On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Argumentation and education. Theoretical foundations and practices

During the last decade, argumentation has attracted growing attention as a means to elicit processes (linguistic, logical, dialogical, psychological, etc.) that can sustain or provoke reasoning and learning. Constituting an important dimension of daily life and of professional activities, argumentation plays a special role in democracies and is at the heart of philosophical reasoning and scientific inquiry. Argumentation, as such, requires specific intellectual and social skills. Hence, argumentation will have an increasing importance in education, both because it is a critical competence that has to be learned, and because argumentation can be used to foster learning in philosophy, history, sciences and in many other domains. Argumentation and Education answers these and other questions by providing both theoretical backgrounds, in psychology, education and theory of argumentation, and concrete examples of experiments and results in school contexts in a range of domains. It reports on existing innovative practices in education settings at various levels.

I have faith in my thing, you know what I mean? Mixed method elements on individual investments on religious markets.

In contemporary society, religious signification and secular systems mix and influence each other. Holistic conceptions of a world in which man is integrated harmoniously with nature meet representations of a world run by an immanent God. On the market of the various systems, the individual goes from one system to another, following his immediate needs and expectations without necessarily leaving any marks in a meaningful long term system. This article presents the first results of an ongoing research in Switzerland on contemporary religion focusing on (new) paths of socialization of modern that individuals and the various (non-) belief systems that they simultaneously develop

Translation to success of surgical innovation.

Contemporary thoracic and cardiovascular surgery uses extensive equipment and devices to enable its performance. As the specialties develop and new frontiers are crossed, the technology needs to advance in a parallel fashion. Strokes of genius or problem-solving brain-storming may generate great ideas, but the metamorphosis of an idea into a physical functioning tool requires a lot more than just a thinking process. A modern surgical device is the end-point of a sophisticated, complicated and potentially treacherous route, which incorporates new skills and knowledge acquisition. Processes including technology transfer, commercialisation, corporate and product development, intellectual property and regulatory routes all play pivotal roles in this voyage. Many good ideas may fall by the wayside for a multitude of reasons as they may not be marketable or may be badly marketed. In this article, we attempt to illuminate the components required in the process of surgical innovation, which we believe must remain in the remit of the modern-day thoracic and cardiovascular surgeon.