"Methodological naturalism" and "metaphysical naturalism" are terms that often surface in the continuing battle between evolutionary biology and creationism/intelligent design. The methodological thesis says that scientific theories shouldn't postulate supernatural entities; the metaphysical thesis says that no such entities exist. In this debate, God is the supernatural entity at issue; the question isn't whether science gets to talk about mathematical entities if Platonism is correct.

Darwin repeatedly used the hypothesis of common ancestry as a platform on which to build his various ideas about testing hypotheses concerning natural selection. He also argued that adaptive similarities provide little or no evidence for common ancestry. Although this second claim needs to be fine-tuned, Darwin was right that ample evidence for common ancestry can exist even if none of the characteristics we observe were caused to evolve by natural selection.

Trait X is fitter than trait Y in a population of organisms if those organisms have other biological traits T and live in an environment that has properties E. The theory of natural selection is filled with statements of this form.

Our own species evolved under the influence of group selection, as Darwin emphasized when he discussed the evolution of altruism.

Evolutionary game theory was originally developed as an alternative to the hypothesis of group selection; now it is clear that game theory models postulate group selection, even if they do not use the g-word.

Earlier attempts to show that simpler theories always have higher prior probabilities have failed, but there is a restricted circumstance in which the claim is right.

Some philosophical arguments (e.g., in connection with the mind/body problem) look pretty good, while others (e.g., those that criticize moral realism) do not.