Humans and other animals are able not only to coordinate their actions with their current sensorimotor state, but also to imagine, plan and act in view of the future, and to realize distal goals. In this paper we discuss whether or not their future-oriented conducts imply (future-oriented) representations. We illustrate the role played by anticipatory mechanisms in natural and artificial agents, and we propose a notion of representation that is grounded in the agent's predictive capabilities. Therefore, we argue that the ability that characterizes and defines a true cognitive mind, as opposed to a merely adaptive system, is that of building representations of the non-existent, of what is not currently (yet) true or perceivable, of what is desired. A real mental activity begins when the organism is able to endogenously (i.e. not as the consequence of current perceptual stimuli) produce an internal representation of the world in order to select and guide its conduct goal-directed: the mind serves to coordinate with the future.