“Whether or not I have effected anything of real value ... is a question for competent judges to decide. Of this, at least, I feel certain, that whatever imperfections may be observed, the fault consists, not in the method proposed, but in the extreme difficulty of any single man putting into full operation all the parts of so vast a scheme. It is on this point, and on this alone, that I feel the need of great indulgence. But, as to the plan itself, I have no misgivings. Of defects in its execution I am not unconscious. I can only plead the immensity of the subject, the shortness of a single life and the imperfection of every single enterprise. I, therefore, wish this work to be estimated, not according to the finish of its separate parts, but according to the way in which those parts have been fused into a complete and symmetrical whole. This, in an undertaking of such novelty and magnitude, I have a right to expect, and I would moreover, add, that if the reader has met with opinions adverse to his own, he should remember, that his views are, perhaps, the same as those which I too once held, and which I have abandoned, because, after a wider range of study, I found them unsupported by solid proof, subversive of the interest of Man, and fatal to the progress of his knowledge. To examine the notions in which we have been educated, and to turn aside from those which will not bear the test, is a task so painful, that they who shrink from the sufferings should pause before they reproach those by whom the suffering is undergone.... Conclusions arrived at in this way are not to be overturned by stating that they endanger some other conclusions; nor can they be even affected by allegation against their supposed tendency. The principles which I advocate are based upon distinct arguments supported by well ascertained facts. The only points, therefore, to be ascertained, are, whether the arguments are fair, and whether the facts are certain. If these two conditions have been obeyed, the principles follow by an inevitable inference.” And why have I sought throughout to follow the spirit of mathematics? Because I have been dealing with ideas and have desired, above all things else, to be right and clear. Ideas have a character of their own—they are right or wrong independently of our hopes and passions and will. In the connection of ideas there is an unbreakable thread of destiny. That is why in his _Mathematical Philosophy_ Professor Keyser has truly said: “Mathematics is the study of Fate—not fate in a physical sense, but in the sense of the binding thread that connects thought with thought and conclusions with their premises. Where, then, is our freedom? What do you love? Painting? Poetry? Music? The muses are _their_ fates. Whoso loves them is free. Logic is the muse of Thought.”