Deductive reasoning

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Deductive reasoning, sometimes called deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is said to be deductive when the truth of the conclusion is purported to follow necessarily or be a logical consequence of the truth of the premises and (consequently) its corresponding conditional is a necessary truth. Deductive arguments are said to be valid or invalid, never true or false. A deductive argument is valid if and only if the truth of the conclusion actually does follow necessarily (or is indeed a logical consequence of) the premises and (consequently) its corresponding conditional is a necessary truth. If the conclusion is false, then at least one of the premises must be false. 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 when it is impossible for both its premises to be true and its conclusion to be false. An argument can be valid even though the premises are false. Note, for example, that the conclusion of the following argument would have to be true if the premises were true, (even though they are, in fact, false):

1. Everyone who eats steak is a quarterback.
2. John eats steak.
3. [Therefore,] John is a quarterback.

The argument, however, is not sound. In order for a deductive argument to be sound, it must not only be valid, 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A theory of deductive reasoning known as categorical or term logic was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.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 is sometimes contrasted with 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).

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.

See also

Argument (logic) Logic Mathematical logic Abductive reasoning Analogical reasoning Correspondence theory of truth Defeasible reasoning Fallacy Hypothetico-deductive method

Logic portal Inquiry Inductive reasoning Inference Logical consequence Propositional calculus Retroductive reasoning Scientific method Soundness Syllogism

References

Further reading

• Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
• Philip Johnson-Laird, Ruth M. J. Byrne, Deduction, Psychology Press 1991, ISBN 9780863771491
• Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002