Modus Tollens

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A Modus Tollens is a Rule of Inference under which the Antecedent of a Conditional is rejected if and only if the Consequent of the Conditional is rejected.


  • (Wikipedia, 2009) ⇒
    • In logic, modus tollendo tollens (Latin for "the way that denies by denying") is the formal name for indirect proof or proof by contraposition ...
    • In classical logic, modus tollens (or modus tollendo tollens)[1] (Latin for "the way that denies by denying")[2] has the following argument form: If P, then Q. ¬Q. Therefore, ¬P.
    • It can also be referred to as denying the consequent, and is a valid form of argument (unlike similarly-named but invalid arguments such as affirming the consequent or denying the antecedent). (See also modus ponens or "affirming the antecedent".)
    • Modus tollens is sometimes confused with indirect proof (assuming the negation of the proposition to be proved and showing that this leads to a contradiction) or proof by contrapositive (proving If P, then Q by a proof of the equivalent contrapositive If not-Q, then not-P).
    • Consider an example: If an intruder is detected, the alarm goes off. The alarm does not go off. Therefore, no intruder is detected.
    • Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.
    • An valid form of argument in which the consequent of a conditional proposition is denied, thus implying the denial of the antecedent. ...
  • CYC Glossary
    • modus tollens: A rule of inference which can be derived from modus ponens under which, given a knowledge base which contains the formulas "Not B" and "A implies B", one may conclude "Not A".
    • modus tollens means "a way of destroying;" symbolically: "If p, then q; not-q; therefore,not-p. (Study 4)
    • Modus Tollens: Consists of a conditional statement and one other premise. The second premise denies the consequent of the conditional, yielding the denied antecedent as the conclusion: IF (IF p THEN q) AND (not-q) THEN (not-p).