Induction, in logic is the process of moving from the particular to the general, and as such is not demonstrative; which means, it does not prove its conclusions through a logical process, like deduction. Ever since induction has been noticed, many philosophers have either been apologetic about it for not being demonstrative, or have tried to show that somehow it really is demonstrative in a roundabout way, or at least respectable in spite of not doing what deduction does. Hume belongs to the group of philosophers who cannot be placed in either of these categories, since his method of dealing with this problem is not a logical one. Since he deals with the problem through the theory of causality in the terms of constant conjunction in the past, despite its general logical usage, induction is not purely a logical problem. Therefore we should look at Hume’s approach to this problem and see, whether he is right in dealing with the problem in a ‘psychological’ way.
In the Introduction to the Treatise, Hume says that ‘as the science of man is the only solid foundation for the other sciences, so the only solid foundation we can give this science itself must be laid on experience and observation.’ These last lines have made a huge difference on me, while I program. Very deep indeed.