Editing Modus ponens (section)

{{redirects here|Forward reasoning||Forward chaining}}
{{short description|Rule of logical inference}}
{{Use dmy dates|date=May 2018}}
{{title language |la}}
{{Infobox mathematical statement
| name = {{lang|la|Modus ponens}}
| type = {{Plainlist|
* [[Deductive reasoning|Deductive]] [[argument form]]
* [[Rule of inference]]
}}
| field = {{Plainlist|
* [[Classical logic]]
* [[Propositional calculus]]
}}
| statement = <math>P</math> implies <math>Q</math>. <math>P</math> is true. Therefore, <math>Q</math> must also be true.
| symbolic statement = <math>P \to Q,\; P\; \vdash\ Q</math>
}}
{{Transformation rules}}

In [[propositional calculus|propositional logic]], '''{{lang|la|modus ponens}}''' ({{IPAc-en|ˈ|m|oʊ|d|ə|s|_|ˈ|p|oʊ|n|ɛ|n|z}}; '''MP'''), also known as '''{{lang|la|modus ponendo ponens}}''' ({{ety|la||mode that by affirming affirms}}),<ref>{{cite book |last=Stone |first=Jon R. |year=1996 |title=Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language |location=London |publisher=Routledge |isbn=0-415-91775-1 |page=[https://archive.org/details/latinforillitera0000ston/page/60 60] |url=https://archive.org/details/latinforillitera0000ston |url-access=registration }}</ref> '''implication elimination''', or '''affirming the antecedent''',<ref>[https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095354544 "Oxford reference: affirming the antecedent"]. ''[[Oxford Reference]]''.</ref> is a [[Deductive reasoning|deductive]] [[argument form]] and [[rule of inference]].<ref>Enderton 2001:110</ref> It can be summarized as "''P'' [[material conditional|implies]] ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true."

''Modus ponens'' is a mixed [[hypothetical syllogism]] and is closely related to another [[Validity (logic)|valid]] form of argument, ''[[modus tollens]]''. Both have apparently similar but invalid forms: [[affirming the consequent]] and [[denying the antecedent]]. [[Constructive dilemma]] is the [[Logical disjunction|disjunctive]] version of ''modus ponens''.

The history of ''modus ponens'' goes back to [[Classical antiquity|antiquity]].<ref>[[Susanne Bobzien]] (2002). "The Development of Modus Ponens in Antiquity", ''Phronesis'' 47, No. 4, 2002.</ref> The first to explicitly describe the argument form ''modus ponens'' was [[Theophrastus]].<ref>[http://plato.stanford.edu/entries/logic-ancient/#StoSyl "Ancient Logic: Forerunners of ''Modus Ponens'' and ''Modus Tollens''"]. ''[[Stanford Encyclopedia of Philosophy]]''.</ref> 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.