Contemporary complexity theory has been instrumental in providing novel rigorous definitions for some classic philosophical concepts, including emergence. In an attempt to provide an account of emergence that is consistent with complexity and dynamical systems theory, several authors have turned to the notion of constraints on state transitions. Drawing on complexity theory directly, this paper builds on those accounts, further developing the constraint-based interpretation of emergence and arguing that such accounts recover many of the features of more traditional accounts. We show that the constraint-based account of emergence also leads naturally into a meaningful definition of self-organization, another concept that has received increasing attention recently. Along the way, we distinguish between order and organization, two concepts which are frequently conflated. Finally, we consider possibilities for future research in the philosophy of complex systems, as well as applications of the distinctions made in this paper.
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