Contrapositus

Part of speech: noun

Definitions

1. A term in logic indicating an assertion that represents the opposite conditions of a given proposition; a construction whereby the negation of a statement's consequent implies the negation of its antecedent; utilized in discussions of conditional statements to denote a specific logical transformation
2. A logical expression formed by contrapositing a conditional statement, wherein the original premise and conclusion are both negated; a method to prove equivalence by showing that one condition leads to the other in a logically inverted manner; often employed in formal arguments and proofs in mathematics and philosophy
3. Referring to the act of reversing a logical implication by switching and negating the components of a statement; a useful strategy in argumentation for establishing validity by confirming that the negation of the conclusion entails the negation of the premise; helps illustrate relationships within logical frameworks

Etymology: "Contrapositus" is the Latin past participle of "contraponere," meaning "to place opposite" or "to set against," built from "contra" (against, opposite) and "ponere" (to put, place). The participle "contrapositus" was used in medieval Latin logic, where a "contrapositio" was the act of placing a proposition in reverse, with its terms swapped and negated. The English noun "contrapositive" entered the vocabulary of logic through this Latin tradition, but the Latin form "contrapositus" itself is rarely used in English as a standalone noun. The reversal at the heart of the idea is simple. A statement such as "if it rains, the ground gets wet" is turned into "if the ground is not wet, it did not rain." The two statements stand or fall together, so proving one proves the other. Medieval logicians such as Peter of Spain treated this operation as one of the standard ways of transforming propositions, and it remains a basic tool of proof today.

Synonyms: contrapositive