# Affirming a disjunct

A formal fallacy in which a positive (affirmative) result for one alternative of an 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 rainorsnow today.

It is raining.

~~Therefore, it will~~notsnow today.

Even if the premise It will rain or snow today

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* disjunction (see: adjunction and contravalence).

Another possibility is an incorrect application of the *Modus tollendo ponens*, especially when mixed with the *Modus ponendo tollens*, can also lead to this fallacy. For comparison, the following table compares the two valid forms with the fallacy:

Modus ponendo tollens (valid inference) | Modus tollendo ponens (valid inference) | Affirming a disjunct (Formal fallacy) |
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---|---|---|---|---|---|---|---|

Premise 1 | A ⊻ B (A or B, but not both) | A ∨ B (A or B, or both) | A ∨ B (A or B, or both) |
||||

Premise 2 | A | B | ⌐A (not A) | ⌐B (not B) | A | B | |

Conclusion | ⌐B (not B) | ⌐A (not A) | B | A | (not B) | (not A) |

### About the name

This form is similar to the *Modus Ponendo Tollens*, in which one side of an exclusive *disjunct* (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 adjunctions (*inclusive* disjunctions) while it is a valid conclusion for contravalent (*exclusive* disjunction) statements.

## When are such inferences valid?

*Affirming a disjunct* is a valid conclusion exactly when the premise contains a contravalence (*exclusive* disjunction) rather than an 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.

Example:

For dessert, you can haveeitheran ice creamora fruit salad.

I’ll have ice cream!

So no fruit salad for you.

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 Modus Ponendo Tollens.

## See also

## More Information

- Affirming a disjunct on
*Wikipedia* - Affirming a Disjunct on
*Logically Fallacious* - Affirming a Disjunct on
*Fallacy Files*