Here's an intuition I have. Suppose that I somehow knew that a dozen of boxes have appeared ex nihilo for no cause (not even a stochastic one) in my office. I open half of them and each one was purple inside. Do I have good reason to think that the others are also purple inside? As long as I hold on to my knowledge that there is no explanation of the boxes' presence and character, I think not. It is rather like when I get heads six times in a row when tossing a fair coin—as long as I get to hold on to my knowledge that the coin is fair, I have no reason to think subsequent tosses will be heads.
This suggests to me that induction requires that the cases we do induction over be non-brute, that they have explanations. But not just any explanations will do. The cases need to have a common type of explanation. If one box was materialized in my office by aliens, and another was delivered by my best friend, and another coalesced from the drippings in a leaky ceiling, and so on, then I don't get to do induction across the cases.
- That all observed Fs are Gs gives me knowledge by induction that all Fs are Gs only if there is a common type of explanation as to why each F is a G.