Context. The author is in the process of explaining the inferences that are drawn from particular causes to particular effects. As he put it at the end of Section 3: "Why we conclude, that such particular causes must necessarily have such particular effects, and why we form an inference from one to the other?" In Section 4, he argues that the inference must begin by establishing the existence of the cause. This is established by there being either an immediate perception of the senses or memory or from an inference from other causes, but such an inference must eventually terminate in an immediate perception. In Section 5, he breaks down the task of explaining causal inferences into that of explaining the original impression, the transition from the original impression to the idea of the cause or effect connected with it, and the nature of the resulting idea. In this section, he turns to the explanation of the transition.

1. The author begins on a negative note. He claims that the inference from cause to effect is not based on a mere inspection of the original impression and the resulting idea by themselves. It might be thought that by a "penetration into their essences" we can discover the causal relation between them, but this would be incorrect. "There is no object, which implies the existence of any other if we consider these objects in themselves, and never look beyond the ideas which we form of them." The author's argument for this claim depends on his principle, first noted in Part 1, Section 3, that distinct perceptions are separable in thought. The impression of the cause and the idea of the effect are distinct from each other, and therefore may be thought separately. In that case, one may separate the impression of the cause from the idea of the effect and substitute any other idea for the latter. Given that this separation can be made, one can conceive of the cause without the effect. But then one cannot discover the connection between the two simply by inspecting the preceptions themselves, which was to be proved. If the connection could be discovered in this way, then it could be the object of knowledge, as described in Part 3, Section 1. But there can be no knowledge of the connection. If there were, the non-existence of the connection would be impossible, in which case it would be inconceivable. It has just been shown that the lack of a connection is conceivable, as the imagination is free to substitute a different idea for the idea of the effect.

2. The author concludes that because the causal inference is not made on the basis of the inspection of the perceptions alone, the inference is made on the basis of EXPERIENCE [which is the only alternative recognized by the author]. The way in which experience contributes to the inference is as follows. First, there is the repeated observation of instances of one "species" of objects are constantly followed by instances of another species. For example, we perceive flame on various occasions, and that perception is accompanied by a sensation of heat. Moreover, there is a "regular order of contiguity and succession" between perceptions of the two species of objects. Upon remembering these facts, "without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other." What distinguishes our inference from the experience on which it is based is that when we reason that a cause or an effect exists, only one of the perceptions is present, "and the other is supply'd in conformity to our past experience."

3. The author now expresses surprise that he has discovered the relation of CONSTANT CONJUNCTION between the perceptions. He had not been looking for it, as he was instead seeking to understand the workings of causal inference. The relation of constant conjunction is essential to causal inference, as the relations of contiguity and succession by themselves are not sufficient to evoke a belief that the contiguous and successive objects are related as cause and effect. We must in addition "perceive, that these two relations are preserv'd in several instances." At this point, we may leave the examination of the relation of cause and effect, focusing instead on the discovery of the nature "of that necessary connection which makes so essential a part of it." The author expresses hope that this new investigation will contribute to the solution to his original question, "tho' to tell the truth, this new-discover'd relation of a constant conjunction seems to advance us but very little in our way." The reason for the author's initial pessimism is this. The nature of a causal inference is to produce a new idea (of a cause or of an effect) when a certain perception is present to the mind. But as was noted earlier, experience only provides us cases where two perceptions are already present, so it is hard to see how constant conjunction does anything more than to multiply the pairings of perceptions. But what we need to explain is how we can "enlarge the objects of our mind." It has been established that we cannot learn from a single observation of an object that it is cause or effect, so how does the observation of a multitude of objects provide us with any useful information? "From the mere repetition of any past impression, even to infinity, there never will arise any new original idea, such as that of a necessary connexion; and the number of impressions has in this case no more effect than if we confin'd ourselves to one only." The author counsels us not to despair to soon, even though "this reasoning seems just and obvious." So he will continue to investigate the inference from particular cause to particular effect, and vice-versa. He then drops an important hint of what is to come. We have been looking for a necessary connection to underpin our causal inferences, but perhaps it will turn out that "the necessary connection depends on the inference." This is indeed how it does turn out, but we must wait until Section 14 to see how this is supposed to work.

