Ontology, reduction, emergence: A general frame

In a scientific context, ontological commitments should be considered as supervenient over accepted scientific theories. This implies that the primarily ontological notions of reduction and emergence of entities of different kinds should be reformulated in terms of relations between existing empirical theories. For this, in turn, it is most convenient to employ a model-theoretic view of scientific theories: the identity criterion of a scientific theory is essentially given by a class of models. Accordingly, reduction and emergence are to be seen as particular kinds of relations between (some) models of different theories that subsume the same (or a similar) “experiential field”. The set-theoretical notion of an echelon-set proves to be crucial for this purpose: The domains in the models of the reduced theory are echelon-sets over the domains of the reducing theory. Finally, it is argued that emergence may plausibly be interpreted as akin to but weaker than reduction.