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.

Il desiderio materno nei casi di maltrattamento infantile

The work of this thesis would like to investigate two particular questions about the care of underage: on the one hand, the maltreatment, and the mother's desire on the other hand. About the first, this proposal try to underscore the elaborate irregularity and disparity related to this phenomenon and his historical evolution. The objective's thesis propose to underline that the abuse crosses the crisis of educational dimension inside and outside the family. We are talking about a type of crisi that places at the origin of a specific clinic and that it is about the maltreatment designated, at the same time, to cope with the educational void and with the ill-treated under age's hardships. The so-called clinic of the maltreatment horns, therefore, with the purpose to join and to set in order the normative and educational aspects. However, the prescriptive requirement is intended to measure against the same one crisis in a paradoxical way; the laws and the juveniles court must make up for the lack absence of the rules that characterized the maltreatment, getting around to use the typical reference that traditionally were been at the base of the educational way's construction. The same crimes on underage often found in the father the responsibility. The requirements and the therapeutic needs has utilized the theoretical construct of the trauma as the key line of clinical practice. On the one hand, the trauma was been paired controversially to the psychoanalytical concepts as the notion of the phantom, in the same manner that the objective truth is been opposed to the notion of the imagination and fantasy; on the other hand, the trauma was gotten to be the mark and the characteristic that defined the individual identity of the mistreated persons, regardless of the person's clinical structure or, generally, regardless of the their individual position. Both the normative demand and therapeutic converge on the idealization of the imaginary figure that is able to supply to every type of maltreatment: the mother. This position is connected on theoretical construct well-established in the mythology, that associated the mother figure to a natural dimension; this is related to the second point at issue: the mother's desire. The awareness of the mother figure in natural and idealized terms describes accusingly and negatively the trauma, without seeing the difference between trauma that helps to give a structure to the individual position from the trauma solely devastating. The mother's mythology, therefore, is in an evident antagonism with the female figure and woman's sexuality. In these way the maltreatment's clinic suggests that a woman is able to be a mother only when she doesn't appreciate the rule of female. This situation preclusives a comparison with own sexuality and gives to the women a complex of castration. The clinic cases reported highlight as these difficulties are the expression of the familiarity's heredity that wasn't been sufficiently elaborated. This condition (into the relation between mother and his child) turn the infant in the incapacity to symbolized and it doesn't help him to accede to the positive trauma, to the language and to the edipic rule; this is the reason why the child toils difficulties to approach to own personality and to orient himself in the relation with his body, with the body of the adults and the same age children.

Changing the awareness of low vitamin D status in a rheumatology population: a pre/post-study.

INTRODUCTION: In 2009 hypovitaminosis D was highly prevalent in a population of Swiss rheumatology patients (86%). We aimed to evaluate the evolution of vitamin D status in the same population two years later, after the results of the first study were disseminated to local physicians and patients, in order to determine the evolution of the problem and the impact of physician information. METHOD: Patients in our rheumatology clinic were screened for 25-OH vitamin D. Results were categorised as: deficient (<10 ng/ml or <25 nmol/l), insufficient (10 to 30 ng/ml or 25 to 75 nmol/l) or normal (>30 ng/ml or >75 nmol/l). We also used another cut-off of 20 ng/ml (50 nmol/l). We evaluated the evolution of 25-OH vitamin D dosages and vitamin D3 prescriptions between 2008 and 2011 in our institution and the number of publications on vitamin D in three important medical journals of the French speaking part of Switzerland. RESULTS: Compared with 2009, significantly more patients had normal results in 2011. Fifty-two percent of patients had levels >20 ng/ml in 2009 and 66% in 2011, difference statistically significant (p = 0.001). During the years separating the two study periods the number of 25-OH vitamin D dosages and the prescription of high doses of vitamin D3 increased in our hospital. In addition the number of publications on vitamin D increased between 2008 and 2011. CONCLUSION: We concluded that lower prevalence in hypovitaminosis D is certainly related to better adherence to daily supplements, and to better information and awareness of the physicians about hypovitaminosis D.

L'hystérie : une entité historique, un trouble psychiatrique ou une maladie neurologique? [Hysteria : an historical entity, a psychiatric condition or a neurological disease?]

