David Hume's great book, Dialogues Concerning Natural Religion, is a fictional report, by Pamphilus to Hermippus, of a conversation of his tutor, Cleanthes, with Demea and Philo on matters pertaining to religion. The main subject is a certain argument, a teleological argument, for the existence of God. Hume's masterfully orchestrated examination of this argument ends with a long rhetorical question and summing up by Philo, who holds that far less than Cleanthes sought can be concluded from facts of apparent design in nature, but that some sort of designer-deity, albeit not a humanly relevant one, can be reasonably inferred. Demea withdraws from the conversation after Philo has drawn it through facts of apparently unnecessary evil and before Cleanthes and Philo have given final statements of their positions, which agree on some points and disagree on others.

Section 1 to follow states the argument, considers its character, and compares it with cosmological arguments. Section 2 dispatches a certain radical objection to the argument and notes several factors relevant to its assessment. Precise Bayesian explications of these factors are developed in Sections 3 and 4.