4. Now that it has been established that the inference from impression to idea is based on past experience and the recollection of the constant conjunction of perceptions of like kind, "the next question is, whether experience produces the idea by means of the undertanding or imagination; whether we are determin'd by reason to make the transition, or by a certain association and relation of perceptions." The author proceeds to show that reason is not what determines us to produce a new idea when we reason causally. He begins by examining how reason might do so, and he claims that "it wou'd proceed upon that principle, 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." Let us refer to this principle as the Principle of the Uniformity of Nature (PUN). [The author does not reveal why reason would have to rely on this principle, but it is pretty clear why he thought it is necessary. The only evidence reason has to work with is the recollection of our past experience. Since the conclusion of any causal inference concerns something that has not been experienced, reason needs a bridge, so to speak, to connect its experience with something beyond it. The only bridge that would be of any value would be one which compares the perception and the idea in terms of their resemblance. After all, the experiences which are relevant to making the inferences are resembling conjunctions of perceptions. It is not clear how the second part of the principle, that nature continues uniformly the same, is related to the first. Perhaps it is a more general principle of which the first is an instance.] In order "to clear up this matter," the author proposes to examine the arguments on which the PUN might be based. And these are of two possible kinds: demonstrative arguments leading to knowledge of its truth, and reasoning that would only make it probably true. "Let us cast our eye on each of these degrees of evidence, and see whether they afford any just conclusion of this nature."

5. As might be expected, the author invokes "our foregoing method of reasoning" to show that "there are no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience. The "foregoing method" was to show that that a change in the course of nature is "not absolutely impossible" because it is conceivable. The author here makes explicit the principle connecting conceivability and possibility: "To form a clear idea of any thing, is an undeniable argument for its possibility." Moreover, such an argument "is alone a refutation of any pretended demonstration against it."

6. The author now turns to probable reasoning. Here, he describes it as discovering the relations of objects, rather than of ideas "consider'd as such." In order to find the relations in objects, probable reasoning involves both impressions and ideas. If there were no impressions involved in this reasoning, we would have no reason to think that the ideas involved have any connection to reality at all, and "the conclusion wo'ld be entirely chimerical." On the other hand, if no idea were produced as the output of the reasoning, we would be left with an impression, in which case the relation "wou'd, properly speaking, be sensation, not reasoning." So in all probable reasoning there must be a present impression ("either seen or remember'd") and an idea inferred from it ("which is not seen nor remember'd").

7. [This paragraph contains the argument for which Hume is most famous.] Our probable reasoning must take us from an impression to an idea, and the only way in which this inference may be made in a "just" way is through the relation of cause and effect. The author concludes from this that the relation of cause and effect is "the only connexion or relation of objects, which can lead us beyond the immediate impressions of our memory or senses." It has been established that the idea of cause and effect is derived from experience, "which informs us, that such particular objects, in all past instances, have been constantly conjoin'd with each other." The inference occurs when we suppose that an object similar to one of the constantly conjoined objects is "immediately present in its impression." At that point, we presume that there exists an object similar to the ones that have been experienced to accompany objects similar to the one supposed to be present. This account of causal reasoning is taken by the author to be "in every point unquestionable." The probable reasoning is based on "the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none." Given that this is the case, the presumption of a resemblance cannot be based on probable reasoning. The reason is that the presumption of a resemblance would be a cause, of which probable reasoning is an effect [see paragraph 4], while probable reasoning is a cause, of which the presumption of a resemblance is an effect. "The same principle cannot be both the cause and effect of another; and this is, perhaps, the only proposition concerning that relation, which is either intuitively or demonstratively certain." [The author ends the paragraph with this statement and does not tell us what follows from the impossibility that the presumption of resemblance is based on probable reasoning. Because the presumption of resemblance is not based on demonstrative reasoning either, it is therefore based on no reasoning at all. But it the presumption of resemblance is based on no reasoning at all, neither is the causal inference on which it is based. This conclusion is first stated explicitly in paragraph 12: "Reason can never show us the connexion of one object with another, tho' aided by experience, and the observation of their constant conjunction of in all past instances."]

8. Having completed his explanation of the way in which inferences from particular causes to particular effects, and vice-versa, are made, the author turns to a possible objection. The objection is that our causal inferences are based on "solid reasoning." But it does not attack the author's claim that there are only two kinds of reasoning, demonstration and probability, and that neither could be the basis of causal reasoning. The author then requests that "the reasoning may be produc'd, in order to be exposed to our examination." He provides a possible candidate for how we reason after we have had "experience of the constant conjunction of certain objects." The claim is that the constant conjunction would not be possible unless the object which has always been found to produce another "was not endow'd with a power of production." If the object does have the power, then its having it necessarily implies that it will have its effect. So, once the power of production is in mind, we reason from the presence of the object to the presence of its cause or effect. "The past production implies a power: The power implies a new production: And the new production is what we infer from the power and the past production."

9. The author asserts that he could easily "show the weakness of this reasoning" by appealing to his earlier conclusion (from Section 2, paragraph 10), that "the idea of production is the same as that of causation." [In that case, the claim that an object has the power of production would be the same as saying that it is the cause of its effect. But the goal of causal reasoning is to show that the object is the cause of the effect, and the reasoning would therefore be question-begging.] Another problem with the reasoning is that the inference from constant conjunction to the claim that a further object has a power cannot be a demonstration that it has one. [In that case, the reasoning would be probable, and the problem of paragraph 7 would recur.] Finally, the author could appeal to what he will later say in Section 14 about the nature of our idea of a power. He will not do this because "such a method of proceeding may seem either to weaken my system, by resting one part of it on another, or to breed a confusion in my reasoning."

