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A theory of deductive reasoning known as categorical or [term logic] was developed by [Aristotle] , but was superseded by [propositional (sentential) logic] and [predicate logic] .

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