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# deduction

[dih-duhk-shuhn]
deduction, in logic, form of inference such that the conclusion must be true if the premises are true. For example, if we know that all men have two legs and that John is a man, it is then logical to deduce that John has two legs. Logicians contrast deduction with induction, in which the conclusion might be false even when the premises are true. Deduction has to do with necessity; induction has to do with probability. The famous Aristotelian syllogism is one species of deductive reasoning, which was greatly extended by the development of symbolic logic.

See R. J. Ackermann, Modern Deductive Logic (1971); P. J. Hurley A Concise Introduction to Logic (1985).

In logic, a type of inference or argument that purports to be valid, where a valid argument is one whose conclusion must be true if its premises are true (see validity). Deduction is thus distinguished from induction, where there is no such presumption. Valid deductive arguments may have false premises, as demonstrated by the example: “All men are mortal; Cleopatra is a man; therefore, Cleopatra is mortal.” Invalid deductive arguments sometimes embody formal fallacies (i.e., errors of reasoning based on the structure of the propositions in the argument); an example is “affirming the consequent”: “If A then B; B; therefore, A” (see fallacy; formal and informal).