Modus Ponens

Lernen

Der 'bejahende Modus': Wenn P dann Q, P ist wahr, also ist Q wahr.

Modus Ponens (Latin for 'mode that affirms') is one of the most fundamental rules of inference in propositional logic. Given a conditional statement 'If P then Q' and the truth of the antecedent P, we can validly conclude Q. This rule is also called 'affirming the antecedent' and forms the basis of much deductive reasoning.

P → Q, P ⊢ Q

• If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.
• If you study hard, you will pass the exam. You study hard. Therefore, you will pass the exam.
• If a number is divisible by 4, it is divisible by 2. 16 is divisible by 4. Therefore, 16 is divisible by 2.

So erkennen Sie es

• Look for an 'If...then...' statement (conditional)
• Check if the 'if' part (antecedent) is affirmed as true
• The conclusion will be the 'then' part (consequent)

Häufige Fehler

• Affirming the consequent (invalid): 'If P then Q, Q is true, therefore P is true' - this does NOT follow
• Example of the fallacy: 'If it rains, the ground is wet. The ground is wet. Therefore it rained.' (Wrong! Sprinklers could cause wet ground)

Übungshinweise

Logische Schlussfolgerung