Physicist P. W. Anderson wrote a seminal article on this topic (look for "More is Different" through Google). I would agree with his vision on the matter - while it is true that, fundamentally, everything follows from the interactions between the tiniest particles, it is neither useful nor feasible to try and reduce every problem to aforementioned tiny particles.
Originally posted by wittywonka Is there such a thing as an emergent property? Or can all physical phenomena in the universe be explained simply by chemical/physical/mathematical reduction?
As KazetNagorra says, the answer is both. There are such things as emergent properties, but they can be explained by simple chemical / physical / mathematical reduction.
So waves on the ocean exist, and are a property of the sea, but we could explain them using the motions and interactions of the individual water molecules, gravity, and possibly the air molecules that create them in the first place. But the emergent property of waves, may have similarities to some other system whose underlying physical basis is completely different. So for example light waves do not involve particles moving in the same form as water waves yet the two exhibit properties of waves that can usefully be compared.