Modus Tollens

MODUS TOLLENS: Latin MODUS "standard, measure" is from the Indo-European root MED- "to take appropriate measures." The second word, TOLLENS, is the present participle of Latin TOLLERE "to take away," from the Indo-European root TELE- "to lift, support." In logic, MODUS TOLLENS is a standard form of argumentation in which you "take away," that is, negate, the consequent of an if-then statement and conclude the negation of the antecedent of that if-then statement. MODUS TOLLENS is equivalent to using the contrapositive of the original if-then statement.

If P, then Q. Not Q, therefore not P.

Modus Tollens - modus tollendo tollens - (Latin for "the mode or way of removing" or in logic "the way that denies by denying")

Denying the consequent.

A valid form of argument (unlike affirming the consequent and denying the antecedent).

1. If A, then B.
2. Not B.
3. Therefore, Not A.

Modus tollens is related to modus ponens. They both have a premise that is a conditional statement. The most important difference lies in the negation of the last two lines.

See also Modus Ponens