ABSTRACT
When we have examined the forms of argument in which premisses entail conclusions and those kinds of propositions which are logically necessary, have we exhausted the scope of logic? On the face of it, there is good reason to suspect that we have not. Valid arguments do not prove the truth of their own universal premisses. The proposition, ‘If all men are mortal and all Greeks are men, all Greeks are mortal’, does not, of course, prove that all men are in fact mortal. But few of us are so sceptical as to deny that we can be said, for all practical purposes, to know that they are. So, if there is a class of non-necessary universal propositions which, as rational men, we are prepared to accept, it is reasonable to assume that there is some form of reasoning, not necessarily deductive, by which we can justifiably arrive at them. Even if generalising is only a convenience, and not an absolute requirement, of our day-to-day lives, the very purpose of science seems to be to establish such propositions. It would be paradoxical to the point of absurdity to dismiss all such generalisations as unjustified simply on the grounds that their truth could not be proved by deductive methods. We have the strongest incentive to accept the possibility of a kind of inference called induction, whereby we may legitimately pass from the recognition of the truth of a number of non-necessary propositions to the formulation of propositions of unrestricted generality or to other particular propositions. And I shall first consider the claims of this alleged kind of reasoning—induction by simple (i.e. incomplete) enumeration—to provide the guarantee that we need for asserting universal propositions, for justifiably moving in our arguments from ‘Some S is P’ to ‘All S is P’.