10. To defeat the objection, the author assumes for the sake of argument (and only for the sake of argument) that "the production of one object by another in any one instance implies a power; and that this power is connected with its effect." The question is then whether one can reason from this object's having the power to another object's having the power. The answer is that one cannot. The problem is that as was shown earlier in Section 2, paragraph 5, there is no perceivable quality in the object that can be identified with the power. Thus, when confronted with the new object, one would have no way of telling whether it possesed the power as well as the original object did. "I ask, why in other instances you presume that the same power still exists, merely upon the appearance of these [sensible] qualities?" Appeal to past experience is useless. At best it can prove that the object that was experienced to produce another had the power at that time, but it cannot be proved that the same power continues to exist in that object, much less that it exists in all other objects with similar sensible qualities. It might be objected that we experience that the powers of objects persist over time and are possessed by similar objects. But even this experience is to no avail, since the author can ask again, "Why from this experience we form any conclusion beyond those past instances, of which we have had experience?" Of course, it could be replied that we have experience that past experience applies to objects that had not yet been experienced. But this invites the same question: why is this experience relevant to other cases? The process of appeal to experience and questioning the relevance of that experience continues even in infinitum, and this "clearly proves, that the foregoing argument had no just foundation."

11. Having dispensed with the objection based on an inference from a power of production, the author takes stock of where his arguments have led. He refers to his earlier claim that "our reason fails us in the discovery of the ultimate connexion of causes and effects," and informs us that reason fails even to inform us why we should relate past experience to what has not "fallen under our observation. We suppose, but are never able to prove, that there must be a resemblance betwixt those of objects, of which we have had experience, and those which lie beyond the reach of our discovery."

12. If it is not reason which leads us beyond our experience, what is it? Here the author appeals to what he has already established (Part 1, Section 3), that there are "certain relations, which make us pass from one object to another, even tho' there be no reason to determine us to that transition." He takes it as a "general rule" that "wherever the mind constantly and uniformly makes a transition without any reason, it is influenc'd by these relations." And this is just what happens in causal reasoning. Even aided by the experience of constant conjunction in all past instances, reason cannot "show us the connexion of one object with another." When the mind makes its transition from an impression of one object to the belief in the existence of another, it is determined by "certain principles, which associate together the ideas of these objects, and unite them in the imagination." Without this principle, we could not make any causal inference, because the objects are not united by reason in the understanding. And in that case, we could not "repose belief in any matter of fact" [beyond what has been experienced].

13. The three principles of union in the imagination are resemblance, contiguity, and [necessary] connection. In each case, "the idea or impression of any object naturally introduces the idea of any other object" to which it is related in one of these ways. The three principles are not "infallible" causes fo a union among ideas, for a person might have an idea in mind for some time without having a related idea. Nor are they "sole" causes of union. This is due to the fact that thought is often quite disorderly: "The thought has evidently a very irregular motion in running along its objects, and may leap from the heavens to the earth, from one end of the creation to the other, without any certain order or method." Despite this "weakness in these three relations, and this irregularity in the imagination," the author asserts that the the three principles are the only "general" ones uniting perceptions in the imaganation.

14. It may seem that there is a fourth principle of union, but it will turn out (see the next paragraph) that this principle is the same as that of cause and effect. There are cases in which, in effect, we are conditioned by experience to form an idea. For example, upon hearing a sound which has always been attached to an object, I form the idea of that object without any intervening thought of the past experience of their constant conjunction. "The imagination of itself supplies the place of this reflection, and is so accustom'd to pass from the word to the idea, that it interposes not a moment's delay betwixt the hearing of the one, and the conception of the other."

15. This is acknowledge by the author "to be a true principle of assocation among ideas," but it is no more than the relation of cause and effect. Indeed, it is "an essential part in all our reasonings from that relation." In anticipation of a view to be developed in more detail in Section 14, the author tells us that our only notion of cause and effect is "that of certain objects, which have been always conjoin'd together, and which in all past instances have been found inseparable." The reason that this conjunction occurs is something that "we cannot penetrate." We observe a thing, and from the constant conjunction, "the objects acquire an union in the imagination." The jump from the given object to its "usual attendant" is immediate. The author claims that as a result, we can incorporate this action into the notion of a belief, that 'tis an idea related to or associated with a present perception.

14. The author now summarizes his position. As a philosophical relation, cause and effect implies priorty, contiguity, and constant conjunction. But we can reason from cause and effect only on the basis of the natural relation of cause and effect, which "produces an union among our ideas." [For the distinction between philosophical and natural relations, see Part 1, Section 5.]