Sources in the History of Mathematics and Physical Sciences 13 Editor G.J. Toomer Advisory Board J.Z. Buchwald P.J. Davis T. Hawkins A.E. Shapiro D. Whiteside Springer New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Andrew I. Dale Pierre-Simon Laplace Philosophical Essay on Probabilities Translated from the fifth French edition of 1825 With Notes by the Translator Springer Andrew I. Dale Department of Mathematical Statistics University of Natal King George V Avenue Durban, Natal 4001 Republic of South Africa Library of Congress Cataloging-in-Publication Data Laplace, Pierre Simon, marquis de. 1749-1827. [Essai philosophique sur les probabilites. English] Philosophical essay on probabilities / Pierre Simon Laplace: translated from the fifth French edition of 1825 by Andrew I. Dale, with notes by the translator. p. cm. - (Sources in the history of mathematics and physical sciences: vol. 13) Includes bibliographical references. I. Probabilities. I. Dale, Andrew I. II. Title. III. Series: Sources in the history of mathematics and physical sciences ; 13. QA273.18.L3713 1994 519.2--dc20 94-25497 Printed on acid-free paper. © 1995 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1995 All rights reserved. This work may not be translated or copied in whole or in part without the written pennission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any fonn of infonnation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. 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Philosophical Essay on Probabilities, Translated from the fifth French edition of 1825, With Notes by the Translator TRANSLATOR'S PREFACE Pierre-Simon Laplace (1749-1827) is remembered today among students of probability for his many memoirs on that subject and, more particularly, for his Theorie Analytique des Probabilites, first published in 1812. The second edition of November 1814 of this work had, as an introduction, an Essai Philosophique sur les Probabilitis, the first edition of which had a~ peared in February of that same year. Here, without the aid of symbolic mathematics, Laplace provided a popular exposition of his Theorie. This Essai was based on a lecture on probability given by Laplace at the Bcoles Normales in 1795. It underwent sweeping changes, almost doubling in size, in the three editions of the Theorie that were published during Laplace's lifetime. Part of this increase was effected by the incorporation of extracts from the first edition of the Theorie Analytique des Probabilites into the Essai. Thus a major part of the first article of Book II of the Theorie appears in this translation in the articles headed "On probability" and "General principles of the probability calculus" , while part of the first paragraph of the second article of the same book appears at the start of the article here entitled "On expectation" . Translations of various editions in different languages have appeared over the years. In 1902 an English translation (stated on the title page of the 1952 reprint as being of the sixth French edition) was published. Ade­ quate as this might have been at the time, it reads awkwardly today, and several mathematical phrases are obscured in translation - for example, who would recognize "generating functions" in the phrase "discriminant functions"? It was the presence of such obscurities that made me take up the task of providing a translation of the Essai. The fifth edition of the Essai has recently been re-issued with new notes and with a preface by Rene Thom and a postscript by Bernard Bru. Other works that proved useful were the German translation of the Essai published by Richard von Mises in 1932 and Karl Pearson's History of Statistics in the 17th & 18th Centuries. vii NOTE ON THE TRANSLATION 'Imnslation is always a more or less crim­ inal act against both author and readers. W.H. Donahue. H it is to read well, a translation must not be too literal, and if it is accu­ rately to reflect the original work, it must not be too free. What is aimed at here, then, is in fact, in some degree, a paraphrase of Laplace's Essai Philosophique sur lea Probabilites. To reproduce Laplace's style in transla.­ tion is impossible, and I have occasionally allowed myself the liberty of a rude rendering to preserve the sense of the original. In his Higher English Rahtz suggests that On the one hand, the paraphrase should contain as much as possible of the meaning of the original, even to the smallest details; and, on the other hand, the result should be a readable bit of prose, developing in logical order and proportion the ideas rather than the words of the original. [1921, p. 327] The production of the best results, he further avers, depends on the taste of the writer and the nature of the subject. Whether I have achieved such production is for the reader to decide, though I would like to be able to say, with Gibbon, The curious reader ... will perhaps accuse me of giving a bold and licentious paraphrase; but, if he considers it with atten­ tion, he will acknowledge that my interpretation is probable and consistent. [1896, vol. 1, p. 429] The difficulties of a translator are well summed up by Lin Yutang in The Wisdom of Confucius as follows: In the actual act of translation, the translator is faced with two jobs after he has grasped the meaning of the sentence. First he is faced with the choice of one of a number of synonyms, and failure to get at the exact word would completely fail to render the meaning of the remark clear to the reader ... In the second ix x Note on the translation place, the translator cannot avoid putting the thought in the more precise concepts of a modern language. [1943, pp. 45-46] Being also assured of the truth of these words, I have not tried to be com­ pletely consistent in my translating. Thus while vraisemblance, hasard and probabilite are given as "likelihood", "chance" and "probability" respec­ tively, Laplace's espemnce is translated sometimes by "hope" (when it is contrasted with "fear") and sometimes by "expectation" (when it is used in its modern probabilistic sense). Ordinary footnotes are labelled with the usual footnote symbols ., t, &c.; these footnotes are usually my comments on the text. Additional words of explanation, my additions, are given in braces { ... }. Numbers in brackets [... ] (some of which may be in the footnotes) refer to the Notes following the translation: all of these notes, unless otherwise indicated, are mine. I have indicated differences between the first and the fifth editions of the Essai by using italic Greek and Roman superscripts. Thus, for exam­ ple, on page 1, the text passage" aof mathematics with Lagrange by decree of the National Conventiona " has a footnote "a-a and which appeared in the Journal de l'Ecole Polytechnique." This means that the text passage between the superscripts appeared in the first edition in the form shown in the footnote. Similarly, the labelling on page 19 of the footnote as "p-p20" indicates that the passage (from the first edition) in the footnote occurs in the main text between the superscripts p and P, the second superscript P appearing on page 20. The appearance of main text between superscripts for which there is no footnote means that the distinguished passage did not appear in the first edition, but is in the fifth.