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Let's Reappraise Carnapian Inductive Logic! View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Kent Academic Repository Let's Reappraise Carnapian Inductive Logic! Thesis submitted in fulfilment of the requirements of the degree of Doctor of Philosophy in Philosophy School of European Culture and Languages, University of Kent Teddy Groves Total word count: 77523 2 Acknowledgements I am very grateful to Maria Groves, Liam Kofi Bright, Hykel Hosni, Gilbert Harman, Richard Pettigrew, Pavel Janda, Jason Konek, Andr´eCarus, Michael Wilde, Ruth Hibbert, Matthew Wittingham, James Angove for their very gen- erous help with and comments on this thesis. I would also like to thank Jon Williamson, J¨urgenLandes and David Corfield for their excellent PhD supervision. The research that led to this thesis was generously funded by the Arts and Humanities Research Council as part of the project From Objective Bayesian Epistemology to Inductive Logic. Finally, I am very grateful to Brigitte Parakenings and Brigitta Arden for help- ing me to access archival material. All such material inside is quoted by per- mission of the University of Pittsburgh. All rights reserved. 3 4 Contents 1 Introduction9 1.1 Reappraising Carnap.........................9 1.2 Structure............................... 11 1.3 Limitations of this analysis..................... 17 2 Carnapian inductive logic 19 2.1 Introduction.............................. 19 2.2 Historical sketch........................... 20 2.2.1 Related programmes..................... 21 2.3 The methodology of scientific research programmes........ 22 2.3.1 Lakatos's methodology.................... 22 2.3.2 The question of truth-directedness............. 23 2.4 Hard core commitments....................... 25 2.4.1 Explication.......................... 26 2.4.2 Systems of inductive logic.................. 28 2.4.3 Tolerance........................... 33 2.4.4 Summary of Carnapian inductive logic's hard core.... 36 2.5 Other components.......................... 36 2.5.1 Protective belt........................ 37 2.5.2 Negative heuristic...................... 37 2.5.3 Positive heuristic....................... 38 2.6 How Carnapian inductive logic developed............. 39 2.6.1 Less restrictive systems of inductive logic......... 39 2.6.2 Different interpretative requirements............ 40 2.6.3 Families of predicates.................... 40 2.6.4 Measure-theoretic reformulation.............. 41 2.6.5 Versatility........................... 41 2.7 Carnapian inductive logic was progressive............. 43 2.8 Discussion............................... 47 2.9 Additional interpretative points................... 49 2.9.1 Blank slate situations.................... 49 2.9.2 The term `logic'....................... 56 2.9.3 Probability1 .......................... 59 5 6 CONTENTS 3 Critiques 63 3.1 Introduction.............................. 63 3.2 Lakatos's critique........................... 63 3.2.1 Historical background.................... 64 3.2.2 Lakatos's argument...................... 65 3.2.3 Why Lakatos was mistaken................. 67 3.2.4 Why did Lakatos go wrong?................. 68 3.2.5 Summary........................... 71 3.3 Grue, projectability and instantial relevance............ 71 3.3.1 Historical background.................... 71 3.3.2 The objection......................... 72 3.3.3 Artificiality.......................... 73 3.3.4 Carnapian inductive logic can formalise assumptions about projectability......................... 74 3.3.5 Why has grue been such a big issue?............ 76 3.4 Salmon on partial entailment.................... 79 3.4.1 Hume's principle....................... 79 3.4.2 Learning from experience.................. 80 3.4.3 Salmon's argument...................... 80 3.4.4 Responses to Salmon's objection.............. 81 3.5 Other critiques of Carnapian inductive logic............ 83 3.5.1 Universal hypotheses..................... 83 3.5.2 Constant exchangeability.................. 84 3.5.3 Reliability in the limit.................... 87 3.6 Discussion............................... 90 3.6.1 Why were there so many critiques?............. 91 3.6.2 What next?.......................... 92 4 Subjective Bayesian inductive logic 93 4.1 Introduction.............................. 93 4.1.1 Inductive logic and epistemology.............. 94 4.1.2 Subjective Bayesian epistemology.............. 95 4.1.3 Subjective Bayesian inductive logic............. 98 4.2 Probabilistic necessity........................ 100 4.2.1 Betting arguments...................... 101 4.2.2 Cox's axiomatic argument.................. 107 4.2.3 Accuracy arguments..................... 111 4.2.4 Are the different arguments for probabilistic necessity mu- tually reinforcing?...................... 