To-day, as in all time, two great wants are felt by man. The first, the most imperious, is that of fixed, immutable principles, which depend upon neither times nor places nor circumstances, and on which the mind reposes with an unbounded confidence. In all investigations, as long as we have seized only isolated, disconnected facts, as long as we have not referred them to a general law, we possess the materials of science, but there is yet no science. Even physics commence only when universal truths appear, to which all the facts of the same order that observation discovers to us in nature may be referred. Plato has said, that there is no science of the transitory. This is our first need. But there is another, not less legitimate, the need of not being the dupe of chimerical principles, of barren abstractions, of combinations more or less ingenious, but artificial, the need of resting upon reality and life, the need of experience. The physical and natural sciences, whose regular and rapid conquests strike and dazzle the most ignorant, owe their progress to the experimental method. Hence the immense popularity of this method, which is carried to such an extent that one would not now condescend to lend the least attention to a science over which this method should not seem to preside. To unite observation and reason, not to lose sight of the ideal of science to which man aspires, and to search for it and find it by the route of experience,--such is the problem of philosophy. Now we address ourselves to your recollections of the last two years:--have we not established, by the severest experimental method, by reflection applied to the study of the human mind, with the deliberation and the rigor which such demonstrations exact,--have we not established that there are in all men, without distinction, in the wise and the ignorant, ideas, notions, beliefs, principles which the most determined skeptic cannot in the slightest degree deny, by which he is unconsciously, and in spite of himself, governed both in his words and actions, and which, by a striking contrast with our other knowledges, are marked with the at once marvellous and incontestable character, that they are encountered in the most common experience, and that, at the same time, instead of being circumscribed within the limits of this experience, they surpass and govern it, universal in the midst of particular phenomena to which they are applied; necessary, although mingled with things contingent; to our eyes infinite and absolute, even while appearing within us in that relative and finite being which we are? It is not an unpremeditated paradox that we present to you; we are only expressing here the result of numerous lectures.[18] It was not difficult for us to show that there are universal and necessary principles at the head of all sciences. It is very evident that there are no mathematics without axioms and definitions, that is to say, without absolute principles.