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Neo-Nagelian Reduction Neo-Nagelian Reduction A Statement, Defence, and Application. Foad Dizadji-Bahmani A thesis submitted to the Department of Philosophy, Logic and Scientific Method of the London School of Economics and Political Science for the degree of Doctor of Philosophy, July 2011. Declaration I certify that the thesis I have presented for examination for the PhD degree of the London School of Economics and Political Science is solely my own work. The copyright of this thesis rests with the author. Quotation from it is permitted, provided that full acknowledgement is made. This thesis may not be reproduced without the prior written consent of the author. I warrant that this authorization does not, to the best of my belief, infringe the rights of any third party. Foad Dizadji-Bahmani 2 Abstract The thesis proposes, defends, and applies a new model of inter-theoretic reduction, called \Neo-Nagelian" reduction. There are numerous accounts of inter-theoretic reduction in the philosophy of science literature but the most well-known and widely-discussed is the Nagelian one. In the thesis I identify various kinds of problems which the Nagelian model faces. Whilst some of these can be resolved, pressing ones remain. In lieu of the Nagelian model, other models of inter-theoretic reduction have been proposed, chief amongst which are so-called \New Wave" models. I show these to be no more adequate than the original Nagelian model. I propose a new model of inter-theoretic reduction, Neo-Nagelian reduction. This model is structurally similar to the Nagelian one, but differs in substantive ways. In particular I argue that it avoids the problems pertaining to both the Nagelian and New Wave models. Multiple realizability looms large in discussions about reduction: it is claimed that multiply realizable properties frustrate the reduction of one theory to another in various ways. I consider these arguments and show that they do not undermine the Neo-Nagelian of reduction of one theory to another. Finally, I apply the model to statistical mechanics. Statistical mechanics is taken to be a reductionist enterprise: one of the aims of statistical mechanics is to reduce thermodynamics. Without an adequate model of inter-theoretic reduction one cannot assess whether it succeeds; I use the Neo-Nagelian model to critically discuss whether it does. Specifically, I consider two very recent derivations of the Second Law of thermodynamics, one from Boltzmannian classical statistical mechanics and another from quantum statistical mechanics. I argue that they are partially successful, and that each makes for a promising line of future research. 3 Outline Acknowledgements 9 Thesis Overview 10 1 Neo-Nagelian Reduction 13 2 New Wave Reductionism 61 3 Multiple Realizability 86 4 Neo-Nagelian Reduction and CSM 119 5 Neo-Nagelian Reduction and QSM 178 Thesis Conclusions 201 Bibliography 205 4 Contents Acknowledgements 9 Thesis Overview 10 1 Neo-Nagelian Reduction 13 1.1 Chapter 1 Introduction . 13 1.2 The External Problem and Methodology . 14 1.2.1 The External Problem . 14 1.2.2 A Better Methodology . 19 1.2.3 Prolegomenon . 21 1.3 Nagelian Reduction . 23 1.3.1 Nagel's Model of Reduction . 23 1.3.2 Nagelian Reduction: Internal Problems . 24 1.4 Neo-Nagelian Reduction . 31 1.4.1 Derivation of the Boyle-Charles Law - A Sketch . 31 1.4.2 Overview of Neo-Nagelian Reduction . 33 1.4.3 Explanation . 38 1.4.4 Pluro-Particularism . 45 1.4.5 Warrant For Auxiliary Assumptions . 52 1.4.6 Warrant For Bridge-Laws . 55 1.4.7 Ontological Simplification . 57 1.5 Chapter Summary and Outlook . 59 2 New Wave Reductionism 61 2.1 Chapter 2 Introduction . 61 2.2 Churchland's New Wave Model of Reduction . 63 2.2.1 Churchland's Wave . 63 5 2.2.2 Problems with Churchland's Wave . 65 2.3 The Hooker-Bickle New Wave Model of Reduction . 71 2.3.1 Hooker's Insights . 72 2.3.2 Bickle's Formal Model . 78 2.4 Chapter Summary . 85 3 Multiple Realizability 86 3.1 Chapter 3 Introduction . 86 3.2 Fodor's Argument Against Reductionism . 90 3.2.1 Stage-Setting . 91 3.2.2 The `Modal' Argument Against Reductionism . 92 3.2.3 The Main Argument Against Reductionism . 94 3.2.4 Fodor's Argument Repudiated . 100 3.3 Multiple Realizability and Explanation . 104 3.3.1 MR Does Not Undermine Explanation . 105 3.3.2 Possible MR Does Not Undermine Explanation . 106 3.3.3 Simplicity and Descriptive Richness . 107 3.4 Multiple Realizability and Ontological Simplification . 109 3.4.1 Simplistic Ontological Simplification . 110 3.4.2 Local Simplistic Ontological Simplification . 111 3.4.3 `Radical' MR . 113 3.4.4 Ontological Simplification Revisited . 116 3.5 Chapter Summary . 118 4 Neo-Nagelian Reduction and CSM 119 4.1 Chapter 4 Introduction . 119 4.2 Thermodynamics . 120 4.2.1 Axiomatic Laws . 