In this paper I offer a straight solution to Hume's problem of induction by defusing the assumptions on which it is based. I argue that Hume's problem only arises if we accept (i) that there is no necessity but logical necessity, or (ii) that it is unreasonable to believe that there is any form of necessity in addition to logical necessity. I show that Hume's arguments in favour of (i) and (ii) are unsound. I then offer a suggestion as to how the weakness of his arguments has escaped detection. Finally, having claimed that there remains a surmountable problem with inductive arguments, I end by characterising that problem and a possible approach to its solution.