Physical emergence, diachronic and synchronic

This paper explicates two notions of emergence which are based on two ways of distinguishing levels of properties for dynamical systems. Once the levels are defined, the strategies of characterizing the relation of higher level to lower level properties as diachronic and synchronic emergence are the same. In each case, the higher level properties are said to be emergent if they are 'novel' or 'irreducible' with respect to the lower level properties. Novelty and irreducibility are given precise meanings in terms of the effects that the change of a bifurcation or perturbation parameter in the system has. (The same strategy can be applied to other ways of separating levels of properties, like the micro/macro distinction.) The notions of emergence developed here are notions of emergence in a weak sense: the higher level emergent properties we capture are always structural properties (or are realized in such properties), that is, they are defined in terms of the lower level properties and their relations. Diachronic and synchronic emergent properties are distinctions within the category of structural properties.