121 4.2.2 Constitutive Laws . 128 4.3 The Kinetic Theory of Gases . 129 4.3.1 Deriving the Boyle-Charles Law . 130 4.3.2 A Rational Reconstruction . 131 4.4 Is Temperature Mean Kinetic Energy? . 138 4.4.1 A Priori Arguments for Identity . 139 4.4.2 Conceptual Arguments Against Identity . 142 4.4.3 Ontological Simplification: The Upward Path . 150 6 4.5 Framework for Classical Statistical Mechanics . 151 4.6 Gibbsian Statistical Mechanics . 153 4.6.1 Re-deriving the Boyle-Charles Law . 154 4.6.2 Gibbsian Statistical Mechanics: Reduction? . 159 4.7 Boltzmannian Statistical Mechanics . 162 4.7.1 Reducing the 2nd Law . 162 4.7.2 The Boltzmannian Framework . 166 4.7.3 The Ergodic Program . 168 4.7.4 Solving Problems with the Ergodic Program . 170 4.7.5 Prospects and Limitations . 177 4.8 Chapter Summary . 177 5 Neo-Nagelian Reduction and QSM 178 5.1 Chapter 5 Introduction . 178 5.2 Albertian and H&Sian QSM . 179 5.3 Aharonovian QSM . 183 5.4 NN Reduction and Aharonovian QSM . 187 5.4.1 Representing Equilibrium . 188 5.4.2 State-averaging and Typicality . 191 5.4.3 Warrant in Aharonovian QSM . 194 5.5 Interventionism . 197 5.5.1 Incredulity . 198 5.5.2 Deus Ex Machina . 198 5.5.3 All for Nothing . 199 5.6 Chapter Summary . 200 Thesis Conclusions 201 Bibliography 205 7 Acknowledgements I thank Roman Frigg and Mikl´osR´edei for their patient and supportive super- vision. Mikl´oshas been a source of inspiration and I learned much from him. I am particularly indebted to Roman. He has provided many insightful comments on my writings, explained important ideas to me, and guided me through this process. I am extremely grateful to them both. I thank all the staff and students at the Department of Philosophy, Logic and Scientific Method at the London School of Economics and Political Science, for creating the excellent academic atmosphere here. In particular, amongst the fac- ulty, I thank Jason McKenzie Alexander, Luc Bovens, Nancy Cartwright, David Makinson, Katie Steele, Max Steuer, Charlotte Werndl, and John Worrall. In particular, amongst the PhD students, I thank Bengt Autzen and Chris Thomp- son, my year-mates, Sheldon Steed, Mauro Rossi, Marilena Di Bucchianico, Alice Obrecht, Ittay Nissan, Dean Peters, Ben Ferguson, Susanne Burri, and Seamus `LATEX' Bradley. I received financial support from the LSE Research Studentship Scheme and a desk from the CPNSS. The latter allowed me to benefit from stimulating con- versations with Isabel Guerra, I~naki San Pedro, and Wolfgang Pietsch, amongst many others. Most importantly it allowed me to share many a great day with Conrad Heilmann. I thank James Ladyman, Stuart Presnell, and Ioannis Votsis for encouraging me to pursue a PhD, and Jeremy Howick and Matt W. Parker for seeing me through. Special thanks go to Phillip Thonemann for introducing me to philoso- phy. I thank all my friends and family for putting up with me whilst I wrote this thesis. Special thanks to my Berlin family, Ayshea, Bex, Lucy, Susannah, Ula, and Mimi. I would not have completed this thesis without Emma, Henry, and Shiv. I am sorry that my father is not here to see me get this far; from what I understand he would have been proud. I thank him, in so far as that makes sense, for being a source of inspiration and strength to my mother, even after all these years. Above all I thank my mother, Farideh Dizadji. She has sacrificed so very much for me, and, despite incredible adversity, has provided me with all the intellectual and emotional support I needed. I owe her everything. 8 For Farideh Dizadji. 9 Thesis Overview In this thesis, I propose, defend, and apply a new model of intertheoretic reduc- tion. I call it the Neo-Nagelian model of intertheoretic reduction. Let us idealise somewhat and suppose that any model of intertheoretic reduc- tion consists of a set of necessary and sufficient criteria for one theory to reduced to another. I make the distinction between two kinds of problems pertaining to any such model: internal and external. By internal problems I mean those to do with how clear and precise the criteria are, whether the criteria are consistent with each other, and whether they afford the putative aims of reduction. Con- trast this with the external problem. The external problem is the problem of establishing what the aims of reduction are, and whether the criteria themselves are the `right' ones. That is, whether in meeting the criteria, one theory does reduce to another. The failure to recognise this distinction has been detrimental to debates about reduction, or so I contend. To solve the external problem, I propose the following: abstract a general model of reduction from a rational reconstruction of the derivation of the Boyle- Charles of thermodynamics from statistical mechanics.
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