Forthcoming in The Oxford Handbook of the Philosophy of Science, edited by Paul Humphreys.
Complexity theory attempts to explain, at the most general possible level, the interesting behaviors of complex systems. Two such behaviors are the emergence of simple or stable high-level behavior from relatively complex low-level behavior, and the emergence of sophisticated high-level behavior from relatively simple low-level behavior; they are often found nested in the same system.
Concerning the emergence of simplicity, this essay examines Herbert Simon's explanation from near-decomposability and a stochastic explanation that generalizes the approach of statistical physics. A more general notion of an abstract difference-making structure is introduced with examples, and a discussion of evolvability follows.
Concerning the emergence of sophistication, this essay focuses on, first, the energetics approach associated with dissipative structures and the
fourth law of thermodynamics, and second, the notion of a
complex adaptive system.