Modus ponens

Modus ponens
Type
Field
Statement implies . is true. Therefore, must also be true.
Symbolic statement

In propositional logic, modus ponens (/ˈmdəs ˈpnɛnz/; 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.

  1. ^ Stone, Jon R. (1996). Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language. London: Routledge. p. 60. ISBN 0-415-91775-1.
  2. ^ "Oxford reference: affirming the antecedent". Oxford Reference.
  3. ^ Enderton 2001:110
  4. ^ Susanne Bobzien (2002). "The Development of Modus Ponens in Antiquity", Phronesis 47, No. 4, 2002.
  5. ^ "Ancient Logic: Forerunners of Modus Ponens and Modus Tollens". Stanford Encyclopedia of Philosophy.