/di duk"sheuhn/, n.1. the act or process of deducting; subtraction.2. something that is or may be deducted: She took deductions for a home office and other business expenses from her taxes.3. the act or process of deducing.4. something that is deduced: His astute deduction was worthy of Sherlock Holmes.5. Logic.a. a process of reasoning in which a conclusion follows necessarily from the premises presented, so that the conclusion cannot be false if the premises are true.[1400-50; late ME deduccioun ( < AF) < L deduction- (s. of deductio) a leading away. See DEDUCT, -ION]
* * *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).
* * *▪ reasonin logic, a rigorous proof, or derivation, of one statement (the conclusion) from one or more statements (the premises)—i.e., a chain of statements, each of which is either a premise or a consequence of a statement occurring earlier in the proof. This usage is a generalization of what the Greek philosopher Aristotle called the syllogism, but a syllogism is now recognized as merely a special case of a deduction. Also, the traditional view that deduction proceeds “from the general to the specific” or “from the universal to the particular” has been abandoned as incorrect by most logicians. Some experts regard all valid inference as deductive in form and, for this and other reasons, reject the supposed contrast between deduction and induction. See also axiomatic method; formal system; inference.
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