deductive reasoning The process of establishing that a conclusion follows validly from premises (i.e., that it must be true given that the premises are true).

deontic reasoning Reasoning about actions that are obligatory, permissible, or impermissible.

formal rules of inference Rules that can be used to derive a conclusion from premises in a way that takes into account only the form, not the meaning, of the premises. Logical calculi rely on formal rules, and so do many psychological theories of reasoning.

implicit reasoning A fast, automatic, and largely unconscious process of making inferences in order to make sense of the world and of discourse (e.g., to select the appropriate sense of a word, or to establish the appropriate referent for a pronoun).

inductive reasoning The process of deriving plausible conclusions from premises.

logic The science of implications among sentences in a formalized language. Logical calculi are systems of proof based on formal rules of inference (proof theory); they have an accompanying semantics (or model theory).

mental models Representations of the world that are postulated to underlie human reasoning; each model represents what is true in a single possibility.

validity An inference is valid if its conclusion must be true given that its premises are true. A valid inference from true premises yields a true conclusion;a valid inference from false premises may yield a true or a false conclusion.

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 calculus—a 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, and more 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.

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