Stephan Hartmann

The papers in this collection were presented at a workshop on Bayesian Epistemology at the 26th International Wittgenstein Symposium in Kirchberg, Austria (August 4–7, 2003), at a workshop on Philosophy and Probability at the conference GAP5 in Bielefeld, Germany (September 20–22, 2003), at a workshop on Bayesian Epistemology at the Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science in London, UK (June 28, 2004), or at the seminar of the research group Philosophy, Probability and Modeling, Center for Junior Research Fellows, University of Konstanz, Germany. We acknowledge the generous support for these events by the Austrian Ludwig Wittgenstein Society, the Gesellschaft für analytische Philosophie e.V., the Centre for Philosophy of Natural and Social Science, the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research and the Program for the Investment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja Award. We thank the organizers of the conferences in Kirchberg and Bielefeld for their support, the authors and referees of the papers for their work, and John Symons for his interest in dedicating a special issue of this journal to Bayesian Epistemology.

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.

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.

The variety of evidence thesis in confirmation theory states that more varied supporting evidence confirms a hypothesis to a greater degree than less varied evidence. Under a very plausible interpretation of this thesis, positive test results from multiple independent instruments confirm a hypothesis to a greater degree than positive test results from a single instrument. We invoke Bayesian Networks to model confirmation on grounds of evidence that is obtained from less than fully reliable instruments and show that the variety of evidence thesis is not sacrosanct when testing is conducted with less than fully reliable instruments: under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than from more independent instruments. In the appendix, we prove certain convergence results for large numbers of positive test results from single versus multiple less than fully reliable instruments.

We develop a utilitarian framework to assess different decision rules for the European Council of Ministers. The proposals to be decided on are conceptualized as utility vectors and a probability distribution is assumed over the utilities. We first show what decision rules yield the highest expected utilities for different means of the probability distri- bution. For proposals with high mean utility, simple bench- mark rules (such as majority voting with proportional weights) tend to outperform rules that have been proposed in the political arena. For proposals with low mean utility, it is the other way round. We then compare the expected utilities for smaller and larger countries and look for Pareto- dominance relations. Finally, we provide an extension of the model, discuss its restrictions, and compare our approach with assessments of decision rules that are based on the Penrose measure of voting power.

The problem of the aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. The dificulty lies in the fact that a seemingly reasonable aggregation procedure, such as propositionwise majority voting, cannot ensure an equally consistent collective outcome. The literature on judgment aggregation refers to such dilemmas as the discursive paradox. So far, three procedures have been proposed to overcome the paradox: the premise-based and conclusion-based procedures on the one hand, and the merging approach on the other hand. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question is how good the merging approach is in tracking the truth, and how it compares with the premise-based and conclusion-based procedures.

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.

Bayes nets are a powerful tool for researchers in statistics and artificial intelligence. This chapter demonstrates that they are also of much use for philosophers and psychologists interested in (Bayesian) rationality. To do so, we outline the general methodology of Bayes nets modeling in rationality research and illustrate it with several examples from the philosophy and psychology of reasoning and argumentation. Along the way, we discuss the normative foundations of Bayes nets modeling and address some of the methodological problems it raises.

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.

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.

According to orthodoxy, there are two basic moods of supposition: indicative and subjunctive. The most popular formalizations of the corresponding norms of suppositional judgement are given by Bayesian conditionalization and Lewisian imaging, respectively. It is well known that Bayesian conditionalization can be generalized (via Jeffrey conditionalization) to provide a model for the norms of partial indicative supposition. This raises the question of whether imaging can likewise be generalized to model the norms of ‘partial subjunctive supposition’. The present article casts doubt on whether the most natural generalizations of imaging are able to provide a plausible account of the norms of partial subjunctive supposition.

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards; they require that the expected utility for the federation be maximized or that the expected utilities for people from different states be equal. We discuss an analytic result that characterizes the decision rule with maximum expected utility, set up a class of models that display interstate dependencies and run simulations for different dependency scenarios in the European Union. We find that, under positive correlations, the welfare distribution tends to be less sensitive to the choice of the decision rule, whereas it can be important under negative correlations. The results that Beisbart and Bovens (SCW 29, p. 581, 2007) have found for two types of models without interstate dependencies are relatively stable. There are exceptions, though, under which the way the welfare distribution is shaped by a decision rule is significantly affected by dependencies.

Modern science is, to a large extent, a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play here? These questions have kept philosophers of science busy for many years, and much work has been done to identify modeling as the central activity of theoretical science. At the same time, these questions have been addressed by methodologically-minded scientists, albeit from a different point of view. While philosophers typically have an eye on general aspects of scientific modeling, scientists typically take their own science as the starting point and are often more concerned with specific methodological problems. There is, however, also much common ground in middle, where philosophers and scientists can engage in a productive dialogue, as the present volume demonstrates. To do so, the editors of this volume have invited eight leading scientists from cosmology, climate science, social science, chemical engeneering and neuroscience to reflect upon their modeling work, and eight philosophers of science to provide a commentary.

