This paper analyses an experiment which studies the acquisition of the linguistic competence required to communicate logical combinations of categories from the wisdom of the crowds perspective. The acquisition of such competence encompasses both the construction of a set of logical categories by each individual agent and of a shared language by the population. The processes of conceptualisation and language acquisition in each individual agent are based on general purpose cognitive capacities such as discrimination, invention, adoption and induction. The construction of a shared language by the population is achieved using a particular type of linguistic interaction, known as the evaluation game, which gives rise to a shared language system of logical constructions as a result of a process of self-organisation of the individual agents’ interactions, when these agents adapt their languages to the expressions they observe are used more often by other agents.