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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, it is not the case that B
Or in logical operators:
¬ 
Where 
denotes a logical assertion.
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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.
Example [edit]
The following argument indicates the invalidity of affirming a disjunct:
- Max is a cat or Max is a mammal.
- Max is a cat.
- Therefore, Max is not a mammal.
This inference is invalid. If Max is a cat then Max is also a mammal. (Remember "or" is defined in an inclusive sense not an exclusive sense.)
- The car is red or the car is large.
- The car is red.
- Therefore, the car is not large.
The above example of an argument also demonstrates the fallacy.
See also [edit]
External links [edit]
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