MODUS PONENS AND MODUS TOLLENS

(Latin: method of affirming and method of de-nying), in propositional logic, two types of inference that can be drawn from a hypothetical propositioni.e., from a proposition of the form If A, then B (symbolically A B, in which signifies If . . . then). Modus ponens refers to inferences of the form A B; A, therefore B. Modus tollens refers to inferences of the form A B; ~B, therefore, ~A (~ signifies not). An example of modus tollens is the following: If an angle is inscribed in a semicircle, then it is a right angle; this angle is not a right angle; therefore, this angle is not inscribed in a semicircle. For disjunctive premises (employing , which signifies either . . . or), the terms modus tollendo ponens and modus ponendo tollens are used for arguments of the forms A B; ~A, therefore B, and A B; A, therefore ~B (valid only for exclusive disjunction: Either A or B but not both). The rule of modus ponens is incorporated into virtually every formal system of logic.