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Roman Frigg

London School of Economics and Political Science, Philosophy, Logic and Scientific Method, Professor

London School of Economics and Political Science, Centre for the Analysis of Time Series, Deputy Director

Ludwig-Maximilians-Universität München, Munich Center for Mathematical Philosophy, Permanent Visiting Professor

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For a complete list of publications go to www.romanfrigg.org
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Address: Houghton Street
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Papers by Roman Frigg

Explaining Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

arXiv (Cornell University), Oct 7, 2013

Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffere... more Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann's proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.

Climate Science, The Philosophy of

Equilibrium in Boltzmannian Statistical Mechanics

Routledge eBooks, Jul 2, 2017

Modelling Climate Change

Philosophy Compass, 2015

Rethinking Boltzmannian Equilibrium

arXiv (Cornell University), Oct 8, 2015

Boltzmannian statistical mechanics partitions the phase space of a system into macro-regions, and... more Boltzmannian statistical mechanics partitions the phase space of a system 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 maximum 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 that equilibrium thus defined corresponds to the largest macro-region. Our derivation is completely general, and does not rely on assumptions about the dynamics or internal interactions.

Boltzmannian Equilibrium in Stochastic Systems

arXiv (Cornell University), Jul 22, 2016

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the not... more Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian α-ε-equilibrium and a Boltzmannian γ-ε-equilibrium (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic microdynamics 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 systems equilibrium macro-regions are large in requisite sense.

Can Somebody Please Say What Gibbsian Statistical Mechanics Says?

arXiv (Cornell University), Jul 11, 2018

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics amo... more 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 coherent interpretation of GSM that provides an account of the status and scope of the principle.

The Philosophy of Climate Science

DEKI Goes Forth

Synthese Library, 2020

In the previous chapter we developed the DEKI account of epistemic representation against the bac... more In the previous chapter we developed the DEKI account of epistemic representation against the backdrop of a material carrier. We begin this chapter by exploring how it applies to carriers that are non-material (Sect. 9.1) and how it answers the Applicability of Mathematics Condition (Sect. 9.2). We then further investigate the nature of keys by discussing an important class of keys based on limits (Sect. 9.3). Finally, we examine DEKI's stance on the demarcation problems with a comparison of epistemic representation in art and science (Sects. 9.4 and 9.5).

Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffere... more Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann’s proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.

Seven Myths About the Fiction View of Models

Logic, Epistemology, and the Unity of Science, 2021

Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scie... more Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scientific models, according to which they are akin to the characters and places of literary fiction. They argue that while some of the criticisms this view has attracted raise legitimate points, others are myths. In this chapter, they first identify and then rebut the following seven myths: (1) that the fiction view regards products of science as falsehoods; (2) that the fiction view holds that models are data-free; (3) that the fiction view is antithetical to representation; (4) that the fiction view trivializes epistemology; (5) that the fiction view cannot account for the use of mathematics in the modeling; (6) that the fiction view misconstrues the function of models in the scientific process; and (7) that the fiction view stands on the wrong side of politics. As a result, they conclude that the fiction view of models, suitably understood (as an account of the ontology of models, rather than their function), remains a viable position.

Taming Abundance: On the Relation between Boltzmannian and Gibbsian Statistical Mechanics

Statistical Mechanics and Scientific Explanation, 2020

Models and Theories in Science

Oxford Bibliographies Online Datasets

Simulation the last two decades of the 20th century. In more recent years, new questions have com... more Simulation the last two decades of the 20th century. In more recent years, new questions have come into focus, in particular the issues of scientific representation, the use of data, and the role of computer simulation in both modeling and theorizing. This entry provides a guide to these intellectual traditions. In doing so, it sets aside a number of related issues, in particular scientific realism, explanation, confirmation, and the application of mathematics. General Overviews Novices to the subject can gain an overview of the different positions and problems in Frigg and

Climate Models and Robustness Analysis – Part I: Core Concepts and Premises

Springer International Publishing eBooks, 2023

Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only reg... more Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only regard a hypothesis as well-supported if all the evidence agrees on it. In contexts like climate science, the evidence in support of a hypothesis often comes in the form of model results. This leads to model-based RA (MBRA), whose core notion is that a hypothesis ought to be regarded as well-supported on grounds that a sufficiently diverse set of models agrees on the hypothesis. This chapter, which is the first part of a two-part review of MBRA, begins by providing a detailed statement of the general structure of MBRA. This statement will make visible the various parts of MBRA and will structure our discussion in the remainder of the chapter. We explicate the core concepts of independence and agreement, and we discuss what they mean in the context of climate modelling. Our statement shows that MBRA is based on three premises, which concern robust properties, common structures, and so-called robust theorems. We analyse what these involve and what problems they raise in the context of climate science. In the next chapter, which is the second part of the review, we analyse how the conclusions of MBRA can be justified.

Konzeptuelle Fragen in den Grundlagen der Klimawissenschaften

Weshalb auf die Wissenschaft hören?

An ineffective antidote for hawkmoths

European Journal for Philosophy of Science

In recent publications we have drawn attention to the fact that if the dynamics of a model is str... more In recent publications we have drawn attention to the fact that if the dynamics of a model is structurally unstable, then the presence of structural model error places in-principle limits on the model’s ability to generate decision-relevant probability forecasts. Writing with a varying array of co-authors, Eric Winsberg has now produced at least four publications in which he dismisses our points as unfounded; the most recent of these appeared in this journal. In this paper we respond to the arguments of Winsberg and his co-workers, and we point out that their criticisms fail. We take this as an opportunity to restate and explain our arguments, and to point to fruitful directions for future research.

Capturing the Scientific Imagination

The Scientific Imagination, 2019

What sort of imagination is involved in scientific models and thought experiments? This chapter d... more What sort of imagination is involved in scientific models and thought experiments? This chapter develops a unifying taxonomy of the different kinds of imagination discussed in aesthetics and philosophy of mind. A crucial distinction is between objectual imagination (imagining an object) and propositional imagination (imagining-that). We characterize propositional imagination through a core of three features: freedom, mirroring, and quarantining. Supposition, counterfactual reasoning, make-believe, and dreaming are varieties of propositional imagination obtained by adding further features to the core. We suggest that the imagination at work in models and thought experiments is make-believe rather than visual imagery, as is often claimed.

Of Barrels and Pipes: Representation-as in Art and Science

On Art and Science, 2019

The influence of footwear on functional outcome after total ankle replacement, ankle arthrodesis, and tibiotalocalcaneal arthrodesis

Clinical biomechanics (Bristol, Avon), 2016

Gait analysis after total ankle replacement and ankle arthrodesis is usually measured barefoot. H... more Gait analysis after total ankle replacement and ankle arthrodesis is usually measured barefoot. However, this does not reflect reality. The purpose of this study was to compare patients barefoot and with footwear. We compared 126 patients (total ankle replacement 28, ankle arthrodesis 57, and tibiotalocalcaneal arthrodesis 41) with 35 healthy controls in three conditions (barefoot, standardized running, and rocker bottom shoes). Minimum follow-up was 2 years. We used dynamic pedobarography and a light gate. relative midfoot index, forefoot maximal force, walking speed. The relative midfoot index decreased in all groups from barefoot to running shoes and again to rocker bottom shoes (p<0.001). The forefoot maximal force increased wearing shoes (p<0.001), but there was no difference between running and rocker bottom shoes. Walking speed increased by 0.06m/s with footwear (p<0.001). Total ankle replacement and ankle arthrodesis were equal in running shoes but both deviated fro...

Scientific Representation

This Element presents a philosophical exploration of the notion of scientific representation. It ... more This Element presents a philosophical exploration of the notion of scientific representation. It does so by focusing on an important class of scientific representations, namely scientific models. Models are important in the scientific process because scientists can study a model to discover features of reality. But what does it mean for something to represent something else? This is the question discussed in this Element. The authors begin by disentangling different aspects of the problem of representation and then discuss the dominant accounts in the philosophical literature: the resemblance view and inferentialism. They find them both wanting and submit that their own preferred option, the so-called DEKI account, not only eschews the problems that beset these conceptions, but further provides a comprehensive answer to the question of how scientific representation works. This Element is also available in the Open Access on Cambridge Core.

