In terms of thermodynamics, the economy cannot be circular. As a human activity, the economy is inherently entropic and the term “circular economy” is close to an oxymoron. Yet, the circular economy seems to be here to stay as a concept in European economic policies and the interconnected worlds of policy, enterprise and science. The aim of this chapter is to move beyond the logical status of concepts such as the circular economy, sustainable growth or humane warfare and ask: If the concept is here to stay, can we fill it with meaningful content? Can there be a responsible narrative of the circular economy that inspires and gives momentum to the sustainability transition while respecting the thermodynamic impossibilities? Inspiration is drawn from a recent initiative by the European Environment Agency of creating “narratives for change” that gives hope for a good future without denying the many painful trade-offs that lie ahead. Irresponsible narratives of the circular economy would be those that either gloss over the stark realities or that prescribe the chasing of impossible goals. A responsible narrative of the circular economy would have to expand the measure of “circularity” beyond material flows and also in terms of the integrity of the biosphere that supports our economic activity.