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.

Pratiquer la religion ensemble : analyse des paroisses et communautés religieuses en Suisse dans une perspective de sociologie des organisations

RESUMÉ DE LA THÈSE EN FRANÇAIS La présente recherche se veut être un examen de la première enquête quantitative menée en Suisse sur les paroisses et communautés religieuses. La recherche vise de à appréhender la dynamique institutionnelle du champ religieux de ce pays. En relation avec une enquête similaire menée aux États-Unis (National Congregations Study, Chaves, 2004) la présente recherche analyse les données récoltées auprès d'un échantillon représentatif de plus de mille responsables spirituels des communautés religieuses de Suisse. Dans la perspective de la sociologie des organisations, elle examine le positionnement des communautés dans le champ institutionnel pour comprendre comment elles s'activent pour se maintenir dans la durée. Les communautés, pour assurer leurs services sur le long terme, sont imbriquées dans des structures confessionnelles avec des contraintes administratives diverses selon leur reconnaissance légale. En conséquence, la dynamique du champ religieux institutionnel est différenciée en trois environnements, selon leur degré de reconnaissance, qui demandent des réponses particulières à chacun pour pouvoir s'adapter et perdurer. Ces trois environnements poussent les groupes qui s'y logent à adopter des structures identiques. Pratiquer la religion ensemble, c'est ainsi se rendre dans une communauté avec une forme de rituel et d'engagement des membres correspondant à la reconnaissance du groupe par la société. Même pratiquée fortuitement, la religion collective est loin d'être un acte fortuit. RESUMÉ DE LA THÈSE EN ANGLAIS Practice the religion together Analysis of parishes and religious congregations in Switzerland in a perspective of sociology of organization This research is intended as a review of the first quantitative survey conducted in Switzerland on parishes and religious communities. The research aims to understand the dynamics of institutional religious field in this country. In connection with a similar survey conducted in the U.S. (National Congregations Study, Chaves, 2004) this research examines data gathered from a representative sample of over a thousand spiritual leaders of religious communities in Switzerland. From the perspective of sociology of organization, it examines the position of communities in the institutional field to understand how they are activated to maintain over time. Communities to ensure their services over the long term, are nested within denominational structures with different administrative constraints according to their legal recognition. Consequently, the dynamics of the religious field is differentiated into three institutional environments according to their degree of recognition, which require specific responses to each in order to adapt and endure. These three environments grow groups staying there to adopt identical structures.

Exploring women's academic careers in cross-national perspective: lessons for equal epportunity eolicies

Purpose - In recent years, several countries and/or higher education institutions have adopted equal opportunity policies to promote women's access to the upper levels of the academic career structure. The purpose of this paper is to argue that there is no universal solution to the glass ceiling that women face within academia. Insofar as the feminisation process evolves according to a variety of models, according to national and occupational context, the solutions adopted in one context may prove to be ineffective elsewhere. Design/methodology/approach - Analysis of the different models of occupational feminisation is based on a secondary analysis of the sociological literature on the subject, combined with recent data on women's access to academic positions in France and Germany. Findings - Although there are similarities in the structure of the academic labour market across countries and in the rate of feminisation of the most prestigious academic positions, the precise mechanisms through which women gain access to an academic career vary significantly from one national context to another. This cross-national variation would tend to suggest that there will also be variation when it comes to defining the most effective policy measures for increasing women's access to the upper echelons of the academic hierarchy. Indeed, different models of gender equality in academia may lead to very different results with regard to existing gender relations. Originality/value - The paper uses the available sociological literature on the feminisation process to examine how different measures adopted to promote women's access to the highest echelons of the academic career structure may have different effects on the reproduction and/or transformation of the dominant sex/gender system.

