Reasoning to and from belief: Deduction and induction are still distinct

Abstract

Along with others we believe there has been a distinct paradigm shift in the psychology of deductive reasoning. Many authors have moved away from a model of rational reasoning based on extensional bivalent logic in favour of a Bayesian approach in which all premises and conclusion are represented with a degree of uncertainty. This leaves the important question of whether deductive reasoning is now distinct from inductive inference, which has traditionally been studied in separate literatures. We argue that induction remains both logically and psychologically distinct from the probabilistic deduction of the new paradigm. Although both forms of inference lead to conclusions with degrees of uncertainty, inductions cannot be probabilistically valid. That is, their conclusions are by their nature more uncertain than their premises. By contrast, valid deduction from uncertain premises cannot increase that uncertainty. The two forms of inference also have distinct purposes: induction adds new beliefs whereas deduction draws out implications from what is already believed.