A type of logical argument, this structure presents two or more alternatives, asserting that at least one of them is true, then denying all but one. The remaining alternative is then affirmed as the conclusion. A common formulation follows this pattern: Either P or Q is true; P is not true; therefore, Q is true. For example: Either the key is in the drawer or it is on the table. The key is not in the drawer. Therefore, the key is on the table. The validity of this form relies on the initial premise establishing a genuine and exhaustive set of possibilities.
This argument form provides a crucial framework for deductive reasoning. It enables the elimination of possibilities, leading to a definitive conclusion when the initial disjunction accurately represents all viable options. Historically, its study has been integral to understanding logical argumentation and constructing sound proofs in various disciplines, including philosophy, mathematics, and law. Its strength lies in its ability to provide certainty, provided the initial premises are correct and complete.
