Deductive reasoning

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Deduction is one of the two main types of reasoning. The other is induction. In deduction, we apply a general rule to a particular case.

Deductive arguments are attempts to show that a conclusion must follow from a set of premises or hypotheses. A deductive argument is valid if the conclusion follows necessarily from the premises.

Aristotle, the first person we know who wrote down laws of deduction, gives this example of deduction:

  • All men are mortal.
  • Socrates is a man.
  • Therefore, Socrates is a mortal.

The first two statements are called "premises". The last statement is called the "conclusion". The conclusion is taken from the premises. If one of the premises is wrong, the conclusion will also be wrong. Mathematicians use deduction to discover new mathematics.