 As Kant had noted in 1787, the theory of deductive inference had not progressed since antiquity.In the 1870s, C S Peirce and Gottlob Frege, unbeknownst to one another, revolutionized deductive logic through vast efforts identifying it with mathematical proof.An American who originated pragmatism—or, since 1905, "pragmaticism", distinguished from more recent appropriations of his original term—Peirce recognized induction, too, but continuously insisted on a third type of inference that Pierce variously termed "abduction", or "retroduction", or "hypothesis", or "presumption".