=1. The Renaissance.=--It would be giving a wrong impression to imply that there was no inquiry, no use of reason in the mediæval world. The problems set by the inheritance of old-world religion and politics, forced themselves upon the builders of castles and cathedrals,[93] of law and of dogma. As indicated above, the universities were centers of discussion in which brilliant minds often challenged received opinions. Men like Roger Bacon sought to discover nature's secrets, and the great scholastics mastered Greek philosophy in the interest of defending the faith. But theological interest limited freedom and choice of theme. It was not until the expansion of the individual along the lines already traced--in political freedom, in the use of the arts, in the development of commerce--that the purely intellectual interest such as had once characterized Greece awoke. A new world of possibilities seemed dawning upon the Italian Galileo, the Frenchman Descartes, the Englishman Francis Bacon. The instruments of thought had been sharpened by the dialectics of the schools; now let them be used to analyze the world in which we live. Instead of merely observing nature Galileo applied the experimental method, putting definite questions to nature and thus preparing the way for a progress step by step toward a positive knowledge of nature's laws. Descartes found in mathematics a method of analysis which had never been appreciated before. What seemed the mysterious path of bodies in curved lines could be given a simple statement in his analytic geometry. Leibniz and Newton carried this method to triumphant results in the analysis of forces. Reason appeared able to discover and frame the laws of the universe--the "principles" of nature. Bacon, with less of positive contribution in method, sounded another note which was equally significant. The human mind is liable to be clouded and hindered in its activities by certain inveterate sources of error. Like deceitful images or obsessions the "idols" of the tribe, of the cave, of the market, and of the theater--due to instinct or habit, to language or tradition--prevent the reason from doing its best work. It needs vigorous effort to free the mind from these idols. But this can be done. Let man turn from metaphysics and theology to nature and life; let him follow reason instead of instinct or prejudice. "Knowledge is power." Through it may rise above the kingdom of nature the "kingdom of man." In his _New Atlantis_, Bacon foresees a human society in which skill and invention and government shall all contribute to human welfare. These three notes, the experimental method, the power of rational analysis through mathematics, and the possibility of controlling nature in the interests of man, were characteristic of the period.