeration means counting each and every individual case: there is no going beyond the particular to the general; there is no going beyond the counting as the counting covers all the cases.
The alternative of formulating rules to negotiate the transition from a limited number of cases to all cases also breaks down. First, cases differ so much in common sense, science, philosophy, history, etc., that it is impossible to formulate rules to cover all cases. Are all politicians corrupt? Are all swans white? Are all men mortal? They are quite different cases and no one set of rules applies. Second, even if there were a set of rules there would be a need for intelligence to select the rules which apply to this particular case, to be able to recognize exceptions, to be able to decide what is similar and what is significantly different. But that is to invoke intelligence and once you invoke intelligence you are beyond an empiricist philosophy. John Stuart Mill formulated five rules for an empirical scientific method: the method of agreement, of difference, of agreement and difference, of residues and of concomitant variation. These are a useful guide towards correct inductions in the field of empirical science; but they require intelligence in applying the laws to particular cases. They do not take the place of intelligence. They are not rules that if followed blindly automatically produce correct conclusions.»