1. What is a causal principle?

Any statement of the form "C causes E" or "E is the effect of C," (where "C" and "E" are any two "objects" (Hume's term) or "events" that are called the "cause" and the "effect" respectively) expresses a causal relation to hold between C and E. Such statements as "fire causes heat" or "temperatures below freezing cause water to turn into ice" are examples of "causal principles."

2. What does it mean to say "C causes E"?

Recall that Hume's empiricism leads him to hold that any idea can be explicated by analyzing it into its simple components and then showing what simple impression each component simple idea copies. The idea of a causal principle in effect includes the ideas of E following C in time and that C and E are necessarily connected, such that when C happens, E must follow, and when E happens, C must have happened previously. The occurrence of the cause thus permits one to infer that the effect has happened or will happen; the occurrence of the effect permits one to infer that the cause happened previously. Any process of reasoning in this way may be called a "causal inference." Thus any causal inference always requires assuming a certain causal principle to hold true, or in other words that a certain "C" and a certain "E" are related as "cause" to "effect". This fact in turn implies that we can know a "causal inference" is a sound inference (all premises are true, so conclusion is true) only if we can know that the relevant causal principle is true.

3. Can we know whether any particular causal principle is true on the basis of demonstrative reasoning?

Hume begins by showing that there is no process of a priori (i.e., not based on sensory experience) "reasoning" or "demonstration" which could ever lead to such knowledge. The only judgments which we can know to be true by reason alone are those Hume calls "judgments of relations of ideas" (analytic judgments). The test for whether any statement expresses a relation of ideas is to try to deny it. If its denial is self-contradictory (logically inconsistent), then it is a judgment of relations of ideas. A judgment such as "all triangles are three sided" expresses a relation of ideas because one cannot consistently think of something which is a triangle and not three sided. Thus we can know by a priori reasoning that this judgment is true.

But there is nothing logically inconsistent in thinking of the occurrence of C and the failure of E to occur. For example, I can think of fire without thinking of heat; it is possible to imagine an idea of a "cold fire." While I have never experienced such a thing and I do in fact associate the impression of a fire with the impression of heat, there is nothing about the idea of "fire" that requires it be connected with "heat." Therefore, no judgments which express causal principles could be reached on the basis of a priori reasoning, and so such judgments must be based on sensory experience.

4. What is there in experience which leads to the belief in any causal principle?

To say a causal principle is not a judgment of relations of ideas is equivalent to saying it must be a judgment of matters of fact.  Hume essentially asks how do we come to believe that any given C and E are causally connected. Since a priori reasoning has been ruled out, it must lie in something we experience. But all we experience is the impression of C followed by the impression of E; we do not have any experience of the alleged necessary connection between them; yet this is part of the idea involved in thinking "C causes E." Furthermore Hume observes that on the experience of a single C-type impression being followed by an E-type impression, we are not likely to conclude that the two are necessarily connected.

However after the repeated experience of the two types of impressions being "constantly conjoined in time" (one following the other), we come to believe that the one, C, causes the other, E.

5. What is there is the experience of the same occurrence repeatedly that was not in the experience of a single occasion where E followed C?

Hume answers it can only be that after repeated experience of C being followed by E, we come to associate the ideas, such that when we think of C occurring we come to expect E to occur. (When we think of having and impression of fire, we expect to have an impression of heat.) Hume calls such an expectation formed by repeated association of C and E a "habit" or "custom" of the mind. He argues that this is the only possible impression from which one can derive the idea of necessary connection which forms part of the complex idea of "C causing E."

6. What is a consequence of this analysis of the idea of causality?

Hume's conclusion that the idea of "C causes E" is derived from the impression of a habit of the mind in expecting E when C happens implies that the basis of our belief in a causal principle is subjective, or in other words determined by the way we think, rather than objective, determined by the nature of C and E. We mistakenly hold that knowledge of a causal principle is based on an objective "power" ("causal efficacy") to produce the effect imagined to be in the cause, but we can have no idea of such a power because we have no corresponding impression.

7. What does this conclusion imply about our knowledge of the truth of any causal principle?

A causal principle maintains that the cause and effect are necessarily connected, which means that whenever C happens, E must follow, or when E happens, C must have preceded it. However, our belief in such a principle is based on experience of repeated cases of C being followed by E and the habit of expecting this pattern to continue into the future. But this basis cannot justify the truth of the conclusion that C will always be followed by E, for the habit of expectation is purely subjective, and, since a causal principle cannot be known as a relation of ideas, no experience of the past conjunction of the two in time can ever establish that they will continue to be so conjoined in the future.

8. Why can't we infer from past instances in which C was followed by E to the conclusion that C will always be followed by E?

Hume refers to such an inference as "experimental or moral reasoning"; today we would call it an "inductive inference" because it reasons from particular premises (past cases of C being followed by E) to a universal conclusion that this connection always holds true. No such inference can ever establish its conclusion to follow with certainty from its premises. Since knowledge requires certainty and no inference to a causal principle can ever be certain, it follows that knowledge of causal principles is impossible. All we can hope for is a possibly fallible belief based on our habit of expecting experienced connections of C and E in the past to be continued into the future.

9. Why can there be no deductive inference to a causal principle?

Hume considers trying to turn the inference to a causal principle into a deductive inference. Such an inference would
look like the following argument:

In the past C has always been followed by E.
The future will resemble the past.

Therefore, in the future C will always be followed by E.
(or in other words C is always followed by E; or
as Hume puts it, C and E are "necessarily connected".)

The first premise can of course be known by experience. But how could we ever know the second premise? This statement is known as the "principle of the uniformity of nature," but it is futile to appeal to it to try to prove a causal principle is true, because we can never know the principle of the uniformity of nature to be true. To see why, we need only repeat the same strategy Hume has used on causal principles. It can't be known by a priori reasoning because its denial is logically possible (it's not a relation of ideas). It can't be known by experience because we have no experience of the future. So just like any specific causal principle, the principle of uniformity of nature is simply a belief based on the habit of expecting the future to resemble the past because in the past what was then the future, when it became the present, turned out to resemble the past. But that, of course, is no grounds for certainty concerning what is still the future. We can conceive of the
possibility that the course of nature could change. Thus there is no way to prove that the course of nature can't change, because having no experience of the future, we cannot establish it on the basis of experience, and since its denial is not self contradictory, we cannot establish it be demonstrative reasoning.  So, in short, the principle of the uniformity of nature cannot be known.

10. Why does this lead to skepticism?

Hume has argued that any knowledge of the world exterior to our mind requires an inference from what we know immediately, our impressions and ideas, to the alleged cause of those impressions in the external world. But what would it require to be able to give any meaning to the sort of causal principle which would be necessary to support such an inference?

We would have to have experience of both C and E conjoined in time. But in this case we can never have any experience of the "C" preceding the "E," because it lies in the "external world" outside our mind, and all we experience is our impressions and ideas. So, having no impression of the presumed cause, we cannot ever ormulate a causal principle which would connect this presumed cause to the impressions as its effect. Hume is not merely saying we cannot know what it is that causes our impressions, but we could possibly believe that they were caused, for example, by physical objects. He is making the much stronger claim that we cannot even give any meaning to the notion of a cause of our impressions lying "outside" the mind, because, by his empiricism, we can only think of that of which we can have experience. But the only things we can experience are impressions and the ideas which copy them, not some presumed "cause" of these impressions. In short we cannot ever infer from our impressions to anything at all which causes them, if indeed there even is such a cause.