Another way to test hypotheses about adaptation is to consider trait variation across a group of species instead of focusing on the trait of a single species. Rather than seeking to explain why polar bears have fur of a certain thickness, one tries to explain why bears in colder climates have thicker fur than bears in warmer climates. The former problem is hard to solve, since it is hard to say exactly what fur thickness polar bears should have if natural selection guided the evolution of that trait.

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.

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.

One influential philosophical position about the use of probability in science holds that probabilities are objective only if they are based on micro-physics; all other probabilities should be interpreted subjectively, as merely revealing our ignorance about physical details. I have argued against this position, contending that the objectivity of micro-physical probabilities entails the objectivity of macro-probabilities.

Evolutionary biologists often appeal to parsimony when they seek to explain why organisms "match" with respect to a given trait. For example, why do almost all the organisms that are alive today on our planet use the same genetic code? If they share a common ancestor, the code could have evolved just once and then been inherited from the most recent common ancestor that present organisms share. On the other hand, if organisms in different species share no common ancestors, the code must have evolved repeatedly.

The big picture, I think, is that common ancestry is evidentially prior to natural selection in Darwin's theory and in contemporary evolutionary biology as well.

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.