Entailment of Ambiguity

AbstractEverything in Rosen's work flows from the principle of ‘closure to efficient cause’, the necessary and sufficient distinguishing feature of complexity, and a necessary distinguishing feature of an organism. Some students of Rosen find considerable confusion over the meaning of ‘closure to efficient cause’. Such confusion is unnecessary. The matter is entirely cleared up by the (M,R)‐system, a set of three algebraic maps. Each map must include one of the others in its co‐domain, and is itself in the co‐domain of the remaining map. Structurally, the three maps form a circular hierarchy of containment. This peculiar structure is Rosen's closure. Since each map represents an efficient cause, they reveal the character of efficient cause. The efficient cause of a process is represented as its ‘dynamical law’, and is a constraint that arises from the intersection of the morphology of the process and the inherent constraints in reality represented by the ‘laws of Nature’.A critical, observable property (evidently unnoticed by Rosen), entailed by the closure, is its inherent ambiguity. From a foundation of ambiguity, the bizarre properties of complexity (e.g., non‐computability, non‐fractionability, undecidability, and incompleteness) follow in a straightforward manner, often with proofs simpler than those that Rosen discovered.