 These various quotations are typical of writing on the foundations of computer science and computational theories of mind. The claims made are true, however, only if the general terms ‘explicitly stated rule’, ‘instruction’, ‘clear recipe composed of simple steps’, and so forth, are restricted in such a way as to refer only to what can be done by means of effective methods. Turing did not show that his machines can solve any problem that can be solved “by instructions, explicitly stated rules, or procedures” (Gregory 1987), and nor did he prove that the universal Turing machine “can compute any function that any computer, with any architecture, can compute” (Dennett 1991). Nor do his results entail that a standard digital computer “can compute any rule-governed input-output function” (Churchland and Churchland 1990).