The entire refutation of the principle of Cause and Effect is contained in a single paragraph in Section III of Part II of Book I. Hume considers the "general maxim in philosophy," that "whatever begins to exist, must have a cause of existence." I think he is justified in claiming that all of traditional metaphysics, theology, and natural science rests on this principle. Here is the paragraph, from start to finish:
"But here is an argument, which proves at once, that the foregoing proposition is neither intuitively nor demonstratively certain. We can never demonstrate the necessity of a cause for every new existence, or new modification of existence, without shewing at the same time the impossibility there is, that any thing can ever begin to exist without some productive principle: and where the latter proposition cannot be prov'd, we must despair of ever being able to prove the former. Now that the latter proposition is utterly incapable of a demonstrative proof, we may satisfy ourselves by considering, that as all distinct ideas are separable from each other, and as the ideas of cause and effect are evidently distinct, 'twill be easy for us to conceive any object to be non-existent this moment, and existent the next, without conjoining to it the distinct idea of a cause or productive principle. The separation, therefore, of the idea of a cause from that of a beginning of existence, is plainly possible for the imagination; and consequently the actual separation of these objects is so far possible, that it implies no contradiction nor absurdity; and is therefore incapable of being refuted by any reasoning from mere ideas; without which 'tis impossible to demonstrate the necessity of a cause."
And with those two hundred and thirteen words, Hume puts paid to all previous philosophy and science. It is not surprising that Kant was, as he said, awakened from his dogmatic slumbers by this savage attack. There were, in the tradition, a number of silly arguments [put forward by some very serious people] in support of the Causal Maxim, and Hume has a bit of fun batting them away. One is that if something does not have a cause, then it must have produced itself, which is impossible [save for God, of course]. Another is that if something does not have a cause, then it must have been produced by nothing, and as we know [although Hume does not add this], ex nihilo nihil fit. " 'Tis sufficient to observe," Hume replies, "that when we exclude all causes we really do exclude them, and neither suppose nothing nor the object itself to be the causes of existence." These arguments actually are good examples of that oft-misused phrase, "begging the question."
There is another possible objection that Hume does not discuss at this point in the text, though he does elsewhere. It might be said that science does not assert absolute necessities, but only probabilities, that scientific reasoning is inductive, not deductive, and hence that Hume's refutation, though certainly telling against anyone who is so unwise as to assert causal judgments in the explanation of nature with the absolute certainty of logic, leaves quite untouched the sorts of scientific explanations that appeal to well-confirmed generalizations, for all that they may fall short of the certainty of syllogistic reasoning. The difficulty with this defense of causal inference, as Hume quite well understands, and as I think we all now recognize, is that it rests on the equally indemonstrable assumption of the Uniformity of Nature. All causal reasoning, Hume will argue in the sections following the present one, takes the form of observing patterns in our experience and then projecting them forward in time or outward in space, leading us to conclude that the portions of the world we have not observed are, in the relevant ways, like the portions we have observed. But induction from present instances to conclusions about the world in general is no better grounded than deduction. Since it is quite easy to imagine that some region of space or time not yet encountered should exhibit different patterns from those already experienced, it "is so far possible, that it implies no contradiction nor absurdity." There simply is no rational ground, Hume insists, for the beliefs that constitute the warp and woof of our conception of the world in which we live.
As often happens in our reading of Hume, his most powerful arguments go by so quickly, with so little sign of stress and strain and heavy lifting, that it is easy for us to overlook just how devastating they are. If Hume is correct, then entire libraries of ancient, medieval, and early modern philosophy must simply be discarded, along with the revolutionary natural science of Galileo, Kepler, Newton, and their contemporaries, not to speak of the corpus of Hebrew, Muslim, and Christian rational theology that was the glory of the Middle Ages. Those of you who followed my Introduction to the Critique of Pure Reason can now see, I think, why Kant concluded that a reply to Hume required the heroic embrace of the proposition that the entire experienced world is merely things as they appear to us, rather than things as they are in themselves.
And yet. And yet. We do believe. No normal, sane, functioning person can actually go through life not believing that events have causes. One cannot even play a game of billiards unless one believes that the striking of one ball by a second causes the first to move. So Hume now pivots from his sceptical attack on the claims of philosophers and scientists, and undertakes to explain our belief in causal judgments, using in his explanations a variety of causal judgments about the workings of the mind and its responses to experience. Norman Kemp-Smith, in his classic 1941 study The Philosophy of David Hume, describes Hume as advancing a theory of "natural belief." It is essentially a psychological account of how beliefs are generated in us, and Hume is quite clear that this account is not intended somehow to invalidate the previous sceptical line of attack. As we shall see, most of the original and exciting doctrines of Book I of the Treatise concern the ways in which the mind constructs a conception of a world of causally connected objects. It was this account, when I first encountered it, that reminded me so powerfully of the theory of a priori synthesis in Kant's First Critique.
In the very last section of Book I, some 190 pages beyond the passages we have just been discussing, Hume writes a passage that is, to my ear, poignant and very touching. Having raised powerful and telling objections to all of the principles on which previous philosophy and science rested, Hume draws back from the abyss he has himself opened up.
"Most fortunately it happens," he says, "that since reason is incapable of dispelling these clouds, nature herself suffices to that purpose, and cures me of this philosophical melancholy and delirium, either by relaxing this bent of mind, or by some avocation, and lively impression of my senses, which obliterate all these chimeras. I dine, I play a game of back-gammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I wou'd return to these speculations, they appear so cold, so strain'd. and ridiculous, that I cannot find in my heart to enter into them any farther."