Since its application to systems, emergence has been explained in terms of levels of observation. This approach has led to confusion, contradiction, and incoherence. When the concept 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 is formally demonstrated with mathematical examples, including the nonorientable, one sided and one edged emergent properties of the Mbius strip. Emergent properties are identified as nonlocal, because of spatially or temporally extended structure. This establishes normative definitions of emergent properties and emergence, which make sense of previous descriptive definitions of emergence. The central insight that emergence is coupled to scope means that emergence is objective, in the sense that it is independent of the knowledge of the observer. This framework is then used to identify fundamental limits to our ability to capture emergence in formal systems, and propose an alternative approach towards identifying system boundaries.