Page:An Investigation of the Laws of Thought (1854, Boole, investigationofl00boolrich).djvu/259

CHAP. XVI.] CHAPTER XVI. ON THE THEORY OF PROBABILITIES. EFORE the expiration of another year just two centuries will have rolled away since Pascal solved the first known question in the theory of Probabilities, and laid, in its solution, the foundations of a science possessing no common share of the attraction which belongs to the more abstract of mathematical speculations. The problem which the Chevalier de Méré, a reputed gamester, proposed to the recluse of Port Royal (not yet withdrawn from the interests of science by the more distracting contemplation of the "greatness and the misery of man"), was the first of a long series of problems, destined to call into existence new methods in mathematical analysis, and to render valuable service in the practical concerns of life. Nor does the interest of the subject centre merely in its mathematical connexion, or its associations of utility. The attention is repaid which is devoted to the theory of Probabilities as an independent object of speculation,—to the fundamental modes in which it has been conceived,—to the great secondary principles which, as in the contemporaneous science of Mechanics, have gradually been annexed to it,—and, lastly, to the estimate of the measure of perfection which has been actually attained. I speak here of that perfection which consists in unity of conception and harmony of processes. Some of these points it is designed very briefly to consider in the present chapter. A distinguished writer has thus stated the fundamental definitions of the science: