Mechanical reductionism, which deals entirely with homogeneous variables, will constrain and enable the activities of richly heterogeneous living systems, but it cannot determine their outcomes. Such indeterminism owes to problems with dimensionality, dynamical logic, intractability, and insufficiency. The order in any living structure arises via an historical series of contingencies that were selected endogenously by stable autocatalytic processes in tandem with, and usually in opposition to, conventional external influences (natural selection). The development of living communities thereby resembles a Heraclitean dialectic between processes that build up and those that tear down. Investigating this unconventional dynamic requires metaphysical assumptions that are complementary to those that have guided science over the past three centuries. The new dynamics can be represented in terms of weighted networks of interacting processes, which facilitate the statement of testable hypotheses. Network analysis thereby implements and tests ideas that heretofore could only be addressed as verbal propositions.