Naturalness and Projectibility
David Lewis offers a lot of work for natural properties in his semantics, his theory of mental content, materialism, supervenience, causation, laws of nature, etc. Strikingly missing in this list (as opposed to the list of Anthony Quinton, "Properties and Classes") is the solution of Goodman's New Riddle of Induction. I don't know why Lewis never mentions this. Two suggestions:
1) He thought it was just too obvious, and he disliked repeating arguments of other philosophers (none of the items on Quinton's list occurs on Lewis').
2) He thought the solution doesn't work. Whether it does seems to depend on the exact definition of projectibility. If at every possible world, the projectible properties are those that work in inductive inferences at our world, projectibility and naturalness could be identified. A more natural definition however would say that at every world, the projectible properties are those that work in inductive inferences at that world. And since the natural properties are the same at every world (why?), there are many worlds where induction only works with certain utterly gruesome properties.