In Chapter 5 we showed that there is a wide range of di erent kinds of inductive inference employed in the sciences. Although the simple rule of enumerative induction needs supplementation, it is a central case of induction with key features in common with most other varieties of induction, so it will be the focus of this chapter. e question to be answered is: on what grounds are we justi ed, from the premises of enumerative induction (or the premises of any inductive inference for that matter), in inferring its conclusion? is is a Level 3 metamethodological question that asks for a justi cation of a core Level 2 principle of method, namely, the rule of enumerative induction. Since the same question can be asked about the justi cation of deductive inferences, §6.1 has a brief discussion of how a metamethodological justi cation of deductive inferences might proceed and problems for this. Hume was the rst to clearly formulate the problem of justifying induction and to argue for the sceptical conclusion that it could not be justi ed. Although we have, and should keep, the habit of making inductive inferences, there is no rational justi cation for this practice. In this chapter we shall not discuss Hume directly but set out an argument that re ects the sceptical position.