How to achieve shared meaning is a significant issue when more than one intelligent agent is involved in the same domain. We define the task of concept convergence, by which intelligent agents can achieve a shared, agreed-upon meaning of a concept (restricted to empirical domains). For this purpose we present a framework that, integrating computational argumentation and inductive concept learning, allows a pair of agents to (1) learn a concept in an empirical domain, (2) argue about the concept's meaning, and (3) reach a shared agreed-upon concept definition. We apply this framework to marine sponges, a biological domain where the actual definitions of concepts such as orders, families and species are currently open to discussion. An experimental evaluation on marine sponges shows that concept convergence is achieved, within a reasonable number of interchanged arguments, and reaching short and accurate definitions (with respect to precision and recall).