Stephan Hartmann

Theoretical models are an important tool for many aspects of scientific activity. They are used, i.a., to structure data, to apply theories or even to construct new theories. But what exactly is a model? It turns out that there is no proper definition of the term "model" that covers all these aspects. Thus, I restrict myself here to evaluate the function of models in the research process while using "model" in the loose way physicists do. To this end, I distinguish four kinds of models. These are (1) models as special theories, (2) models as a substitute for a theory, (3) toy models and (4) developmental models. I argue that models of the types (3) and (4) are considerably useful in the process of theory construction. This will be demonstrated in an extended case-study from High-Energy Physics.

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.

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.

Das Thema dieses Bandes ist die Frage, ob die Wissenschaftstheorie eine normative Disziplin ist. Zunächst überrascht die Frage, denn für viele Wissenschaftstheoretiker ist die Antwort ein klares „Ja“; sie halten es für einen Allgemeinplatz, dass die Wissenschaftstheorie ein normatives Unternehmen ist. Bei genauerem Hinsehen stellt sich jedoch heraus, dass die Frage unterschiedliche Interpretationen zulässt, die einzeln diskutiert werden müssen. Dies geschieht im ersten Abschnitt. Im zweiten Abschnitt suchen wir nach möglichen Erklärungen dafür, warum die Wissenschaftstheorie bisher bei dem Projekt, eine allseits akzeptable Methodologie wissenschaftlichen Schließens zu formulieren und zu begründen, so wenig Erfolg hatte. Eine mögliche Erklärung für den ausbleibenden Erfolg ist der Partikularismus, wonach Methoden keine allgemeine, sondern nur eine lokale, bereichsabhängige Gültigkeit haben. Im dritten Abschnitt wollen wir an Hand des Bayesianismus zeigen, dass die Methodologie doch nicht so schlecht da steht, wie es zunächst den Anschein hat. Der Bayesianismus ist für viele Wissenschaftstheoretiker der aussichtsreichste Kandidat für eine allgemeine Theorie induktiven Räsonierens. Wir besprechen seine Vorzüge, stellen aber auch dar, welche Konzessionen er an den Partikularismus machen muss.

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?