Discourse on Method, Part 3.
[1965]. As demonstration is the showing the agreement or disagreement of two ideas, by the intervention of one or more proofs, which have a constant, immutable, and visible connexion one with another; so probability is nothing but the appearance of such an agreement or disagreement, by the intervention of proofs, whose connexion is not constant and immutable, or at least is not perceived to be so, and it is enough to induce the mind to judge the proposition to be true or false, rather than contrary.—Locke, John.
An Essay concerning Human Understanding, Bk. 4, chap. 15, sect. 1.
[1966]. The difference between necessary and contingent truths is indeed the same as that between commensurable and incommensurable numbers. For the reduction of commensurable numbers to a common measure is analogous to the demonstration of necessary truths, or their reduction to such as are identical. But as, in the case of surd ratios, the reduction involves an infinite process, and yet approaches a common measure, so that a definite but unending series is obtained, so also contingent truths require an infinite analysis, which God alone can accomplish.—Leibnitz.
Philosophische Schriften [Gerhardt] Bd. 7 (Berlin, 1890), p. 200.
[1967]. The theory in question [theory of probability] affords an excellent illustration of the application of the theory of permutation and combinations which is the fundamental part of the algebra of discrete quantity; it forms in the elementary parts an excellent logical exercise in the accurate use of terms and in the nice discrimination of shades of meaning; and, above all, it enters into the regulation of some of the most important practical concerns of modern life.—Chrystal, George.
Algebra, Vol. 2 (Edinburgh, 1889), chap. 36, sect. 1.
[1968]. There is possibly no branch of mathematics at once so interesting, so bewildering, and of so great practical importance as the theory of probabilities. Its history reveals both the wonders that can be accomplished and the bounds that cannot be transcended by mathematical science. It is the link between rigid deduction and the vast field of inductive science. A complete theory of probabilities would be the complete theory of the formation of belief. It is certainly a pity then, that, to quote M. Bertrand, “one cannot well understand the calculus of probabilities without having read Laplace’s work,” and that “one cannot read Laplace’s work without having prepared oneself for it by the most profound mathematical studies”—Davis, E. W.
Bulletin American Mathematical Society, Vol. 1 (1894-1895), p. 16.
[1969]. The most important questions of life are, for the most part, really only problems of probability. Strictly speaking one may even say 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, induction and analogy, the principal means for discovering truth, are based on probabilities, so that the entire system of human knowledge is connected with this theory.—Laplace.