RUSSELL‘S PHILOSOPHICAL APPROACH TO LOGICAL ANALYSIS BERTRAND RUSSELL‘S PHILOSOPHICAL APPROACH TO LOGICAL ANALYSIS, 1897-1905. By JOLEN GALAUGHER, B.A.H; M.A. A Thesis Submitted to the School of Graduate Studies in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy. McMaster University © Copyright by Jolen Galaugher, December, 2011 McMaster University DOCTOR OF PHILOSOPHY (2011) Hamilton, Ontario (Philosophy) TITLE: Bertrand Russell‘s Philosophical Approach to Logical Analysis, 1897-1905 AUTHOR: Jolen Galaugher, B.A.H (University of Winnipeg); M.A. (McMaster University) SUPERVISOR: Professor Nicholas Griffin NUMBER OF PAGES: viii, 291. ii ABSTRACT In what is supposed to have been a radical break with neo-Hegelian idealism, Bertrand Russell, alongside G.E Moore, advocated the analysis of propositions by their decomposition into constituent concepts and relations. Russell regarded this as a breakthrough for the analysis of the propositions of mathematics. However, it would seem that the decompositional-analytic approach is singularly unhelpful as a technique for the clarification of the concepts of mathematics. The aim of this thesis will be to clarify Russell‘s early conception of the analysis of mathematical propositions and concepts in the light of the philosophical doctrines to which his conception of analysis answered, and the demands imposed by existing mathematics on Russell‘s logicist program. Chapter 1 is concerned with the conception of analysis which emerged, rather gradually, out of Russell‘s break with idealism and with the philosophical commitments thereby entrenched. Chapter 2 is concerned with Russell‘s considered treatment of the significance of relations for analysis and the overturning of his ―doctrine of internal relations‖ in his work on Leibniz. Chapter 3 is concerned with Russell‘s discovery of Peano and the manner in which it informed the conception of analysis underlying Russell‘s articulation of logicism for arithmetic and geometry in PoM. Chapter 4 is concerned with the philosophical and logical differences between Russell‘s and Frege‘s approaches to logical analysis in the logicist definition of number. Chapter 5 is concerned with connecting Russell‘s attempt to secure a theory of denoting, crucial to mathematical definition, to his decompositional conception of the analysis of propositions. iii ACKNOWLEDGMENTS It is a pleasure to express my heartfelt thanks to those who have helped and encouraged me in writing this thesis. I am exceptionally grateful to my supervisor, Nicholas Griffin, who exemplifies a rare combination of supervisory virtues and has a knack for raising my morale enough for me to try to meet his sometimes exacting expectations. I could not have had written this thesis without his incisive criticism and surprising patience. I feel fortunate to have belonged to a supportive and collegial department and am grateful for the continual encouragement I received from the McMaster department of philosophy. I am exceedingly grateful to Ric Arthur for the invaluable insights he contributed to earlier drafts, especially in all that concerns the philosophy of Leibniz. I also am especially grateful to Sébastien Gandon, whose comments and questions led me to think matters through more carefully and whose work on logicism is a paradigm of Russell scholarship that has informed my own work significantly. I owe a debt of gratitude to Michael Beaney, who patiently introduced me to Frege, and who has since offered support and feedback from which I have benefitted tremendously. I am thankful to Kenneth Blackwell, Rosalind Carey, Arlene Duncan, Kevin Klement, Ilmari Kortelainen, Gregory Landini, Bernard Linsky, Consuelo Preti, and Russell Wahl, who have each, in a unique and important way, contributed to my project. I would also like to acknowledge SSHRC for supporting my research. My warmest thanks to my family, to my grandparents, and especially to my mom, who is a constant source of love and generosity; to my amazing friend, Matt Grellette, for challenging me and cheering me up; to Rachel, for her constant helpfulness and supportive presence; to Jeff for his caring and understanding, to Jeremy and Rebecca for good discussion, Alanda for keeping me motivated, and Val for setting a great example in life and work. Finally, thanks to my siblings, Tara Galaugher and Bryan Galaugher, for being themselves; I dedicate this thesis to them. iv TABLE OF CONTENTS ABSTRACT ............................................................................................................................. iii ACKNOWLEDGMENTS…………………………………………………………………………………………………………………iv LIST OF ABBREVIATIONS......................................................................................................... vi INTRODUCTION ...................................................................................................................... 