1. There is a non-zero probability that Naturalism is necessarily false.
2. With respect to the data of good and evil, any overall advantage in accuracy that naturalism has over theism is relatively small.
3. With respect to other data, theism is much more accurate than naturalism.
4. Any other epistemic advantage that theism has over naturalism is relatively large and significant.
CONCLUSION: Therefore, Naturalism is very probably false.
For a defense of premise 1, see my post titled: Who Bears the Burden of Proof?
For a defense of premise 2, see my posts titled: Flourishing and Languishing of Sentient Beings, Evolution is Antecedently More Probable on Naturalism, Pain and Pleasure, and Limited Altruism, and Limited Moral and Religious Knowledge, and the Systematic Lack of Any Discernable Moral Ends.
For a defense of premise 3, see my post titled: The Fallacy of Understated Evidence.
For a defense of premise 4, see the article attached below by Paul Draper, and my post titled: An Emergent Case for Theism
The CONCLUSION is a bit tricky. Theism is just one of the ways in which naturalism can be false. Thus, the falsity of naturalism must be at least as probable as the truth of theism. But then it does follow that if theism is much more probable than naturalism, then naturalism is very probably false.