Roman Frigg

London School of Economics and Political Science | LSE · Department of Philosophy, Logic and Scientific Method

Statistical mechanics is the third pillar of modern physics, next to quantum theory and relativity theory. It aims to account for the behaviour of macroscopic systems in terms of the dynamical laws that govern their microscopic constituents and probabilistic assumptions about them. In this Element, the authors investigate the philosophical and foun...

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...

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...

Climate science is an umbrella term referring to scientific disciplines studying aspects of the Earth’s climate. It includes, among others, parts of atmospheric science, oceanography, and glaciology. In the wake of public discussions about an appropriate reaction to climate change, parts of decision theory and economics have also been brought to be...

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 from scientific models. This leads to model-based RA (MBRA), whose core notion is that a hypothesi...

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 hyp...

Die Philosophie der KlimawissenschaftenKlimawissenschaften ist ein Teilgebiet der Wissenschaftstheorie, das sich mit den Methoden und Grundbegriffen der Klimawissenschaften auseinandersetzt. Ziel dieses Kapitels ist es, eine überblickende Darstellung der wichtigsten Probleme und Fragen in den Klimawissenschaften zu liefern. Nach einführenden Erläut...

Extreme weather events like hurricanes occur rarely, but when they occur, they cause immense damage. How should decision-makers, both public and private, make decisions about such events? Such decisions face significant and often poorly understood uncertainty. We rework the so-called “confidence approach” to tackle decision-making under severe unce...

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 fo...

This is a book-length discussion of philosophical issues that pertain to models and theories.

In their “DEKI, Denotation, and the Fortuitous Misuse of Maps” Jared Millson and Mark Risjord take the DEKI account to task for being unable to “distinguish justified surrogative inferences from unjustified ones”, which is problem because an analysis of representation “must block unjustified surrogative inferences” (p. 5). This, they say, means tha...

Extreme weather events like hurricanes occur rarely, but when they occur, they cause immense damage. How should decision-makers, both public and private, make decisions about such events? Such decisions face significant and often poorly understood uncertainty. We rework the so-called “confidence approach” to tackle decision-making under severe unce...

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 hyp...

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 from scientific models. This leads to model-based RA (MBRA), whose core notion is that a hypothesi...

Climate change adaptation is largely a local matter, and adaptation planning can benefit from local climate change projections. Such projections are typically generated by accepting climate model outputs in a relatively uncritical way. We argue, based on the IPCC’s treatment of model outputs from the CMIP5 ensemble, that this approach is unwarrante...

This paper presents an in-depth analysis of the anatomy of both ther-modynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represente...

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented...

Many scientific models are not objects that one can hold in one’s hands, and yet they seem to be objects of some sort. But of what sort? This chapter offers an answer to this question in terms of Walton’s pretence theory and argues the models should be understood in terms of games of make-believe. This also provides answers to other important issue...

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 th...

Veritism, the position that truth is necessary for epistemic acceptability, seems to be in tension with the observation that much of our best science is not, strictly speaking, true when interpreted literally. This generates a paradox: (i) truth is necessary for epistemic acceptability; (ii) the claims of science have to be taken literally; (iii) m...

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian e...

Maps are often invoked as a way to understanding scientific modelling: a model represents its target as a map represents its territory. However, without an account of how maps represent this analogy is suggestive at best. We reverse the direction of explanation and show that maps represent like models. Utilising the DEKI account of representation,...

This chapter provides synoptic discussion of the fiction view of models and shows how this view can be developed using Walton's pretence theory.

The fiction view of models submits that scientific models are akin to the characters and places of literary fiction. This view has attracted a number of criticisms. While some of these criticisms raise legitimate points, others are myths. In this paper we first identify and then rebut the following seven myths: (1) that the fiction view regards pro...

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics (SM) is one of the major conceptual issues in the foundations the discipline. In their celebrated review of SM Paul Ehrenfest and Tatjana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values...

Many policy decisions take input from collections of scientific models. Such decisions face significant and often poorly understood uncertainty. We rework the so-called “confidence approach” to tackle decision-making under severe uncertainty with multiple models, and illustrate the approach with a case study: insurance pricing using hurricane model...

