The work of Boden on the nature of creativity has been extremely influential, particularly the hypothesis that the highest form of creativity results from transformation of a conceptual space. We consider how these ideas could be made more precise, and hence become amenable to empirical testing. This requires some reconsideration of foundational assumptions about computational ty. We set down the abstract requirements for a conceptual space, review some possible types of formal model, and discuss how it might be possible experimentally to falsify (or corroborate) this hypothesis. We conclude that the central terms (conceptual space, transformation) are still too vaguely defined to support falsifiable claims, but that this is not an obstacle to writing creative computer programs. Keywords Transformational Creativity, Conceptual Space, Exploratory Creativity, Computational Creativity.