Stephan Hartmann

Bayesianism is our leading theory of uncertainty. Epistemology is defined as the theory of knowledge. So “Bayesian Epistemology” may sound like an oxymoron. Bayesianism, after all, studies the properties and dynamics of degrees of belief, understood to be probabilities. Traditional epistemology, on the other hand, places the singularly non-probabilistic notion of knowledge at centre stage, and to the extent that it traffics in belief, that notion does not come in degrees. So how can there be a Bayesian epistemology?

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.

Social epistemology is a relatively new and booming field of research. It studies the social dimension of the pursuit of acquiring true beliefs and requires philosophical as well as sociological and economic expertise. The insights gained in social epistemology are not only of theoretical interest; they also improve our understanding of social and political processes, as the field includes the analysis of group deliberation and group decision-making. However, surprisingly little work has so far been done on the epistemic properties of group deliberation, belief aggregation, and decision-making procedures. To close this gap, the construction and analysis of formal models are especially promising as formal modeling combines representational adequacy with instructive analytical results. This special issue collects papers that follow this strategy from the point of view of different disciplines.

Nancy Cartwright is one of the most distinguished and influential contemporary philosophers of science. Despite the profound impact of her work, there is neither a systematic exposition of Cartwright’s philosophy of science nor a collection of articles that contains in-depth discussions of the major themes of her philosophy. This book is devoted to a critical assessment of Cartwright’s philosophy of science and contains contributions from Cartwright's champions and critics. Broken into three parts, the book begins by addressing Cartwright's views on the practice of model building in science and the question of how models represent the world before moving on to a detailed discussion of methodologically and metaphysically challenging problems. Finally, the book addresses Cartwright's original attempts to clarify profound questions concerning the metaphysics of science. With contributions from leading scholars, such as Ronald N. Giere and Paul Teller, this unique volume will be extremely useful to philosophers of science the world over.

One of the major problems that artificial intelligence needs to tackle is the combination of different and potentially conflicting sources of information. Examples are multi-sensor fusion, database integration and expert systems development. In this paper we are interested in the aggregation of propositional logic-based information, a problem recently addressed in the literature on information fusion. It has applications in multi-agent systems that aim at aggregating the distributed agent-based knowledge into an (ideally) unique set of propositions. We consider a group of autonomous agents who individually hold a logically consistent set of propositions. Each set of propositions represents an agent’s beliefs on issues on which the group has to make a collective decision. To make the collective decision, several aggregation procedures have been proposed in the literature. Assuming that all propositions in question are factually right or wrong, we ask how good belief fusion is as a truth tracker. Will it single out the true set of propositions? And how does information fusion compare with other aggregation procedures? We address these questions in a probabilistic framework and show that information fusion does especially well for agents with a middling competence of hitting the truth of an individual proposition.

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.

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.

The roles models play in science have long been recognised and sparked rich and varied philosophical debates. In recent years attention has also been paid to the computational techniques used in the sciences, and the question arose what the implications were of the use of computer simulations for our understanding of scientific modelling, and science more generally. This was the subject of the conference “Models and Simulations”, which took place at the IHPST in Paris in June 2006. Selected papers of that conference appeared in a special issue of this journal (Synthese 169(3) (2009)). After the conference there was a general feeling that there still was much ground to cover, and so we decided to organize a follow up a year later. “Models and Simulations 2” took place in October 2007 at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in the Netherlands. The conference was made possible due to generous financial support from IHPST (Paris, CNRS), Universitat de Barcelona, TiLPS (Tilburg Center for Logic and Philosophy of Science) and the Evert Willem Beth Foundation. The papers in this special issue were presented at the conference and selected after a double-blind review process. We would like to thank the authors and referees of the papers for their work, and Vincent Hendricks and John Symons for their support of the project of another special issue on models and simulations.

Combining testimonial reports from independent and partially reliable information sources is an important epistemological problem of uncertain reasoning. Within the framework of Dempster–Shafer theory, we propose a general model of partially reliable sources, which includes several previously known results as special cases. The paper reproduces these results on the basis of a comprehensive model taxonomy. This gives a number of new insights and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete information.

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth.

Die Frage, was eine wissenschaftliche Erklärung ist, stellt seit mehr als einem halben Jahrhundert ein zentrales Thema der Wissenschaftsphilosophie dar. Die heutige Diskussion begann mit einer richtungsweisenden Arbeit von Carl Hempel im Jahre 1942 über den Erklärungsbegriff in der Geschichtswissenschaft. In dieser Arbeit gab Hempel, frühere Überlegungen von John Stuart Mill, Karl Popper und anderen präzisierend, eine formale Definition der Erklärung eines singulären Faktums.1 Mit seiner dem zugrunde liegenden Auffassung, dass die Wissenschaften sehr wohl in der Lage sind, Erklärungen zu liefern, setzt sich Hempel ab von den zur damaligen Zeit vorherrschenden antimetaphysisch gestimmten Erklärungsskeptikern wie Pierre Duhem. Es ist jedoch wichtig zu betonen, dass Hempels Definition des Konzeptes der wissenschaftlichen Erklärung nicht wesentlich über das Deskriptive hinaus geht und damit auch und gerade von Empiristen akzeptiert werden kann. Bekanntlich versteht man unter einer Erklärung in Hempels Deduktiv-Nomologischen (D-N) Modell ein deduktiv gültiges Argument, zu dessen Prämisse (dem sog. Explanans) mindestens ein universelles Gesetz und eine Menge von singulären Sätzen gehört und dessen Konklusion das zu erklärende Faktum (das sog. Explanandum) ist.

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 is that it is an unsettled question what the epistemic goal of toy modeling 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 paper 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.