The Tractatus Paradox Reza Mosmer A thesis submitted to the University of Birmingham for the degree of DOCTOR OF PHILOSOPHY Department of philosophy School of Philosophy, Theology and Religion College of Art and Law University of Birmingham May 2013 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract In the penultimate remark of the Tractatus Logico-Philosophicus Wittgenstein declares that anyone who understands him judges the book to be nonsense. The immediate reaction to this paradoxical statement is to reject the insights of the book that this assessment is based on; that is, to reject the book’s theories of logic and language. Commentators have tried to save the book’s fundamental philosophical ideas by blocking this immediate response. In this thesis I characterise and explore different attempts to do so. I discuss attempts of Russell, Carnap, Max Black, Malcolm, Hacker’s Ineffability interpretation and Conant’s (and Diamond’s) Therapeutic interpretation. I argue that the Therapeutic reading is the most promising attempt in its main ideas. Nonetheless, current versions of the Therapeutic readings do not seem successful. I borrow ideas from Grice’s pragmatic theory of conversation and Davidson’s account of metaphor to explain how the book is to be read therapeutically. I argue that the book is a long conversation between Wittgenstein and his audience which eventually turns out to be a pointless series of remarks. The book, however, works metaphorically in such a way that it affects its readers and helps them to divest themselves of the inclination to do philosophy. Acknowledgements I would like to express my gratitude to my supervisors Alex Miller (2009-2012), Jussi Suikkanen and Darragh Byrne (2012-2013). This thesis would not have been possible without their patience, generous help and encouragement. I will always be grateful that I have had this opportunity to learn from them. I would also like to thank my committee members Scott Sturgeon, Denis McManus and Nikk Effingham. I would like to dedicate this thesis to my parents Azizeh Hajefeizi and Habib Mosmer who have supported me endlessly. Contents Introduction.............................................................................................................................1 Chapter 1: Historical background.......................................................................................12 1.0 Introduction.......................................................................................................................12 1.1. Kant on Logic and Mathematics......................................................................................15 1.2 Criticisms of Kant’s Concept of Logic...............................................................................18 1.3 Function-argument Analysis.............................................................................................20 1.4 The Theory of Descriptions...............................................................................................23 1.5 Frege and Russell on Analyticity......................................................................................25 1.6 Frege’s Concept of Numbers............................................................................................29 1.7 Russell’s Paradox .............................................................................................................32 1.8 Russell’s Theory of Types................................................................................................33 1.9 Frege’s and Russell’s Theories of Language...................................................................36 1.9.1 The Context Principle and the Sense-Reference distinction.........................................37 1.9.2 Russell’s theory of judgement........................................................................................42 Chapter 2: Logic, Metaphysics and Language in the Tractatus.......................................45 2.0 Introduction.......................................................................................................................45 2.1 Logic.................................................................................................................................48 2.1.1 Wittgenstein’s conception of logic..................................................................................48 2.1.2 An Argument against logical objects..............................................................................51 2.1.3 The significance of the concept of logic ........................................................................53 2.2 Metaphysics......................................................................................................................55 2.3 Language..........................................................................................................................68 2.3.1 The General Theory of Depiction...................................................................................68 2.3.1 (a) Depiction and Representation..................................................................................70 2.3.1 (b) The Logical Form of Depiction and the Pictorial Relationship..................................71 2.3.1 (c) Bipolarity and Bivalence...........................................................................................73 2.3.1 (d) Depicting and Displaying..........................................................................................74 2.3.2 Transcendental Argument for Simple Objects...............................................................76 2.3.3 Language as a Depiction...............................................................................................79 2.3.4 The Sentence-Name Distinction and the Context Principle...........................................81 2.3.5 Inferential Role Semantics and the Notion of Senselessness.......................................90 Chapter 3: The Tractatus Paradox and the Reductio Response......................................98 3.0 Introduction.......................................................................................................................98 3.1 Wittgenstein’s Criticisms of Russell’s Theory of Types..................................................100 3.1 (a). Russell’s Theory of Types is Nonsense....................................... ...........................105 3.1 (b). Russell’s Appeal to the Theory of Types is Unnecessary........................................106 3.2 The Saying-Showing Distinction.....................................................................................107 3.3 The Tractatus Paradox...................................................................................................112 3.4 The Reductio Response....................................... .........................................................117 Chapter 4: Early Attempts to Block the Reductio Response; Russell, Carnap and Black....................................................................................................................................122 4.0Introduction......................................................................................................................122 4.1 Russell’s Metalinguistic Solution.....................................................................................124 4.2 Carnap’s Metalinguistic Solution.....................................................................................129 4.2.1 The Argument for Meta-language................................................................................132 4.2.2 The Argument for Senselessness................................................................................135 4.2.3 The Relation Between Two Arguments.......................................................................140 4.3. Objections to Metalinguistic Solutions...........................................................................143 4.3.1 External Evidence........................................................................................................144 4.3.2 Internal Evidence.........................................................................................................145 4.4 Black’s Two Arguments..................................................................................................147 4.4.1 The Book-as-Tautology Argument...............................................................................149 4.4.2 The Mental Labour Argument......................................................................................155 4.5 Conclusion......................................................................................................................161 Chapter 5: The Ineffability Attempt to Block the Reductio Response; the case of Hacker..................................................................................................................................162 5.0 Introduction.....................................................................................................................162