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.

Effect of levodopa on both verbal and motor representations of action in Parkinson's disease: a fMRI study.

Previous studies have demonstrated that non-demented Parkinson's disease (PD) patients have a specific impairment of verb production compared with noun generation. One interpretation of this deficit suggested the influence of striato-frontal dysfunction on action-related verb processing. The aim of our study was to investigate cerebral changes after motor improvement due to dopaminergic medication on the neural circuitry supporting action representation in the brain as mediated by verb generation and motor imagery in PD patients. Functional magnetic resonance imaging on 8 PD patients in "ON" dopaminergic treatment state (DTS) and in "OFF" DTS was used to explore the brain activity during three different tasks: Object Naming (ObjN), Generation of Action Verbs (GenA) in which patients were asked to overtly say an action associated with a picture and mental simulation of action (MSoA) was investigated by asking subjects to mentally simulate an action related to a depicted object. The distribution of brain activities associated with these tasks whatever DTS was very similar to results of previous studies. The results showed that brain activity related to semantics of action is modified by dopaminergic treatment in PD patients. This cerebral reorganisation concerns mainly motor and premotor cortex suggesting an involvement of the putaminal motor loop according to the "motor" theory of verb processing.

An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

L'usage du narratif dans le Testament de Joseph

(Résumé de l'ouvrage) Seventeen innovative studies are collected in this volume which has been produced under the aegis of the Centre for Biblical Studies, University of Manchester, and L'Institut des sciences bibliques, Université de Lausanne. The majority of the studies engage with narrative through providing insightful working examples. Building on the many contributions of recent narratological research, for the most part the studies in this collection avoid the technical language of narratology as they present fresh insights at many levels. Some essays focus more on the implied author, some on the implied reader or hearer, and some on the way particular messages are constructed; some of the studies consider how author, message and reader are all interconnected. There are several creative proposals for refining genre definition, from law and wisdom to gospel and apocryphal writings. Some studies highlight the way in which narratives can contain ethical, religious, and cultural messages. Sensitivity to narrative is also shown by some contributors to expose in intruing ways the redactional processes behind the final form of texts. Students of narrative in the ancient world will find much to consider in this book, and others engaged with literary studies more generally will discover that scholars of the worlds of the Bible and Late Antiquity have much to offer them.

Dynamics of phonological-phonetic encoding in word production: Evidence from diverging ERPs between stroke patients and controls.

While the dynamics of lexical-semantic and lexical-phonological encoding in word production have been investigated in several event-related potential (ERP) studies, the estimated time course of phonological-phonetic encoding is the result of rather indirect evidence. We investigated the dynamics of phonological-phonetic encoding combining ERP analyses covering the entire encoding process in picture naming and word reading tasks by comparing ERP modulations in eight brain-damaged speakers presenting impaired phonological-phonetic encoding relative to 16 healthy controls. ERPs diverged between groups in terms of local waveform amplitude and global topography at ∼400ms after stimulus onset in the picture naming task and at ∼320-350ms in word reading and sustained until 100ms before articulation onset. These divergences appeared in later time windows than those found in patients with underlying lexical-semantic and lexical-phonological impairment in previous studies, providing evidence that phonological-phonetic encoding is engaged around 400ms in picture naming and around 330ms in word reading.

The God of the Book of Acts

(Résumé de l'ouvrage) Seventeen innovative studies are collected in this volume which has been produced under the aegis of the Centre for Biblical Studies, University of Manchester, and L'Institut des sciences bibliques, Université de Lausanne. The majority of the studies engage with narrative through providing insightful working examples. Building on the many contributions of recent narratological research, for the most part the studies in this collection avoid the technical language of narratology as they present fresh insights at many levels. Some essays focus more on the implied author, some on the implied reader or hearer, and some on the way particular messages are constructed; some of the studies consider how author, message and reader are all interconnected. There are several creative proposals for refining genre definition, from law and wisdom to gospel and apocryphal writings. Some studies highlight the way in which narratives can contain ethical, religious, and cultural messages. Sensitivity to narrative is also shown by some contributors to expose in intruing ways the redactional processes behind the final form of texts. Students of narrative in the ancient world will find much to consider in this book, and others engaged with literary studies more generally will discover that scholars of the worlds of the Bible and Late Antiquity have much to offer them.

Inadequate and infrequent are not alike : ERPs to deviant prosodic patterns in spoken sentence comprehension

The current study on German investigates Event-Related brain Potentials (ERPs) for the perception of sentences with intonations which are infrequent (i.e. vocatives) or inadequate in daily conversation. These ERPs are compared to the processing correlates for sentences in which the syntax-to-prosody relations are congruent and used frequently during communication. Results show that perceiving an adequate but infrequent prosodic structure does not result in the same brain responses as encountering an inadequate prosodic pattern. While an early negative-going ERP followed by an N400 were observed for both the infrequent and the inadequate syntax-to-prosody association, only the inadequate intonation also elicits a P600.