Question

What is modus ponen and modus tollen? Write one example of each.

Answer 1

Modus ponens and modus tollens,( Latin: “method of affirming” and “method of denying”) in propositional logic, two types of inference that can be drawn from a hypothetical proposition—i.e., from a proposition of the form “If A, then B” (symbolically A ⊃ B, in which ⊃ signifies “If . . . then”). Modus ponensrefers 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 ofmodus 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 termsmodus 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.