CHAPTER XV. Concerning the Benefits of Institutions which Depend upon the Probability of Events 149 CHAPTER XVI. Concerning Illusions in the Estimation of Probabilities 160 CHAPTER XVII. Concerning the Various Means of Approaching Certainty 176 CHAPTER XVIII. Historical Notice of the Calculus of Probabilities to 1816 185 ERRATA. Page 89, line 22, _for_ Pline _read_ Pliny " 102, lines 14, 16, " minutes " days " 143, line 25, " sun " soil " 177, lines 15, 17, 18, 21, 22, 24, _for_ primary _read_ prime " 182, line 5, _for_ conjunctions _read_ being binary A PHILOSOPHICAL ESSAY ON PROBABILITIES. CHAPTER I. _INTRODUCTION._ This philosophical essay is the development of a lecture on probabilities which I delivered in 1795 to the normal schools whither I had been called, by a decree of the national convention, as professor of mathematics with Lagrange. I have recently published upon the same subject a work entitled _The Analytical Theory of Probabilities_. I present here without the aid of analysis the principles and general results of this theory, applying them to the most important questions of life, which 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; so that the entire system of human knowledge is connected with the theory set forth in this essay. Doubtless it will be seen here with interest that in considering, even in the eternal principles of reason, justice, and humanity, only the favorable chances which are constantly attached to them, there is a great advantage in following these principles and serious inconvenience in departing from them: their chances, like those favorable to lotteries, always end by prevailing in the midst of the vacillations of hazard. I hope that the reflections given in this essay may merit the attention of philosophers and direct it to a subject so worthy of engaging their minds. CHAPTER II. _CONCERNING PROBABILITY._