Contemporary dynamic theories of cognition and functional theories of linguistics fall into two general camps: "traditional" and "emergent" approaches. Building on work of the linguist Paul Hopper, I identify four characteristics of emergent phenomena: feedback properties; sociohistorical embeddedness; language and language-like "structures"; and what I call "recursivity," the feedback-based presence of system-analytic elements within the cognitive systems they seem to explain. This latter feature, especially, raises questions about whether "emergence" is a phenomenon, a theory, an approach, etc. I suggest that emergence offers at least a refreshingly ordinary framework for theories of empirical cognition, which nevertheless flow to the "deep" levels claimed by rule-based cognitive explanations.