In relation to mathematics Bertrand Russell has said: “Logic is the youth of mathematics, mathematics is the manhood of logic.” This brilliant _mot_ of the eminent philosopher of mathematics is no doubt just and is profoundly significant; the least it can teach us is that it is useless to try to find a dividing line between logic and mathematics, for no such line exists; to seek for one serves merely to betray one’s ignorance of mathematical philosophy. Elsewhere Mr. Russell says: “The hope of satisfaction to our more human desires, the hope of demonstrating that the world has this or that ethical characteristic, is not one which, so far as I can see, philosophy can do anything whatever to satisfy.” By “philosophy” he means mathematical philosophy—a philosophy that is rigorously scientific, not vaguely speculative. I am entirely unable to agree with him that such a philosophy can make no contribution to ethics. On the contrary, I contend, and in this book I hope to show, that by mathematical philosophy, by rigorously scientific thinking, we can arrive at the true conception of what a human being really is and that in thus discovering the characteristic nature of man we come to the secret and source of ethics. Ethics as a science will investigate and explain the essential nature of man and the obligations which the essential nature of man imposes upon human beings. It will be seen that to live righteously, to live ethically, is to live in accordance with the laws of human nature; and when it is clearly seen that man is a natural being, a part of nature literally, then it will be seen that the laws of human nature—the only possible rules for ethical conduct—are no more _super_natural and no more _man_-made than is the law of gravitation, for example, or any other natural law. It is no cause for wonder that mathematical thinking should lead to such a result; for Man is a _natural_ being, man’s mind is a _natural agency_, and the results of rigorous thinking, far from being artificial fictions, are natural facts—natural revelations of natural law. I hope I have not given the impression, by repeated allusion to mathematical science, that this book is to be in any technical sense a mathematical treatise. I have merely wished to indicate that the task is conceived and undertaken in the mathematical spirit, which must be the guiding spirit of Human Engineering; for no thought, if it be non-mathematical in spirit, can be trusted, and, although mathematicians sometimes make mistakes, the spirit of mathematics is always right and always sound.