1. Hume rightly maintains that some degree of resemblance must always exist between the various instances upon which a generalisation is based. For they must have this, at least, in common, that they are instances of the proposition which generalises them. Some element of analogy must, therefore, lie at the base of every inductive argument. In this chapter I shall try to explain with precision the meaning of analogy, and to analyse the reasons, for which, rightly or wrongly, we usually regard analogies as strong or weak, without considering at present whether it is possible to find a good reason for our instinctive principle that likeness breeds the expectation of likeness.

2. There are a few technical terms to be defined. We mean by a generalisation a statement that all of a certain definable class of propositions are true. It is convenient to specify this class in the following way. Iff(x) is true for all those values of x for which ϕ(x) is true, then we have a generalisation about ϕ and f which we may write g(ϕ,f). If, for example, we are dealing with the generalisation, ‘All swans are white’, this is equivalent to the statement, “x is white” is true for all those values of x for which “x is a swan” is true’.