Deductive reasoning

Deductive reasoning, also called Deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is deductive when its conclusion is a logical consequence of the premises. 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:

All men are mortal
Socrates is a man
(Therefore,) Socrates is mortal

Deductive reasoning is sometimes contrasted with inductive reasoning.

1 Deductive logic
2 Natural deduction
3 See also
4 References
5 Further reading

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.

Everyone who eats steak is a quarterback.
John eats steak.
[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A theory of deductive reasoning known as categorical or term logic was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.

Deductive reasoning can be contrasted with inductive reasoning, in which one moves from a set of specific facts to a general conclusion. 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).

Natural deduction

Main article: Natural deduction

Deductive 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.

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