Popper's Justification of Induction
Science does not rely on induction. Rather, science deduces
possible observations from conjectured hypotheses, and rejects the
hypotheses if these possible observations are contradicted by
experience. Since "All A are B" is deductively falsified by any A
that is not B, the problem of induction does not arise.
Literature
Popper 1971 is the most
succinct presentation of this, and has the most marvellously
arrogant opening of any philosophical paper I have ever read. Do
not imitate this in your essays!
Problems
We never have any reason to believe any of our conjectures: all we
know is that we don't yet know them to be false.