Stephan Hartmann

Der Begriff ‘Modell’ leitet sich vom Lateinischen ‘modulus’ (das Maß) ab, im Italienischen existiert seit dem 16. Jh. ‘modello’ und R. Descartes verwendet im 17. Jh. ‘modèlle’. Während der Begriff in Architektur und Kunst schon seit der Renaissance gängig ist, wird er in den Naturwissenschaften erst im 19. Jh. verwendet.1 Dort greifen wissenschaftliche Modelle die für eine gegebene Problemstellung als wesentlich erachteten Charakteristika (Eigenschaften, Beziehungen, etc.) eines Untersuchungsgegenstandes heraus und machen diesen so einem Verständnis bzw. einer weiterführenden Untersuchung zugänglich. Es ist üblich, zwischen Skalenmodellen, Analogmodellen und theoretischen Modellen zu unterscheiden.

Wann ist Kohärenz ein Indiz für Wahrheit? Können Informationsmengen immer entsprechend ihrer Kohärenz geordnet werden? Welche Rolle spielt Kohärenz bei der Theoriewahl in der Wissenschaft? Unter welchen Umständen kann eine wissenschaftliche Theorie mit nur teilweise zuverlässigen Messinstrumenten bestätigt werden? Ist die Belegvielfaltsthese wahr? Warum sind übereinstimmende Aussagen unabhängiger Zeugen so gewichtig? Dies sind einige der Fragen, die in diesem Buch in einem wahrscheinlichkeitstheoretischen Kontext und auf der Grundlage konkreter Modelle behandelt werden. Darüber hinaus bietet das Buch eine elementare Einführung in die Theorie der Bayesianischen Netzwerke und zeigt Verbindungen auf zu Debatten in der Kognitionswissenschaft (Tversky und Kahnemans Linda Problem), Sozialwahltheorie (Condorcet Jury Theorem) und Informatik (Repräsentation von Glaubenssystemen). Das Buch richtet sich an alle, die sich für die Anwendung wahrscheinlichkeitstheoretischer Methoden in der Philosophie interessieren.

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.

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 aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same 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 such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.".

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.

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.

Models are a principle instrument of modern science. They are built, applied, tested, compared, revised and interpreted in an expansive scientific literature. Throughout this paper, I will argue that models are also a valuable tool for the philosopher of science. In particular, I will discuss how the methodology of Bayesian Networks can elucidate two central problems in the philosophy of science. The first thesis I will explore is the variety-of-evidence thesis, which argues that the more varied the supporting evidence, the greater the degree of confirmation for a given hypothesis. However, when investigated using Bayesian methodology, this thesis turns out not to be sacrosanct. In fact, under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than more instruments, and from evidence that confirms one rather than more testable consequences of the hypothesis. The second challenge that I will investigate is scientific theory change. This application highlights a different virtue of modeling methodology. In particular, I will argue that Bayesian modeling illustrates how two seemingly unrelated aspects of theory change, namely the (Kuhnian) stability of (normal) science and the ability of anomalies to over turn that stability and lead to theory change, are in fact united by a single underlying principle, in this case, coherence. In the end, I will argue that these two examples bring out some metatheoretical reflections regarding the following questions: What are the differences between modeling in science and modeling in philosophy? What is the scope of the modeling method in philosophy? And what does this imply for our understanding of Bayesianism?

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. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework.