Modus tollens

A rule of inference that denies a conditional’s consequent to conclude that its antecedent is false. In symbolic form, from P → Q and ¬Q, it infers ¬P.

Material conditional: A logical connective whose formula P → Q is false only when P is true and Q is false. Its truth conditions make the inference from a false consequent to a false antecedent valid.
Proposition: A declarative statement that can be assigned a truth value. P and Q stand for propositions whose truth values determine whether the inference applies.
Denying the antecedent: An invalid argument form that infers ¬Q from P → Q and ¬P. It resembles modus tollens but denies the conditional’s antecedent instead of its consequent.
Reductio ad absurdum: A proof method that derives a contradiction from an assumption to establish that the assumption is false. A reductio often uses modus tollens to reject an assumption that entails a contradiction.
Aristotle: An ancient Greek philosopher whose works shaped logic, science, and philosophy. Aristotle discussed inference patterns equivalent to modus tollens in his treatment of hypothetical reasoning.
Modus ponens: A rule of inference that affirms a conditional’s antecedent to conclude its consequent. It uses the same conditional structure but affirms P rather than denying Q.
Logical negation: The operation that reverses a proposition’s truth value, represented by ¬. The rule depends on denying Q and concluding the denial of P.
Affirming the consequent: An invalid argument form that infers P from P → Q and Q. It reverses the valid move: a true consequent does not establish the antecedent.
Falsifiability: The property of a claim being testable by observations that could show it false. A prediction can be rejected by modus tollens when its expected observation fails.
Stoic logic: The system of propositional logic developed by ancient Stoic philosophers. Stoic logicians formalized conditional arguments that include the pattern later called modus tollens.

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