On a widely shared assumption, our mental states supervene on our microphysical properties - that is, microphysical supervenience is true. When this thesis is combined with the apparent truism that human persons have proper parts, a grave difficulty arises: what prevents some of these proper parts from being themselves thinkers as well? How can I know that I am a human person and not a smaller thinker enclosed in a human person? Most solutions to this puzzle make radical, if not absurd, claims. Recently, however, Michael Burke and Howard Robinson proposed conservative solutions that, according to them, do not have such undesired consequences. This paper argues that the conservative solutions tacitly assume at least one of the radical ones, and therefore they provide no alternative to the extreme solutions.