Deductive reasoning

Deductive reasoning

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Deductive reasoning

Deductive reasoning is reasoning which uses deductive arguments to move from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true.^[1]

The classic example of deductive reasoning, given by Aristotle, is

All men are mortal. (major premise)
Socrates is a man. (minor premise)
Socrates is mortal. (conclusion)

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.

Background
Deductive logic
Natural deduction
Cultural references
Further reading
References
See also

Background

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]

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion.^[3]

Alternative to deductive reasoning is inductive reasoning. The basic difference between the two can be summarized in the deductive dynamic of logically progressing from general evidence to a particular truth or conclusion; whereas with induction the logical dynamic is precisely the reverse. Inductive reasoning starts with a particular observation that is believed to be a demonstrative model for a truth or principle that is assumed to apply generally.

Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to impute a general principle. 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).

Deductive logic

Deductive reasoning is supported by deductive logic

For example:

All apples are fruit.

All fruits grow on trees.

Therefore all apples grow on trees.

All apples are fruit.

Some apples are red.

Therefore some fruits are red.

The first premise may be false yet anyone accepting the premises is compelled to accept the conclusion.

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.

Cultural references

Sherlock 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 abduction.