The indispensability argument says (roughly) that if you have ample reason to accept an empirical scientific theory that makes indispensable use of mathematics, and that theory entails that numbers exist, then you have ample reason to accept that numbers exist. The argument affirms the antecedent of this conditional, and concludes that you have ample reason to believe that numbers exist. What is striking about this argument is that it seems to show that the empirical reasons that suffice for accepting a scientific theory also suffice for accepting a metaphysical claim.

Darwin and his successors have railed against the fallacy of confusing the current utility of a trait with the reason the trait evolved. For example, Darwin argued that skull sutures in mammals did not evolve because they facilitate live birth; the sutures were in place well before live birth evolved. Checking the chronological order in which different traits evolved in a lineage is one way to test an adaptive hypothesis; the fact of common ancestry is what makes that checking possible.

I think that the existence of Beethoven is remarkable, but I do not bristle at the suggestion that this event had a low probability given the initial state of the universe.

The indispensability argument seeks to assimilate the epistemology of metaphysical statements to the epistemology of statements that are obviously empirical. I think it fails to achieve this goal. The argument does not refute the Carnapian thesis that scientific theories and metaphysical claims differ epistemologically - observations can provide evidence for the former, but not for the latter.

Methodological naturalism gives advice to scientists about what they should include in their theories. There is a second type of methodological naturalism that gives advice to philosophers, which I call "methodological naturalismp." It says that the methods that philosophers should use in assessing philosophical theories are limited to the methods that scientists ought to use in assessing scientific theories.

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.

Creationists have long held that evolutionary theory is atheistic; defenders of the theory do the theory no favor when they agree.