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Deductive reasoning

** Deductive reasoning ** , also called ** Deductive logic ** , is [reasoning] which constructs or evaluates deductive [argument] s.

In [logic] , an argument is deductive when its conclusion is a [logical consequence] of the [premise] s. Deductive arguments are [valid] or invalid, never true or false. A deductive argument is valid [if and only if] the conclusion does follow necessarily from the premises. If the conclusion is false, then at least one of the premises must be false. And if a deductive argument is not valid then it is invalid. A valid deductive argument with true premises is said to be [sound] ; a deductive argument which is invalid or has one or more false premises or both is said to be not sound (unsound).

An example of a deductive argument and hence of deductive reasoning:

** 1 ** All men are mortal

** 2 ** [Socrates] is a man

** 3 ** ( [Therefore] ,) Socrates is mortal

Deductive reasoning is sometimes contrasted with [inductive reasoning] .

** Deductive logic **

An argument is * valid * if it is impossible both for its premises to be true and its conclusion to be false. An argument can be valid even though the premises are false.

This is an example of a valid argument. The first premise is false, yet the conclusion is still true.

** 1 ** Everyone who eats steak is a quarterback.

** 2 ** John eats steak.

** 3 ** [Therefore,] John is a quarterback.

This argument is valid but not [sound] . For a deductive argument to be considered sound the argument must not only be valid, but the premises must be true as well.

A theory of deductive reasoning known as categorical or [term logic] was developed by [Aristotle] , but was superseded by [propositional (sentential) logic] and [predicate logic] .

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