- The Evidential Argument from Scale: compares naturalism to theism conjoined with various auxiliary hypotheses about God’s potential reasons for giving or not giving humans a privileged position in the universe.
- The Evidential Argument from the Flourishing and Languishing of Sentient Beings: compares naturalism conjoined with Darwnism to theism conjoined with Darwinism
- The Evidential Argument from the Self-Centeredness and Limited Altruism of Human Beings: compares naturalism conjoined with Darwnism to theism conjoined with Darwinism
- The (Evidential) Fine-Tuning Argument: compares theism to naturalism conjoined with the multiverse hypothesis
In the explanatory argument schema described above, it may be possible to defeat premise (3) by showing that an auxiliary hypothesis is evidentially significant in the relevant way, i.e., that A sufficiently raises Pr(F | H1) or lowers Pr(F | H2). In order to assess the evidential significance of such hypotheses, we would need to apply the theorem of the probability calculus known as the theorem of total probability.
One way to show that H2 has a higher final probability than H1 is to show that the ratio of each multiplicand on the right-hand side of Bayes’s Theorem in its compound odds form is also less than 1, i.e.,
This enables us to define the following schema for cumulative case arguments.
 I owe this schema to Paul Draper.
 Draper 1989.
 Draper 1989.