Logic and Reasoning

Logic captures the implications among sentences. A logical calculus consists of a precise definition of a language and a set of rules of inference that can be used to derive conclusions from premises. The rules are formal, that is, they operate on the form of sentences, not their meaning. The calculus, however, may have a semantics, which provides interpretations for all the sentences in the language.Modern logic lies at the heart of the development of computers and computer programming languages. However, logic is not easy to use in the evaluation of everyday inferences because no algorithm exists for translating such inferences into sentences in a logical calculusFa gap that the logician Bar-Hillel once referred to as the scandal of logic. Logic is also not a theory of how human beings reason. That topic is the province of psychology. Although psychologists studied deductive reasoning for almost the entire 20th century, they began to formulate theories of the process only in the past 25 years. Deductive reasoning is now under intensive investigation, andmore is known about it than any other variety of thinking. The aim of this article is accordingly to outline the general principles of logic; to describe current theories of human reasoning, which owe much to logic; and to outline what is known about the role of the brain in reasoning.