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.

Tackling Societal Challenges Related to Ageing and Transport Transition: An Introduction to Philosophical Principles of Causation Adapted to the Biopsychosocial Model

In geriatrics, driving cessation is addressed within the biopsychosocial model. This has broadened the scope of practitioners, not only in terms of assessing fitness to drive, but also by helping to maintain social engagements and provide support for transport transition. Causes can be addressed at different levels by adapting medication, improving physical health, modifying behaviour, adapting lifestyle, or bringing changes to the environment. This transdisciplinary approach requires an understanding of how different disciplines are linked to each other. This article reviews the philosophical principles of causality between fields and provides a framework for understanding causality within the biopsychosocial model. Understanding interlevel constraints should help practitioners overcome their differences, and favor transversal approaches to driving cessation.

Self-deception as affective coping. An empirical perspective on philosophical issues.

In the philosophical literature, self-deception is mainly approached through the analysis of paradoxes. Yet, it is agreed that self-deception is motivated by protection from distress. In this paper, we argue, with the help of findings from cognitive neuroscience and psychology, that self-deception is a type of affective coping. First, we criticize the main solutions to the paradoxes of self-deception. We then present a new approach to self-deception. Self-deception, we argue, involves three appraisals of the distressing evidence: (a) appraisal of the strength of evidence as uncertain, (b) low coping potential and (c) negative anticipation along the lines of Damasio's somatic marker hypothesis. At the same time, desire impacts the treatment of flattering evidence via dopamine. Our main proposal is that self-deception involves emotional mechanisms provoking a preference for immediate reward despite possible long-term negative repercussions. In the last part, we use this emotional model to revisit the philosophical paradoxes.