To another group of the Cartesian sciences, however, Vico seems to grant a privileged position, one, that is, not of consciousness but of science strictly so called, in the sphere not of certitude but of truth; namely, the mathematical sciences. These, according to him, form the only region in which man's knowledge is identical in character with God's, perfect and demonstrative. This is not due, as Descartes supposed, to their self-evident character. Self-evidence, when employed in physical science and in matters of action, does not yield truth of the same conclusiveness as in mathematics. Nor is mathematics in itself self-evident. What clear and distinct idea can lead, for instance, to the conception of a line as composed of points having no parts? But the indivisible point which cannot be conceived in the world of reality, can be nevertheless denned. By defining certain names, man creates the elements of mathematics; by the postulates, he carries them on to infinity; by the axioms, he establishes certain eternal truths; and, disposing these elements with the help of these infinities and this eternity, he creates the truth which he teaches. The validity of mathematics then arises not from the Cartesian principle, but precisely from Vico's other proposition, the conversion of knowledge with creation. "We demonstrate mathematics, because we create their truth" (_mathematica demonstramus, quia verum facimus_). Man assumes unity and multiplicity, points and figures, and creates numbers and quantities which he knows perfectly because they are his own work. Mathematics is a constructive science; not only in its problems, but even in its theorems, which are commonly supposed to be mere objects of contemplation. For this reason it is a science which demonstrates _per causas,_ in opposition to that other common view which excludes from mathematics the concept of causation. It is in fact the only one among all the human sciences which truly demonstrates by causes. Hence its extraordinary accuracy. The whole secret of the geometrical method lies first in defining the terms, that is, creating the concepts which are to be the subject matter of our reasoning; secondly, in establishing certain common principles by mutual consent of the disputants; and lastly, if required, in making certain postulates of such a nature that they can be granted, to enable us to proceed with our deductions, which without such an agreement could make no progress; then, upon these principles, to advance by degrees from the demonstration of the simplest truths to the most complex, and not to affirm the complex propositions before examining singly their component parts.