Affirming a Disjunct
Taxonomy: Logical Fallacy > Formal Fallacy > Propositional Fallacy > Affirming a Disjunct
Alias:
- Affirming One Disjunct1
- The Fallacy of the Alternative Syllogism2
- Asserting an Alternative
- Improper Disjunctive Syllogism1
| 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:
A disjunction is a statement of the "either-or" form, and a disjunct is one of the components that make it up. For instance, "It's either raining or snowing" is a disjunction, and "it's raining" and "it's snowing" are its disjuncts.
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.
Exception:
As mentioned in the Exposition section, above, the form of Affirming a Disjunct is non-validating, which means that not every argument of that form is valid. This doesn't mean that every argument that affirms a disjunct is invalid; rather, it means that some arguments of that form are invalid. There are arguments of that form that are formally valid, but all of them are such that the second premiss alone implies the conclusion, that is, the immediate inference from the second premiss to the conclusion is valid. Therefore, before pronouncing an instance of affirming a disjunct invalid, check to see whether the second premiss implies the conclusion.
Exposure:
- Types of Disjunction: Most logic texts claim that "or" has two meanings:
- Inclusive (or "weak") disjunction: One or both of the disjuncts is true, which is what is meant by the "and/or" of legalese. Affirming a Disjunct is a non-validating form of argument when "or" is inclusive, as it is usually interpreted in propositional logic.
- Exclusive (or "strong") disjunction: Exactly one of the disjuncts is true.
So, to affirm a disjunct of an exclusive disjunction is a validating form of argument, and it's only fallacious to affirm one in an inclusive disjunction. For this reason, if the textbook account is correct, there is a problem of ambiguity in applying the fallacy. In order to accuse an argument of committing this fallacy, we must first determine in which sense the "or" in the disjunctive premiss is used.
- Enthymemes: Even assuming that the disjunction in such an argument is inclusive, there is a further difficulty: As with other propositional fallacies, an argument which affirms a disjunct is most likely to seem valid when we take into consideration some further information not explicitly mentioned in the argument. In the case of Affirming a Disjunct, this is:
Suppressed Premiss: Not both p and q.
If we have some reason to believe that the two disjuncts are contraries, then the argument may be a valid enthymeme. In other words, even if the "or" in the disjunctive premiss is not inclusive, it may be a matter of fact that both disjuncts cannot be true, in which case the argument would be valid with an additional premiss stating this fact. However, if we cannot rule out the truth of both disjuncts, then the argument is fallacious.
Acknowledgment: Thanks to Noah Cooper and Pedro G. Rodrigues for criticisms that led me to revise this entry.
Notes:
- Robert Audi (General Editor), The Cambridge Dictionary of Philosophy (Second Edition), 1995, p. 316.
- William L. Reese, Dictionary of Philosophy and Religion (Humanities Press, 1980), p. 169. An "alternative" is Reese's term for an "inclusive" disjunction―see, above, under "Types of Disjunction" in the Exposure section.