A Treatise of Human Nature, Hume proceeds to explore the bases of our knowledge. We possess two faculties, memory and imagination, for dealing with the ideas that we receive. The memory preserves the ideas in the exact order in which they entered the mind. The imagination, on the other hand, is free to arrange the ideas in any manner that is desired. However, contrary to what might be expected, our imaginations do not function at random. Instead, we imagine ideas in ordered sequences, so that whenever a particular idea comes to mind, related ideas automatically follow it, according to certain principles of the association of ideas that Hume calls “a kind of ATTRACTION, which in the mental world will be found to have as extraordinary effects as in the natural.” Ideas tend naturally to be associated when they are similar or when they are contiguous in time or space or when they stand in the relation of cause and effect. The importance of association is brought out when Hume comes to discuss causality in part 3.

Before applying these “discoveries” about the way we think, Hume takes up a few other questions. He argues first for a point the philosopher George Berkeley had previously made, that we possess no abstract general ideas but only ideas of particular things. General terms, such as “man” or “triangle,” designate the collections of similar particular ideas that we have acquired from experience.

Hume then tries to explain mathematics as being about particular experiences. He knew relatively little about mathematics and based many of his views on comments in philospher Pierre Bayle’s The Historical and Critical Dictionary (1695-1697). Hume’s empirical mathematical theory has generally been regarded as, perhaps, the weakest part of his book, though he was always proud of having shown that mathematics is “big with absurdity and contradiction.” Hume conceived of arithmetic as being a demonstrable science dealing with relations of quantity, whereas geometry was thought of as an empirical science dealing with observable points. Because of the limitation of our ability to see and count the points, the theorems in geometry are always to some degree uncertain.

The most famous part of A Treatise of Human Nature is the third part of book 1, which treats “Of Knowledge and Probability.” Genuine knowledge is gained by an intuitive inspection of two or more ideas to see if they stand in a particular relationship to each other. We can be completely certain by intuition that two ideas do or do not resemble each other, or that they differ from each other, or that one has more or less of a given quality than another—for instance, that one is darker than another. Such knowledge is certain in that it depends solely on what one “sees” when two or more ideas are brought together by the imagination, but it gives us relatively little information. By connecting a series of intuitions, we gain the sort of demonstrative knowledge that occurs in arithmetic and algebra. Intuition and demonstration are the sole sources of complete certainty and knowledge.

Our information about the causal relation of ideas does not arise from an intuitive examination of our ideas, and almost all of our information about what is happening beyond our immediate experience is based upon causal reasoning. How do we decide which ideas are causally related? When we examine two ideas, or two impressions that we think are so related, we find that we do not perceive any necessary or causal connection between them. We perceive only that the ideas are contiguous and successive. We do not, however, perceive that they are necessarily connected in any way, although we do feel that there must be more to the sequence than merely one idea following after another. We believe that one of the ideas must make the other occur. However, Hume asks, what evidence do we have for such a belief, and where do we acquire the belief? If we admit that we do not perceive any necessary connection between events, then Hume suggests that we ought to ask ourselves why we believe that every event must have a cause and why we believe that particular causes necessarily must have certain effects.

When the first problem is examined, we discover something that is surprising. Even though we all believe that every event must have a cause, this proposition is not intuitively obvious, nor can it be demonstrated. When we conceive of events, we neither see them as caused nor necessarily think of them in terms of their causes. Because of the freedom of our imagination, each event can be thought of separately and independently. If events can be thought of as uncaused, it is also possible that they occur uncaused. If that is a genuine possibility, then there can be no valid demonstration proving the impossibility of uncaused events. The demonstrations that had been offered by previous philosophers, Hume believed, are all unsatisfactory. They beg the question in that they assume what they are attempting to prove: namely, that every event has a cause. Apparently the causal principle, which is neither self-evident nor demonstrable, is so basic that we all accept it for reasons that seem to be unknown.

To explore the matter further, Hume turns to the other problem: What is the basis for our belief that particular causes have particular effects, and how do we infer one from the other? The actual constituents of our causal reasoning, he asserts, are a present impression of sense or memory, an imagined idea of a related event, and an unknown connection between them. When we hear a certain sound, we think of somebody ringing the doorbell. Why and how do we infer from the impression to its supposed cause? Many other ideas might have come to mind. When we hear the sound, we do not, at the same time, experience its cause, yet we implicitly believe that said cause must also be occurring to produce the perceived effect. This reasoning process is not a logical one, Hume maintains, since there is no reason for us to think of one idea rather than another when a particular experience takes place.

If reason cannot be what makes us connect events causally, perhaps experience is responsible. We find that when a sequence of events is constantly repeated in our experience, and when the events are conjoined, we tend to associate ideas about them in our minds. Then, when we experience just one of the events, we also think of the other. One of them we call the cause and the other, the effect. What is there in the fact that certain events have been constantly conjoined in the past that leads us to think of them as causally related? Hume points out that if the process involved were a rational one, we would have to presuppose that the principle of the uniformity of nature was true. This principle asserts that “instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same.”