It would appear, then, that we are incapable of apprehending any kind of necessary connection between events. All we can intelligibly say is that one event follows another. The same holds in body-body interactions, mind-body interactions, and mind-mind interactions. Events may appear conjoined, but never connected. And because there is no simple impression related to necessary connection, it would seem that that term is meaningless, both in philosophy and in common life.
However, Hume does provide some positive response to the skepticism presented in the first part of Section VII. If one event has invariably, in our experience, followed another, we become quite confident in predicting upon the appearance of the first event that the second will follow, and we come to call the first event the "cause" and the second event the "effect." We feel these two events to be connected in the imagination. Thus, when we say that two events are connected, we simply mean that they have acquired a connection in our minds. This conclusion is quite satisfactory to the skepticism Hume has been employing, since the conclusion rests upon a certain weakness in human reason.
The principle of cause and effect is crucial to science and one that we should know if we claim to know anything. Yet we have no experience of any kind of secret power or necessary connection in nature. All we can claim is that some objects or events are constantly conjoined. Thus, Hume provides two possible definitions of cause: the first is "an object, followed by another, and where all the objects similar to the first, are followed by objects similar to the second" and the second is "where, if the object had not been, the second [would] never ha[ve] existed." Drawing on the connection created by our imagination between cause and effect, Hume provides a third definition: "an object followed by another, and whose appearance always conveys the thought to that other."
The second part of section VII provides us with a positive spin on the skepticism we encountered in the first part regarding necessary connection. Hume by no means suggests that we can rationalize necessary connection, but he does provide some explanation for necessary connection that might give some meaning to the term "cause" in both philosophical and everyday discussions.
The problem we encountered was that we could find no rational foundation to our idea of necessary connection even though we all believe in it. To be able to speak rationally about necessary connection, we needed to identify some simple impression that the idea of necessary connection is built upon. In the absence of such a simple impression, we had to acknowledge that we could not speak rationally about necessary connection.
Hume's rescue effort here is to identify that, though there may be no observable necessary connection in nature, the mind does imagine a necessary connection between two events when it perceives that they are constantly conjoined. We return once more to Hume's discussion of probability in section VI. There he points out that belief is what probability impresses upon the imagination. That is, if a certain event follows from a certain other event with good regularity, that second event impresses itself upon our imagination and leads us to believe that that second event will indeed follow. If that second event invariably follows from the first event, our belief becomes quite strong, and we are led to create a necessary connection in our minds between the first event and the second. Thus, the impression of the first event invariably leads to the idea of the second event in our minds. We begin to speak of the first event as "causing" the second event.
The conclusion Hume reaches, then, is that we can perceive only constant conjunction between two events, and not necessary connection. Constant conjunction, to reiterate, is simply the observation that two events seem to go together quite frequently. Necessary connection is the perception of some connection between the two events that explains why they go together. While Hume undercuts any rational basis for believing in necessary connection, he suggests that the mind projects the idea of necessary connection onto events that it observes to be constantly conjoined. Our notion of causation is then not the combination of constant conjunction and necessary connection, but rather the combination of constant conjunction and the determination of thought that conjures up the idea of necessary connection.
Part 2 rescues us from the extreme skepticism of Part 1 by suggesting that there is a way in which talk of necessary connection and causation can be meaningful. Hume remains skeptical to the extent that he does not believe in a necessary connection that outstrips constant conjunction. While he concludes that we can speak meaningfully about causation and necessary connection, these terms have been limited to the extent that they now bear no more metaphysical weight than talk about constant conjunction. To talk about causes or necessary connections is no more than to talk about the combination of constant conjunction and a determination in our thoughts. As a result, it is not clear how we can meaningfully speak about a metaphysical connection between two events that goes beyond their constant conjunction and the belief that there is some necessary connection.
We might want to say "yes, I may not perceive the necessary connection between a flame and its power to burn, but there is something more than simply a constant conjunction between the flame and the burning." Hume's argument is that there is no intelligible way to talk about that "something." We cannot call it a cause, since he has reduced the term "cause" to being a combination of constant conjunction and a determination of thought. If all our terms must be reducible to simple impressions, and if there is no simple impression of that "something" which connects cause and effect, then there is no intelligible way to talk about cause and effect that goes beyond Hume's somewhat unsatisfying limitations.