Stephan Hartmann

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.

The first edition of Peter Lipton's Inference to the Best Explanation, which appeared in 1991, is a modern classic in the philosophy of science. Yet in the second edition of the book, Lipton proves that even a classic can be improved. Not only does Lipton elaborate and expand on the themes covered in the first edition, but he also adds a new chapter on Bayesianism. In particular, he attempts a reconciliation between the Bayesian approach and that offered by Inference to the Best Explanation (IBE).

Let me first state that I like Antti Revonsuo’s discussion of the various methodological and interpretational problems in neuroscience. It shows how careful and methodologically reflected scientists have to proceed in this fascinating field of research. I have nothing to add here. Furthermore, I am very sympathetic towards Revonsuo’s general proposal to call for a Philosophy of Neuroscience that stresses foundational issues, but also focuses on methodological and explanatory strategies.2 In a footnote of his paper, Revonsuo complains – as many others do today – about what is sometimes called “physics imperialism”. This is the view that physics dominates the philosophy of science. I am not sure if this is still the case nowadays, but it is certainly historically correct that almost all work in the field of methodology centered around cases from physics. Although this has been changing, there are still plenty of special sciences philosophers did not worry about much. Admittedly, I am myself a trained physicist and not a neuroscientist and will therefore probably be biased negatively. As it is, I will discuss some examples from physics in order to illustrate my points.

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.

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on those propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to that problem as the discursive dilemma. In this paper, we motivate that many groups do not only want to reach a factually right conclusion, but also want to correctly evaluate the reasons for that conclusion. In other words, we address the problem of tracking the true situation instead of merely selecting the right outcome. We set up a probabilistic model analogous to Bovens and Rabinowicz (2006) and compare several aggregation procedures by means of theoretical results, numerical simulations and practical considerations. Among them are the premise-based, the situation-based and the distance-based procedure. Our findings confirm the conjecture in Hartmann, Pigozzi and Sprenger (2008) that the premise-based procedure is a crude, but reliable and sometimes even optimal form of judgment aggregation.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses, whereas the witnesses in Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. 1 Claim (C) examined for Olsson's characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion.

Quantum mechanical entangled configurations of particles that do not satisfy Bell’s inequalities, or equivalently, do not have a joint probability distribution, are familiar in the foundational literature of quantum mechanics. Nonexistence of a joint probability measure for the correlations predicted by quantum mechanics is itself equivalent to the nonexistence of local hidden variables that account for the correlations (for a proof of this equivalence, see Suppes and Zanotti, 1981). From a philosophical standpoint it is natural to ask what sort of concept can be used to provide a “joint” analysis of such quantum correlations. In other areas of application of probability, similar but different problems arise. A typical example is the introduction of upper and lower probabilities in the theory of belief. A person may feel uncomfortable assigning a precise probability to the occurrence of rain tomorrow, but feel comfortable saying the probability should be greater than ½ and less than ⅞. Rather extensive statistical developments have occurred for this framework. A thorough treatment can be found in Walley (1991) and an earlier measurement-oriented development in Suppes (1974). It is important to note that this focus on beliefs, or related Bayesian ideas, is not concerned, as we are here, with the nonexistence of joint probability distributions. Yet earlier work with no relation to quantum mechanics, but focused on conditions for existence has been published by many people. For some of our own work on this topic, see Suppes and Zanotti (1989). Still, this earlier work naturally suggested the question of whether or not upper and lower measures could be used in quantum mechanics, as a generalization of..