The life of one man is short, and to very few is it given to achieve much in their lifetime. Extensive achievements are made almost entirely by many men taking up the work done by a discoverer. In such a case, we arrive at a _complete_ “truth,” not by the production of one man but by a chain of men, but the initial discovery not only has to be produced but correctly defined before it can be used and that is the important point to be made. What we do not realize is the tremendous amount of mental work that is lost by an incorrect use of words.
Human thought—that unique, subtle and yet most energetic phenomenon of nature—is in the main wantonly wasted, because we do not use, or take pains to use, suitable language; at the same time, false definitions lead to consequences not merely wasteful but positively harmful. When ideas and facts are falsely defined, they tend to bring us to false conclusions, and false conclusions lead us in wrong directions, and life and knowledge greatly suffer in consequence. Our progress is not a well ordered pursuit after truth, as pure chance plays too large a part in it.
Until lately, logic was supposed to be the science of correct thinking, but modern thought has progressed so far that the old logic is not able to handle the great accumulated volume—the great complicated mass of existing ideas and facts—and so we are forced to look for another instrument much more expedient and powerful. There is no need to establish a new science to replace logic; we simply have to look closer into the sciences at hand and realize the fact, which was with us all the time, namely, that mathematics and mathematical reasoning is nothing else than the true logic of nature—nature’s universal tongue—the one means of expression that is the same for all peoples. This is not a play on words, it is a fact which, after investigation, everybody must admit. Everybody who wants to think logically must think mathematically or give up any pretense of correct thinking—there is no escape and all who refuse to investigate the justice of this statement put themselves outside the pale of logically thinking people. The application of rigorous thinking to life will even revolutionize scientific methods by the introduction of right definitions, correct classifications, just language, and so will lead to trustworthy results. Very probably all our doctrines and creeds will have to be revised; some rejected, some rectified, some broadened; bringing about unanimity of all sciences and thus greatly increasing their effectiveness in the pursuit of truth. This application of mathematics to life will even revolutionize mathematics itself. In App. I it is suggested tentatively how this may be accomplished.