====== Modus Tollendo Ponens ======

Also abbreviated <abbr :la "Modus tollendo ponens">MTP</abbr>. One of the elementary (valid) logical conclusion figures. It is based on a [[glossary:disjunction|disjunction]] and has the form:

> <span "A or B">''A ∨ B''</span>    –    (<q><var>A</var> or <var>B</var></q>)
> <span "nicht A">''¬A''</span>    –    (<q>not <var>A</var></q>)
> <span conclusio><span "therefore B">''∴ B''</span>    –    (<q>therefore <var>B</var></q>)</span>


For example, the following is a valid <abbr :la "Modus tollendo ponens">MTP</abbr>:

> Today will be rain //or// fog.
> There is //no// rain today.
> <span conclusio>//Therefore// there will be fog today.</span>

===== Name =====

The name of this form can be freely translated as "method of infering an affirmative sstatement by denying".

==== Other names ====

  * Disjunctive syllogism

===== Fallacies =====

As with other forms of logical reasoning, there are several fallacies that can on incorrect application of the <abbr :la "Modus tollendo ponens">MPT</abbr>:

The following table compares the <i :la>Modus tollendo ponens</i> and the most important related fallacies:

<div print-wide">
| ^  //Modus tollendo ponens// \\ (valid inference)  ^^ ^  [[logic:formal_fallacies:denying_a_conjunct|Denying a Conjunct]]  \\ (fallacy)  ^^  [[logic:formal_fallacies:affirming_a_disjunct|Affirming a Disjunct]]  \\ (fallacy)  ^^
^Premise 1 |  <span "A or [incl.] B">A ∨ B</span> \\ <small>(A //or// B)</small>  || |  <span "A or B, aber nicht beides">A ⊻ B</span> \\ <small>(A //or// B, //but not both//)</small>  ||  <span "A or [incl.] B">A ∨ B</span> \\ <small>(A //or// B)</small>  ||
^Premise 2 |  <span "not A">⌐A</span> <small>(not A)</small>  |  <span "not B">⌐B</span> <small>(not B)</small>  | |  <span "not A">⌐A</span> <small>(not A)</small>  |  <span "not B">⌐B</span> <small>(not B)</small>  |  A  |  B  |
^Con­clusion |  B  |  A  | |  <span invalid short>B</span>  |  <span invalid short>A</span>  |  <span "not B (invalid)" invalid short2>⌐B</span> <small>(not B)</small>  |  <span "not A (invalid)" invalid short2>⌐A</span> <small>(not A)</small>  |
</div>

===== See also =====

  * [[glossary:disjunction|Disjunction]]
  * [[logic:inferences:modus_ponendo_tollens|Modus Ponendo Tollens]]

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

  * [[wp>Disjunctive syllogism]] on //Wikipedia//

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