The conceptual modelling community has no clear, agreed semantics for its models; or more plainly, there is no general agreement on what the models model. One mainstream proposal is that they model concepts, but there is no clear semantics for this; no clear description of what concepts are and how they relate to their domain. This creates theoretical problems; for example, it is difficult to build accurate meta-models, as these have to encompass the semantic structure. It also creates practical problems; practitioners will approach building a model of the concept of a business differently from modelling the business itself. We aim to exploit research undertaken in philosophy to construct a framework that classifies the broad semantic options. Using this we identify two major options: concept-mediated and direct-domain semantics. We focus on the concept-mediated option and examine how philosophy has analysed what a concept is; identifying three main options and exploring the issues they raise. While not wishing to advocate choices at this stage, we note that the concept-mediated view - in particular, the version prevalent in conceptual modelling, that concepts are representations – faces serious challenges as a practical semantics for modelling and languages.