Type | |
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Field | |
Statement | implies . is true. Therefore, must also be true. |
Symbolic statement |
In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'),[1] implication elimination, or affirming the antecedent,[2] is a deductive argument form and rule of inference.[3] It can be summarized as "P implies Q. P is true. Therefore, Q must also be true."
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens.
The history of modus ponens goes back to antiquity.[4] The first to explicitly describe the argument form modus ponens was Theophrastus.[5] It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal.