Section VI is a short section entitled "Of Probability." Hume asserts that there is no such thing as chance in the workings of the universe, but that our ignorance of the real causes of events leads us to a belief in chance. Hume conjectures that belief differs from fiction simply in this: what we believe is more forcefully imprinted upon our imagination because it is more likely to arise. Belief, Hume asserts, is just what is confirmed by experiment.
In section VII, "Of the Idea of Necessary Connection," Hume suggests that no idea in metaphysics is more obscure and uncertain than what is variously termed "force," "power," "energy," or "necessary connection." As he has argued in section II, all ideas and complex impressions are initially formed by simple impressions, which are vivid, sensible, and unambiguous. For a complex idea like causation to have any meaning, we must be able to trace it from the simple impression from whence it is derived.
Hume argues that there is no simple impression that could inform us of necessary connection. He examines in turn our impressions of interactions between two bodies, between mind and body, and within the mind, and argues that in each case we do not perceive, by experiment or reason, any secret power of necessary connection.
Hume has already discussed the body-body interaction of billiard balls. All we observe is that the motion of the first billiard ball is followed by the motion of the second billiard ball: we cannot observe the act of causation. Nor does the mind perceive the workings of cause and effect: otherwise we could determine what effects would follow from causes without ever having to rely on observation.
Next, Hume looks at the mind-body interactions according to which an act of volition can cause the movement of limbs. Hume points out that while we are aware of our ability to move our body, we are by no means aware of the connection between the act of volition and the bodily movement. The connection between mind and body is poorly understood at best, nor do we understand why we are so capable of moving, say, our fingers but not of controlling, say, our heart. Furthermore, Hume points out that there is a long chain of muscle and nerve reactions between the act of volition and the movement of the body. Our mind wills that the arm should move, but it actually produces a whole series of effects which it in no way wills.
Finally, Hume looks at mind-mind interactions, whereby we focus the mind or produce ideas, and fails to locate any necessary connection. First, he points out that we are unaware of how the mind can conjure an idea out of nothing. Further, he points out that experience teaches us that the mind has varying degrees of control, so that it has more power over reason than the passions, or that it has greater self-command when it is healthy. That we learn these things from experience suggests that we are observing only a constant conjunction and not some necessary connection.