307. The understanding knows what it makes; but this is not all that it knows; for it has truths which neither are nor can be its works, since they are the basis of all its works, as, for example, the principle of contradiction. Can the impossibility of a thing being and not being at the same time be said to be the work of our reason? Assuredly not. Reason itself is impossible if this principle be not supposed; the understanding finds it in itself as an absolutely necessary law, as a condition _sine qua non_ of all its acts. Here, then, Vico's criterion fails: "the understanding knows only the truth it makes:" and yet the understanding knows but does not make the truth of the principle of contradiction. 308. Facts of consciousness are known by reason, although they are not its production. These facts are not only present to consciousness, but are also objects of the combinations of reason: here, then, Vico's criterion again fails. 309. Although in those things that are a purely intellectual work, the understanding knows what it makes, it does not make whatever it chooses; for then we should have to say that science is perfectly arbitrary: instead of the geometrical results we now have, we might have others as numerous as the individuals who deal in lines, surfaces, and solids. This shows reason to be subject to certain laws, its constructions to be connected with conditions which it cannot abstract. One of these conditions is the principle of contradiction, which would, were it to fail, annihilate all knowledge. True, by a series of intellectual constructions one may ascertain the size of a sphere; but can two understandings obtain two different values of it? They cannot, for that would be an absurdity: they may choose different ways, or express their demonstrations and conclusions in different terms; but the value is the same: if there be any discrepancy, it is because one or the other has fallen into an error. 310. If we thoroughly examine this matter, we shall perceive that the intellectual construction, of which Vico speaks, is a fact generally admitted. There are in this philosopher's system two new things, the one good, the other bad; the good, is to have indicated one reason of the certainty of mathematics; the bad, is to have exaggerated the value of his criterion. We have said that his system expressed a fact generally recognized, but exaggerated by him. The understanding undoubtedly creates, in some sense, ideal sciences; but in what sense? Solely by taking postulates, and combining its data in various ways. Here ends its creative power, for in these postulates and combinations it discovers truths not placed there by itself.