====== Modus Ponens ======

Also abbreviated <abbr :la "Modus Ponens">MP</abbr> or <abbr :la "Modus Ponendo Ponens">MPP</abbr>, is one of the most elementary (valid) logical inferences. It is based on a [[glossary:conditional|conditional]] and the //affirmation// of its [[glossary:antecedent|antecedent]].

> <span "If A, then B">''A → B''</span>   –   <q>if <var>A</var>, then <var>B</var>.</q>
> <span "A is true">''A''</span>   –   <q><var>A</var> is true.</q>
> <span conclusio><span "therefore B [is true]">''∴ B''</span>   –   <q>therefore <var>B</var> [is true].</q></span>

The following is an example of a valid <i :la>Modus Ponens</i>:

> //If// it is raining, [//then//] the street will get wet.
> It is raining,
> <span conclusio>Therefore: The street will get wet.</span>

===== Name =====

The full name of this form is "<i :la "way of setting up a [new statement] by setting [a statement]">Modus ponendo ponens</i>". Loosely, this could be translated as the "mode of inferring an affirmative [consequent statement] by affirmation [of the antecedent statement]".

==== Other names ====

  * Implication elimination
  * Affirming the antecedent
  * <i :la>Affirmatio conditionis</i>

===== Fallacies =====

Although the <abbr :la "Modus ponens">MP</abbr> is intuitively understandable to most people, it is not uncommon for people to draw erroneous conclusions based on it.

The following table contrasts the <i :la>modus ponens</i> with its most common fallacies:

<div print-wide">
| ^  <i :la>Modus ponens</i> \\ (valid inference)  ^ ^  [[logic:formal_fallacies:affirming_the_consequent|Affirming the consequent]] \\ (formal fallacy)  ^  [[logic:formal_fallacies:denying_the_antecedent|Denying the antecedent]] \\ (formal fallacy)  ^
^Premise 1 |  <span "If A, then B">A → B</span> \\ <small>(if A, then B)</small>  | |  <span "If A, then B">A → B</span> \\ <small>(if A, then B)</small>  |  <span "if A, then B">A → B</span> \\ <small>(if A, then B)</small>  | 
^Premise 2 |  A  | |  B  |  <span "not A">⌐A</span> <small>(not A)</small>  | 
^Conclusion |  B  | |  <s invalid short">A</s>  |  <s "nicht-B" invalid short2">⌐B</s> <small>(not B)</small>  |
</div>
===== See also =====

  * [[glossary:conditional|(Material) Conditional]]
  * [[logic:inferences:constructive_dilemma|Constructive dilemma]]
  * [[logic:inferences:modus_tollens|Modus Tollens]]

===== More information =====

  * [[wp>Modus ponens]] on //Wikipedia//

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