For history, lines exist of the movement of human wills, one end of which is hidden in the unknown but at the other end of which a consciousness of man’s will in the present moves in space, time, and dependence on cause.
The more this field of motion spreads out before our eyes, the more evident are the laws of that movement. To discover and define those laws is the problem of history.
From the standpoint from which the science of history now regards its subject on the path it now follows, seeking the causes of events in man’s free will, a scientific enunciation of those laws is impossible, for however man’s free will may be restricted, as soon as we recognize it as a force not subject to law, the existence of law becomes impossible.
Only by reducing this element of free will to the infinitesimal, that is, by regarding it as an infinitely small quantity, can we convince ourselves of the absolute inaccessibility of the causes, and then instead of seeking causes, history will take the discovery of laws as its problem.
The search for these laws has long been begun and the new methods of thought which history must adopt are being worked out simultaneously with the self-destruction toward which—ever dissecting and dissecting the causes of phenomena—the old method of history is moving.
All human sciences have traveled along that path. Arriving at infinitesimals, mathematics, the most exact of sciences, abandons the process of analysis and enters on the new process of the integration of unknown, infinitely small, quantities. Abandoning the conception of cause, mathematics seeks law, that is, the property common to all unknown, infinitely small, elements.