The idea that science involves inductive inference was first adumbrated by Aristotle in his Organon, where he speaks of a way of getting knowledge of the universal by induction from our knowledge of particulars, his term being epagoge, literally meaning “to lead on”. Our term “induction” comes from the Latin “inducere” meaning much the same. Francis Bacon, in his Novum Organum, also gave pride of place to induction in science, although he did not think much of the rule of enumerative induction as an example of it (see §5.3). In contrast, as we have seen in §3.4, Newton's third and fourth rules appeal to induction. However, nobody thought that induction was a deeply problematic form of inference until Hume sharply formulated an argument that shows that all inductive inference lacks justification, thereby challenging a deep philosophical assumption. The problem of justifying induction is discussed in Chapter 6; in this chapter we shall be concerned with some of the different kinds of inductive inference used in science.

Scientific methods are intimately bound up with rules of inference. Few would characterize science so narrowly as to say that it is only the collection of the perforce finite number of disparate reports we make about what we can directly observe. Such a naive view of science has no role for inference-making. In recognizing the need to transcend the meagre amount of data we can collect, we must make inferences, drawing out two broad kinds of conclusion.