====== Affirming a disjunct ======

A [[logic:formal_fallacies:index|formal fallacy]] in which a positive (affirmative) result for one alternative of an [[glossary:adjunction|adjunct]] statement is (mis-)interpreted to imply a negative result for the other option

The following is an example of an affirmation of a disjunction:

> It will rain //or// snow today.
> It is raining.
> <span conclusio><s class="invalid">Therefore, it will //not// snow today.</s></span>

Even if the premise <q>It will rain or snow today</q> holds //true//, the conclusion does not necessarily so – it is quite possible that there may be //both//, rain //and// snow, during the same day (or even at the same time).

===== Description =====

In most cases, the underlying error is likely to be a confusion between //inclusive// and //exclusive// [[glossary:disjunction|disjunction]] (see: [[glossary:adjunction|ad­junction]] and [[glossary:contravalence|contra­valence]]).

Another possibility is an incorrect application of the <i :la>[[logic:inferences:modus_tollendo_ponens|Modus tollendo ponens]]</i>, especially when mixed with the <i :la>[[logic:inferences:modus_ponendo_tollens|Modus ponendo tollens]]</i>, can also lead to this fallacy. For comparison, the following table compares the two valid forms with the fallacy:

<div print-wide>
| ^  <i :la>[[logic:inferences:modus_ponendo_tollens|Modus ponendo tollens]]</i> \\ (valid inference)  ^^  <i :la>[[logic:inferences:modus_tollendo_ponens|Modus tollendo ponens]]</i> \\ (valid inference)  ^^ ^  Affirming a disjunct  \\ (Formal fallacy)  ^^
^ <span nobreak>Premise 1</span>|  <span "A or B, but not both">A ⊻ B</span> \\ <small>(A <i>or</i> B, <i nobreak>but not both</i>)</small>  ||  <span "A or [incl.] B">A ∨ B</span> \\ <small>(A <i>or</i> B, <i nobreak>or both</i>)</small>  || |  <span "A or [incl.] B">A ∨ B</span> \\ <small>(A <i>or</i> B, <i nobreak>or both</i>)</small>  ||
^ <span nobreak>Premise 2</span>|  A  |  B  |  <span "not A">⌐A</span> \\ <small>(not A)</small>  |  <span "not B">⌐B</span> \\ <small>(not B)</small>  | |  A  |  B  |
^ <span nobreak>Con­clu­sion</span>|  <span "not B">⌐B</span> \\ <small>(not B)</small>  |  <span "not A">⌐A</span> \\ <small>(not A)</small>  |  B  |  A  | |  <s "not B"  invalid short2>⌐B</s> \\ <small>(not B)</small>  |  <s "not A" invalid short2>⌐A</s> \\ <small>(not A)</small>  |
</div>

==== About the name ====

This form is similar to the <i :la>[[logic:inferences:modus_ponendo_tollens|Modus Ponendo Tollens]]</i>, in which one side of an exclusive //disjunct// ([[glossary:contravalence|contravalence]]) is //negated// and it follows that the other is //affirmative//. In this fallacy, the part of the disjunct statement is instead //affirmed// and it is (incorrectly) assumed that the other side must be //negated//.

However, the use of the term “disjunction” is somewhat misleading in this context, as this deduction is invalid only for certain kinds of disjunct statements, namely [[glossary:adjunction|adjunctions]] (//inclusive// disjunctions) while it is a valid conclusion for [[glossary:contravalence|contravalent]] (//exclusive// disjunction) statements.

===== When are such inferences valid? =====

//Affirming a disjunct// is a valid conclusion exactly when the premise contains a [[glossary:contravalence|contravalence]] (//exclusive// disjunction) rather than an [[glossary:adjunction|adjunction]] (//inclusive// disjunction). Furthermore, it must be ensured that the set of options is //complete//, i.e., that there are no other possibilities than the ones put forward.

<div keep-together>
Example:
> For dessert, you can have //either// an ice cream //or// a fruit salad.
> I’ll have ice cream!
> <span conclusio>So no fruit salad for you.</span>
</div>

By phrasing with "either … or" it is implied that there is an //exclusive// choice to be made: You can choose //either// ice cream //or// fruit salad, //but not both//! (However, the possibility that one might not want any dessert at all is not considered here).

If the above premises are fulfilled, this is valid inferrence, namely a [[logic:inferences:modus_ponendo_tollens|Modus Ponendo Tollens]].

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

  * [[glossary:disjunction|Disjunction]]
  * <i :la>[[logic:inferences:modus_ponendo_tollens|Modus Ponendo Tollens]]</i>
  * [[logic:formal_fallacies:denying_a_conjunct|Denying a Conjunct]]
  * [[errors:sherlock_holmes_fallacy|Sherlock-Holmes fallacy]]

===== More Information =====

  * [[wp>Affirming a disjunct]] on //Wikipedia//
  * [[https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/13/Affirming-a-Disjunct|Affirming a Disjunct]] on //Logically Fallacious//
  * [[http://www.fallacyfiles.org/afonedis.html|Affirming a Disjunct]] on //Fallacy Files//