Pierre-Simon, marquis de Laplace (1749-1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He wrote in the Introduction to this 1812 book, “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… as professor of mathematics with Lagrange… 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… nearly all our knowledge is problematical; and… even in the mathematical sciences themselves … are based on probabilities; so that the entire system of human knowledge is connected with the theory set forth in this essay… in considering, even in the eternal principles of reason, justice, and humanity, only the favorable changes which are constantly attached to them, there is a great advantage in following these principles and serious inconvenience in departing from them.” (Pg. 1-2)
He notes, “the transcendent results of calculus are, like all the abstractions of the understanding, general signs whose true meaning may be ascertained only by repassing by metaphysical analysis to the elementary ideas which have led to them; this often presents great difficulties, for the human mind tries still less to transport itself into the future than to retire within itself. The comparison of infinitely small differences with finite differences is able similarly to shed great light upon the metaphysics of infinitesimal calculus.” (Pg. 44)
He observes, “Amid the variable and unknown causes which we comprehend under the name ‘chance,’ and which render uncertain and irregular the march of events, we see appearing, in the measure that they multiply, a striking regularity which seems to hold to a design and which has been considered as a proof of Providence. But in reflecting upon this we soon recognize that this regularity is only the development of the respective possibilities of simple events which ought to present themselves more often when they are probable.” (Pg. 60)
Concerning jury trials, he points out, “In a jury of twelve members, if the plurality demanded for the condemnation is eight of twelve votes, the probability of the error to be feared is … a little more than one eighth, it is almost 1/22nd if this plurality consists of nine votes. In the case of unanimity the probability of the error to be feared is … more than a thousand times less than in our juries. This supposes that the unanimity results only from proofs favorable or contrary to the accused… the probability of the decision is too feeble in our juries, and I think that in order to give a sufficient guarantee to innocence, one ought to demand at least a plurality of nine votes in twelve.” (Pg. 139)
He comments, “[Leibnitz] imagined, since God can be represented by unity and nothing by zero, that the Supreme Being had drawn from nothing all beings, as unity with zero expresses all the numbers in this system of arithmetic. This idea was so pleasing to Leibnitz that he communicated it to the Jesuit Grimaldi… in the hope that this emblem of creation would convert to Christianity the emperor there who particularly loved the sciences. I report this incident only to show to what extent the prejudices of infancy can mislead the greatest men.” (Pg. 169)
He suggests, “Man, made for the temperature which he enjoys, and for the element which he breathes, would not be able, according to all appearance, to live upon the other planets. But ought there not to be an infinity of organization relative to the various constitutions of the globes of this universe? If the single difference of the elements and of the climates make so much variety in terrestrial productions, how much greater the difference ought to be among those of the various planets and of their satellites! The most active imagination can form no idea of it; but their existence is very probable.” (Pg. 181)
This book will be of interest not just to students of the history of science, but to students of probability and related areas.