Explaining Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

arXiv (Cornell University), Oct 7, 2013

Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffere... more Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann's proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.

Climate Science, The Philosophy of

Equilibrium in Boltzmannian Statistical Mechanics

Routledge eBooks, Jul 2, 2017

Modelling Climate Change

Philosophy Compass, 2015

Rethinking Boltzmannian Equilibrium

arXiv (Cornell University), Oct 8, 2015

Boltzmannian statistical mechanics partitions the phase space of a system into macro-regions, and... more Boltzmannian statistical mechanics partitions the phase space of a system 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 maximum 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 that equilibrium thus defined corresponds to the largest macro-region. Our derivation is completely general, and does not rely on assumptions about the dynamics or internal interactions.

Boltzmannian Equilibrium in Stochastic Systems

arXiv (Cornell University), Jul 22, 2016

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the not... more Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian α-ε-equilibrium and a Boltzmannian γ-ε-equilibrium (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic microdynamics 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 systems equilibrium macro-regions are large in requisite sense.

Can Somebody Please Say What Gibbsian Statistical Mechanics Says?

arXiv (Cornell University), Jul 11, 2018

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics amo... more 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 coherent interpretation of GSM that provides an account of the status and scope of the principle.

The Philosophy of Climate Science

DEKI Goes Forth

Synthese Library, 2020

In the previous chapter we developed the DEKI account of epistemic representation against the bac... more In the previous chapter we developed the DEKI account of epistemic representation against the backdrop of a material carrier. We begin this chapter by exploring how it applies to carriers that are non-material (Sect. 9.1) and how it answers the Applicability of Mathematics Condition (Sect. 9.2). We then further investigate the nature of keys by discussing an important class of keys based on limits (Sect. 9.3). Finally, we examine DEKI's stance on the demarcation problems with a comparison of epistemic representation in art and science (Sects. 9.4 and 9.5).

Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffere... more Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann’s proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.

Seven Myths About the Fiction View of Models

Logic, Epistemology, and the Unity of Science, 2021

Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scie... more Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scientific models, according to which they are akin to the characters and places of literary fiction. They argue that while some of the criticisms this view has attracted raise legitimate points, others are myths. In this chapter, they first identify and then rebut the following seven myths: (1) that the fiction view regards products of science as falsehoods; (2) that the fiction view holds that models are data-free; (3) that the fiction view is antithetical to representation; (4) that the fiction view trivializes epistemology; (5) that the fiction view cannot account for the use of mathematics in the modeling; (6) that the fiction view misconstrues the function of models in the scientific process; and (7) that the fiction view stands on the wrong side of politics. As a result, they conclude that the fiction view of models, suitably understood (as an account of the ontology of models, rather than their function), remains a viable position.

Taming Abundance: On the Relation between Boltzmannian and Gibbsian Statistical Mechanics

Statistical Mechanics and Scientific Explanation, 2020

Models and Theories in Science

Oxford Bibliographies Online Datasets

Simulation the last two decades of the 20th century. In more recent years, new questions have com... more Simulation the last two decades of the 20th century. In more recent years, new questions have come into focus, in particular the issues of scientific representation, the use of data, and the role of computer simulation in both modeling and theorizing. This entry provides a guide to these intellectual traditions. In doing so, it sets aside a number of related issues, in particular scientific realism, explanation, confirmation, and the application of mathematics. General Overviews Novices to the subject can gain an overview of the different positions and problems in Frigg and

Climate Models and Robustness Analysis – Part I: Core Concepts and Premises

Springer International Publishing eBooks, 2023

Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only reg... more Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only regard a hypothesis as well-supported if all the evidence agrees on it. In contexts like climate science, the evidence in support of a hypothesis often comes in the form of model results. This leads to model-based RA (MBRA), whose core notion is that a hypothesis ought to be regarded as well-supported on grounds that a sufficiently diverse set of models agrees on the hypothesis. This chapter, which is the first part of a two-part review of MBRA, begins by providing a detailed statement of the general structure of MBRA. This statement will make visible the various parts of MBRA and will structure our discussion in the remainder of the chapter. We explicate the core concepts of independence and agreement, and we discuss what they mean in the context of climate modelling. Our statement shows that MBRA is based on three premises, which concern robust properties, common structures, and so-called robust theorems. We analyse what these involve and what problems they raise in the context of climate science. In the next chapter, which is the second part of the review, we analyse how the conclusions of MBRA can be justified.