123 4.2.5 Conclusion: probabilistic necessity has not yet been es- tablished........................... 129 4.3 Probabilistic sufficiency....................... 129 4.3.1 Grue-based arguments.................... 130 4.3.2 Dominance-avoidance.................... 132 4.3.3 Howson's logical argument.................. 133 4.3.4 Probabilistic sufficiency has not been established..... 139 CONTENTS 7 4.4 Which kind of inductive logic is best?............... 139 4.4.1 Philosophical comparison.................. 139 4.4.2 Methodological comparison................. 140 4.4.3 Conclusion.......................... 141 5 Objective Bayesianism 143 5.1 Introduction.............................. 143 5.2 Objective Bayesian epistemology.................. 144 5.2.1 Norms of rational belief................... 144 5.2.2 Are the norms justified?................... 146 5.2.3 Methods of representing evidence.............. 146 5.3 Objective Bayesian inductive logic................. 148 5.3.1 Scope for formalising different inductive assumptions... 150 5.3.2 Evidence about physical probabilities........... 151 5.3.3 Evidence about relevance.................. 152 5.3.4 Conclusion.......................... 157 5.4 The assimilative approach...................... 159 5.4.1 Objective Bayesian epistemology as a system of inductive logic.............................. 160 5.4.2 Advantages of the assimilative approach.......... 162 5.4.3 Problem: unconnectedness.................. 165 5.4.4 Assessment of the assimilative approach.......... 166 5.5 Conclusion.............................. 167 6 An application 169 6.1 Introduction.............................. 169 6.2 Statistical model-choice....................... 170 6.2.1 Statistical models....................... 170 6.2.2 Gelman and Shalizi's arguments.............. 170 6.3 The Carnapian account....................... 173 6.4 Advantages of the Carnapian account............... 177 6.4.1 Technical fruitfulness..................... 177 6.4.2 Philosophical foundations.................. 179 6.4.3 Conclusion.......................... 182 7 Conclusion 185 7.1 The current state of the reappraisal................. 185 7.1.1 Historical reappraisal..................... 185 7.1.2 Substantive reappraisal................... 186 7.2 The case for ongoing reappraisal.................. 188 7.2.1 Reassessing the context of Carnapian inductive logic... 188 7.2.2 Carnap's conception of logic................. 189 7.2.3 Other ways of evaluating research programmes...... 190 7.2.4 Carrying out the assimilative approach........... 190 7.2.5 Imprecise probability..................... 191 7.2.6 Double-counting....................... 193 8 CONTENTS 7.3 Conclusion.............................. 193 Chapter 1 Introduction 1.1 Reappraising Carnap Sometimes the scholarly community comes to realise that it should have a second look at an old idea. Sometimes circumstances change so that the old idea acquires extra salience. Sometimes, for one reason or another, it turns out that an old idea had not previously been understood correctly. When this happens and the old idea is re-examined, prompting a change in the general consensus as to its nature and importance, a reappraisal has taken place. In recent times scholars of twentieth century philosophy have begun to recon- sider their views about the German philosopher Rudolf Carnap and the `logical positivist' movement that he championed. Carnap and the other logical pos- itivists had previously been understood as continuing the tradition of British empiricists such as Locke, who sought to establish that sensory experience was the foundation of all human knowledge. Lately, works such as Friedman(1999) and Richardson(1998) have argued convincingly that the logical positivists were not primarily interested in this foundational project, and that their work is better understood in the context of Austro-German neo-Kantianism. Logi- cal positivism had been thought of as an apolitical movement, if not one with reactionary tendencies: a well-informed activist once commented \I cant see anything progressive. coming out of positivism. It just seems to exclude it completely." Chomsky et al.(1988). Recent scholarship, for example Carus (2010) and Yap(2010), has revealed that many of the logical positivists saw their work as part of an emancipatory social project and that that their ideas can make interesting and useful contributions to current such projects. Close examination of the historical record has also overthrown the previous view that the positivists held academic activities other than physics in disregard. For example, Galison(1990) and Potochnik and Yap(2006) unearth connections between the logical positivists and the Bauhaus movement. 9 10 CHAPTER 1. INTRODUCTION This sustained rethinking of Carnap's place in
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