There is a certain tendency to consider that, whereas approaches based on artificial life may be appropriate for lower-level cognition, the computational theory of mind based primarily on the manipulation of symbolic representations is the only possible approach to high-level cognition. This article contests that view, and argues that a constructivist approach to cognition rooted in elementary living organisms leads to a radically new understanding of phenomena such as communication, representation, intentional action and language. Whatever the level of cognition, the computational paradigm is necessarily objectivist, whereas the constructivist paradigm is non-objectivist. It is suggested that within the field of Artificial Life, objectivism is appropriate from an engineering perspective, but that constructivism is appropriate from a biological perspective aimed at modelling living organisms as autonomous systems.