Yet not exactly with the Descartes of positive history, but with Descartes as a doubter, as perhaps the most notable progenitor of the modern confession and the modern use of doubt, are we now directly concerned; for without the license of this broader view we might lose a large part of the advantage of the centuries that lie between Descartes' time and our own. He had many disciples, and these disciples uncovered much in the Cartesian philosophy that Descartes himself failed to see, or saw only imperfectly. He was not without faults, too, some moral and some intellectual, if the two are separate, and these faults we shall not consider, though the conscientious historian should never play to the sentimentalist by disregarding them. But with our present task we can afford to forget the faults; just as we cannot afford to lose the interpretations and corrections of the disciples. With interests as vital and personal as ours, we seek something more than matter of fact. Our interest is very near to that of the historical novel, but needless to say, this book is an essay in philosophy, not a novel. Past men and past times can be really useful to us, only if, belonging as we do not to the seventeenth but to the twentieth century, we really use them. What we ourselves are able to find in any period or in any human career is always truer or realer, possibly in a sense it is also better history, than what lay on the surface at the time or than what was seen, however profoundly, even by contemporaries. So much better did Descartes and all really great men build than they knew or even willed.

Descartes came into European life at a crucial moment. The period of the Renaissance, with its rediscovery of the old world and its stirring vision of the new, had culminated in the Reformation, not merely in the religious reformation that set Protestant against Catholic, but in the reformation that appeared in every department of man's life—in art, literature, and science, in morals and in politics, as well as in religion. Man asserted his independence of established authority in any form. Man, not king, not pope, not even God, became the real centre of the universe. Justification by his own faith was simply overflowing with a meaning that knew no bounds in his experience.

But the birth of Descartes was fifty years after the death of Luther, and by the time he had reached his intellectual majority, as might well be expected, the Reformation had changed from a spiritual enthusiasm—whether among those who were its great leaders or among those who, not less devoutly, were bent on summarily checking its progress—into a practical, thoroughly worldly situation. The two opposing parties, without exaggeration, seem to have settled down to real business, and not less in the thought of one than in that of the other the end justified any means.

The society of Jesus was definitely organized and began its notable career in 1640, and although its members, the Jesuits, have given to history many wonderful examples of devotion and heroism, Jesuitry itself is synonymous with the extreme materialism to which the Roman Church resorted in its desperate defence against the Protestants. And on the other side, men became not less sensuous and worldly, giving as good as they got. They simply met, or opposed, like with like. Reading the history of the time with its controversies and jealousies and intrigues and persecutions, one can only conclude that the honours were about even. If Catholicism felt justified in her acts of sensuous brutality, of almost hellish violence, which culminated in the massacre of St. Bartholomew, Protestantism was made the specious, yet not less welcome, excuse for worldliness, general materialism, and sensualism out of the Church and in it. Any religious reform, or reform of any sort, must always bring an unscrupulous lawlessness with it, and the great Reformation was by no means an exception to this rule. Extreme humanists, naturalists, atheists, sensationalists, social and physical atomists, Machiavellists, sceptics and opportunists of all sorts, swarmed in every capital of Europe, and especially in Paris.[1]

But the extravagant, more or less unconventional things of any time are often the best signs of its inner life, since in them we see a few men boldly, if not prudently, stepping over the bounds of custom, and sometimes even of decency, and giving expression to what is actively present, though often suppressed or concealed, in the lives of all. Thus contemporary with Descartes, and from one side or another expressing the materialism of his day, there were at least three very significant movements, all of them endorsed by parties, of course under different names, from both of the contending churches, or from their outside echoes or reflections, and all of them at least in some degree when not in great degree beyond the bounds of common conventional respectability. These movements in one church or in the other, or in neither, as the case might be, were, first, a scoffing scepticism; second, a dogmatic mysticism; and third, a most visionary gnosticism.

1. Vanini (1585-1619) in Italy, Montaigne (1533-1592) in France, and Bacon (1560-1620) in England, among many others that might be named, were more or less extravagantly, not mere doubters, but satirical, often derisive, scoffing doubters of everything in human life. Conceit of knowledge, whenever asserted, in church or state, in everyday consciousness or in science, was declared idolatry and held up to constant ridicule. Could man's wisdom at its best be anything more than a blinding folly?