Il a été suggéré que l'hystérie avait disparu et n'était qu'un concept ancien, stigmatisant et péjoratif, voire erroné, reflétant l'incapacité de la communauté médicale à établir parfois un diagnostic. Actuellement ces troubles, appelés troubles dissociatifs ou de conversion, restent pourtant une réalité clinique fréquente et invalidante pour les patients. Plusieurs études et revues ont tenté de mieux décrire la présentation clinique, mais également de mieux comprendre les mécanismes neurobiologiques impliqués dans ces troubles grâce au développement de certaines techniques d'imagerie cérébrale. Si les corrélats neurobiologiques sont mieux compris, des traitements efficaces manquent encore et seule une prise en charge multidisciplinaire (généralistes, neurologues et psychiatres) et individualisée peut apporter un bénéfice au patient. It has been suggested that hysteria had waned and was an old-fashioned, stigmatizing and false concept, reflecting the incapacity of the medical community to establish a diagnosis in certain situations. Nowadays, however, those disturbances, now referred to as conversion or dissociative disorders, still remain a frequent and incapacitating condition that every clinician faces. These past decades, several studies have tried to better describe their clinical presentation and their neurobiological mechanisms, with the help of the development of new neuroimaging techniques. If the neurobiological correlates are now better understood, efficient treatments are still lacking and only a multidisciplinary (general practitioners, neurologists and psychiatrists) and individually-tailored therapy might be beneficial to the patients.

Prevalence, awareness, treatment and control of hypertension in a Swiss general population: the CoLaus Study

Objective: To assess the prevalence levels of awareness, treatment and control of hypertension and associated factors in Switzerland. Methods: Population-based cross-sectional study of 6,182 subjects (52.5% women) aged 35-75 years living in Lausanne, Switzerland. Hypertension was defined as blood pressure ≥140/90 mm Hg or current antihypertensive medication. Results: The overall prevalence of hypertension was 36% (95% CI: 35-38%). Among hypertensive participants, 63% were aware of having hypertension. Among aware hypertensives, 78% were treated, and among treated hypertensives 48% were controlled (BP <140/90 mmHg). In multivariate analysis, prevalence of hypertension was associated with older age, male gender, low educational level, high alcohol intake, awareness of diabetes, awareness of dyslipidaemia, obesity and parental history of myocardial infarction (MI). Awareness of hypertension was associated with older age, female gender, awareness of diabetes, awareness of dyslipidaemia, obesity and parental history of MI. Control was associated with younger age, higher educational level and no alcohol intake. Alone or in combination, sartans were the most often prescribed antihypertensive medication category (41%), followed by diuretics, beta-blockers, ACE inhibitors and calcium channel blockers. Only 31% of treated hypertensives were taking ≥2 antihypertensive medications. Conclusion: Although more than half of the participants with hypertension were aware of being hypertensive and more than three quarters of them received a pharmacological treatment, less than half of those treated were adequately controlled. Treated hypertensive subjects should be followed up more closely.

Historical Profile of Water Regime in Switzerland (1870-2000).

Analyse comparée de la formation et des effets des régimes institutionnels de ressources naturelles en Suisse. Partant du constat de l'accroissement significatif et généralisé de la consommation des ressources naturelles, le projet a pour ambition d'examiner, dans le cas de la Suisse, quels sont les types de régimes institutionnels -régimes composés de l'ensemble des droits de propriété de disposition et d'usages s'appliquant aux différentes ressources naturelles, de même que des politiques publiques d'exploitation et de protection les régulant- susceptibles de prévenir des processus de surexploitation et de dégradation de ces ressources. Dans le cadre de ce projet de recherche financé par le Fonds national suisse de la recherche scientifique (FNRS), il s'agit, dans un premier temps, d'analyser les trajectoires historiques d'adaptation et de changements des régimes institutionnels des différentes ressources sur une durée d'environ un siècle (1900-2000). C'est l'objet des différents screenings. Dans un second temps et à l'aide d'études de cas, ces transformations de (ou au sein des) régimes institutionnels sont analysées sous l'angle de leurs effets sur l'état de la ressource. L'ambition finale de cette recherche est de comprendre les conditions l'émergence de "régimes intégrés" capables de prendre en compte un nombre croissant de groupes d'usagers agissant à différents niveaux (géographiques et institutionnels) et ayant des usages de plus en plus hétérogènes et concurrents de ces différentes ressources. Le champ empirique de la recherche porte plus particulièrement sur cinq ressources que sont: l'eau,l'air, le sol, le paysage et la forêt.