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This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively.

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I will present results from a novel analysis of complexity definitions. I will argue that the vast majority of complexity definitions can be interpreted as requiring di↵erent combinations of di↵erent technical embodiments of five core criteria for complexity: the three dynamical criteria of the existence of many components, determinism and indeterminism; and the two phenomenological criteria of regularity and irregularity. Furthermore, I will show thatwhile di↵erent complexity definitions require di↵erent and even exclusive combinations of these criteria-all complexity definitions require contrasting dynamical and phenomenological criteria, i.e. determinism in combination with irregularity or indeterminism in combination with irregularity. Therefore, a contrast between dynamics and phenomenology appears to constitute the conceptual heart of complexity science. I will then propose that the existence of such dyanmics-phenomenology contrasts should be used as a minimal definition of the concept of complexity. Furthermore, I will show that such contrasts constitute a kind of epistemological emergence.

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