What does contraposition mean?
Contraposition is a formal-logical operation that transforms a conditional statement of the form “if P, then Q” into “if not Q, then not P.” The transformed statement is called the contrapositive, and it is logically equivalent to the original conditional: whenever the first is true, so is the second. Contraposition is especially useful because it makes the dependencies in an argument explicit, revealing what would have to be false if a conclusion were false. It should not be confused with simply reversing a conditional into “if Q, then P,” which is its converse, or with denying its antecedent. Outside philosophy, mathematics, and closely related technical fields, the word is relatively uncommon, though it can also refer more generally to placing things in contrast or in opposite positions. Recognising the term helps readers distinguish a valid logical reformulation from the several superficially similar transformations that may not be valid.
nounIn formal logic, contraposition is the transformation of a conditional statement of the form “if P, then Q” into the logically equivalent conditional “if not Q, then not P.” More generally and rarely, it means the placing of things side by side in contrast or in opposite positions.
- The logical transformation of a conditional statement “if P, then Q” into “if not Q, then not P.”
- The placing of two things side by side in contrast or in opposite positions.
"The proof uses contraposition to establish that if the conclusion is false, its necessary premise must also be false."
"The proof uses contraposition to rewrite the conditional in a form that exposes its hidden dependency."
"Counsel used contraposition, reasoning that if the duty had not arisen, the statutory condition could not have been met."
Rare; the plural is chiefly used in technical writing referring to several conditionals or logical transformations.
"These contrapositions are all logically equivalent to their original conditionals."
Move “If P, then Q” around and logic lands on its mirror image: “If not Q, then not P.”
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does contraposition come from?
Contraposition comes from Late Latin contrapositio, formed from contra- (“against” or “opposite”) and positio (“a placing”), ultimately from Latin ponere (“to put”). The term entered English in the seventeenth century as vocabulary in formal logic. Its Latin relatives position, proposition, composition, and deposition preserve the same etymological family of meanings involving placement, setting forth, or putting forward.
Related word forms
How contraposition is actually used
Chiefly formal and technical, especially in logic, philosophy, mathematics, and legal argument. In general prose it can sound specialist or archaic, and its use is not notably region-specific.
Easily confused with contraposition
Contraposition is the operation or process of transforming a conditional, whereas the contrapositive is the transformed conditional statement itself.