The term emergence, or irreducibility, has been used in a great variety of senses over the years, and different senses are useful in different discursive contexts. In this paper the focus is on one specific context, that of methodologically oriented social theory, and the question to answer is, what might be the most useful sense(s) of emergent irreducibility in that field? To answer that question, key intuitions of emergence are first abstracted from the concept’s history. Three main senses of the term are distinguished based on those different intuitions. Then the likely linguistic functions of emergence in each of those main senses are gauged in social theory and methodology. It is argued that one of the senses – here called “contingently epistemological irreducibility” – is in fact more useful as regards social scientific methodology than the others.