In “A Computational Foundation for the Study of Cognition” David Chalmers articulates, justifies and defends the computational suf ficiency thesis (CST). Chalmers advances a revised theory of computational implementation, and argues that implementing the right sort of computational structure is sufficient for the possession of a mind, and for the possession of a wide variety of mental properties. I argue that Chalmers’s theory of implementation is consistent with the nomological possibility of physical systems that possess different entire minds. I further argue that this brain-possessing-two-minds result challenges CST in three ways. It implicates CST with a host of epistemological problems;it undermines the underlying assumption that the mental supervenes on the physical; and it calls into question the claim that CST provides conceptual foundations for the computational science of the mind.