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Mental

Deductive Reasoning

Deductive reasoning draws conclusions that must be true whenever the premises they start from are true.

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The idea

Deductive reasoning is the process of drawing valid inferences. An inference is valid when its conclusion follows logically from its premises, the statements it starts from. In a valid argument, it is impossible for the premises to be true and the conclusion to be false. A classic example starts from the premises that all men are mortal and that Socrates is a man, and it concludes that Socrates is mortal.

Valid does not mean true. An argument is sound only if it is valid and all of its premises are true. If a premise is false, a valid argument can still reach a false conclusion. Valid deductive arguments follow rules of inference, such as modus ponens and modus tollens. Modus ponens says that if P leads to Q, and P is true, then Q is true. Modus tollens says that if P leads to Q, and Q is false, then P is false. An argument that does not follow a rule of inference is called a formal fallacy.

Deduction differs from inductive and abductive reasoning. In those kinds of reasoning, the premises give weaker support, making a conclusion likely without guaranteeing it. In exchange, they can provide genuinely new information, while a deductive conclusion only spells out what the premises already hold. Research on how people reason finds that they draw valid inferences more often with modus ponens than with modus tollens, and more often with concrete cases than abstract ones.

Check yourself

Question 1 of 3

What makes a deductive argument sound?

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Composition

what it's made of

  • Premises — The starting statements that an argument takes as given.
  • Conclusion — The statement the argument claims follows from the premises.
  • Validity — An argument is valid if its premises cannot all be true while its conclusion is false.
  • Soundness — An argument is sound if it is valid and all its premises are true.
  • Rules of inference — Patterns such as modus ponens and modus tollens that lead from premises to a conclusion by form alone.

Connection

how it relates

Under Logic and Reasoning

Related

  1. Constructing Argumentsstrength 80 of 100

    Building a strong argument often means arranging premises so the conclusion follows deductively.

  2. Identifying Assumptionsstrength 70 of 100

    A valid deduction is only as trustworthy as its premises, so spotting unstated assumptions matters.

  3. Evaluating Evidencestrength 50 of 100

    Deduction cannot show that a premise is true; checking evidence for the premises does that job.

Change

how and why it evolves

Past
Logic has been studied since ancient times, and Aristotelian logic focused on deductive arguments in the form of syllogisms.
Now
Today deductive reasoning underlies mathematical proofs and computer logic, and psychologists study why people find some valid forms harder than others.
Next
Software that checks proofs automatically will likely play a larger role in mathematics, though people will still have to judge whether the premises are true.

Knowledge you can walk. Read the idea, then step up, across or down.

Deductive Reasoning

Deductive reasoning draws conclusions that must be true whenever the premises they start from are true.

Learn, discuss, create, buy or invest

The idea

Deductive reasoning is the process of drawing valid inferences. An inference is valid when its conclusion follows logically from its premises, the statements it starts from. In a valid argument, it is impossible for the premises to be true and the conclusion to be false. A classic example starts from the premises that all men are mortal and that Socrates is a man, and it concludes that Socrates is mortal.

Valid does not mean true. An argument is sound only if it is valid and all of its premises are true. If a premise is false, a valid argument can still reach a false conclusion. Valid deductive arguments follow rules of inference, such as modus ponens and modus tollens. Modus ponens says that if P leads to Q, and P is true, then Q is true. Modus tollens says that if P leads to Q, and Q is false, then P is false. An argument that does not follow a rule of inference is called a formal fallacy.

Deduction differs from inductive and abductive reasoning. In those kinds of reasoning, the premises give weaker support, making a conclusion likely without guaranteeing it. In exchange, they can provide genuinely new information, while a deductive conclusion only spells out what the premises already hold. Research on how people reason finds that they draw valid inferences more often with modus ponens than with modus tollens, and more often with concrete cases than abstract ones.

Check yourself

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