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian e...

In a series of recent papers we have developed what we call the DEKI account of scientific representation, according to which models represent their targets via keys. These keys provide a systematic way to move from model-features to features to be imputed to their targets. We show how keys allow for accurate representation in the presence of ideal...

We now address the issues faced by Representation-As and develop it into a full-fledged account of epistemic representation. The result of this endeavour is what we call the DEKI account, where the acronym is formed from the names of the account’s defining features: denotation, exemplification, keying-up, and imputation. In this chapter we introduc...

In its most basic guise, the similarity view of representation says that something represents something else by being similar to it. A photograph represents its subject matter by being similar to it; a statue represents its object by being similar to it; and a painting represents by being similar to what it portrays. In the context of a discussion...

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 and how it answers the Applicability of Mathematics Condition. We then further investigate the nature of keys by discussing an important cla...

Scientific modelling involves a creative act of the imagination. This, and the fact that at least parts of the content of what is imagined deviates from reality, motivates a family of approaches that analyse modelling and representation by drawing analogies with literary fiction. We begin by outlining the guiding intuitions behind the fiction view...

General Griceanism is the radical proposal that all types of representation can be explained in a unified way as deriving from a more fundamental kind of representations, namely mental states. The view thus holds that there is no problem of scientific representation, or of any other form of epistemic representation like images, diagrams, or graphs....

In this chapter we discuss accounts of scientific representation that analyse representation in terms of the inferential role that models play in scientific investigations. According to the accounts discussed earlier, a model’s inferential capacity – its capacity to ground surrogative reasoning – dropped out of an analysis of epistemic representati...

In this chapter we discuss approaches that depart from Goodman’s notion of “representation-as”, which is based on the notion that both works of art and scientific representations represent their subject matters as being thus or so. The chapter begins with a discussion of the demarcation problems in the context of representation-as, and then explore...

The structuralist view of scientific representation originated in the so-called semantic view of theories, which came to prominence in the second half of the twentieth century. Many defenders of the semantic view of theories take models to be structures, which represent their target systems in virtue of there being some kind of mapping (isomorphism...

What questions does a philosophical account of scientific representation have to answer and what conditions do these answers have to satisfy? Different authors have focussed on different issues and framed the problem in different ways. There is neither a shared understanding of the problems that an account of scientific representation has to addres...

This paper aims to shed light on the relation between Boltzmannian statistical mechanics and Gibbsian statistical mechanics by studying the Mechanical Averaging Principle, which says that, under certain conditions, Boltzmannian equilibrium values and Gibbsian phase averages are approximately equal. What are these conditions? We identify three condi...

Many models function representationally. Considerable differences notwithstanding, most accounts of representation involve the notion that models denote their targets. Denotation is a dyadic relation that obtains between certain symbols and certain objects. This does not sit well with the fact that many models are not concrete objects. If a model d...

According to the fiction view of models, scientific models are akin to places and characters in literary fiction. The chapter introduces this view and develops a specific version of the view based on the pretense account of fiction. It then turns to the question of how models represent their targets and formulates an account of representation based...

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 characteriz...

(Link: https://plato.stanford.edu/entries/models-science/) Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and g...

This monograph offers a critical introduction to current theories of how scientific models represent their target systems. Representation is important because it allows scientists to study a model to discover features of reality. The authors provide a map of the conceptual landscape surrounding the issue of scientific representation, arguing that i...

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...

Many models function representationally. Considerable differences notwithstanding, most accounts of representation involve the notion that models denote their targets. Denotation is a dyadic relation that obtains between certain symbols and certain objects. This does not sit well with the fact that many models are not concrete objects. If a model d...

Theoreticians working in statistical mechanics seem to be spoilt for choice. The theory offers two different theoretical approaches, one associated with Boltzmann and the other with Gibbs. These approaches are neither theoretically equivalent nor in any obvious way inter-translatable. This raises the question about the relation between them. We arg...

According to the fiction view of models, scientific models are akin to places and characters in literary fiction. The chapter introduces this view and develops a specific version of the view based on the pretense account of fiction. It then turns to the question of how models represent their targets and formulates an account of representation based...

