Modus Ponens

Le 'mode affirmatif' : Si P alors Q, P est vrai, donc Q est vrai.

Apprendre

Le 'mode affirmatif' : Si P alors Q, P est vrai, donc Q est vrai.

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.

Comment le reconnaître

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)

Erreurs fréquentes

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)

Résolution étape par étape

S'il pleut, le sol est mouillé. Il pleut. Que conclure ?

Identifiez le conditionnel : 'S'il pleut, le sol est mouillé'
Vérifiez l'antécédent : 'Il pleut' = OUI
Appliquez Modus Ponens : P vrai donc Q vrai
Concluez : Le sol est mouillé

Réponse: The ground is wet

Conseils de pratique

Déduction Logique