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.
Hume goes on to examine and attack the occasionalist picture, which suggests that what we perceive as "causes" are in fact "occasions" and that God is the ultimate cause of all change. Considering the limitations of the human intellect, Hume ponders what stroke of logic could possibly produce such unsupported and outlandish conclusions. Further, he questions how we might know the forces that are operated by the mind of God if we cannot even decipher the forces that are operated by our own minds and bodies.
The motivation behind Hume's brief discussion of probability might not be readily apparent. Considering his emphasis on the scientific method, we should not be surprised that Hume carries a deterministic worldview: nothing that happens happens purely by chance. We may not be able to predict the outcomes of dice rolls, but this is simply because we cannot adequately calculate all the relevant factors. Hume will address the difficult question of how free will might be reconciled with this determinism in section VIII.
Hume's determinism should suggest to us that his skepticism is epistemological and not metaphysical. That is, Hume does not believe that it is pure coincidence that billiard ball collisions always happen in the same way. Rather, he believes that we are incapable of rationalizing the causal connection. We might read Hume as saying that everything that happens happens according to some sort of law or necessity, but that these laws or necessities are beyond our understanding.
We invent the notion of probability and chance, Hume suggests, because we cannot actually determine precisely how things will happen. These probabilities are determined by experience. For instance, if car crashes kill passengers 80 percent of the time, I will judge it highly probable that a car crash will result in death. Other probabilities are 100 percent certain: for instance, flames always burn. This certainty does not then result from observing directly some power of causation or necessary connection, but comes instead from a calculation of probability based on experience. Hume's discussion of probability explains his tendency to see reasoning about matters of fact as determined by habit and experience rather than by an understanding of causation.
A little more straightforward in its intent and methodology, section VII returns to the central line of Hume's argument in the Enquiry. This section is meant to establish what precisely we mean when we talk about causation.
Before we continue, perhaps we should clear up the distinction between causation and necessary connection. Generally speaking, we can say that A causes B if B temporally succeeds A, if A and B are spatially contiguous, and if B always follows A. However, if I always hum while striking a match, we can hardly say that my humming causes the match to burst into flame, even though it satisfies all the above criteria. Causation must also rely on some kind of necessary connection: the match could still burst into flame if I didn't hum, but it couldn't burst into flame if I didn't strike it. The question for Hume, then, is how we can know or perceive this necessary connection. What is it about the striking of the match and not my humming that connects to the match's bursting into flame?
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.