Turing’s (1950) article on the Turing test is often interpreted as supporting the behaviouristic view that human intelligence can be represented in terms of input/output functions, and thus emulated by a machine. We show that the properties of functions are not decidable in practice by the behaviour they exhibit, a result, we argue, of which Turing was likely aware. Given that the concept of a function is strictly a Platonic ideal, the question of whether or not the mind is a program is a pointless one, because it has no demonstrable implications. Instead, the interesting question is what intelligence means in practice. We suggest that Turing was introducing the novel idea that intelligence can be reliably evidenced in practice by finite interactions. In other words, although intelligence is not decidable in practice, it is testable in practice. We explore the connections between Turing’s idea of testability and subsequent developments in computational complexity theory.