Emergence made ontological ? Computational vs. combinatorial approaches

Abstract
This paper challenges the usual approach of emergence in terms of properties of wholes “emerging” upon properties of parts (“combinatorial approach”). I show that this approach mostly fails to face the requirement of non triviality, since it makes a whole bunch of ordinary properties emergent. As most of authors recognize, this meaning of emergence is mostly epistemological. On the contrary, by defining emergence as the incompressibility of a simulation process, we come up with an objective meaning of emergence since I argue that the difference between the processes satisfying the incompressibility criterion and the others do not depend upon our cognitive abilities. Then I show that this definition may fulfil the non triviality requirement and the scientific adequacy requirement better than the computational approach, provided that we think emergence as a predicate of processes rather than properties, and that we make use of the descriptive language of computational mechanics (Crutchfield and Hanson). Finally, I answer an objection by Epstein, concerning agent-based models, that pretends to show that in this context emergence is either impossible or trivial.
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