In everyday life, as well as in science, we have to deal with and act on the basis of partial (i.e. incomplete, uncertain, or even inconsistent) information. This observation is the source of a broad research activity from which a number of competing approaches have arisen. There is some disagreement concerning the way in which partial or full ignorance is and should be handled. The most successful approaches include both quantitative aspects (by means of probability theory) and qualitative aspect (by means of graphical or causal models or logic). Some of these approaches have important impacts on various disciplines including philosophy, computer science, statistics, mathematics, physics, and social science. Most notably, the relation between causal and probabilistic information is a topic of interest in all of these fields. The general question of how uncertainty is related to ignorance, and the connection thereof to causality, have been the key topics of the international summer school at the University of Konstanz, Germany, in August 2004. This was the third event in a series of summer schools organized by the interdisciplinary research group “Philosophy, Probability, and Modeling”. The group was in operation from September 1st, 2001, until August 31, 2005. The first summer school, held in September 2002, focused on the application of probability theory to topics of philosophical interest. Problems and questions that arise when probabilistic models and techniques are being applied in the special sciences were then discussed during the second summer school, held in July 2003. The fourth and final event in the series, in August 2005, was devoted to philosophical questions related to the application and interpretation of probabilities in physics. Each of the four summer schools attracted 40–50 people from many different countries. It was an inspiring forum for an interdisciplinary discussion among researchers and students from many different areas. This special issue collects a selection of the invited and contributed papers presented at the summer school in 2004. We acknowledge the generous support of the Center for Junior Research Fellows at the University of Konstanz, the Gesellschaft für analytische Philosophie e.V., the Centre for Philosophy of Natural and Social Science at the London School of Economics, the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research and the Program for the Investment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja Award. We thank the referees of the papers for their work, and James Moor for his interest in dedicating a special issue of this journal to Causality, Uncertainty and Ignorance.

The formalism of quantum mechanics provides us with the probabilities for certain events to occur—this much is uncontroversial. But how are we to understand these probabilities? The essays in this special issue approach this question from different angles. The first three contributions take as their point of departure the philosophy of probability and discuss what the two main outlooks—objective and subjective interpretations of probability—have to offer in the context of quantum mechanics. The following five papers explore the question of how probabilities in particular interpretations of quantum mechanics—modal interpretations, relative state interpretations, Bohmian mechanics, and GRW theory—can be interpreted. The last three essays address specific issues: non-standard probability and algebraic quantum field theory, quantum propensities, and the relation between decoherence and the interpretation of probability.

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)

Science presents us with a variety of accounts of the world. While some of these accounts posit deep theoretical structure and fundamental entities, others do not. But which of these approaches is the right one? How should science conceptualize the world? And what is the relation between the various accounts? Opinions on these issues diverge wildly in philosophy of science. At one extreme are reductionists who argue that higher-level theories should, in principle, be incorporated in, or eliminated by, the basic-level theory. According to this view, higher-level theories do not ultimately exhibit conceptual integrity or provide genuine explanations. At the other extreme are pluralists who take higher levels of description and explanation seriously and argue for their independence and indispensability. It was the aim of the first Sydney–Tilburg conference on “Reduction and the Special Sciences”, which took place at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in Tilburg, The Netherlands, over the 10–12th April 2008, to bring researchers working on these questions together and provide a platform to discuss them in a focused way. The papers in this special issue were presented at this conference. We would like to thank the Royal Netherlands Academy of Art and Sciences (KNAW), the Sydney Centre for the Foundations of Science at the University of Sydney and TiLPS for financial and institutional support. We also thank the authors and referees of the papers for their work, and Hans Rott for his support of this project.

A federal assembly consists of a number of representatives for each of the nations (states, Länder, cantons,...) that make up the federation. How many representatives should each nation receive? What makes this issue worth quibbling about is that the model of representation that is instituted will have an impact on the welfare distribution over the nations in the federation that will ensue over due course. We will investigate what models of representation yield welfare distributions that score higher on a utilitarian measure. First, we construct a continuum of models of representation ranging from equal to proportional representation. In between these extremes are models of degressive proportionality. We run a Monte-Carlo simulation in which a large number of motions are voted up or down within different contexts of evaluation and investigate how well the resulting welfare distributions score on the utilitarian measure. Subsequently, we will provide matching analytical results for a slightly idealized case. We conclude with a discussion of the significance of our results and of the role of simulations and analytical results and point to further work.

Computational modeling should play a central role in philosophy. In this introduction to our topical collection, we propose a small topology of computational modeling in philosophy in general, and show how the various contributions to our topical collection ft into this overall picture. On this basis, we describe some of the ways in which computational models from other disciplines have found their way into philosophy, and how the principles one found here still underlie current trends in the feld. Moreover, we argue that philosophers contribute to computational modeling not only by building their own models, but also by thinking about the various applications of the method in philosophy and the sciences. In this context, we note that models in philosophy are usually simple, while models in the sciences are often more complex and empirically grounded. Bridging certain methodological gaps that arise from this discrepancy may prove to be challenging and fruitful for the further development of computational modeling in philosophy and beyond.

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 longstanding question is the extent to which "reasonable doubt" may be expressed simply in terms of a threshold degree of belief. In this context, we examine the extent to which learning about possible alternatives may alter one's beliefs about a target hypothesis, even when no new "evidence" linking them to the hypothesis is acquired. Imagine the following scenario: a crime has been committed and Alice, the police's main suspect has been brought to trial. There are several pieces of evidence that raise the probability that Alice committed the crime. Her attorney's defense strategy is not to challenge this evidence, but instead to provide personal details about Alice's neighbour, Jane. While Jane is one of many people the police spoke to, they saw no reason to investigate her further. You now learn that Jane, too, had access to the shed where the murder weapon was stored, just like Alice. To what extent should this alter your beliefs about Alice's guilt? In this paper, we provide a formal description of the problem and a solution indicating circumstances under which learning about Jane will more or less impact beliefs about Alice.