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.

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.

Future hotspots of terrestrial mammal loss.

Current levels of endangerment and historical trends of species and habitats are the main criteria used to direct conservation efforts globally. Estimates of future declines, which might indicate different priorities than past declines, have been limited by the lack of appropriate data and models. Given that much of conservation is about anticipating and responding to future threats, our inability to look forward at a global scale has been a major constraint on effective action. Here, we assess the geography and extent of projected future changes in suitable habitat for terrestrial mammals within their present ranges. We used a global earth-system model, IMAGE, coupled with fine-scale habitat suitability models and parametrized according to four global scenarios of human development. We identified the most affected countries by 2050 for each scenario, assuming that no additional conservation actions other than those described in the scenarios take place. We found that, with some exceptions, most of the countries with the largest predicted losses of suitable habitat for mammals are in Africa and the Americas. African and North American countries were also predicted to host the most species with large proportional global declines. Most of the countries we identified as future hotspots of terrestrial mammal loss have little or no overlap with the present global conservation priorities, thus confirming the need for forward-looking analyses in conservation priority setting. The expected growth in human populations and consumption in hotspots of future mammal loss mean that local conservation actions such as protected areas might not be sufficient to mitigate losses. Other policies, directed towards the root causes of biodiversity loss, are required, both in Africa and other parts of the world.

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.

Historical review: Negative efficacy and the constitutive activity of G-protein-coupled receptors.

The idea that a receptor can produce signalling without agonist intervention and that several antagonists can be 'active' in repressing such spontaneous activity is contained in the concept of ligand-induced conformational changes. Yet, this idea was neglected by pharmacologists for many years. In this article, we review the events that brought inverse agonism and constitutive activity to general attention and made this phenomenon a topic of current research. We also suggest a classification of antagonists based on the cooperativity that links their primary site of interaction with other functional domains of the receptor.