Konzeptuelle Fragen in den Grundlagen der Klimawissenschaften

Weshalb auf die Wissenschaft hören?

An ineffective antidote for hawkmoths

European Journal for Philosophy of Science

In recent publications we have drawn attention to the fact that if the dynamics of a model is str... more In recent publications we have drawn attention to the fact that if the dynamics of a model is structurally unstable, then the presence of structural model error places in-principle limits on the model’s ability to generate decision-relevant probability forecasts. Writing with a varying array of co-authors, Eric Winsberg has now produced at least four publications in which he dismisses our points as unfounded; the most recent of these appeared in this journal. In this paper we respond to the arguments of Winsberg and his co-workers, and we point out that their criticisms fail. We take this as an opportunity to restate and explain our arguments, and to point to fruitful directions for future research.

Capturing the Scientific Imagination

The Scientific Imagination, 2019

What sort of imagination is involved in scientific models and thought experiments? This chapter d... more What sort of imagination is involved in scientific models and thought experiments? This chapter develops a unifying taxonomy of the different kinds of imagination discussed in aesthetics and philosophy of mind. A crucial distinction is between objectual imagination (imagining an object) and propositional imagination (imagining-that). We characterize propositional imagination through a core of three features: freedom, mirroring, and quarantining. Supposition, counterfactual reasoning, make-believe, and dreaming are varieties of propositional imagination obtained by adding further features to the core. We suggest that the imagination at work in models and thought experiments is make-believe rather than visual imagery, as is often claimed.

Of Barrels and Pipes: Representation-as in Art and Science

On Art and Science, 2019

The influence of footwear on functional outcome after total ankle replacement, ankle arthrodesis, and tibiotalocalcaneal arthrodesis

Clinical biomechanics (Bristol, Avon), 2016

Gait analysis after total ankle replacement and ankle arthrodesis is usually measured barefoot. H... more Gait analysis after total ankle replacement and ankle arthrodesis is usually measured barefoot. However, this does not reflect reality. The purpose of this study was to compare patients barefoot and with footwear. We compared 126 patients (total ankle replacement 28, ankle arthrodesis 57, and tibiotalocalcaneal arthrodesis 41) with 35 healthy controls in three conditions (barefoot, standardized running, and rocker bottom shoes). Minimum follow-up was 2 years. We used dynamic pedobarography and a light gate. relative midfoot index, forefoot maximal force, walking speed. The relative midfoot index decreased in all groups from barefoot to running shoes and again to rocker bottom shoes (p<0.001). The forefoot maximal force increased wearing shoes (p<0.001), but there was no difference between running and rocker bottom shoes. Walking speed increased by 0.06m/s with footwear (p<0.001). Total ankle replacement and ankle arthrodesis were equal in running shoes but both deviated fro...

Scientific Representation

This Element presents a philosophical exploration of the notion of scientific representation. It ... more This Element presents a philosophical exploration of the notion of scientific representation. It does so by focusing on an important class of scientific representations, namely scientific models. Models are important in the scientific process because scientists can study a model to discover features of reality. But what does it mean for something to represent something else? This is the question discussed in this Element. The authors begin by disentangling different aspects of the problem of representation and then discuss the dominant accounts in the philosophical literature: the resemblance view and inferentialism. They find them both wanting and submit that their own preferred option, the so-called DEKI account, not only eschews the problems that beset these conceptions, but further provides a comprehensive answer to the question of how scientific representation works. This Element is also available in the Open Access on Cambridge Core.