The only kind of judgments that are the expression of true knowledge must, therefore, be synthetic judgments that are _a priori_. That is to say, they must express some new relation between ideas that is also universally and necessarily true. By _a priori_ Kant means the universal and necessary; and, furthermore, he maintains that the universal and necessary, and nothing else, constitutes knowledge. He points out that we make such judgments. When we say that the three angles of a triangle equal two right angles, or that every event has a cause, we are saying something universal and necessary, something not founded on experience. No one would admit that there were exceptions to these propositions. The question, then, that Kant tries to answer in his _Critique of Pure Reason_ is, How are synthetic judgments _a priori_ possible? Or since to Kant knowledge consists of synthetic judgments _a priori_, under what conditions is knowledge possible?[56] For the sake of clearness, let us state this problem of Kant in another way. It is the nature of man to try by mere thinking to discover the nature of reality. The dogmatic school of Rationalists had attempted, without calling in experience to its aid, to weave out of pure thought answers to the questions about God, immortality, and nature. It had maintained that clear and distinct notions have a reality corresponding to them, and are therefore real. Judgments formed in this way are analytic _a priori_; but it is evident that while such analyses of thought have a cogency for thought, they do not necessarily have a corresponding reality. On the other hand, conclusions based on experience have a kind of validity for the real world, but they yield no certain truth about it. These are synthetic judgments _a posteriori_. If Hume is right in saying that these are the only judgments dealing with nature, then we have no certain truth about nature. They give generalizations that are useful on the whole, but their conclusions range only from possibility to high probability, and never reach certainty. Besides (1) conceptual knowledge and (2) “knowledge of matters of fact,” Kant pointed out that there is a third kind. This is the only valid kind. This knowledge is based on synthetic judgments _a priori_. Such knowledge arises independently of experience, _i. e._ is _a priori_, and yet is valid for experience, _i. e._ is synthetic. Hume’s statement that such knowledge is synthetic _a posteriori_ is not accepted by Kant. Kant is, therefore, bound to show how this third class of synthetic judgments _a priori_ is possible, and how pure thought can be binding on experience.