of relations, a complete system having nothing external to itself. The unity of the system, i.e. the unity of nature, is presupposed in all knowledge, and is the basis and gauge of its certainty. In mathematics this certainty is undoubtedly more stable, and rests upon a surer foundation, but we are not therefore justified in placing the exact, a priori, necessary science in opposition to the a posteriori and contingent natural sciences. In reality, mathematics, like other sciences, is the result of experience, in the sense that it consists in the analysis of the unconscious products of primordial mental creation, and that it rediscovers in things the relations unconsciously infused into them by thought. Its one and only claim to superiority lies in the fact that it is based on the simple and general conditions governing the existence of natural objects, that is to say, on quantitative and spatial conditions, of which it is possible to conceive apart from all others. The natural sciences, on the other hand, are not contingent, as is thought by those who place them in opposition to mathematics, since induction is not based on experience, analogy, or custom derived from many repetitions, which could never be sufficient authority for laying down a universal law. We do not pass from the known to the unknown, since such a transition would be unintelligible, nor from like to like, since we should have no authority for such a transition, but from identical to identical. In order to assert that that which has been recognised as true in one case holds good of a whole class, we must know that all the cases in question, whether they have come under observation or not, are identical as regards a certain aspect, that is to say, as regards that relation at all events to which the present induction refers.
The conditions of a natural phenomenon are extremely numerous and are never repeated, hence it follows that at times some of them may escape us; a geometrical problem, on the other hand, depends only upon conditions with which we are thoroughly acquainted, therefore
