Publications des Archives Henri-Poincaré Publications of the Henri Poincaré Archives Textes et Travaux, Approches Philosophiques en Logique, Mathématiques et Physique autour de 1900 Texts, Studies and Philosophical Insights in Logic, Mathematics and Physics around 1900 Éditeur/Editor: Gerhard Heinzmann, Nancy, France Louis Couturat−Traite´ de Logique algorithmique Edited by Oliver Schlaudt and Mohsen Sakhri, with an introduction and annotations by Oliver Schlaudt Birkhäuser Editors: Dr. Oliver Schlaudt Dr. Mohsen Sakhri Universitat¨ Heidelberg Laboratoire d’ Histoire des Sciences et de Philosophisches Seminar Philosophie - Archives Henri Poincare´ Schulgasse 6 UMR 7117 CNRS - Nancy-Universite´ 69117 Heidelberg Universite´ Nancy 2 Germany 91 avenue de la Libe´ ration - BP 454 54001 Nancy Cedex France ISBN 978-3-0346-0410-9 e-ISBN 978-3-0346-0411-6 DOI 10.1007/978-3-0346-0411-6 Library of Congress Control Number: 2010927519 © Springer Basel AG 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. Printed on acid-free paper Springer Basel AG is part of Springer Science+Business Media www.birkhauser.ch Preface Louis Couturat (1868–1914) was an outstanding intellectual of the turn of the nineteenth to the twentieth century. He is known for his work in the philosophy of mathematics, for his critical and editorial work on Leibniz, for his attempt to popularise modern logic in France, for his commitment to an international auxiliary language, as well as for his extended correspondence with scholars and mathematicians from Great Britain, the United States, Italy, and Germany. From his correspondence we know of four unpublished manuscripts on logic and its history, which were largely complete and some of which must have been of considerable size. We publish here for the first time in a critical edition the only one of these manuscripts that has been rediscovered: the Traité de Logique algorithmique, presumably written in the years 1899–1901. It is a highly interesting document of the academic reception and popularisation of symbolic logic in France. It provides evidence of the discussions and controversies which accompanied the creation of logic as a new branch of science. At the same time it completes the picture of Couturat’s work, which has been opened up to systematic study by the publication of important parts of his correspondence during the last decade. We append the article on Symbolic Logic of 1902 which Couturat wrote in collaboration with Christine Ladd- Franklin for Baldwin’s Dictionary of Philosophy and Psychology. This article, as now becomes evident, is a sort of résumé of the Traité; at the same time it points the way to Couturat’s Algèbre de la Logique of 1905. It thus helps to situate the Traité in Couturat’s œuvre. The same purpose is served by the second document appended, a short part of Couturat’s report of the first International Congress of Philosophy, which took place in Paris in 1900. This report documents Couturat’s reception of Platon Poretsky, whose work was of considerable importance for the outline of L’Algèbre de la Logique and marks the main difference between this later work and the Traité. – Since history of modern logic already attracts a lot of attention, the introduction focusses on Couturat and his perspective on modern logic in order to provide information the reader may lack. Finally a critical apparatus should help the reader to find his way through the Traité and to understand its genesis. Acknowledgements We are much obliged to the Laboratoire d’Histoire des Sciences et de Philosophie – Archives Henri Poincaré (UMR 7117 CNRS / Nancy-Université), especially to Gerhard Heinz- mann, for the generous intellectual and material support which rendered possible the realisation of this project, as well as to the CDELI (Centre de documentation et d’étude sur la langue internationale) at the municipal library of La Chaux-de-Fonds (Switzerland) for granting the printing licence for the manuscript. We are furthermore indebted to vi Preface a number of colleagues for their help and advice which were essential for our project. We would like to thank Paolo Mancuso (Berkeley), Peter McLaughlin (Heidelberg), Philippe de Rouilhan (Paris), Fabien Schang (Nancy/Dresden), Anne-Françoise Schmid (Lyon/Paris), Christian Thiel (Erlangen), and Paul Ziche (Utrecht). Contents I Introduction 1 I. Presentation of the Manuscript 3 II. Biographical Note 3 III. Dating of the Manuscript 5 IV. Origin and Meaning of the Term “Logique algorithmique” 7 V. Characterisation of the Manuscript 9 VI. Couturat’s Interest in Algebraic Logic 11 VII. Editorial Policy 32 VIII. Editorial Symbols in the Presentation of the Text 33 II Transcription of the Manuscript 35 Tome I 37 I. Définitions et notations : A. Logique des concepts 37 