Philosophy: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:
- [math]\displaystyle{ p \vee q }[/math]
- [math]\displaystyle{ p }[/math]
- [math]\displaystyle{ {} \vdash {} }[/math] ¬ [math]\displaystyle{ q }[/math]
Where [math]\displaystyle{ {} \vdash {} }[/math] 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
- Exclusive disjunction
- Logical disjunction
- Syllogistic fallacy
External links
- Fallacy files: affirming a disjunct
- Bennett, Robert "Bo". "Affirming a Disjunct" (in en). Logically Fallacious. https://www.logicallyfallacious.com/logicalfallacies/Affirming-a-Disjunct.
References
- ↑ 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. https://pubmed.ncbi.nlm.nih.gov/34813968/.
- ↑ Lay, Steven. Introduction to Analysis with Proof, 5th edition. ISBN 978-0321747471. https://www.amazon.com/Analysis-Introduction-Proof-5th-Steven/dp/032174747X/ref=sr_1_1?crid=13UMHL6N7WEKN&keywords=introduction+to+analysis+with+proof&qid=1704598871&sprefix=introduction+to+analysis+with+proof%2Caps%2C131&sr=8-1.
- ↑ Rosen, Kenneth H.. "Discrete Mathematics and its Applications: Kenneth H. Rosen". https://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-author-dp-1260091996/dp/1260091996/ref=dp_ob_title_bk.
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