In the middle of the twentieth century, Wittgenstein warned that "the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws…leads…into complete darkness" (1958, p. 18). At the time, few philosophers and even fewer scientists were prepared to heed his warning. A half-century later, however, the reductive method of science—the method famously defined by Descartes, brilliantly exemplified by Newtonian physics, and long upheld as the gold standard of scientific explanation—seems to have finally lost its luster. While reduction is still widely defended, in the last decades alternative views have gained credibility, to the extent that a "non-reductive science" is no longer dismissed as an oxymoron.