kontraposition

Kontraposition is a rule of inference in propositional and predicate logic. It states that from a conditional statement of the form “If P then Q” one may infer its contrapositive, “If not Q then not P.” In classical logic the contrapositive is logically equivalent to the original statement: P → Q is true exactly when ¬Q → ¬P is true. Consequently, proving the contrapositive provides a proof of the original statement, and vice versa. The contrapositive is a common technique in mathematical proofs and formal reasoning.

Extensions and caveats: The same form applies to predicates in predicate logic. When quantifiers are present, care is needed with scope, but the basic equivalence typically holds under classical semantics. In non-classical logics, such as intuitionistic logic, the contrapositive may not be an equivalent reformulation of the original statement; some implications that hold classically may fail to hold constructively.

Examples:

- If it is raining, then the streets are wet. Contrapositive: if the streets are not wet, then it is not raining.

- If a number n is even, then n^2 is even. Contrapositive: if n^2 is not even (i.e., is odd), then n is not even (i.e., is odd).

Limitations: While contrapositive is valid for many mathematical and formal arguments, translating statements with vague natural-language content may introduce ambiguities. The contrapositive focuses on logical form rather than causal or empirical readings of a statement.