 Leibniz gives various formulations to his Principle of Contradiction or Law of Identity, but the central idea is that a proposition and its negation cannot both be true (G 7: 299). Leibniz hoped to be able to construct a logical calculus that would enable all significant truths to be demonstrated, since every concept must include, be included in, or exclude every other. A concept such as ‘human,’ he maintained, included the concepts ‘animal,’ ‘rational,’ ‘bipedal,’ etc., so that a true statement such as ‘Humans are animals’ was true in virtue of the inclusion of the predicate in the subject. Though the magnitude of Leibniz’s contribution to combinatorial mathematics and logic remained unknown until the twentieth century, Kant offers some skeptical remarks to what he takes to be the Leibnizian programme in Section II of the New Elucidation. Later, he offers two specific criticisms of the Principle of Contradiction taken not in a logical, but in an ontological sense: