The psychology of reasoning was dominated by the deduction paradigm from around 1960 to 2000, in which untrained participants are asked to assess the validity of logical arguments. As evidence of logical error and content-dependent thinking amassed, the paradigm has shifted recently with more emphasis on probabilistic and pragmatic processes. This chapter is focused particularly on the dual-process theories that arose from traditional studies of deductive reasoning but that now form part of a more general set of theories of higher cognition. It is argued that the “received” view of dual-process theory, which was established around 2000, actually incorporates a number of false beliefs and fallacies, which are discussed in this chapter. While dual-process theory rightly remains the focus of much current research, it is important to understand and avoid these fallacies.