This essay begins by addressing the role of the so-called Parity Principle in arguments for extended cognition. It is concluded that the Parity Principle does not, by itself, demarcate cognition and that another mark of the cognitive must be sought. The second section of the paper advances two arguments against the extended view of cognition, one of which - the conservatism-or-simplicity argument - appeals to principles of theory selection, and the other of which - the argument from demarcation - draws on a systems-based theory of cognition. The final section contests the claim, made by Andy Clark, that empirical work done by Wayne Gray and colleagues supports the extended view.