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.

Family relationships and learning experiences in anxious vs. non-anxious families: Are there differences ?

L'objectif principal de ce travail était d'explorer les relations parent-enfant et les processus d'apprentissage familiaux associés aux troubles anxieux. A cet effet, des familles ayant un membre anxieux (la mère ou l'enfant) ont été comparées avec des familles n'ayant aucun membre anxieux. Dans une première étude, l'observation de l'interaction mère-enfant, pendant une situation standardisée de jeu, a révélé que les mères présentant un trouble panique étaient plus susceptibles de se montrer verbalement contrôlantes, critiques et moins sensibles aux besoins de l'enfant, que les mères qui ne présentaient pas de trouble panique. Une deuxième étude a examiné les perceptions des différents membres de la famille quant aux relations au sein de la famille et a indiqué que, par comparaison aux adolescents non-anxieux, les adolescents anxieux étaient plus enclins à éprouver un sentiment d'autonomie individuelle diminué par rapport à leurs parents. Finalement, une troisième étude s'est intéressée à déterminer l'impact d'expériences d'apprentissage moins directes dans l'étiologie de l'anxiété. Les résultats ont indiqué que les mères présentant un trouble panique étaient plus enclines à s'engager dans des comportements qui maintiennent la panique et à impliquer leurs enfants dans ces comportements, que les mères ne présentant pas de trouble panique. En se basant sur des recherches antérieures qui ont établi une relation entre le contrôle parental, la perception de contrôle chez l'enfant et les troubles anxieux, le présent travail non seulement confirme ce lien mais propose également un modèle pour résumer l'état actuel des connaissances concernant les processus familiaux et le développement des troubles anxieux. Deux routes ont été suggérées par lesquelles l'anxiété pourrait être transmise de manière intergénérationnelle. Chacune de ces routes attribue un rôle important à la perception de contrôle chez l'enfant. L'idée est que lorsque les enfants présentent une prédisposition à interpréter le comportement de leurs parents comme hors de leur contrôle, ils seraient plus enclins à développer de l'anxiété. A ce titre, la perception du contrôle représenterait un tampon entre le comportement de contrôle/surprotection des parents et le trouble anxieux chez l'enfant. - The principal objective of the present work was to explore parent-child relationships and family learning processes associated with anxiety disorders. To this purpose, families with and without an anxious family member (mother or child) were compared. In a first study, observation of mother-child interaction, during a standard play situation, revealed that mothers with panic disorder were more likely to display verbal control and criticism, and less likely to display sensitivity toward their children than mothers without panic disorder. A second study examined family members' perceptions of family relationships and indicated that compared to non-anxious adolescents, anxious adolescents were more prone to experience a diminished sense of individual autonomy in relation to their parents. Finally a third study was interested in determining the effect of less direct learning experiences in the aetiology of anxiety. Results indicated that mothers with panic disorder were more likely to engage in panic-maintaining behaviour and to involve their children in this behaviour than mothers without panic disorder. Based on previous research showing a relationship between parental control, children's perception of control, and anxiety disorders, the present work not only further adds evidence to support this link but also proposes a model summarizing the current knowledge concerning family processes and the development of anxiety disorders. Two pathways have been suggested through which anxiety may be intergenerationally transmitted. Both pathways assign an important role to children's perception of control. The idea is that whenever children have a predisposition towards interpreting their parents' behaviour as beyond of their control, they may be more prone to develop anxiety. As such, perceived control may represent a buffer between parental overcontrolling/overprotective behaviours and childhood anxiety disorder.

Application of contrast media in post-mortem imaging (CT and MRI).

The application of contrast media in post-mortem radiology differs from clinical approaches in living patients. Post-mortem changes in the vascular system and the absence of blood flow lead to specific problems that have to be considered for the performance of post-mortem angiography. In addition, interpreting the images is challenging due to technique-related and post-mortem artefacts that have to be known and that are specific for each applied technique. Although the idea of injecting contrast media is old, classic methods are not simply transferable to modern radiological techniques in forensic medicine, as they are mostly dedicated to single-organ studies or applicable only shortly after death. With the introduction of modern imaging techniques, such as post-mortem computed tomography (PMCT) and post-mortem magnetic resonance (PMMR), to forensic death investigations, intensive research started to explore their advantages and limitations compared to conventional autopsy. PMCT has already become a routine investigation in several centres, and different techniques have been developed to better visualise the vascular system and organ parenchyma in PMCT. In contrast, the use of PMMR is still limited due to practical issues, and research is now starting in the field of PMMR angiography. This article gives an overview of the problems in post-mortem contrast media application, the various classic and modern techniques, and the issues to consider by using different media.