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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).

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

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).

Learn more about deduction with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Deduction can refer to one of the following usages:

- Deductive reasoning, inference in which the conclusion is of no greater generality than the premises
- Natural deduction, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs

Relating to taxation:

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Last updated on Monday June 16, 2008 at 10:39:57 PDT (GMT -0700)

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