What do people do when they reason? Prima facie, this would seem to be a straightforward question with a straightforward answer. When people reason, they draw (or at least attempt to draw) logical inferences. Reasoning, by this approach, is about classical logic. In classical logic, ¹ a valid inference is one in which the conclusion necessarily follows from the premises (what is assumed to be given as true): if the premises are true, so is the conclusion. So reasoning helps us determine what is true and what is false. In psychology, the foremost representatives of this approach are Inhelder and Piaget (1958): their theory depicts ‘formal operations’ – that is, logical thinking – as the pinnacle of human cognitive development. Similarly, in philosophy, Copi’s (2013) influential introduction to logic still refers to logic as the way to achieve correct, fully reliable reasoning. Retrospectively dubbed ‘logicism’ (Evans, 2002; Oaksford & Chater, 1991), ‘the deduction paradigm’ (Evans, 2002), ‘the binary paradigm’ (Over, 2009), or simply ‘the traditional paradigm’ (Elqayam & Over, 2012), this view dominated psychology of reasoning for a long time: that logic at least is the correct norm showing how humans ought to reason, and perhaps even a good theory describing how we actually do reason.