This should not be interpreted to mean that Leibniz denied the "freedom of the will." What he denied is a notion of freedom which seemed to him at once unverifiable, useless, and irrational. There is a conception of freedom which Leibniz not only accepts, but insists upon. Such a notion of freedom is indeed his ethical ideal. Its three traits are contingency, spontaneity, and rationality of action. How action can be at the same time contingent and determined is perhaps difficult to understand; but Leibniz takes the position that it is. His first step is to distinguish between physical, mathematical, metaphysical, and moral necessity. There are truths which are eternal, truths which are absolutely necessary, because their opposites involve contradiction. They cannot be violated without involving us in absurdity. There are other truths which are "positive," that is, ordained for good reason. These truths may be _a priori_, or rational, and not merely empirical; for they have been chosen for reasons of advantage. God always chooses and ordains the best of a number of possibilities; but he does it, not because the opposite is impossible, but because it is inferior. Truths whose opposites are impossible have metaphysical and mathematical necessity. Positive truths have moral necessity. The principle of causation _must_ be true; the three interior angles of a triangle _must_ be equal to two right angles. But that God shall choose the better of two courses is a moral necessity only. It invokes no absolute logical contradiction to conceive him choosing some other way. Upon moral necessity depends the physical. The particular laws of nature are necessary, not because their opposites are logically absurd, but because these laws are most in accordance with the general principles of good and order, in agreement with which God chooses. Physical and moral action is therefore in all cases contingent. (Contingency does not of itself, of course, constitute freedom, but conjoined with the characteristics of rationality and spontaneity, does so.)