2. And religion, the religion of a few, as if in acknowledged sympathy with these sceptics, surrendered everything but God—God being more a longing than an actual fact; a spirit than a positive thing or person. Even within the Catholic Church the Oratory of Jesus, a society energetically opposed for good and sufficient reasons by the Jesuits, was organized in the interests of a purified, truly spiritual Christianity; and among those who had broken with the Catholics appeared new sects of many names, such as the "Friends of God," "Collegiants," and the "Brotherhood of the Christian Life," but with one ideal, the direct untrammelled worship of God. "God is," they proclaimed in so many words; "and God, just God, is all. Church and creeds and rites and priests are hindrances, not helps, to true religion." This attitude, commentary as of course it was on the conditions of the day, had almost more satire in it and more doubt than any of the words of the most active scoffers; it was so unconscious; so quietly and so piously it picked up the crumbs that the scoffers left. Indeed, the sceptics and their devout, pure-minded contemporaries, Pierre Charron (1541-1603) and Jakob Boehme (1595-1624), both advocates of religious purity against theology and sensuous ritual, must be said not to have engaged in separate activities, but to have shared the labour of a single activity. Scepticism and such mysticism are but two sides of the same shield.

3. But with the scoffing scepticism and its complementary counterpart, the dogmatic mysticism of religion, there was associated also a most visionary gnosticism. Thus the science of mathematics was heralded as a key to all the secrets of the universe. A few simple applications of mathematics to physical phenomena had been successfully made by the scientists—for example, by Galilei—and ere long certain men in the world of the intellectual life went wild over the possibilities of mathematics. Obliged, as soon they were, to abandon every other field of knowledge—theology, politics, material science, tradition, and convention—they needed but little encouragement to give themselves heart and soul to this last resort. Their enthusiasm for mathematics doubtless had a deeper source than this simple account of its rise would suggest, for an intellectual atmosphere in which just such a purely logical, abstract science would develop was the natural product of medievalism; but Galilei's successes may be said to have precipitated the movement, and in any case for many mathematics became, both in its principles and in its method, an intellectual cure-all, and in consequence not only were remarkable advances made in the science itself, but men went to the extreme of applying the methods and the formulæ of mathematics in every conceivable direction. Religion, morality, and politics, as well as natural science, were all subjected to mathematical treatment. Among the surviving monuments to this activity the Ethics, so called, of Benedict Spinoza (1632-77) is certainly the most noteworthy; a work of five books on God, mind, emotions, bondage, and freedom—each with its special quota of axioms, propositions, corollaries, scholia, and the like, and the procedure of the whole amazingly consistent with that of Euclid. Excuse, also, a personal reminiscence. I can myself recall how in the enthusiasm of a first course in geometry I formulated a Euclidean proof of the proposition: Knowledge is power. I, too, had my axioms, my special demonstrations, my corollaries, and my final Q.E.D.'s. But any present-day resort to mathematics or its methods is only a shadow, or an echo, of the movement of the seventeenth century. At that time it was a movement of last resort and all the passion of a deceived intellect, of a mind given over to the most far-reaching doubts, and a disappointed faith, once more acquiring hope, was present in it. The truths and methods of mathematics—what but veracity incarnate, the very mind of God made manifest to mankind!

Nor, furthermore, does it take much reflection to appreciate that mathematics was after all a very appropriate form for credible knowledge to take in a time of scepticism and of religion turning to purism. Trustworthy knowledge of actual things—that is to say, real concrete knowledge—being held impossible, there was nothing left but knowledge of the strictly formal relations of things. Formal principles, just like those of mathematics, are altogether innocent of the confusion in actual things and persons, in particular events and current issues; and accordingly in the seventeenth century, just by reason of this innocence, they were peculiarly timely. Doubt seemed quite unable to touch them; controversy was turned to agreement before them; and even a truth-loving God, so to speak, could appeal to them in support of his right to rule the minds and the lives of men. You and I might question the reality of the things we count or the justice of the ratio between our wealth and the wealth of certain others in the world, but we could not easily question that two and two are four, or in matters of wealth that one thousand and two thousand dollars are in the same ratio as two million and four million. Such knowledge as this may not settle any actual quarrels that we have, for example, over the number of acres we own or the taxes we pay or the prices charged by our butchers or grocers; but what of that? The quarrels are idle any way, and our mathematical wisdom, being exact from the start and self-evident, is a basis of perfect agreement between man and man and men and God.

In short, mathematics is exact and universally credible just because it is so empty and so logically formal, being always "in the abstract," in that ideal, wholly blessed region, where there is no disputing, where all men readily admit anything that can be suggested; and its being exact for this cause made it the only credible knowledge for Descartes' time, a time at once of scepticism and mysticism. With Vanini, then, and Charron, who were separately engaged, as was remarked, in a single activity, we may associate the mathematicians of the day, among whom none were more distinguished than Descartes himself and the members of the Cartesian school. To Descartes we are largely indebted for the Analytic Geometry, and Pascal did important work in the Theory of Equations.