One of the key deficiencies of the Semantic Web is its lack of cognitive plausibility. We argue that by accounting for people's reasoning mechanisms and cognitive representations, the usefulness of information coming from the Semantic Web will be enhanced. More specifically, the utilization and integration of conceptual spaces is proposed as a knowledge representation that affords two important human cognitive mechanisms, i.e., semantic similarity and concept combination. Formal conceptual space algebra serves as the basis for the Conceptual Space Markup Language (CSML), which facilitates the engineering of ontologies using a geometric framework. We demonstrate the usefulness of the approach through a concrete example and suggest directions for future work, especially the need for combining geometric representations and reasoning mechanisms with existing Semantic Web structures.