Roman Frigg

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 the discussion in the remainder of the chapter. The chapter explicates the core concepts of independence and agreement, and it discusses what they mean in the context of climate modeling. The statement shows that MBRA is based on three premises, which concern robust properties, common structures, and so-called robust theorems. The chapter analyzes 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, an analysis of how the conclusions of MBRA can be justified is provided.

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 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 second part of a two-part review of MBRA, addresses the thorny issue of justifying the inferential steps taking us from the premises to the conclusions. The chapter begins by making explicit what exactly the problem is. It then turns to a discussion of two broad families of justificatory strategies, namely top-down and bottom-up justifications. In the latter group, one can distinguish between the likelihood approach, independence approaches, and the explanatory approach. This discussion leads to the sober conclusion that multimodel situations raise issues that are not yet fully understood and that MBRA has not yet reached a stage of maturity. Important questions remain open, and these will have to be addressed in future research.

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 general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science.

The aim of this paper is two-fold. Recently, Lewis has presented an argument, now known as the `counting anomaly', that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that the composition principle, which holds true in Standard Quantum Mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of collapse interpretations. Once this flaw is uncovered, the anomaly vanishes.

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought.

Background: 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 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. Main outcome measures: relative midfoot index, forefoot maximal force, walking speed. Findings: 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 0.06 m/s with footwear (p < 0.001). Total ankle replacement and ankle arthrodesis were equal in running shoes but both deviated from healthy controls (total ankle replacement/ankle arthrodesis smaller RMI p = 0.07/0.017; increased forefoot maximal force p = 0.757/0.862; slower walking speed p < 0.001). In rocker bottom shoes, this ranking remained the same except the relative midfoot index merged to similar values. Tibiotalocalcaneal arthrodesis were inferior in both shoes. Interpretation: Runners are beneficial and the benefit is greater for fusions and replacements. Rocker bottom shoes have little added benefit. Total ankle replacement and ankle arthrodesis were equal but inferior to healthy controls. Tibiotalocalcaneal arthrodesis has an inferior outcome.

Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at length the dynamical properties of a system consisting of two or three spinning spheres with homogenous mass distributions gravitationally interacting only with each other. Population biologists study the evolution of one species procreating at a constant rate in an isolated ecosystem. And when studying the exchange of goods, economists consider a situation in which there are only two goods, two perfectly rational agents, no restrictions on available information, no transaction costs, no money, and dealings are done immediately. Their surface structure notwithstanding, no competent scientist would mistake descriptions of such systems as descriptions of an actual system: we know very well that there are no such systems. These descriptions are descriptions of a model-system, and scientists use model-systems to represent parts or aspects of the world they are interested in. Following common practice, I refer to those parts or aspects as target-systems. What are we to make of this? Is discourse about such models merely a picturesque and ultimately dispensable façon de parler? This was the view of some early twentieth century philosophers. Duhem (1906) famously guarded against confusing model building with scientific theorizing and argued that model building has no real place in science, beyond a minor heuristic role. The aim of science was, instead, to construct theories, with theories understood as classificatory or representative structures systematically presented and formulated in precise symbolic..

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. 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 systems equilibrium macro-regions are large in requisite sense.

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 and show how field variables fit into the framework of our own version of BSM, the long-run residence time account of BSM. The introduction of field variables into the theory makes it possible to give a full macroscopic characterisation of the approach to equilibrium.

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 and the multi-mushroom gas.

Models and theories are of central importance in science, and scientists spend substantial amounts of time building, testing, comparing and revising models and theories. It is therefore not surprising that the nature of scientific models and theories has been a widely debated topic within the philosophy of science for many years. The product of two decades of research, in this book Roman Frigg provides an accessible yet critical introduction to the debates about models and theories within analytical philosophy of science since the 1920s. Models and Theories is the first book to address the topic from a philosophical perspective, making it essential reading for advanced undergraduates, researchers, and professional philosophers working in philosophy of science, philosophy of mathematics, and philosophy of technology. It will also be of interest to philosophically minded readers working in physics, computer sciences and STEM fields more broadly.

This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions.

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 scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature.