Critical discussions can often require conceptual engineering, a process in which speakers are engaged in revising each other’s concepts. We show that the analysis of conceptual engineering can benefit from integrating argumentation theory with models of conceptual representation. Argumentation theory accounts for the argumentative moves of the discussants, allowing the detection of speakers’ conceptual disagreements, for which some fallacies can be seen as cues. Models of conceptual representation, such as Conceptual spaces and the theory of meeting of minds, allow us (...) to study the cognitive side of engineering practices. However, when this integrated framework is applied to practical scenarios, conceptual engineering faces different challenges. In particular, assuming a psychological view about concepts, revisionary strategies are significantly narrowed down, if not impossible, in practice. These criticisms lead to a kind of dilemma for conceptual engineers, highlighting the necessity of further work on the definition of concept embraced by this research program. (shrink)