# Philosophy:Affirming a disjunct

__: Formal fallacy__

**Short description**The formal fallacy of **affirming a disjunct** also known as **the fallacy of the alternative disjunct** or a **false exclusionary disjunct** occurs when a deductive argument takes the following logical form:^{[1]}

- A or B
- A
- Therefore, not B

Or in logical operators:

- [math]\displaystyle{ p \vee q }[/math]
- [math]\displaystyle{ p }[/math]
- [math]\displaystyle{ {} \vdash {} }[/math] ¬ [math]\displaystyle{ q }[/math]

Where [math]\displaystyle{ {} \vdash {} }[/math] denotes a logical assertion.

## Explanation

The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of equivocation between the operations OR and XOR.

Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.

## Examples

The following argument indicates the unsoundness of affirming a disjunct:

- Max is a mammal or Max is a cat.
- Max is a mammal.
- Therefore, Max is not a cat.

This inference is unsound because **all** cats, by definition, are mammals.

A second example provides a first proposition that appears realistic and shows how an obviously flawed conclusion still arises under this fallacy.

- To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful.
- This month's cover was a celebrity.
- Therefore, this celebrity is not very beautiful.

## See also

- Exclusive disjunction
- Logical disjunction
- Syllogistic fallacy

## External links

## References

- ↑ Sinnott-Armstrong, Walter; Simmons, Claire (2021-12-15). "Some common fallacies in arguments from M/EEG data".
*NeuroImage***245**: 118725. doi:10.1016/j.neuroimage.2021.118725. ISSN 1095-9572. PMID 34813968. https://pubmed.ncbi.nlm.nih.gov/34813968/.

Original source: https://en.wikipedia.org/wiki/Affirming a disjunct.
Read more |