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:

${\displaystyle p\vee q}$

${\displaystyle p}$

${\displaystyle {}\vdash {))$ ¬ ${\displaystyle q}$

Where ${\displaystyle {}\vdash {))$ 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.^[2]

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.^[3]

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.