Classical logic and logicism in human thought

This chapter explores the role of classical logic as a theory of human reasoning. I distinguish between classical logic as a normative, computational and algorithmic system, and review its role is theories of human reasoning since the 1960s. The thesis I defend is that psychological theories have been moving further and further away from classical logic on all three levels. I examine some prominent example of logicist theories, which incorporate logic in their psychological account, including mental logic and mental models, showing that they differ in the role they accord to logic in general and the classical variants in particular on all three levels. However, even mental logic theories, with the strongest logicist leanings, limit the algorithmic role of classical logic, although they accept it as a computational and normative system. I examine in particular three prominent features of classical logic: monotonicity, bivalence and extensionality, reviewing the empirical evidence against them as characteristics of human reasoning. Moving on to non-logicist and anti-logicist accounts, I review two of the influential proposals, the Bayesian rational analysis and the dual-process hypothetical thinking theory. Lastly, I examine the role of classical logic in the big debate on human rationality.