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deduction
(redirected from deductions)

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deduction, in logic logic, the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference.
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, 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 induction, in logic , a form of argument in which the premises give grounds for the conclusion but do not necessitate it. Induction is contrasted with deduction , in which true premises do necessitate the conclusion.
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, 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 syllogism, a mode of argument that forms the core of the body of Western logical thought. Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years.
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 is one species of deductive reasoning, which was greatly extended by the development of symbolic logic symbolic logic or mathematical logic, formalized system of deductive logic, employing abstract symbols for the various aspects of natural language.
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Bibliography

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


deduction

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).


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