Affirming a disjunct

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:

¬

Where 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.

See also

References

  1. ^ 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.
  2. ^ Lay, Steven (2014). Introduction to Analysis with Proof, 5th edition. Pearson. ISBN 978-0321747471.
  3. ^ Rosen, Kenneth H. (2019). Discrete Mathematics and its Applications: Kenneth H. Rosen. McGraw-Hill. ISBN 978-1260091991.
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