The scientific mind holds it as self-evident that all natural phenomena are bound by the laws of nature. We study such laws in physics and express them in the language of mathematics. The idea that all natural phenomena are also reducible to a sum of their parts, that micro components (iteratively down to sub-atomic particles) both describe and predict macro behavior, is called reductionism. Introduced by Descartes, its current proponents include Dennett, Dawkins, and Pinker.
The idea that reductionism has limits, particularly for highly complex systems like the biosphere and human culture (a wholly natural phenomenon), has also been around since at least Aristotle ("the whole is more than a sum of its parts"). Emergentism, as this hypothesis is called (or holism), claims that the fundamental laws of nature eventually run out of descriptive and predictive steam—not due to the inadequacy of our science but due to irreducible and unpredictable properties inherent in complex systems. Both reductionism and emergentism remain epistemological (as opposed to scientific) claims, though reductionism can boast of some inductive success on the verification front.
Stuart Kauffman, a scientist at the forefront of the idea of emergence, has written a new book, Reinventing the Sacred: A New View of Science, Reason and Religion, where he fleshes out this concept in more detail. Here is a brief excerpt:
Emergence is therefore a major part of the new scientiﬁc worldview. Emergence says that, while no laws of physics are violated, life in the biosphere, the evolution of the biosphere, the fullness of our human historicity, and our practical everyday worlds are also real, are not reducible to physics nor explicable from it, and are central to our lives. Emergence, already both contentious and transformative, is but one part of the new scientiﬁc worldview I embrace.
Even deeper than emergence and its challenge to reductionism in this new scientific worldview is what I call breaking the Galilean spell. Galileo rolled balls down incline planes and showed that the distance traveled varied as the square of the time elapsed. From this he obtained a universal law of motion. Newton followed with his Principia, setting the stage for all of modern science. With these triumphs, the Western world came to the view that all that happens in the universe is governed by natural law. Indeed, this is the heart of reductionism. Another Nobel laureate physicist, Murray Gell-Mann, has deﬁned a natural law as a compressed description, available beforehand, of the regularities of a phenomenon. The Galilean spell that has driven so much science is the faith that all aspects of the natural world can be described by such laws. Perhaps my most radical scientific claim is that we can and must break the Galilean spell. Evolution of the biosphere, human economic life, and human history are partially indescribable by natural law. This claim ﬂies in the face of our settled convictions since Galileo, Newton, and the Enlightenment.