I think what Hume was trying to get at here is that we do not experience one thing causing another. We only experience an event followed by a subsequent event. Since according to Hume all knowledge comes from experience, we cannot deduce that one thing "caused" another. He argues that we have innate ideas and causation is not a feature of the physical world but an association that our minds impose onto our experience of the physical world.

Quote Originally Posted by Xei View Post
I think it's clear that science and induction can never be proof, but what is our justification for even suspecting that, for instance, all swans are white, or if you drop an object it will fall to Earth? Does science even imply that we should suspect these things? If not, what use is science?
The scientific method is setup in a way that allows for inductive statements to be falsified in the future. For example "all swans are white" just means all swans are white until we observe a swan that isn't white. Likewise the hydrogen atom is the lightest and most common element in the universe until we observe otherwise.