In Chapter 5 we showed that there is a wide range of different 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. The question to be answered is: on what grounds are we justified, from the premises of enumerative induction (or the premises of any inductive inference for that matter), in inferring its conclusion? This is a Level 3 metamethodological question that asks for a justification of a core Level 2 principle of method, namely, the rule of enumerative induction. Since the same question can be asked about the justification of deductive inferences, §6.1 has a brief discussion of how a metamethodological justification of deductive inferences might proceed and problems for this. Hume was the first to clearly formulate the problem of justifying induction and to argue for the sceptical conclusion that it could not be justified. Although we have, and should keep, the habit of making inductive inferences, there is no rational justification for this practice. In this chapter we shall not discuss Hume directly but set out an argument that reflects the sceptical position.