A Newtonian and mechanistic notion of physical law, hale for almost 400 years, has been weakened in the 20th Century by scientists who stumbled upon a non-deterministic quantum reality, and may be terminally ill. Stuart Kaufmann's answer to the 2009 Edge question, "What game-changing scientific ideas and developments do you expect to live to see?" makes a similar point about biological reductionism.
All of the explanatory arrows do not point downward. Key question:
Can a physical system be completely describable using physical law? For now, the answer appears to be "no," or if "yes" - yes in a way that is currently incomprehensible.