Affirming a Disjunct

Taxonomy: Logical Fallacy > Formal Fallacy > Propositional Fallacy > Affirming a Disjunct

Alias:

Forms
p or q.
p.
Therefore, not-q.
p or q.
q.
Therefore, not-p.
Similar Validating Forms (Disjunctive Syllogism)
p or q.
Not-p.
Therefore, q.
p or q
Not-q.
Therefore, p.
Examples
Either it's raining or the sun is shining.
It's raining.
Therefore, the sun is not shining.
Either it's raining or the sun is shining.
The sun is shining.
Therefore, it's not raining.
Counter-Examples
Either Thomas Jefferson or John Adams died on the fourth of July, 1826.
Thomas Jefferson died on the fourth of July, 1826.
Therefore, John Adams did not die on the fourth of July, 1826.
Either Thomas Jefferson or John Adams died on the fourth of July, 1826.
John Adams died on the fourth of July, 1826.
Therefore, Thomas Jefferson did not die on the fourth of July, 1826.

Exposition:

Affirming a disjunct is a form of argument in which one disjunct of a disjunctive premiss is affirmed as a premiss, while the other disjunct is denied as a conclusion. There are two forms of the argument―see the table under "Forms", above―because there are two disjuncts that could be affirmed.

To deny a disjunct and affirm the other disjunct as a conclusion is a validating form of argument in propositional logic which is called "disjunctive syllogism"―see the Similar Validating Forms, above. Since these forms are similar, it is possible that one source of the fallacy is confusing affirming a disjunct with disjunctive syllogism. For a brief introduction to propositional logic, see the entry for propositional fallacy.

However, affirming a disjunct in order to deny the other is non-validating: if both disjuncts are true, then the premisses of the argument will be true and the conclusion false―but see "Types of Disjunction", below. This can also be seen from the Examples above: though raining while the sun is shining may be an unusual phenomenon, many of us have seen this happen. Therefore, if either of these arguments were made on such an occasion, the premisses would be true while the conclusion was false, and thus the argument would be invalid. Finally, the Counter-Examples also displayed above are invalid arguments with the forms of the fallacy, and are specifically designed to show that the form is not validating; surprisingly, both Thomas Jefferson and John Adams died on July Fourth, 1826.

Exposure:

Sources:

Acknowledgment: Thanks to Noah Cooper and Pedro G. Rodrigues for criticisms that led me to revise this entry.