The conversation between Demea, Cleanthes, and Philo begins with a question concerning education: when is it best to begin teaching students theology? Demea argues that theology should only be taught to a mature mind: a student should first study logic, ethics, and physics, and only then should they turn to theology. He has two reasons for preferring this order. First, by studying the other disciples first, the mind is trained and readied for the most difficult subject of all, theology. Second, and more to the point of the Dialogues, he wants his students to first see how very limited philosophy really is. He wants them to see, for instance, that learned men can rarely reach firm conclusions amongst themselves, and that the wisest often come up with the most absurd hypotheses. By revealing the limits of philosophy to his students, Demea believes that he ensures that they will not be so arrogant as to think that they can use reason to overthrow religious beliefs.
Demea's second motivation sounds a great deal like a fideist position. Philo picks up on this fideist strain and expands upon it. He stresses just how weak and limited human reason really is, and also the importance of this realization (i.e. of reason's limits) for piety. Given how frail human reason is, he contends, it is ill-advised to try to apply it to matters as difficult and important as theology.
Cleanthes, of course, is appalled that his two friends are proposing to rest religious faith on philosophical skepticism rather than on reason. He spends the rest of the chapter trying to expose Philo's skepticism as insincere. Philo responds by continually revising his skeptical position into more and more subtle forms. Initially, it sounds as if Philo is claiming that we cannot really believe anything. Cleanthes asks, then, whether he will leave by the door or by the window when they finish their discussion: that is, is he skeptical enough about the laws of gravity that he will leap several stories?
Philo tells Cleanthes that he has mischaracterized his skeptical position: Philo does believe what his reason tells him to believe, but he proportions his belief to the evidence. In areas where we have a great deal of experience, and thus much evidence on which to base our conclusions (areas such as everyday life, morals, politics, trade, jumping out of windows), Philo explains, we can believe strongly in our conclusions. But when it comes to those subjects about which we have no direct experience, such as the formation of the world, or the nature of God, we have no basis on which to rationally justify any of our conclusions. Instead of a very radical claim that we cannot believe anything, Philo is actually making the much more modest claim that we should only believe what we have good evidence to believe, and that we only have good evidence in those areas of knowledge where we have direct experience.
Cleanthes, though, is not satisfied with this modest skeptical claim. He points out that Philo and his skeptical colleagues seem to have no trouble drawing conclusions when it comes to the speculative sciences. For instance, they seem to trust in the conclusions drawn by Newton, Copernicus, and Galileo even though these concern topics very remote from our everyday experience. It is pure prejudice, he declares, that prevents them from allowing the same method of reasoning in theology. If human reason is good enough to justify theoretical scientific theories, in other words, it is good enough to justify theological theories. He concludes by asserting that there is really no difference between a skeptic and an atheist.
Philo defends himself against the claim of atheism, affirming his strong belief in God's existence. However, he points out that religious institutions actually seem to go back and forth in their opinion of skepticism: they embrace skepticism whenever reason seems to threaten their power, and they embrace reason when it becomes the only way to keep their influence.
Philo's brand of philosophical skepticism is immediately familiar to readers of Hume's other works, in particular readers of the Treatise on Human Nature and the Enquiry Concerning Human Understanding. Hume was continually interested in showing that we are not justified in believing something that we thought we were justified in believing; and he often shows that our beliefs are irrational by showing that we have no experience of the relevant kind.
Even if you are not familiar with Hume's other works, it helps to have some familiarity with his other skeptical arguments in order to better understand his position in the Dialogue. The most famous of his skeptical arguments is his argument concerning causal reasoning. In the Treatise and the Enquiry he argues that we cannot rationally justify the inductive inferences we make from observed events to those that are unobserved—that is, no matter how many times we see A followed by B, this evidence will never show us that B will continue to follow A in the future. To give one of his more famous examples, no matter how many times we see the sun rise in the morning (presumably, many, many times) we never attain rational justification for believing that it will rise the following morning. This does not mean that we should not believe that the sun will rise. We should do so, and in fact, if we do not believe this we are unwise. The point is only that we are not rationally justified in believing it.
Why are we not rationally justified in believing that the sun will rise tomorrow? We would have to be justified either through our use of reason or through experience (since these are the only faculties available to us for coming to know things). Reason does not prove that the sun will continue to rise tomorrow, because according to Hume, reason can only prove something by showing that to deny it leads to contradiction (and thus reason cannot be used to prove any matters of fact), and there is no logical contradiction in the statement, "the sun will not rise tomorrow." Experience cannot justify this belief either, though, because all that we have ever experienced is what has happened in the past. In order to infer anything about the future from what we have observed about the past, we would have to know that there is some eternal law that the future tends to resemble the past. But we cannot know that this is true, because we could only justify believing in this law through experience or through reason. We cannot know it through reason because, once again, there is no contradiction in the statement, "the future will not resemble the past." We cannot know it through experience, because in order to get this law from experience, we would need this very law, and the argument would be circular.
Hume's argument that we cannot reason from induction reveals a lot about Philo's position. First of all, it shows us that Philo is not afraid to turn his skeptical eye on even the most everyday sort of conclusions. Second, it shows us the positions that are at work behind Philo's skepticism. Philo believes that there are only two ways to obtain rational justification for a belief: a priori (through the use of pure reason, unaided by any specific experience), and a posteriori (through investigating the world and reasoning from observed phenomena to unobserved phenomena). He believes that a priori reasoning cannot yield any knowledge concerning matters of fact because a priori reasoning only reveals conceptual truths whose opposite involves a contradiction. Philo thus believes that only a posteriori reason can justify any matters of fact, such as truths of science, or morality, or of theology. Whenever he is skeptical, then, it will be because he does not think that experience affords us enough evidence. This is why he tells Cleanthes that a person should be least skeptical when it comes to the areas in which he has the most direct experience (morals, politics, trade) and the most skeptical when it comes to areas where he has no direct experience (such as theology).
Cleanthes responds to this assertion by pointing out that Philo believes in the conclusions of theoretical science. Philo does not directly responds to this objection. Given the background knowledge concerning Hume's other skeptical argument, it is interesting to try to figure out what Philo's response to this objection might have been. He might simply have said that there is a great deal more experiential evidence when it comes to judgments of theoretical science, than when it comes to judgments of theology. After all, Newton, Galileo, and Copernicus did not simply think up their theories out of thin air; they based their theories on careful observation, and tried to confirm their theories with accurate predictions. The strength of a scientific theory, in fact, is determined by how well the theory fits the evidence we find in experience.
Philo does make this very comparison between the relative experiential evidence in the case of science and theology later in the book, but he does not make it here, and we can only wonder why. Perhaps Hume does not really think that these scientific theories are rationally justified, strictly speaking. After all, they are all based on a form of reasoning that he has cast into doubt (i.e. inferring unobserved phenomena from observed). To launch into his subtle skepticism regarding these scientific theories, though, would only needlessly complicate matters and draw attention away from the topic at hand—that is, the question of whether religious beliefs can be rationally justified. This might be why Hume chose not to let Philo respond to this question at all: to reply without giving his full opinion would be intellectually dishonest; to reply and give his full opinion would get us far from the main point of the dialogue.