Emergence is coupled to scope, not level

Since its application to systems, emergence has been explained in terms of levels of observation. This approach has led to confusion, contradiction, incoherence and at times mysticism. When the idea of level is replaced by a framework of scope, resolution and state, this confusion is dissolved. We find that emergent properties are determined by the relationship between the scope of macrostate and microstate descriptions. This establishes a normative definition of emergent properties and emergence that makes sense of previous descriptive definitions of emergence. In particular, this framework sheds light on which classes of emergent properties are epistemic and which are ontological, and identifies fundamental limits to our ability to capture emergence in formal systems.