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The hypothesis that religious belief can, in fact, be justified by experiential evidence is commonly called "empirical theism." It is empirical because it looks for evidence in experience, and it is theistic because it believes in a personal deity. In Dialogues Concerning Natural Religion the position of empirical theism is represented by the character of Cleanthes.
At the time that Hume was writing, the argument from design was the most popular basis on which to rest a belief in empirical theism. According to the argument from design we can use the evidence of the natural world to arrive at knowledge about the nature of God in the following way: We see that the universe is like a machine insofar as it is perfectly and intricately ordered so that every part, from smallest to largest, fits harmoniously with every other part. We take note of the fact that every machine we have ever come across in our experience has been the product of intelligent design. Seeing the similarity between the universe and machines, we reason that since they are so analogous, they must certainly have analogous causes. We conclude, therefore, that the universe must also be caused by an intelligent designer. We thus arrive at knowledge about God's nature: we know that he resembles human intelligence.
Sir Isaac Newton was a proponent of the argument by design, as were many other British luminaries of Hume's day. The most famous version of the argument by design was put forward just a few years after Hume published Dialogues Concerning Natural Religion by a man named William Paley. In his book Natural Theology, Paley presents the consideration often dubbed the "Universal Watchmaker." Though Hume could not have possibly had this version of the argument in mind when he wrote Dialogues Concerning Natural Religion it is still a helpful way to better understand the argument by design. According to the "Universal Watchmaker" line of reasoning, the universe is as intricate and as finely-tuned as a watch. If we were walking through the desert and stumbled upon a watch we would never once doubt that it was created by human intelligence. No one would be so silly as to suppose that all the parts of the watch just happened to come together by chance and to function so perfectly. The same, says Paley, could be said about our universe. Our universe is like a watch in that it runs so perfectly, everything being so well adapted to our survival and happiness. To conjecture that all of this could have come together by sheer chance is as absurd as maintaining that a watch could have come together by sheer chance.
Hume takes the argument by design to be the best case available to the empirical theist and so he spends the greater part of the book attacking this argument. However, many of his objections (such as the objection from the problem of evil) work equally well against any plausible argument for empirical theism. The brunt of his message is simply that there is not enough evidence in nature to justify our drawing any substantive conclusions about the world's ultimate cause. Empirical theism in any guise, in other words, cannot be made to work.