Toward a comprehensive conceptualization of business organizations and their members from a sensemaking perspective. Lessons learned from Picassoâeuro?s cubism

Until recently, much of the discussion regarding the type of organization theory needed in management studies focused on normative vs. descriptive roles of management science. Some authors however noticed that even a descriptive theory can have a normative impact. Among others, management theories are used by practitioners to make sense of their identity and roles in given contexts, and so guide their attitude, decision process, and behavior. The sensemaking potential of a theory might in this view represent an important element for predicting the adoption of a theory by practitioners. Accordingly, theories are needed which better grasp the increased complexity of today's business environment in order to be more relevant for practitioners. This article proposes a multi-faceted perspective of organizations. This implies leaving a simplistic view of organizations and building a 'cubist' conception. Picasso's cubism paintings are characterized by the use of multiple perspectives within a single drawing. Similarly, I argue here that managers must learn not only to add multiple responsibilities in their work, but to develop an integrated conception of their managerial identity and of their organizations in which the multiple social and economic dimensions are enmeshed. Social entrepreneurship is discussed as illustration of typical multi-faceted business.

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.

The normative dimension of social life from a second-person perspective

This thesis argues that insofar as we want to account for the normative dimension of social life, we must be careful to avoid construing that normative dimension in such a way as to exclude that which the second-person perspective reveals is important to social life and our ability to participate in it.¦The second-person perspective reveals that social life ought to be understood as a mix or balance of the regular and the irregular, where, in addition, those one interacts with are always to some extent experienced as other in a way that is neither immediately, nor perhaps ultimately, understandable. For persons to be able to participate in social life, conceived of in this way, they must have abilities that allow them to be, to some extent, hesitant and tentative in their relations with others, and thus tolerant of ambiguity, uncertainty and unpredictability, and responsive to and capable of learning from the otherness of others in the course of interacting with them.¦Incorporating the second-person perspective means we have to make some changes to the way we think about the normative in general, and the normative dimension of social life in particular. It does not mean giving up on the distinction between the normative and the regular - that continues to be fundamentally important but it does mean not excluding, as part of social life and as worthy of explanation, all that which is irregular. A radical way of putting it would be to say that there must be a sense in which the irregular is part of the normative. A less radical way, and the way adopted by this thesis, is to say that any account of the normative dimension of social life must not be such as to exclude the importance of irregularity from social life. This will mean 1) not characterising conventions, norms and rules as determinants of appropriateness and inappropriateness; 2) not thinking of them as necessary; 3) not thinking of them as necessarily governing minds; and 4) not thinking of them as necessarily shared.¦-¦L'argument principal de la thèse est que, pour rendre compte de la dimension normative de la vie sociale, il faut veiller à ne pas exclure la perspective de la deuxième personne - une perspective importante pour comprendre la vie sociale et la capacité requise pour y participer.¦Cette perspective nous permet d'imaginer la vie sociale comme un mélange ou un équilibre entre le régulier et l'irrégulier, l'interaction entre des individus pouvant être appréhendée comme l'expérience de chaque personne avec «l'autre» d'une manière qui n'est pas immédiatement compréhensible, et qui ne peut pas, peut-être, être ultimement comprise. Pour participer à la vie sociale, l'on doit avoir la capacité de rester hésitant et «réactif» dans ses relations avec les autres, de rester ouvert à leur altérité et de tolérer l'ambiguïté, l'incertitude et l'imprévisibilité des interactions sociales.¦Adopter une perspective «à la deuxième personne» conduit à une autre manière de penser la normativité en général, et la dimension normative de la vie sociale en particulier. Cela ne veut pas dire qu'il faut abandonner la distinction entre le normatif et le régulier - une distinction qui garde une importance fondamentale - mais qu'il faut reconnaître l'irrégulier comme faisant partie de la vie sociale et comme étant digne, en tant que tel, d'être expliqué. Une conception radicale pourrait même concevoir l'irrégulier comme faisant partie intégrante de la normativité. Une approche moins radicale, qui est celle adoptée dans cette thèse, est de dire que tout compte-rendu de la dimension normative de la vie sociale doit prendre en considération l'importance de l'irrégularité dans la vie sociale. Une telle approche implique que les conventions, normes et règles (1) ne déterminent pas ce qui est approprié ou inapproprié; (2) ne sont pas toujours nécessaires ; (3) ne gouvernent pas le fonctionnement de l'esprit ; et (4) ne sont pas nécessairement partagées.