reduct, Craig See CRAIG ‘S INTERPOLATION THEO -. RE. reductio ad absurdum. (1) The principles (A / — A) / -A and (-A / A) / A. (2) The argument forms ‘If A then B and not-B; therefore, not-A’ and ‘If not-A then B and not-B; therefore, A’ and arguments of these forms. Reasoning via such arguments is known as the method of indirect proof. (3) The rules of inference that permit (i) inferring not-A having derived a contradiction from A and (ii) inferring A having derived a contradiction from not-A. Both rules hold in classical logic and come to the same thing in any logic with the law of double negation. In intuitionist logic, however, (i) holds but (ii) does not. See also DOUBLE NEGATION , MATHEMATICAL INTU — ITIONIS. G.F.S.