modus tollens

/ ˈməʊdəs ˈtɒlˌɛnz /

noun

1. logic the principle that whenever a conditional statement and the negation of its consequent are given to be true, the negation of its antecedent may be validly inferred, as in if it's Tuesday this must be Belgium and this isn't Belgium so it's not Tuesday

Word History and Origins

Origin of modus tollens¹

literally: mood that denies

Example Sentences

It consisted primarily of modus ponens—“If A is true, then B is true. A is true. Therefore, B is true”—and modus tollens—“If A is true, then B is true. B is not true. Therefore, A is not true.”

From Scientific American

“Modus ponens is O.K. when you’re doing the informal proofs, but modus tollens can be tough,” Murphy said as he packed his books and pens.

From New York Times

Again, take an example of the Modus Tollens— If rain has fallen, the streets are wet.

From Project Gutenberg

Two Moods are usually recognised the Modus ponens, in which the antecedent of the hypothetical major premise is affirmed; and the Modus tollens, in which its consequent is denied.

From Project Gutenberg

Rule of the Modus tollens: The consequent of the major premise being denied in the minor premise, the antecedent is denied in the conclusion.

From Project Gutenberg