Formal fallacy

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Affirming a disjunct is a fallacy

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:

- $p\vee q$
- $p$
- ${}\vdash {))$ ¬ $q$

Where ${}\vdash {))$ denotes a logical assertion.

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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.

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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.