Weak Emergence, Ontological Hierarchies, and Computational Equivalence

This paper examines the implications of Bedau’s notion of weak emergence when combined with both a hierarchical ontological model and Wolfram’s principle of computational equivalence. I argue that if a system exhibits weak emergence, the very fact of weak emergence of some of its states must itself be a weakly emergent state. Interpreted through Wolfram’s principle of computational equivalence, this implies that a system with weakly emergent states would need to ‘decide’ whether its own dynamical trajectories are incompressible—which contradicts with the formal undecidability of the incompressibility predicate. I term this aporetic conclusion the paradox of weak emergence. After evaluating possible responses, I contend that Bedau’s approach exemplifies what I call the derivational account of metaphysical relations, a framework that I will show to be highly problematic insofar as it implies a mismatch between the intrinsic limitations of formal derivations and the explanatory ambitions of metaphysical notions.