Stephan Hartmann

The way in which philosophers have thought about the scientific method and the nature of good scientific reasoning over the last few centuries has been consistently and heavily influenced by the examples set by physics. The astounding achievements of 19th and 20th century physics demonstrated that physicists had successfully identified methodologies and reasoning patterns that were uniquely well suited to discovering fundamental truths about the natural world. Inspired by this success, generations of philosophers set themselves the goal of taxonomising, codifying, formalising and evaluating these reasoning patterns. Many will concede that this has been a tremendously fruitful exercise that has served both to illuminate characteristic methodological and epistemological features of the physical sciences, and to inform the way that philosophers think about the epistemic ideals served by science more generally. However, as has been widely noted, the great challenges confronted by contemporary physics have led to a number of fundamental shifts in the way that physicists formulate, assess and apply their theories of the physical world. The most prominent examples of this trend occur in the realm of theoretical high energy physics, where many of the most influential theories advocated by physicists lie beyond the reach of extant experimental methods, and are therefore extremely difficult to test empirically. The fact that whole communities of physicists have devoted so much time and effort to evaluating theories that are largely disconnected from experiments and empirical testing suggests that existing philosophical accounts of the epistemology of physics, based as they are on a broadly empiricist conception of physics, are no longer completely apt, or are at least somewhat out of date. This in turn suggests that it is time for philosophers to redirect their attention towards the characteristic reasoning strategies at play in contemporary physics. As well as clarifying the epistemic structure of 21st century physics and providing new stimulation for general debates surrounding the epistemology of science, this will also allow more philosophers to confront and engage with the existential methodological debates currently raging within physics. There is currently intense and wide spread disagreement surrounding what kinds of reasoning strategies can legitimately be employed in the assessment of competing physical theories and research programs. This special issue aims to facilitate the further engagement of philosophers in this crucial debate by collecting eight contributions that both highlight the deep philosophical issues at stake in debates surrounding the proper methodology for theory assessment in physics, and present novel philosophical perspectives on specific reasoning strategies in the physical sciences.

A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian account of reasoning according to which “argumentation is learning”. We show that the asymmetry must appear for certain prior probability distributions, under the assumption that the conditional inference provides the agent with new information that is integrated into the existing knowledge by minimizing the Kullback-Leibler divergence between the posterior and prior probability distribution. We also show under which conditions we would expect the opposite pattern, an MT-MP asymmetry

Scientific theories are used for a variety of purposes. For example, physical theories such as classical mechanics and electrodynamics have important applications in engineering and technology, and we trust that this results in useful machines, stable bridges, and the like. Similarly, theories such as quantum mechanics and relativity theory have many applications as well. Beyond that, these theories provide us with an understanding of the world and address fundamental questions about space, time, and matter. Here we trust that the answers scientific theories give are reliable and that we have good reason to believe that the features of the world are similar to what the theories say about them. But why do we trust scientific theories, and what counts as evidence in favor of them?

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners.

In this article, we address a major outstanding question of probabilistic Bayesian epistemology: how should a rational Bayesian agent update their beliefs upon learning an indicative conditional? A number of authors have recently contended that this question is fundamentally underdetermined by Bayesian norms, and hence that there is no single update procedure that rational agents are obliged to follow upon learning an indicative conditional. Here we resist this trend and argue that a core set of widely accepted Bayesian norms is sufficient to identify a normatively privileged updating procedure for this kind of learning. Along the way, we justify a privileged formalization of the notion of ‘epistemic conservativity’, offer a new analysis of the Judy Benjamin problem, and emphasize the distinction between interpreting the content of new evidence and updating one’s beliefs on the basis of that content.

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.

This book successfully achieves to serve two different purposes. On the one hand, it is a readable physics-based introduction into the philosophy of science, written in an informal and accessible style. The author, himself a professor of physics at the University of Notre Dame and active in the philosophy of science for almost twenty years, carefully develops his metatheoretical arguments on a solid basis provided by an extensive survey along the lines of the historical development of physics. On the other hand, this book supplies one long argument for Cushing´s own attitude in the philosophy of science. While former studies of the author, from which this book draws in part, focused each on one special episode in the history of science, this book gathers case material from many different parts of physics and epochs. The main goal of this book is ”to impress upon the reader the essential and ineliminable role that philosophical considerations have played in the actual practice of science” (p. xv)

