by 
David Hume
[...]If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects."[8] One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced or inferior people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If he is right, then the justification of induction can be only inductive. But this begs the question; as induction is based on an assumption of the connection, it cannot itself explain the connection.
Karl Popper
Karl Popper, a philosopher of science, sought to resolve the problem of induction in the context of the scientific method. He argued that science does not rely on induction, but exclusively on deduction, by making the modus tollens argument form the centerpiece of his theory. Knowledge is gradually advanced as tests are made and failures are accounted for.
Wesley C. Salmon critiques Popper's falsifiability by arguing that in using corroborated theories, induction is being used. Salmon stated, "Modus tollens without corroboration is empty; modus tollens with corroboration is induction."
I didn't quote the other relevant sections but you can read it summerized here to get the full picture:
http://en.wikipedia.org/wiki/Problem_of_induction
Basically my question would be if we need some "component" of deductive reasoning to solve the "problem of induction"? I hope this is not a false dichotomy and I reckon there's also abductive reasoning although it seems to be fallacious.
