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Deductive reasoning, sometimes called deductive logic, is reasoning which uses deductive arguments to move from given statements (premises) to conclusions, which must be true if the premises are true.[1] An example of deductive reasoning, given by Aristotle, is
For a detailed treatment of deduction as it is understood in philosophy, see Logic. For a technical treatment of deduction as it is understood in mathematics, see mathematical logic. Deductive reasoning is often contrasted with inductive reasoning, which reasons from a large number of particular examples to a general rule.
[edit] BackgroundThe theory of deductive reasoning was developed by Aristotle, Thales, Pythagoras, and other Greek philosophers of the Classical Period (600 to 300 B.C.). Aristotle, for example, relates a story of how Thales used his skills to deduce that the next season's olive crop would be a very large one. He therefore bought all the olive presses and made a fortune when the bumper olive crop did indeed arrive.[2] An argument is valid when its conclusion must be true if its premises are true. If the premises are not true or the argument is not valid, the conclusion may or may not be true. Alternative to deductive reasoning is inductive reasoning. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data). [edit] Deductive logicDeductive reasoning is supported by deductive logic, for example, the following is a valid deduction:
Note that the validity of deduction is not affected by the truth of the premise or the truth of the conclusion. The following deduction is perfectly valid:
The argument, however, is not sound. In order for a deductive argument to be sound, the deduction must be valid and the premise must be true. [edit] Natural deductionDeductive reasoning should be distinguished from the related concept of natural deduction, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs. [edit] Cultural referencesSherlock Holmes, the fictional detective created by Sir Arthur Conan Doyle, is well known for referring to deductive reasoning in numerous of Doyle's stories. However, Holmes' most famous inferences were arguably cases of abductive reasoning. [edit] Further reading
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