The Collaborative International Dictionary
Contraposition \Con"tra*po*si"tion\, n. [Pref. contra- + position: cf. f. conterposition.]
A placing over against; opposite position. [Obs.]
--F. Potter.(Logic) A so-called immediate inference which consists in denying the original subject of the contradictory predicate; e. g.: Every S is P; therefore, no Not-P is S.
Douglas Harper's Etymology Dictionary
Wiktionary
n. (context logic English) The statement of the form "if not Q then not P", given the statement "if P then Q".
Wikipedia
In traditional logic, contraposition is a form of immediate inference in which from a given proposition another is inferred having for its subject the contradictory of the original predicate, and in some cases involving a change of quality (affirmation or negation). For its symbolic expression in modern logic see the rule of transposition. Contraposition also has distinctive applications in its philosophical application distinct from the other traditional inference processes of conversion and obversion where equivocation varies with different proposition types.
In logic, contraposition is a law that says that a conditional statement is logically equivalent to its contrapositive. The contrapositive of the statement has its antecedent and consequent inverted and flipped: the contrapositive of P → Q is thus ¬Q → ¬P. For instance, the proposition "All bats are mammals" can be restated as the conditional "If something is a bat, then it is a mammal". Now, the law says that statement is identical to the contrapositive "If something is not a mammal, then it is not a bat."
The contrapositive can be compared with three other relationships between conditional statements:
Inversion (the inverse), ¬P → ¬Q: "If something is not a bat, then it is not a mammal." Unlike the contrapositive, the inverse's truth value is not at all dependent on whether or not the original proposition was true, as evidenced here. The inverse here is clearly not true.Conversion (the converse), Q → P: "If something is a mammal, then it is a bat." The converse is actually the contrapositive of the inverse and so always has the same truth value as the inverse, which is not necessarily the same as that of the original proposition.
Negation, ¬(P → Q): "There exists a bat that is not a mammal. " If the negation is true, the original proposition (and by extension the contrapositive) is false. Here, of course, the negation is false.
Note that if P → Q is true and we are given that Q is false, ¬Q, it can logically be concluded that P must be false, ¬P. This is often called the law of contrapositive, or the modus tollens rule of inference.
Usage examples of "contraposition".
This was creative light, divine energy in the pure state, like the ignition of a keg of powder, which at first is black granules compressed into an opaque mass, and then all of a sudden it is an expansion of flames, a concentrate of lightning that spreads to its own extreme confine, beyond which, in contraposition, darkness is created (even if the explosion occurs at day).