> Context . Realism has difficulty using the language of mind-independent dynamics to explicate autonomous cognition. Constructivism has difficulty locating the purposive originator of adaptive cognitive reconstruction. Enactivism derives purpose from self-maintaining dynamics, but has difficulty describing how the autopoietic subject emerges. > Problem . We seek to resolve these difficulties by asking: What kind of dynamically embodied system could ever be autonomous in the sense of being the causally accountable originator of its own purposeful, yet spontaneous, cognitive constructions? >Method . We identify causal accountability as the key obstacle to naturalizing autonomy, and employ a multi-level selection argument from evolutionary theory to overcome it. We demonstrate the feasibility of our solution in a computer simulation model. > Results . Our argument leads us to postulate the Stabilization Thesis: Autonomy, learning, evolution and life are expected properties of dynamical systems whose structure upwardly conditions their dynamical flow, and whose flow downwardly selects their structural variation. Such systems exhibit stabilization - the spontaneous, purposeful construction of hierarchical modularity. This generates three claims: no pre-programmed behavior, architecture or learning rules can implement autonomy; autonomy entails non-local flows that establish identity by downwardly stabilizing its structure against exogenous irritations; constructivism's postulate of a cognizing subject entails a view of concepts as fundamentally dynamical skills (as opposed to categories).