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.

Engorgement des centres d'urgences: une raison légitime de refuser l'accès aux patients non urgents [Emergency department overcrowding: a legitimate reason to refuse access to urgent care for non-urgent patients?].

Non-urgent cases represent 30-40% of all ED consults; they contribute to overcrowding of emergency departments (ED), which could be reduced if they were denied emergency care. However, no triage instrument has demonstrated a high enough degree of accuracy to safely rule out serious medical conditions: patients suffering from life-threatening emergencies have been inappropriately denied care. Insurance companies have instituted financial penalties to discourage the use of ED as a source of non-urgent care, but this practice mainly restricts access for the underprivileged. More recent data suggest that in fact most patients consult for appropriate urgent reasons, or have no alternate access to urgent care. The safe reduction of overcrowding requires a reform of the healthcare system based on patients' needs rather than access barriers.

La communication médicale avec les patients migrants allophones : difficultés de compréhension dans les consultations spécialisées centrées sur les douleurs musculo-squelettiques chroniques

Les suivis spécialisés de douleurs chroniques comportent des enjeux communicationnels sensibles liés notamment à la subjectivité des ressentis douloureux et aux fréquentes divergences de vue entre médecins et patients quant à l'origine du problème de santé et à son traitement. Centré sur ces suivis, ce travail de thèse a cherché à appréhender comment les situations sociolinguistiques des patients migrants allophones se répercutent sur la communication médicale et, plus particulièrement, sur la compréhension mutuelle dans les consultations. Il a emprunté une approche discursive s'appuyant sur l'analyse interactionnelle de consultations filmées et sur un riche corpus de données contextuelles recueillies dans des interviews de patients et de cliniciens. Les analyses réalisées ont, entre autres, mis en évidence que les difficultés de compréhension non résolues se concentrent dans les consultations des patients les moins à l'aise en français et que ces difficultés renferment pour la plupart une charge problématique certaine en termes de qualité des soins. Il apparaît également que lorsque des malentendus ou incompréhensions cliniquement pertinents ne peuvent être résolus, le caractère limité des compétences de français de base des patients migrants n'est jamais seul en cause. Des facteurs de complexité médicaux (ex. surestimations des connaissances médicales de base des patients), relationnels (ex. non-signalement de malentendus par les patients pour éviter de faire perdre la face au médecin) et discursifs (ex. nécessité de traiter de discours ou « voix » venant de l'extérieur de la consultation dans le cadre d'une polyphonie particulièrement marquée) jouent également des rôles de premier plan dans les difficultés non résolues les plus problématiques au plan clinique et sont généralement étroitement intriqués avec le langagier au sens strict. En termes pratiques, les résultats soulignent le rôle décisif de l'autoréflexivité chez les médecins, ainsi que de leur capacité à ajuster de manière flexible leurs styles communicationnels afin, par exemple, d'éviter le cumul de facteurs de complexités favorisant des malentendus ou incompréhensions problématiques. Les observations effectuées rappellent également l'importance du recours à des ressources d'interprétariat.