  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.
