On many episodes we've mentioned in passing, or given some author's criticism of, the classic arguments for the existence of God:
-The cosmological argument, which deduces from the fact that everything has a cause (or everything is contingent, or everything moves... there are several variations of this) that there must be a first cause, i.e. God. This argument dates at least back to Aristotle but was given its most famous formulations by Thomas Aquinas.
-The teleological argument, or argument from design, which says that since nature looks designed (i.e. uniformity, complicated structures that achieve impressive results), there must be a designer, i.e. God. This was given its most famous formulation in William Paley's metaphor about finding a watch on the beach: of course, we'd assume that had a designer.
We'd planned an episode on these arguments from the very beginning of the podcast, but merely reading the source materials linked above would take us about 10 minutes. Well, we found (recommended in both theist and atheist sources) a book that does a pretty exhaustive job analyzing these major arguments: J.L. Mackie'sThe Miracle of Theism: Arguments For and Against the Existence of God
Mackie (who worked at Oxford and died before this book was published) provides substantial chunks of Descartes, Hume, Aquinas, Leibniz, Kierkegaard, Pascal, James, and others, and systematically goes through all the possible points of weakness and the responses available to defend the arguments.
A key point of value in the book is bringing it up to the modern era: his chief opponent is Richard Swinburne (also at Oxford, and still publishing into the 2000's), who takes a very rationalist approach to religion, seeing his existence as a scientifically respectable theory that explains the world better than the alternatives. Mackie, too, has written in philosophy of science, and his critiques, e.g. of miracles show a lot of subtlety in that respect.
We read chapters 1-3, 5-6, 8, and 11. Buy the book
Note that we even had an actual theist in on this discussion: Robert from Cape Town, aka Kid Charlemagne.