The first part of section VII could be read as the negative phase of Hume's argument. With body-body, mind-body, and mind-mind interactions, Hume shows that there is no evidence of necessary connection. If we knew of necessary connection purely through reason, we would not need experience to show us that two events are necessarily connected. However, in each case, Hume shows us that it is experience that teaches us of this connection. Furthermore, we do not actually experience the necessary connection itself: we only infer it from the constant conjunction that we observe between two events. Here, Hume's discussion of probability comes in once more. We observe that in 100 percent of cases, one billiard ball striking a second billiard ball is followed by the movement of the second billiard ball. This observation leads us to infer that there must be some necessary connection between the collision and the movement of the second ball even though we cannot directly observe that connection.
That all ideas and complex impressions are derived from simple impressions is central to Hume's thinking. For our idea of necessary connection to have any coherence, it must be related to some simple impression. However, Hume's arguments show us that there is no simple impression that produces the idea of necessary connection. As we mentioned before, Hume is not suggesting that it is pure coincidence that the second billiard ball invariably moves when it is struck. Instead, he is suggesting that whatever causal connection there might be between the two events cannot be rationalized by us.
At the end of the first part of section VII, Hume touches on occasionalism, most famously represented by Nicolas Malebranche (1638-1715). A proper discussion of occasionalism is beyond the scope of the present commentary, but we should note that Hume displays a great deal of intellectual courage and integrity in not shying away from the skeptical consequences of his argument. Unfortunately, he was rewarded for this with accusations of atheism that plagued him his entire life.