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234When does a Boltzmannian equilibrium exist?In Daniel Bedingham, Owen Maroney & Christopher Timpson (eds.), Quantum Foundations of Statistical Mechanics, Oxford University Press. 2016.The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we stat…Read more
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82DeterminismIn Kevin Timpe, Meghan Griffith & Neil Levy (eds.), Routledge Companion to Free Will., Routledge. 2017.This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.
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21Equilibrium in Gibbsian Statistical MechanicsIn Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics, Routledge. 2022.
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24Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-epsilon-equilibrium. This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic s…Read more
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13Boltzmannian Non-Equilibrium and Local VariablesIn Cristián Soto (ed.), Current Debates in Philosophy of Science: In Honor of Roberto Torretti, Springer Verlag. pp. 275-287. 2023.Boltzmannian statistical mechanics (BSM) partitions a system’s space of micro-states into cells and refers to these cells as ‘macro-states’. One of these cells is singled out as the equilibrium macro-state while the others are non-equilibrium macro-states. It remains unclear, however, how these states are characterised at the macro-level as long as only real-valued macro-variables are available. We argue that physical quantities like pressure and temperature should be treated as field-variables …Read more
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6When Does a Boltzmannian Equilibrium Exist?In Cristián Soto (ed.), Current Debates in Philosophy of Science: In Honor of Roberto Torretti, Springer Verlag. pp. 247-273. 2023.We present a definition of equilibrium for Boltzmannian statistical mechanics based on the long-run fraction of time a system spends in a state. We then formulate and prove an existence theorem which provides general criteria for the existence of an equilibrium state. We illustrate how the theorem works with toy example. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas …Read more
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12Model-Selection Theory: The Need for a More Nuanced Picture of Use-Novelty and Double-CountingBritish Journal for the Philosophy of Science 69 (2): 351-375. 2018.This article argues that common intuitions regarding (a) the specialness of ‘use-novel’ data for confirmation and (b) that this specialness implies the ‘no-double-counting rule’, which says that data used in ‘constructing’ (calibrating) a model cannot also play a role in confirming the model’s predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuit…Read more
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9Deterministic Versus Indeterministic Descriptions: Not That Different After All?In Alexander Hieke & Hannes Leitgeb (eds.), Reduction, abstraction, analysis: proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008, De Gruyter. pp. 63-78. 2009.
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357On the history of the isomorphism problem of dynamical systems with special regard to von Neumann’s contributionArchive for History of Exact Sciences 66 (1): 71-93. 2012.This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to…Read more
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36Statistical Mechanics: A Tale of Two TheoriesThe Monist 102 (4): 424-438. 2019.There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statisti…Read more
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399Explaining Thermodynamic-Like Behavior in Terms of Epsilon-ErgodicityPhilosophy of Science 78 (4): 628-652. 2011.Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something …Read more
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61Demystifying TypicalityPhilosophy of Science 79 (5): 917-929. 2012.A gas prepared in a non-equilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilon-ergodic are typical with respect to the Whitney topology.…Read more
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60The Diversity of Model Tuning Practices in Climate SciencePhilosophy of Science 83 (5): 113-114. 2016.Many examples of calibration in climate science raise no alarms regarding model reliability. We examine one example and show that, in employing Classical Hypothesis-testing, it involves calibrating a base model against data that is also used to confirm the model. This is counter to the "intuitive position". We argue, however, that aspects of the intuitive position are upheld by some methods, in particular, the general Cross-validation method. How Cross-validation relates to other prominent Class…Read more
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118Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existenceStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49 19-31. 2015.In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a m…Read more
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509Rethinking boltzmannian equilibriumPhilosophy of Science 82 (5): 1224-1235. 2015.Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing th…Read more
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126On Defining Climate and Climate ChangeBritish Journal for the Philosophy of Science 67 (2): 337-364. 2016.The aim of the article is to provide a clear and thorough conceptual analysis of the main candidates for a definition of climate and climate change. Five desiderata on a definition of climate are presented: it should be empirically applicable; it should correctly classify different climates; it should not depend on our knowledge; it should be applicable to the past, present, and future; and it should be mathematically well-defined. Then five definitions are discussed: climate as distribution ove…Read more
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29Mind the Gap: Boltzmannian versus Gibbsian EquilibriumPhilosophy of Science 84 (5): 1289-1302. 2017.There are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is a prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong. There are important cases in which the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibriums exists are different for Gibbsian and Boltzmannian sta…Read more
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29The Precautionary Principle: Science, Evidence and Environmental Policy (review)Economics and Philosophy 32 (1): 162-169. 2016.
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156Do microbes question standard thinking in the philosophy of biology? (review)Analysis 73 (2): 380-387. 2013.This is a highly welcome book that offers a fresh perspective on the philosophy of biology. It is of interest to both philosophers and biologists and to experienced readers as well as novices. The book is structured into four sections ‘Science’, ‘Biology’, ‘Microbes’ and ‘Humans’ and consists of a collection of articles written by John Dupré over the past few years.
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447Model-Selection Theory: The Need for a More Nuanced Picture of Use-Novelty and Double-CountingBritish Journal for the Philosophy of Science. 2016.This article argues that common intuitions regarding (a) the specialness of ‘use-novel’ data for confirmation and (b) that this specialness implies the ‘no-double-counting rule’, which says that data used in ‘constructing’ (calibrating) a model cannot also play a role in confirming the model’s predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuit…Read more
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5Rezension:: Rationalität in der Angewandten EthikKriterion - Journal of Philosophy 19 (1): 44-54. 2005.
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4Rezension:: Rationalität in der Angewandten EthikKriterion - Journal of Philosophy 1 (19): 44-54. 2005.
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36Can Somebody Please Say What Gibbsian Statistical Mechanics Says?British Journal for the Philosophy of Science 72 (1): 105-129. 2021.Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the averaging principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coh…Read more
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121Philosophy of climate science part I: observing climate changePhilosophy Compass 10 (12): 953-964. 2015.This is the first of three parts of an introduction to the philosophy of climate science. In this first part about observing climate change, the topics of definitions of climate and climate change, data sets and data models, detection of climate change, and attribution of climate change will be discussed.
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110Philosophy of climate science part II: modelling climate changePhilosophy Compass 10 (12): 965-977. 2015.This is the second of three parts of an introduction to the philosophy of climate science. In this second part about modelling climate change, the topics of climate modelling, confirmation of climate models, the limits of climate projections, uncertainty and finally model ensembles will be discussed.
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57Can somebody please say what Gibbsian statistical mechanics says?British Journal for the Philosophy of Science 1-27. 2018.Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coh…Read more
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19When do Gibbsian phase averages and Boltzmannian equilibrium values agree?Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72 46-69. 2020.
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125Climate Science, The Philosophy ofInternet Encyclopedia of Philosophy. 2020.The Philosophy of Climate Science Climate change is one of the defining challenges of the 21st century. But what is climate change, how do we know about it, and how should we react to it? This article summarizes the main conceptual issues and questions in the foundations of climate science, as well as of the … Continue reading Climate Science, The Philosophy of →
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26Philosophy of the Precautionary Principle, Daniel Steel. Cambridge University Press, 2015, xv + 256 pages (review)Economics and Philosophy 32 (1): 162-169. 2016.