Affirming a disjunct
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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:
- A or B
- A
- Therefore, not B
Or in logical operators:
- ¬
Where denotes a logical assertion.
Explanation[edit]
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[edit]
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.