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Language and Logic in Wittgenstein's Tractatus Logico-Philosophicus

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Language and Logic in Wittgenstein's Tractatus Logico-Philosophicus LANGUAGE AND LOGIC IN WITTGENSTEIN’S TRACTATUS LOGICO-PHILOSOPHICUS Daniele Mezzadri Submitted for the degree of Doctor of Philosophy Department of Philosophy University of Stirling July 2010 Acknowledgements I would like to express my gratitude to my supervisors; Peter Sullivan, for his scrupulous but always patient and encouraging supervision. His help and guidance in getting me to develop and shape my research plans – from the initial to the final level – has been invaluable; Colin Johnston, for his support and friendly assistance (extending beyond the scope of my thesis work) in the late stages of my research. I would like to thank everybody in the Department of Philosophy at the University of Stirling – academics, members of support staff, fellow graduate students – for creating a friendly, supportive and stimulating environment to carry out research. I have learned a lot, not only about philosophy, from being part of this community. My work was conducted while holding a PhD scholarship provided by the Department of Philosophy, University of Stirling, and a Royal Institute of Philosophy Bursary. I gratefully acknowledge their support. Finally, I would like to express special thanks to my parents, for their constant support throughout the years. Without them my work would not have been possible. This thesis is dedicated to them, with gratitude and love. 1 Abstract This thesis discusses some central aspects of Wittgenstein‟s conception of language and logic in his Tractatus Logico-Philosophicus and brings them into relation with the philosophies of Frege and Russell. The main contention is that a fruitful way of understanding the Tractatus is to see it as responding to tensions in Frege‟s conception of logic and Russell‟s theory of judgement. In the thesis the philosophy of the Tractatus is presented as developing from these two strands of criticism and thus as the culmination of the philosophy of logic and language developed in the early analytic period. Part one examines relevant features of Frege‟s philosophy of logic. Besides shedding light on Frege‟s philosophy in its own right, it aims at preparing the ground for a discussion of those aspects of the Tractatus‟ conception of logic which derive from Wittgenstein‟s critical response to Frege. Part two first presents Russell‟s early view on truth and judgement, before considering several variants of the multiple relation theory of judgement, devised in opposition to it. Part three discusses the development of Wittgenstein‟s conception of language and logic, beginning with Wittgenstein‟s criticism of the multiple relation theory and his early theory of sense, seen as containing the seeds of the picture theory of propositions presented in the Tractatus. I then consider the relation between Wittgenstein‟s pictorial conception of language and his conception of logic, arguing that Wittgenstein‟s understanding of sense in terms of bipolarity grounds his view of logical complexity and of the essence of logic as a whole. This view, I show, is free from the internal tensions that affect Frege‟s understanding of the nature of logic. 2 Table of Contents Introduction 5 Part One: Frege’s Conception of Logic [1] Logic: Thoughts and the Predicate ‘True’ 17 [1.1] The Predicate „True‟ 17 [1.2] Thoughts 20 [2] Is Logic Normative or Descriptive? 26 [2.1] Laws of Truth and Laws of Thought 26 [2.2] From Laws of Thought to Laws of Truth: Logic as Normative and Descriptive 29 [2.3] Normativity, Descriptivity, Generality 32 [3] Is Logic Formal? 37 [3.1] Formality of Logic and the Begriffsschrift 37 [3.2] Frege and Kant on the Formality of Logic 47 [3.3] Concluding Remarks 50 [4] Is Logic ‘Constitutive’ of Thought? 53 [4.1] The Idea of „Constitutivity‟, and its Problems 53 [4.2] Logical Aliens 57 [4.3] Some Interpretations 60 [4.4] Logic, Thought and Rationality 71 [4.5] Conclusion 76 Part Two: Russell on the Nature of Judgement [5] Propositional Unity, Truth and Judgement in 1903-1905 80 [5.1] Terms and Propositions 80 [5.2] The Unity of the Proposition 87 [5.3] Truth and Judgement 91 [6] The Multiple Relation Theory of Judgement in 1910-1912 99 [6.1] Truth and the 1910 Multiple Relation Theory of Judgement 99 [6.2] The 1912 Multiple Relation Theory of Judgement 110 [7] The Multiple Relation Theory of Judgement in 1913 115 [7.1] Propositional Thought, Understanding and Judgement 115 [7.2] Logical Form 118 [7.3] Logical Form and Judgement 122 [7.4] Conclusion 130 3 Part Three: the Tractatus on Language and Logic [8] Wittgenstein’s Criticism of Russell’s Theory of Judgement 133 [8.1] Introduction 133 [8.2] Types 135 [8.3] Unity 141 [8.4] Forms 146 [8.5] Russell‟s