The 'induction problem'

'Inductive' argument: argument for a general proposition based upon particular propositions. [Definitions: e.g., Popper 1935.]

The 'induction problem' is supposed to be the problem that induction is never conclusive because, always, future evidence may falsify the conclusion. This problem particularly infects general statements about 'empirical' (fatual) matters, such as statements of natural laws.

Actually, the 'induction problem' is not a problem of induction.

Induction in the sense under consideration (the conclusion to general propositions based on particular propositions) may well be conclusive. Example: Castor is male; Pollux is male; hence, Dioscuri are male. 

Also the 'induction problem' is not a problem peculiar of empirical premises (as is largely supposed).

Induction by empirical premises may well be conclusive: Let us assume that we have a singular event e which continues for two hours. Let us further assume that we have observed its development in the first and in the second hour, singly. Let us further assume that these observations consistently ascribe a certain feature, f, to e. And let us finally assume that it is no longer possible to receive information about e. Then we can conclusively reason as follows: e was f in the first hour of its existence; e was f in the second hour of its existence; e is a singular instance; hence in general (always), e is f.

In fact, the 'induction problem' is specifically attached to cases where it is possible to obtain falsifying evidence in the future (this may, but need not at all, occur with empirical matters; and it may, but need not at all, be involved in an inductive argument).