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.

Neo/adjuvant chemotherapy does not improve outcome in resected primary synovial sarcoma: a study of the French Sarcoma Group.

BACKGROUND: There are only scarce data about the benefit of adjunctive chemotherapy in patients with localized synovial sarcoma (SS). PATIENTS AND METHODS: Data from 237 SS patients recorded in the database of the French Sarcoma Group were retrospectively analyzed. The respective impact of radiotherapy, neo-adjuvant chemotherapy and adjuvant chemotherapy on overall survival (OS), local recurrence-free survival (LRFS) and distant recurrence-free survival (DRFS) were assessed after adjustment to prognostic factors. RESULTS: The median follow-up was 58 months (range 1-321). Adjuvant, neo-adjuvant chemotherapy and postoperative radiotherapy were administered in 112, 45 and 181 cases, respectively. In all, 59% of patients treated with chemotherapy received an ifosfamide-containing regimen. The 5-year OS, LRFS and DRFS rates were 64.0%, 70% and 57%, respectively. On multivariate analysis, age >35 years old, grade 3 and not-R0 margins were highly significant independent predictors of worse OS. After adjustment to prognostic factors, radiotherapy significantly improved LRFS but not DRFS or OS. Neither neo-adjuvant nor adjuvant chemotherapy had significant impact on OS, LRFS or DRFS. CONCLUSION: As for other high-grade soft-tissue sarcomas, well-planned wide surgical excision with adjuvant radiotherapy remains the cornerstone of treatment for SS. Neo-adjuvant or adjuvant chemotherapy should not be delivered outside a clinical trial setting.

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.

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.

Multicenter trial of neo-adjuvant chemotherapy followed by extrapleural pneumonectomy in malignant pleural mesothelioma.

BACKGROUND: The aim of this multicenter trial was to prospectively evaluate neo-adjuvant chemotherapy followed by extrapleural pneumonectomy (EPP) and radiotherapy, including quality of life as outcome. PATIENTS AND METHODS: Eligible patients had malignant pleural mesothelioma of all histological types, World Health Organization performance status of zero to two and clinical stage T1-T3, N0-2, M0 disease considered completely resectable. Neo-adjuvant chemotherapy consisted of three cycles of cisplatin and gemcitabine followed by EPP. Postoperative radiotherapy was considered for all patients. RESULTS: In all, 58 of 61 patients completed three cycles of neo-adjuvant chemotherapy. Forty-five patients (74%) underwent EPP and in 37 patients (61%) the resection was complete. Postoperative radiotherapy was initiated in 36 patients. The median survival of all patients was 19.8 months [95% confidence interval (CI) 14.6-24.5]. For the 45 patients undergoing EPP, the median survival was 23 months (95% CI 16.6-32.9). Psychological distress showed minor variations over time with distress above the cut-off score indicating no morbidity with 82% (N = 36) at baseline and 76% (N = 26) at 3 months after surgery (P = 0.5). CONCLUSIONS: The observed rate of operability is promising. A median survival of 23 months for patients undergoing EPP compares favourably with the survival reported from single center studies of upfront surgery. This approach was not associated with an increase in psychological distress.

Genetic structure of Gymnures (genus Hylomys; Erinaceidae) on continental islands of Southeast Asia: Historical effects of fragmentation

Eustatic sea level changes during Pleistocene climatic fluctuations produced several cycles of connection-isolation among continental islands of the Sunda shelf. To explore the potential effects of these fluctuations, we reconstructed a model of the vicariant events that separated these islands, based on bathymetric information. Among many possible scenarios, two opposite phylogenetic patterns of evolution were predicted for terrestrial organisms living in this region: one is based on the classical allopatric speciation mode of evolution, while the other is the outcome of a sequential dispersal colonization of the archipelago. We tested the applicability of these predictions with an analysis of sequence variation of the cytochrome b gene from several taxa of Hylomys. They were sampled throughout SE-Asia and the Sunda islands. High levels of haplotype differentiation characterize the different island taxa. Such levels of differentiation support the existence of several allopatric species, as was suggested by previous allozyme and morphological data. Also in accordance with previous results, the occurrence of two sympatric species from Sumatra is suggested by their strongly divergent haplotypes. One species, Hylomys suillus maxi, is found both on Sumatra and in Peninsular Malaysia, while the other, H. parvus, is endemic to Sumatra. Its closest relative is H. suillus dorsalis from Borneo. Phylogenetic reconstructions also demonstrate the existence of a Sundaic clade composed of all island taxa, as opposed to those from the continent. Although there is no statistical support for either proposed biogeographic model of evolution, we argue that the sequential dispersal scenario is more appropriate to describe the genetic variation found among the Hylomys taxa. However, despite strong differentiation among island haplotypes, the cladistic relationships between some island taxa could not be resolved. We argue that this is evidence of a rapid radiation, suggesting that the separation of the islands may have been perceived as a simultaneous event rather than as a succession of vicariant events. Furthermore, the estimates of divergence times between the haplotypes of these taxa suggest that this radiation may actually have predated the climatic fluctuations of the Pleistocene. Further refinement of the initial palaeogeographic models of evolution are therefore needed to account for these results.