Theory of Judgement and Wittgenstein‟s Objection 149 [9] Sense and Propositional Unity in the Notes on Logic 152 [9.1] „A Correct Theory of Propositions‟ 152 [9.2] Names and Forms 154 [9.3] Wittgenstein, Russell, Frege 157 [9.4] The Picturing Analogy 160 [10] Sense and Propositional Unity in the Tractatus 162 [10.1] Introduction 162 [10.2] Propositions as Pictures 163 [10.3] Propositional Constituents, Identity of Structure and Isomorphism 169 [10.4] Realism and Identity of Structure 181 [10.5] From the Notes on Logic to the Tractatus 186 [11] Language and Logic in the Tractatus 189 [11.1] Language, Truth and Logic: Pictures and Truth-functions 189 [11.2] The Internal Unity of Language and Logic 194 [11.3] Propositional Complexity and the Functional Model 197 [12] The Logic of the Tractatus 204 [12.1] Bipolarity, ab-functions and Logic 204 [12.2] Truth-operations 210 [12.3] The Grundgedanke of the Tractatus 220 [12.4] Truth and Logical Truth 224 [12.5] Entailment 233 [13] Frege and Wittgenstein: The Nature of Logic 240 [13.1] Introduction 240 [13.2] The Generality of Logic 242 [13.3] Frege and Wittgenstein on the Formality of Logic 249 [13.4] Frege and Wittgenstein on the Normative Status of Logic 253 [13.5] Wittgenstein and the Constitutivity of Logic: The Impossibility of Illogical Thought 258 Bibliography 264 4 Introduction It is perhaps trite to remark that Wittgenstein‟s Tractatus Logico-Philosophicus was influenced by Frege and Russell. Wittgenstein himself acknowledges this in the Preface to the Tractatus by claiming that he is “indebted to Frege‟s great works and to the writings of my friend Bertrand Russell for much of the stimulation of my thoughts” [TLP: p. 3]. Frege‟s and Russell‟s impact on Wittgenstein‟s thought is, however, twofold; on the one hand, the Tractatus develops some important philosophical insights which it owes to Frege and Russell; on the other hand, it can be seen as a critical reaction to some crucial aspects of Frege‟s and Russell‟s philosophy. In the thesis I concentrate on the latter point; the guiding thought is that the Tractatus‟ conception of the nature of language should be understood as the culmination of Wittgenstein‟s critical insights about Russell‟s theory of judgement, while the conception of logic as tautologous, which derives from the pictorial understanding of the nature of the proposition, is to be seen as embedding a rejection of some aspects of Frege‟s conception of the nature of logic. The outcome of the thesis is that, while Wittgenstein‟s pictorial conception of language stands in a fundamental opposition to Russell‟s conception of judgement, seen as involving a misapprehension of the nature of propositional articulation, the Tractatus‟ conception of logic should not be thought as implying a rejection of Frege‟s views on logic as a whole. The conception of logic presented in the Tractatus is better understood as dispelling tensions in Frege‟s thought on 5 logic, and thus as rejecting some of Frege‟s views on the matter while retaining and developing others. The structure of the thesis implements this general idea as follows; in part one I discuss some internal tensions in Frege‟s conception of logic that bear a direct relation to Wittgenstein‟s understanding of the nature – and the essence – of logic and of logical propositions. In the second part I address Russell‟s views on the nature the proposition and the development of his views on judgement from 1903 to 1913, when his work was abandoned in consequence of Wittgenstein‟s criticism. Part one and two should thus be conceived of as two independent beginnings of the thesis, aimed at analysing those views of Frege‟s and Russell‟s that are rejected in the Tractatus. In part three I discuss Wittgenstein‟s conception of language and logic in the Tractatus, showing how his mature view of the nature of the proposition (the picture theory) arises – via the early account of sense presented in the Notes on Logic – out of Wittgenstein‟s criticism of Russell‟s theory of judgement. I then consider how Wittgenstein‟s pictorial account of language grounds his understanding of the nature of logical constants and of logical propositions. I argue that the philosophy of logic that derives from it helps to resolve the tensions present in Frege‟s conception of logic, discussed in the first part of the thesis. Part three thus analyses Wittgenstein‟s answer, in the Tractatus, to the problems in Frege‟s and Russell‟s philosophy, and thus connects the discussion of Frege‟s and Russell‟s conceptions of logic, language and judgement dealt with separately in the previous two parts of my work. 6 In the first part of the thesis, after a preliminary discussion of some of Frege‟s basic ideas on the essence of logic, I address, in chapter 2, Frege‟s conception of logic as a normative and descriptive science.
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