1 CHAPTER 1: ANALYSIS AND THE DECOMPOSITION OF IDEALISM ................................................ 8 1.1 CONTEXTUALIZING RUSSELL’S BREAK WITH IDEALISM.................................................. 8 1.2 TRANSCENDENTAL DEDUCTIONS .............................................................................. 25 1.3 INTERNAL RELATIONS AND THE CONTRADICTION OF RELATIVITY................................ 43 CHAPTER 2: RELATIONS IN ANALYSIS ..................................................................................... 54 2.1 EXTERNAL RELATIONS AND THE PRIMITIVE DIVERSITY OF LOGICAL SUBJECTS: THE IMPORT OF RUSSELL’S WORK ON LEIBNIZ ....................................................................... 54 2.2 THE INTENSIONAL DOCTRINE OF RELATIONS AND THE PHILOSOPHICAL APPROACH TO ANALYSIS ...................................................................................................................... 99 CHAPTER 3: LOGICISM AND THE ANALYSIS OF MATHEMATICAL PROPOSITIONS ..................... 118 3.1 LOGICISM AND EXISTING MATHEMATICS ................................................................ 118 3.2 MORE LOGICISM: THE FORM OF IMPLICATIONS AND THE ROLE OF EXPLICIT DEFINITIONS .................................................................................................................................. 136 3.3 THE LOGIC OF RUSSELL’S LOGICISM AND THE CONTRADICTION ................................ 157 CHAPTER 4: LOGIC AND ANALYSIS IN RUSSELL’S DEFINITION OF NUMBER.............................. 174 4.1 RUSSELL’S AND FREGE’S LOGICIST DEFINITIONS OF NUMBER ................................... 174 4.2 RUSSELL’S REJECTION OF FREGE’S (AMENDED) DEFINITION...................................... 194 CHAPTER 5: TOWARD A NEW THEORY OF DENOTING ........................................................... 225 5.1 FAMILIAR WOES: DENOTING CONCEPTS.................................................................. 225 5.2 MATHEMATICAL FUNCTIONS AND DENOTING COMPLEXES ...................................... 245 CONCLUSION...................................................................................................................... 273 BIBLIOGRAPHY ................................................................................................................... 281 v LIST OF ABBREVIATIONS LH Bodemann, E. 1895. Die Leibniz-Handschriften der Koniglichen offentlichen. Hanover: Bibliothek zu Hannover. PL Bradley, F.H. 1967. The Principles of Logic. 2nd Ed. London: Oxford University Press. A&R 1893. Appearance and Reality: A Metaphysical Essay. London: Swan Sonnenschein. BLA Frege, Gottlob. 1964. The Basic Laws of Arithmetic. Montgomery Furth, trans. Berkeley: University of California Press. CO ―On Concept and Object,‖ in The Frege Reader, Michael Beaney, Ed. Oxford: Blackwell, 181–93. CP 1984. Collected Papers on Mathematics, Logic and Philosophy. B. McGuinness, Ed. Oxford/New York: Basil Blackwell. FA 1980. The Foundations of Arithmetic. J.L. Austin, trans. Illinois: Northwestern University Press. GG 1893–1903. Grundgesetze der Arithmetik. Jena: Verlag Hermann Pohle. PMC 1980. Philosophical and Mathematical Correspondence. Gabriel, Gottfried, et al., Eds. Oxford: Basil Blackwell. PW 1979. Posthumous Writings. Hans Hermes, Friedrich Kambartel, Friedrich Kaulbach, Eds. Chicago: University of Chicago Press. G Leibniz, G.W. 1965. Die Philosophische Schriften von Leibniz, 7 vols., C.I. Gerhardt (ed). Hildesheim: Olms. I Moore, G.E. 1900-1. ―Identity,‖ Proceedings of the Aristotelian Society vol. 1, 103-127. N 1900. ―Necessity,‖ Mind vol. 9, no. 35, 289–304. NJ 1899. ―The Nature of Judgment,‖ Mind vol. 8, no. 30, 176-93. PE 1903. Principia Ethica. Cambridge: Cambridge University Press. vi SW Peano, Giuseppe. 1990. Selected Works of Giuseppe Peano. H.C. Kennedy, Ed. Toronto and London: University of Toronto Press. AMR Russell, Bertrand. 1898. ―An Analysis of Mathematical Reasoning Being an Inquiry into the Subject-Matter, the Fundamental Conceptions, and the Necessary Postulates of Mathematics,‖ in Papers 2, 155–242. AOG 1899. ―The Axioms of Geometry,‖ in Papers 2, 390–415. COR 1899. ―The Classification of Relations,‖ in Papers 2, 136–146. EAE 1898. ―Are Euclid‘s Axioms Empirical?‖ in Papers 2, 322–338. EFG 1897. An Essay on the Foundations of Geometry. Cambridge: Cambridge University Press. FIAM ―The Fundamental Ideas and Axioms of Mathematics,‖ in Papers 2, 261– 305. FN 1904. ―Fundamental Notions,‖ in Papers 4, 111-259. FUND 1905. ―On Fundamentals,‖ in Papers 4, 359-413. IMP 1919. Introduction to Mathematical Philosophy. London: G. Allen & Unwin. LOR 1901. ―The Logic of Relations