Do non-human animals have rights? The answer to this question depends on whether animals have morally relevant mental properties. Mindreading is the human activity of ascribing mental states to other organisms. Current knowledge about the evolution and cognitive structure of mindreading indicates that human ascriptions of mental states to non-human animals are very inaccurate. The accuracy of human mindreading can be improved with the help of scientific studies of animal minds. But the scientific studies by themselves do not by themselves solve the problem of how to map psychological similarities (and differences) between humans and animals onto a distinction between morally relevant and morally irrelevant mental properties. The current limitations of human mindreading – whether scientifically aided or not – have practical consequences for the rational justification of claims about which rights (if any) non-human animals should be accorded.