Helen Beebee in The Philosopher's Magazine:
Hume’s account of causation has a good claim to being one of the most influential views in the history of philosophy. It not only set much of the agenda for large swathes of analytic philosophy in the 20th century and beyond, but it also awoke Immanuel Kant from his “dogmatic slumber” – as he put it in his Prolegomena to any Future Metaphysics – and prompted him to write the mighty Critique of Pure Reason, itself a hugely influential work and arguably the starting-point for the continental tradition in philosophy.
So why has Hume’s view on causation proved to be so influential? Well, let’s start with the state of play in philosophy at the time Hume was writing. The dominant view of causation at the time was a part of what Edward Craig (in The Mind of God and the Works of Man calls the “Image of God doctrine”. The idea here is, as the name suggests, that we are made in God’s image: our mental faculties are of course rather feeble compared to God’s, but they are of the same kind as God’s. If you were in the grip of the Image of God doctrine, you might think something like this. Our mental faculties are at their most perfect – their most God-like – when we’re engaged in a priori reasoning, for example when we’re constructing a mathematical proof. And in a mathematical proof, we can (if we’re really good at maths) just “see” or “intuit” that each successive stage of the proof follows from, or is entailed by, the preceding stage. So, if our mental faculties generally are God-like, then the same kind of thing must be going on when we turn our attention to the causal structure of the world. At least in principle, if I look at some event – the cue ball hitting the black ball in snooker, say – I can tell, just by observing that event, what must happen next: I can infer, on the basis of just that experience, what the collision will cause, just as I can in principle tell just by looking at a mathematical theorem what follows from it.
Hume’s fundamental insight when it comes to causation is that that story cannot possibly be right. No matter how hard I look, and no matter how much I know about the size and shape and weight of the balls and their position on the table, nothing whatsoever follows about what the collision is going to cause. Of course, what I expect to happen is that the black ball will move off in a certain direction and (let’s suppose) land in the corner pocket. But that is not something I can deduce just from careful observation of the collision. As Hume puts it: “If we reason a priori, any thing may appear able to produce anything”.