"Imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes."

“The most important questions of life... are indeed for the most part only problems of probability. Strictly speaking it may even be said that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, the principal means for ascertaining truth—induction and analogy—are based on probabilities.”

“It is to the influence of the opinion of those whom the multitude judges best informed, and to whom it has been accustomed to give its confidence in regard to the most important matters of life, that the propagation of those errors is due, which in times of ignorance, have covered the face of the earth. Magic and astrology offer us two great examples. These errors... having for a basis only universal credence, have maintained themselves during a very long time; but at last the progress of science has destroyed them in the minds of enlightened men, whose opinion consequently has caused them to disappear... through the power of imitation and habit which had so generally spread them... This power, the richest resource of the moral world, establishes and conserves in a whole nation ideas entirely contrary to those... elsewhere... What indulgence ought we not then to have for opinions different from ours, when this difference often depends only upon the various points of view where circumstances have placed us! Let us enlighten those whom we judge insufficiently instructed; but first let us examine critically our own opinions, and weigh with impartiality, their respective probabilities.”

“Nature laughs at the difficulties of integration.”

“All these efforts in the search for truth tend to lead it back continually to the vast intelligence... but from which it will always remain infinitely removed. This tendency peculiar to the human race is that which renders it superior... and their progress in this respect distinguishes nations and ages and constitutes their true glory.”

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

“The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought.”