Affirming a Disjunct

Alias:

• Affirming One Disjunct
• The Fallacy of the Alternative Syllogism
• Asserting an Alternative
• Improper Disjunctive Syllogism

Exposition:

Affirming a Disjunct is a non-validating form of argument when "or" is inclusive (see below), as it is standardly interpreted in propositional logic. 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 contrast, if we cannot rule out the truth of both disjuncts, then the argument is fallacious.

Exposure:

Most logic texts claim that "or" has two meanings:

1. Inclusive (or "weak") disjunction: One or both of the disjuncts is true, which is what is meant by the "and/or" of legalese.
2. Exclusive (or "strong") disjunction: Exactly one of the disjuncts is true.

As a form of argument, Affirming One Disjunct is perfectly valid for the exclusive sense of "or". It is only for the inclusive sense that it is a non-validating form. For this reason, if the textbook account is correct, there is a problem of ambiguity in the above two argument forms, which faces the application of Affirming One Disjunct as a fallacy. In order to accuse an argument of committing this fallacy, we must determine in which sense the "or" in the first premiss is used.

Sources:

• 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.