International Monthly, Vol. 4 (1901), p. 93.
[1960]. An assemblage (ensemble, collection, group, manifold) of elements (things, no matter what) is infinite or finite according as it has or has not a part to which the whole is just equivalent in the sense that between the elements composing that part and those composing the whole there subsists a unique and reciprocal (one-to-one) correspondence.—Keyser, C. J.
The Axioms of Infinity; Hibbert Journal, Vol. 2 (1903-1904), p. 539.
[1961]. Whereas in former times the Infinite betrayed its presence not indeed to the faculties of Logic but only to the spiritual Imagination and Sensibility, mathematics has shown ... that the structure of Transfinite Being is open to exploration by the organon of Thought.—Keyser, C. J.
Lectures on Science, Philosophy and Art (New York, 1908), p. 42.
[1962]. The mathematical theory of probability is a science which aims at reducing to calculation, where possible, the amount of credence due to propositions or statements, or to the occurrence of events, future or past, more especially as contingent or dependent upon other propositions or events the probability of which is known.—Crofton, M. W.
Encyclopedia Britannica, 9th Edition; Article, “Probability”
[1963]. The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which ofttimes they are unable to account. If we consider the analytical methods to which this theory has given birth, the truth of the principles on which it is based, the fine and delicate logic which their employment in the solution of problems requires, the public utilities whose establishment rests upon it, the extension which it has received and which it may still receive through its application to the most important problems of natural philosophy and the moral sciences; if again we observe that, even in matters which cannot be submitted to the calculus, it gives us the surest suggestions for the guidance of our judgments, and that it teaches us to avoid the illusions which often mislead us, then we shall see that there is no science more worthy of our contemplations nor a more useful one for admission to our system of public education.—Laplace.
Théorie Analytique des Probabilitiés, Introduction; Oeuvres, t. 7 (Paris, 1886), p. 153.
[1964]. It is a truth very certain that, when it is not in our power to determine what is true, we ought to follow what is most probable.—Descartes.