Modus Tollens

Le 'mode négatif' : Si P alors Q, Q est faux, donc P est faux.

Apprendre

Le 'mode négatif' : Si P alors Q, Q est faux, donc P est faux.

Modus Tollens (Latin for 'mode that denies') is a fundamental rule of inference that works by denying the consequent. Given a conditional 'If P then Q' and knowing that Q is false, we can validly conclude that P must also be false. This rule is logically equivalent to Modus Ponens applied to the contrapositive.

P → Q, ¬Q ⊢ ¬P

If it is raining, the ground is wet. The ground is not wet. Therefore, it is not raining.
If the battery is charged, the phone will turn on. The phone does not turn on. Therefore, the battery is not charged.
If a number is prime and greater than 2, it is odd. 8 is not odd. Therefore, 8 is not a prime number greater than 2.

Comment le reconnaître

Look for an 'If...then...' statement (conditional)
Check if the 'then' part (consequent) is denied/negated
The conclusion negates the 'if' part (antecedent)

Erreurs fréquentes

Denying the antecedent (invalid): 'If P then Q, P is false, therefore Q is false' - this does NOT follow
Example of the fallacy: 'If it rains, the ground is wet. It is not raining. Therefore the ground is not wet.' (Wrong! Sprinklers could still make it wet)

Résolution étape par étape

Si la batterie est chargée, le téléphone s'allume. Le téléphone ne s'allume pas. Que conclure ?

Identifiez le conditionnel : 'Si batterie chargée, téléphone s'allume'
Vérifiez le conséquent : 'Téléphone ne s'allume pas' = Q est faux
Appliquez Modus Tollens : Q faux donc P faux
Concluez : La batterie n'est pas chargée

Réponse: The battery is not charged

Conseils de pratique

Déduction Logique