The inquiry now turns from the origin of ideas to their cognitive value or their validity, beginning (in the concluding chapters of the second book) with the accuracy of single ideas, and advancing (in Book iv., which is the most important in the whole work) to the truth of judgments. An idea is real when it conforms to its archetype, whether this is a thing, real or possible, or an idea of some other thing; it is adequate when the conformity is complete. The idea of a four-sided triangle or of brave cowardice is unreal or fantastical, since it is composed of incompatible elements, and the idea of a centaur, since it unites simple ideas in a way in which they do not occur in nature. The layman’s ideas of law or of chemical substances are real, but inadequate, since they have a general resemblance to those of experts, and a basis in reality, but yet only imperfectly represent their archetypes. Nay, further, our ideas of substances are all inadequate, not only when they are taken for representations of the inner essences of things (since we do not know these essences), but also when they are considered merely as collections of qualities. The copy never includes all the qualities of the thing, the less so since the majority of these are powers, i.e., consist in relations to other objects, and since it is impossible, even in the case of a single body, to discover all the changes which it is fitted to impart to, or to receive from, other substances. Ideas of modes and relations