Suppose that we acquire various items of information from various sources and that our degree of confidence in the content of the information set is sufficiently high to believe the information. Now a new item of information is being presented by a new information source. Are we justified to add this new item of information to what we already believe? Consider the following parable: “I go to a lecture about wildlife in Greenland which was supposed to be delivered by an expert in the field. When I arrive I notice that the expert has excused himself and that the biology department has sent a newcomer to fill in for him. I have no beliefs about wildlife in Greenland, but I do have some beliefs about Greenland’s climate and about the kinds of climate conditions that various types of wildlife favor. Suppose that our newcomer proclaims that large colonies of elk roam in a particular valley on the southern tip of Greenland. Then I would certainly be willing to accept this item of information. But suppose that he proclaims that large colonies of armadillos roam in the same valley. Then I would not be willing to accept this item of information. Why do I accept the former but not the latter item of information? Let us suppose that neither item of information is logically inconsistent with what I already believe. Clearly, the former item of information is not inconsistent. But also the latter item is not: after all, there may be small pockets of Greenland with special climatological conditions and some Texan sailors may have set loose a pair of armadillos as a practical joke. But whereas the former item of information is quite plausible given my previous beliefs, the latter item of information is not. And this is what makes for the difference. Now suppose that our newcomer proclaims that large colonies of wild boars roam this valley in Greenland. I am not that sure anymore. Given everything I believe, I find wild boars in Greenland more plausible than armadillos in Greenland, but certainly less plausible than elk in Greenland. Had our expert presented the lecture and provided precisely the 2 same information, then I would have been willing to adopt the belief that there are wild boars in Greenland, but, with our newcomer delivering the lecture, I am not willing to do so. It is not that I would believe anything out of the expert’s mouth: also he could not have convinced me that there are armadillos in Greenland. But when it comes to wild boars, the difference between the expert’s and the newcomer’s credentials simply makes for the difference.” What we learn from this story is that the question of belief expansion has something to do with the reliability of the information source as well as with the plausibility of the new information, given what I already believe. The more reliable the information source is, the less plausible the new information needs to be given what I already believe, for me to be justified to add the belief to our belief set. The more plausible the new information is given what I already believe, the less reliable the information source needs to be given what I already believe, for me to be justified to add the belief to my belief set. The challenge is: can a precise account of this relationship be provided?

Toy models are highly idealized and extremely simple models. Although they are omnipresent across scientific disciplines, toy models are a surprisingly under-appreciated subject in the philosophy of science. The main philosophical puzzle regarding toy models concerns what the epistemic goal of toy modelling is. One promising proposal for answering this question is the claim that the epistemic goal of toy models is to provide individual scientists with understanding. The aim of this article is to precisely articulate and to defend this claim. In particular, we will distinguish between autonomous and embedded toy models, and then argue that important examples of autonomous toy models are sometimes best interpreted to provide how-possibly understanding, while embedded toy models yield how-actually understanding, if certain conditions are satisfied. _1_ Introduction _2_ Embedded and Autonomous Toy Models _2.1_ Embedded toy models _2.2_ Autonomous toy models _2.3_ Qualification _3_ A Theory of Understanding for Toy Models _3.1_ Preliminaries and requirements _3.2_ The refined simple view _4_ Two Kinds of Understanding with Toy Models _4.1_ Embedded toy models and how-actually understanding _4.2_ Against a how-actually interpretation of all autonomous toy models _4.3_ The how-possibly interpretation of some autonomous toy models _5_ Conclusion

According to an argument by Colin Howson, the no-miracles argument is contingent on committing the base-rate fallacy and is therefore bound to fail. We demonstrate that Howson’s argument only applies to one of two versions of the NMA. The other version, which resembles the form in which the argument was initially presented by Putnam and Boyd, remains unaffected by his line of reasoning. We provide a formal reconstruction of that version of the NMA and show that it is valid. Finally, we demonstrate that the use of subjective priors is consistent with the realist implication of the NMA and show that a core worry with respect to the suggested form of the NMA can be dispelled.

McGee argues that it is sometimes reasonable to accept both x and x-> without accepting y->z, and that modus ponens is therefore invalid for natural language indicative conditionals. Here, we examine McGee's counterexamples from a Bayesian perspective. We argue that the counterexamples are genuine insofar as the joint acceptance of x and x-> at time t does not generally imply constraints on the acceptability of y->z at t, but we use the distance-based approach to Bayesian learning to show that applications of modus ponens are nevertheless guaranteed to be successful in an important sense. Roughly, if an agent becomes convinced of the premises of a modus ponens argument, then she should likewise become convinced of the argument's conclusion. Thus we take McGee's counterexamples to disentangle and reveal two distinct ways in which arguments can convince. Any general theory of argumentation must take stock of both.

Does y obtain under the counterfactual supposition that x? The answer to this question is famously thought to depend on whether y obtains in the most similar world in which x obtains. What this notion of ‘similarity’ consists in is controversial, but in recent years, graphical causal models have proved incredibly useful in getting a handle on considerations of similarity between worlds. One limitation of the resulting conception of similarity is that it says nothing about what would obtain were the causal structure to be different from what it actually is, or from what we believe it to be. In this paper, we explore the possibility of using graphical causal models to resolve counterfactual queries about causal structure by introducing a notion of similarity between causal graphs. Since there are multiple principled senses in which a graph G* can be more similar to a graph G than a graph G**, we introduce multiple similarity metrics, as well as multiple ways to prioritize the various metrics when settling counterfactual queries about causal structure.

Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach is overall better supported by the empirical evidence. So, to develop philosophical theories of mind on the basis of a realist interpretation of results from Bayesian cognitive science is unwarranted. Naturalistic philosophers of mind should instead adopt an anti-realist attitude towards these results and remain agnostic as to whether Bayesian models are true. For continuing on with an exclusive focus and praise of Bayes within debates about the predictive processing theory will impede progress in philosophical understanding of scientific practice in computational cognitive science as well as of the architecture of the mind.

We present a Bayesian analysis of the epistemology of analogue experiments with particular reference to Hawking radiation. Provided such experiments can be externally validated via universality arguments, we prove that they are confirmatory in Bayesian terms. We then provide a formal model for the scaling behaviour of the confirmation measure for multiple distinct realisations of the analogue system and isolate a generic saturation feature. Finally, we demonstrate that different potential analogue realisations could provide different levels of confirmation. Our results thus provide a basis both to formalise the epistemic value of analogue experiments that have been conducted and to advise scientists as to the respective epistemic value of future analogue experiments.

Deliberation is a standard procedure to make decisions in not too large groups. It has the advantage that the group members can learn from each other and that, at the end, often a consensus emerges that everybody endorses. But a deliberation procedure also has a number of disadvantages. E.g., what consensus is reached usually depends on the order in which the different group members speak. More specifically, the group member who speaks first often has an unproportionally high impact on the final decision: She anchors the deliberation process. While the anchoring effect undoubtably appears in real deliberating groups, we ask whether it also appears in groups whose members are truth-seeking and rational in the sense that they take the information provided by their fellow group members properly into account by updating their beliefs according to plausible rules. To answer this question and to make some progress towards explaining the anchoring effect, a formal model is constructed and analyzed. Using this model, we study the anchoring effect in homogenous groups, for which we provide analytical results, and in inhomogeneous groups, for which we provide simulation results.

A widely shared view in the cognitive sciences is that discovering and assessing explanations of cognitive phenomena whose production involves uncertainty should be done in a Bayesian framework. One assumption supporting this modelling choice is that Bayes provides the best approach for representing uncertainty. However, it is unclear that Bayes possesses special epistemic virtues over alternative modelling frameworks, since a systematic comparison has yet to be attempted. Currently, it is then premature to assert that cognitive phenomena involving uncertainty are best explained within the Bayesian framework. As a forewarning, progress in cognitive science may be hindered if too many scientists continue to focus their efforts on Bayesian modelling, which risks to monopolize scientific resources that may be better allocated to alternative approaches.

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework.

This paper focuses on the question of how to resolve disagreement and uses the Lehrer-Wagner model as a formal tool for investigating consensual decision-making. The main result consists in a general definition of when agents treat each other as epistemic peers (Kelly 2005; Elga 2007), and a theorem vindicating the “equal weight view” to resolve disagreement among epistemic peers. We apply our findings to an analysis of the impact of social network structures on group deliberation processes, and we demonstrate their stability with the help of numerical simulations.

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix.

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" (PSE) in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing papers coming from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​

Here P is the density operator of the system under consideration, and σ ± and σ 3 are the usual Pauli matrices, acting on atom i whose states are |1 > or |0 >, representing, respectively, the atom being in an excited state or in the ground state. B and C are appropriate decay constants and s has been called the pumping parameter [1]. It varies from s = 0 for pure damping to s = 1 for full laser action. To solve the corresponding quantum master equations, three approaches have been taken: First, one focuses on the case of one atom. Second, one truncates eq. (1) and derives semi-classical models. Third, one employs numerical simulation methods such as the quantum trajectory method. While the latter method is very popular, it should be noted that the numerical complexity of the problem increases exponentially with the number of atoms, and so numerical methods soon become unfeasible.

Vacuum (leer, frei) bezeichnete bis zum 19. Jahrhundert allein den körperlosen Raum. Unter dem Einfluss physikalischer (Feld-) Theorien meint der Terminus inzwischen diejenige residuale physische Entiät, die einen vorgegebenen Raum ausfüllt bzw. im Prinzip ausfüllen würde, nachdem alles, was mit physikalischen Mitteln entfernt werden kann, aus dem Raum entfernt wurde. Theorien über das V. sind daher eng mit Theorien über die Struktur des Raumes, die Bewegung, die physikalischen Gegenstände und deren Wechselwirkungen verbunden. In der Quantentheorie bezeichnet V. den Zustand niedrigster Energie (Grundzustand) eines Systems.

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it does not re- place it or aim at replacing it.

There is a long philosophical tradition of addressing questions in philosophy of science and epistemology by means of the tools of Bayesian probability theory (see Earman (1992) and Howson and Urbach (1993)). In the late '70s, an axiomatic approach to conditional independence was developed within a Bayesian framework. This approach in conjunction with developments in graph theory are the two pillars of the theory of Bayesian Networks, which is a theory of probabilistic reasoning in artificial intelligence. The theory has been very successful over the last two decades and has found a wide array of applications ranging from medical diagnosis to safety systems for hazardous industries.