II. Définitions et notations : B. Logique des propositions 49 III. Principes 63 IV. Lois de la multiplication et de l’addition 75 V. Lois de la négation 93 VI. Développement des fonctions 107 VII. Théorie des équations 121 Appendice II. Sur les opérations inverses : Soustraction et division 145 Tome II 157 VIII. Théorie des inégalités 157 IX. Calcul des propositions constantes 185 viii Contents X. Calcul des jugements variables (ou des probabilités) 205 XI. Comparaison avec la Logique classique 225 XII. Conclusions 241 Editor’s Appendix: 251 A: Louis Couturat and Christine Ladd-Franklin: Symbolic Logic, 1902 251 B: Couturat on Schröder and Poretsky, on the Ist International congress 258 of Philosophy, Paris 1900 III Critical Apparatus 261 Variants and Annotations 263 Table of Correspondence with L’Algèbre de la Logique 294 List of Signs and Abbreviations 295 Table of Figures 296 Bibliography 297 Index Nominum 311 Index Rerum 312 Part I Introduction I. Presentation of the Manuscript The present text is a transcription of Louis Couturat’s manuscript entitled “Traité de Logique algorithmique”. Of this manuscript, only the tenth chapter has been published – posthumously in 1917. The present edition of the entire text is based on the only known copy, an undated handwritten version preserved at the CDELI (Centre de documentation et d’étude sur la langue internationale) at the library of La Chaux-de-Fonds in Switzerland. It was found there by Mohsen Sakhri in 2003 in the course of his research on Couturat’s work on international auxiliary languages. With dismay we must note that according to the CDELI the remaining papers of Couturat, including the manuscript of the Traité, have in the meantime been seriously damaged and partly destroyed by water during construction work. The only version available for study thus is a photocopy of the manuscript kept at the Archives Henri Poincaré at Nancy University (France). The manuscript consisted of two volumes of about 200 sheets each. The sheets are mostly used on one side; if used, the versos contain additional notes or corrections. Three handwritings can be distinguished: The rather uniform main text is in Couturat’s clear and easily legible handwriting; additional notes in different ink were presumably added by Couturat himself; and some notes that correspond to the 1917 edition of chapter X of the manuscript are in a different hand. On the last two pages of the second volume are placed a table of contents and a table of figures. The table of contents additionally indicates three appendices: I. Sur les signes adoptés, II. Soustraction et division (15 p.), and III. Solutions générales symétriques. However only one of them – on the logical operations of division and substraction – is given at the end of the first volume. II. Biographical Note Alexandre-Louis Couturat was an outstanding intellectual of the French Third Republic. He was born on January 17, 1868 in Ris-Orangis near Paris and died on August 3, 1914, on the eve of the First World War, when on the way from Paris to his country house in Bois le Roi he was involved in a fatal traffic accident with an army transporter during the mobilisation of the French army.1 Couturat is today still known as a Leibniz scholar and as an important figure in the propagation of modern logic in France. Couturat’s most creative period as a philosophical writer as well as a tireless propagator of the international auxiliary language Ido in the name of peace and internationalism coincided with the impact of the Dreyfus Affair on the French society. He expressed his pacifist convictions – coupled with profound knowledge in the history of philosophy – in a 1The main sources of his biography are André Lalande’s synopsis L’Œuvre de Louis Couturat, published in 1914 in the Revue de métapysique et de morale, and the obituary Couturat’s friend Louis Benaerts published in 1915 in L’annuaire de l’Association amicale de secours des Anciens Elèves de l’Ecole Normale Supérieure. These articles have been reprinted together with Arnold Reymond’s short obituary from 1915, but this booklet is difficult to find today. There are two monographs on Couturat, one from the Argentinean historian of mathematics Claro C. Dassen (1873–1941) from 1939, and a more recent one from Ubaldo Sanzo, published in 1991. Dassen’s book, reviewed by Quine in 1940, benefits from the author’s correspondence with Couturat from January 1902 until at least 1911 on the subject of Ido. O. Schlaudt, M. Sakhri (eds.), Louis Couturat – Traité de Logique algorithmique, Publications des Archives Henri Poincaré, DOI 10.1007/978-3-0346-0411-6_1, © Springer Basel AG 2010 4 Introduction polemic over Kant’s notion of war with the conservative writer Ferdinand Brunetière, a key figure of the Dreyfus Affair.