Publications des Archives Henri-Poincaré Publications of the Henri Poincaré Archives

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2 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

3 Louis Couturat Traitéde Logique algorithmique Edited by Oliver Schlaudt and Mohsen Sakhri, with an introduction and annotations by Oliver Schlaudt Birkhäuser

4 Editors: Dr. Oliver Schlaudt Universität Heidelberg Philosophisches Seminar Schulgasse Heidelberg Germany Dr. Mohsen Sakhri Laboratoire d Histoire des Sciences et de Philosophie - Archives Henri Poincar é UMR 7117 CNRS - Nancy-Université Universit é Nancy 2 91 avenue de la Libération - BP Nancy Cedex France ISBN e-isbn DOI / Library of Congress Control Number: 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

5 Preface Louis Couturat ( ) 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 From his correspondence we know of four unpublished manuscripts on logic and its history, which were largely complete and some of which must have been of considerable size.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 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 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 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 Heinzmann, 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

6 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).

7 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

8 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, 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