Lena Zuchowski

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values agree with Gibbsian phase averages. In this paper, we analyse their argument, which is still important today, and point out that its scope is limited to dilute gases.

In this paper, I argue that epidemic modeling of disease spreading involves both multi-model as well as multi-methodology reasoning. I demonstrate that epidemic modeling includes two different modeling methodologies: compartment and network modeling. Furthermore, within each of those methodologies, models are often constructed as structured groups of models, rather than as single models. I analyse the epistemic advantages of this mode of modeling, including complementary reasoning with different modeling methodologies and the ability to easily compare explanatory advantages of different models.

The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It also evaluates the link between entropy and visible disorder, and the related claim of an alignment of the Arrow of Time with a development from order to visible disorder. The Element identifies three different entropy-groundings for the Arrow of Time: (i) the Empirical Arrow of Time, (ii) the Universal Statistical Arrow of Time, and (iii) the Local Statistical Arrow of Time. The Element will also demonstrate that it is unlikely that high entropy states will always coincide with visible disorder. Therefore, it will dispute that there is a strong link between the Arrow of Time and visible disorder.

This article highlights and discusses the Ehrenfests’ use of toy models to explore irreversibility in statistical mechanics. In particular, we explore their urn and P–Q models and highlight that, while the former was primarily used to provide a simple counter-example to Zermelo’s objection to Boltzmann’s statistical mechanical underpinning of the Second Law of Thermodynamics, the latter was intended to highlight the role and importance of the Stoßzahlansatz as a cause of the tendency of systems to exhibit entropy increase. We also explain the sense in which these models are toy models and why agents can use them, as the Ehrenfests’ did, to carry out this important work, despite the fact that they do not represent any real system.

Die multiparadigmatische Struktur der Wissenschaften (kurz MSW) ist eine hoch interessante Aufsatzsammlung, welche an die Arbeit eines von 1996–2002 bestehen Spezialforschungsbereichs an der Universität Salzburg zum Thema „Theorien- und Paradigmenpluralismus in den Wissenschaften“ anknüpft. Die Arbeit dieser Forschungsgruppe und auch die in dem Buch zusammengefassten Untersuchungen zeichnen sich durch einen hohen Grad an Multidisziplinarität aus. MSW enthält Beiträge aus den Politikwissenschaften, den Erziehungswissenschaften, der Musikpädagogik, der Sportwissenschaft, der Linguistik, der Geschichte der Physik, der Soziologie und natürlich auch der Wissenschaftstheorie selbst. Es ist besonders hervorzuheben, dass jeder dieser Beiträge von Fachwissenschaftlern geschrieben wurde. Eine solche Multidisziplinarität und Zusammenarbeit mit den Fachwissenschaften wird in der Wissenschaftstheorie oft gewünscht, lässt sich jedoch nur selten realisieren. Diese Konstellation an sich zeichnet MSW aus: Das Buch ist eine einmalige Dokumentation der Anwendung eines wissenschaftstheoretischen Konzepts auf zahlreiche Fachwissenschaften und als solche grundsätzlich zu empfehlen.

I will present a refutation of 6 and 7 inconsistency claim. Using the proof by Kiessling, I will show that Classical Electrodynamics can be applied consistently and can preserve energy conservation to the problem of charged, accelerated particles. This refutes the core of Frisch's inconsistency claim. Additionally, I will argue that Frisch's proof and the resulting debate is based on a comparison of different, approximate, explicit solutions to the Maxwell–Lorentz equations. However, in order to be informative on the foundations of CED, an analysis would have to be focussed on the Maxwell–Lorentz equations as coupled system of equations.

I analyse in detail the construction of asymptotic surfaces in Sections 16–19 of Poincaré, also known as the prize paper. There are two prime reasons for doing so. Firstly, this part of the prize paper contains an interesting argumentative strategy, which I call Poincaré׳s gestalt switch. Secondly, it has been claimed that the prize paper contains one of the first descriptions of chaotic motion. I will argue that the latter claim is false, although both the gestalt switches and the graphical representation which Poincaré chose for the asymptotic surfaces might well have provided the inspiration for later works in chaos theory.

This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively.