Argument
Modus ponens
Overview
In propositional logic, modus ponens (; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. 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. The first to explicitly describe the argument form modus ponens was Theophrastus. 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.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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For generally, not he that hath skill in geometry, or any other science speculative, but only he that understandeth what conduceth to the good and government of the people, is called a wise man. Now that no author of sedition can be wise in this acceptation of the word, is sufficiently proved, in that it hath been already demonstrated, that no pretence of sedition can be right or just. And therefore the authors of…
Thomas Hobbes, The English works of Thomas Hobbes of Malmesbury, Volume 04
States what Modus ponens is; the author is tied to Modus ponens in the knowledge graph.
But because in sense, to one and the same thing perceived, sometimes one thing, sometimes another succeedeth, it comes to passe in time, that in the Imagining of any thing, there is no certainty what we shall Imagine next; Onely this is certain, it shall be something that succeeded the same before, at one time or another.
Thomas Hobbes, Leviathan
States what Modus ponens is; the author is tied to Modus ponens in the knowledge graph.
Hence, in the conclusion of a syllogism we restrict a predicate to a certain object, after having thought it in the major in its whole extent under a certain condition. This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions.
Immanuel Kant, The Critique of Pure Reason
States what Modus ponens is.
Philosophers who discussed Modus ponens
Related ideas
- Artificial intelligence
- Argument
- Deontic logic
- Hamlet
- Propositional logic
- Modus tollens
- Validity (logic)
- Principia Mathematica
- Rule of inference
- Sequent calculus
- Classical antiquity
- Curry–Howard correspondence
- Soundness
- Thomas Hobbes
- Truth
- Susanne Bobzien
- Stanford Encyclopedia of Philosophy
- Logical consequence
- Metalogic
- Boolean algebra (structure)
- Formal system
- Deductive reasoning
- Material conditional
- Affirming the consequent
Place in the tradition
Part of Doxastic logic.