Deductive reasoning encyclopedia topics

Deductive reasoning

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

An argument is valid when its conclusion must be true if its premises are true. If the premises are not true or the argument is not valid, the conclusion may or may not be true. Alternative to deductive reasoning is 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).

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.

Or

All animals are mortal

All humans are animal

Therefore all humans are mortal (copi, logic)

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.

References

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.

An argument is valid when its conclusion must be true if its premises are true. If the premises are not true or the argument is not valid, the conclusion may or may not be true. Alternative to deductive reasoning is 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).

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.

Or

All animals are mortal

All humans are animal

Therefore all humans are mortal (copi, logic)

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.

Background

Deductive logic

Natural deduction

Cultural references

Further reading

References

See also

Background

Deductive logic

Natural deduction

Cultural references

Further reading

References

See also