Consilience in Causation: Causal Emergence Is Found Across Measures of Causation.

Causation is fundamentally important to science, and yet our understanding of causation is spread out across disparate fields, with different measures of causation having been proposed in philosophy, statistics, psychology, and other areas. Here we examined over a dozen popular measures of causation, all independently developed and widely used, originating in different fields. We identify a high degree of consilience, in that measures are often very similar, or indeed often rediscovered. This is because, we show, measures of causation are based on a small set of related "causal primitives": sufficiency and necessity, or alternatively, determinism and degeneracy. These primitives are ways of capturing the degree of uncertainty inherent in causal relationships. In turn, these results help us understand the phenomenon whereby macroscales can reduce the uncertainty in causal relationships, leading to stronger causes at macroscales-an outcome known as "causal emergence". First identified using the effective information and later the integrated information in model systems, causal emergence has been found in real data across the sciences since. But is it simply a quirk of these original measures? Using a simple model system, we demonstrate how the consilience of causation guarantees that causal emergence is commonly found in causal measures, identifying instances across all measures analyzed. This finding sets the mathematical understanding of emergence on firmer ground, opening the door for the detection of natural scales of causal interaction in complex systems, as well as assisting with scientific modeling and experimental interventions.