Modus Tollens

El 'modo negante': Si P entonces Q, Q es falso, por lo tanto P es falso.

Aprender

El 'modo negante': Si P entonces Q, Q es falso, por lo tanto P es falso.

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.

Cómo reconocerlo

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

Errores comunes

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)

Resolución paso a paso

Si la batería está cargada, el teléfono se enciende. El teléfono no se enciende. ¿Qué podemos concluir?

Identifica el condicional: 'Si batería cargada, teléfono se enciende'
Comprueba el consecuente: 'Teléfono no se enciende' = Q es falso
Aplica Modus Tollens: si Q es falso, P debe ser falso
Concluye: La batería no está cargada

Respuesta: The battery is not charged

Orientación para practicar

Deducción Lógica