Hume begins by noting the difference between impressions and ideas. Impressions come through our senses, emotions, and other mental phenomena, whereas ideas are thoughts, beliefs, or memories that we connect to our impressions. We construct ideas from simple impressions in three ways: resemblance, contiguity, and cause and effect.
Next, Hume distinguishes between relations of ideas and matters of fact. Relations of ideas are usually mathematical truths, so we cannot negate them without creating a contradiction. Matters of fact are the more common truths we learn through our experiences. We understand matters of fact according to causation, or cause and effect, such that our experience of one event leads us to assume an unobserved cause. But Hume argues that assumptions of cause and effect between two events are not necessarily real or true. It is possible to deny causal connections without contradiction because causal connections are assumptions not subject to reason.
We cannot justify our assumptions about the future based on past experience unless there is a law that the future will always resemble the past. No such law exists. We can deny the relationship without contradiction and we cannot justify it with experience. Therefore, we have no rational support for believing in causation. Hume suggests that our assumptions are based on habit, not reason, and that, ultimately, our assumptions about matters of fact are based in probability. If experience teaches us that two events occur together repeatedly, we will assume a link between them. So, Hume explains, we must be able to reduce all meaningful concepts to the simple impressions on which they are built. Since no simple impression of causation or necessary connection exists, these concepts might appear meaningless. Rather than dismiss these assumed connections entirely, however, Hume acknowledges their usefulness and limits them to being nothing more than simple observations of repeated conjunction between two events. Further, he concludes that if there is no cause and effect, then our actions are not predetermined, and we enjoy true free will.
At the end of the Enquiry, Hume pursues a number of tangential discussions. He argues that humans and animals possess similar capacities and methods for reason. He denies that any rational justification exists for belief in either miracles or most forms of religious and metaphysical philosophy. Although we can rationally justify our skepticism regarding the existence of an external world, that doubt destroys our ability to act or judge. The instinctual beliefs formed by custom help us get along in the world. As long as we restrict our thinking to relations of ideas and matters of fact, we are acting within the limits of reason, but we should abandon all metaphysical speculations as useless, impossible to resolve, and nonsensical.
Hume seeks to explain our understanding of the world rather than try to justify our beliefs or prove anything. Here, he does not address the existence of necessary connections between events but states merely that we cannot know what those connections are. Ultimately, Hume argues for a mitigated skepticism. We have no good reason to believe much of what we believe about the world, but human nature helps us function in all the ways that reason cannot. However, we must limit ourselves by accepting that matters of fact are our sole source of true information. If past experience cannot teach us about the future, it becomes difficult to function on a practical level. The elimination of causation would make it impossible for us to function, if it meant that we began to act as if causation didn’t exist. Whether or not we can know of a necessary connection between two events is not worth arguing about. Similarly, Hume does not think we should spend time and energy on questions such as whether God exists, what the soul is, or whether the soul is immortal. He claims that because the mind is not meant to help us discover and define truths, we will never be able to come to any definite and rational conclusions about abstract matters.
Hume is skeptical about his own explanation of why we cannot rationally make necessary connections between two events. He stops short of saying that it is impossible to predict future events based on past experience and explains only that we lack any solid reason to believe this is the case. Hume admits that, if we observe that one event repeatedly follows another, it is natural that we assume the two events will always occur together in this pattern. He also admits that we must necessarily make such assumptions to live our lives. Such assumptions are practical and useful but not completely reliable or passable as proof. We are wrong to justify these beliefs by claiming that reason supports them or that we can absolutely know that one event causes the other.