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]
Or in logical operators:
Where ⊢ ⊢ --> {\displaystyle {}\vdash {}} denotes a logical assertion.
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]
The following argument indicates the unsoundness of affirming a disjunct:
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]
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