The DEKI account of representation, which builds on Goodman and Elgin’s notion of representation-as, explicates representation in terms of denotation, exemplification, keying up, and imputation. Originally formulated as an account of scientific representation, it is here used to account for representation in the arts and to highlight the commonalit...

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...

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...

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...

How are properties encoded in GRW theory? In this chapter I discuss an influential answer to this question, the so-called Fuzzy Link. Lewis (1997) argued that GRW theory, when interpreted in terms of the Fuzzy Link, implies that arithmetic does not apply to ordinary objects, an argument now known as the ‘counting anomaly’. I take this argument as t...

Nancy Cartwright’s work has been influential in establishing the now widely accepted view that scientific models are the primary representational units of science. This view brings with it the question of scientific representation: in virtue of what do scientific models represent parts, or aspects, of the world (their ‘target systems’). In this pap...

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 where the Boltzmannian and Gibbsian equilib...

Many scientific models are representations. Building on Goodman and Elgin’s notion of representation-as we analyse what this claim involves by providing a general definition of what makes something a scientific model, and formulating a novel account of how they represent. We call the result the DEKI account of representation, which offers a complex...

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structure...

Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian α-ɛ-equilibrium and a Boltzmannian γ-ɛ-equilibrium (Werndl and Frigg, Stud Hist Philos Mod Phys 44:470–479, 2015a; Philos Sci 82:1224–1235, 2015b). This was done in a deterministic context. We now consider systems with a stochasti...

Models are of central importance in many scientific contexts. We study models and thereby discover features of the phenomena they stand for. For this to be possible models must be representations: they can instruct us about the nature of reality only if they represent the selected parts or aspects of the world we investigate. This raises an importa...

Climate change adaptation is largely a local matter, and adaptation planning can benefit from local climate change projections. Such projections are typically generated by accepting climate model outputs in a relatively uncritical way. We argue, based on the IPCC’s treatment of model outputs from the CMIP5 ensemble, that this approach is unwarrante...

Climate change adaptation is largely a local matter, and adaptation planning can benefit from local climate change projections. Such projections are typically generated by accepting climate model outputs in a relatively uncritical way. We argue, based on the IPCC's treatment of model outputs from the CMIP5 ensemble, that this approach is unwarrante...

Background Pedobarography offers dynamic information about the foot, but the interpretation of its large data is challenging. In a prior study it was shown that attention can be restricted to pedobarographic midfoot load data. We aim to verify this observation in ankle osteoarthritic and contralateral feet. Methods We assessed both feet of 120 pati...

Background Pedobarography offers dynamic information about the foot, but the interpretation of its large data is challenging. In a prior study it was shown that attention can be restricted to pedobarographic midfoot load data. We aim to verify this observation in ankle osteoarthritic and contralateral feet. Methods We assessed both feet of 120 pati...

Equilibrium 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 (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions...

In this paper we explore the constraints that our preferred account of scientific representation places on the ontology of scientific models. Pace the Direct Representation view associated with Arnon Levy and Adam Toon we argue that scientific models should be thought of as imagined systems, and clarify the relationship between imagination and repr...

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 equi...

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. Methods: We compared 126 patients (total ankle replacement 28, ankle arthrodesis 57, and tibiotalocalcaneal arthrodesis 41) with 35 hea...

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world?s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientif...

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.

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.

Boltzmannian statistical mechanics partitions the phase space 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...

The United Kingdom Climate Impacts Programme’s UKCP09 project makes high-resolution projections of the climate out to 2100 by post-processing the outputs of a large-scale global climate model. The aim of this paper is to describe and analyse the methodology used and then urge some caution. Given the acknowledged systematic, shared errors of all cur...

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...

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been under-appreciated, namely structural model error (SME). A model has SME if the model-dynamics differ from the dynamics in the target system. If a nonl...

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide u...

The United Kingdom Climate Impacts Program’s UKCP09 project makes high-resolution forecasts of climate during the twenty-first century using state of the art global climate models. The aim of this article is to introduce and analyze the methodology used and then urge some caution. Given the acknowledged systematic errors in all current climate mode...

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show th...