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.

The joint influence of gender and amount of smoking on weight gain one year after smoking cessation.

Weight gain is often associated with smoking cessation and may discourage smokers from quitting. This study estimated the weight gained one year after smoking cessation and examined the risk factors associated with weight gain in order to identify socio-demographic groups at higher risk of increased weight after quitting. We analyzed data from 750 adults in two randomized controlled studies that included smokers motivated to quit and found a gradient in weight gain according to the actual duration of abstinence during follow-up. Subjects who were abstinent for at least 40 weeks gained 4.6 kg (SD = 3.8) on average, compared to 1.2 kg (SD = 2.6) for those who were abstinent less than 20 weeks during the 1-year follow-up. Considering the duration of abstinence as an exposure variable, we found an age effect and a significant interaction between sex and the amount of smoking before quitting: younger subjects gained more weight than older subjects; among light smokers, men gained more weight on average than women one year after quitting, while the opposite was observed among heavy smokers. Young women smoking heavily at baseline had the highest risk of weight gain after quitting.

Missing value imputation in longitudinal measures of alcohol consumption

Attrition in longitudinal studies can lead to biased results. The study is motivated by the unexpected observation that alcohol consumption decreased despite increased availability, which may be due to sample attrition of heavy drinkers. Several imputation methods have been proposed, but rarely compared in longitudinal studies of alcohol consumption. The imputation of consumption level measurements is computationally particularly challenging due to alcohol consumption being a semi-continuous variable (dichotomous drinking status and continuous volume among drinkers), and the non-normality of data in the continuous part. Data come from a longitudinal study in Denmark with four waves (2003-2006) and 1771 individuals at baseline. Five techniques for missing data are compared: Last value carried forward (LVCF) was used as a single, and Hotdeck, Heckman modelling, multivariate imputation by chained equations (MICE), and a Bayesian approach as multiple imputation methods. Predictive mean matching was used to account for non-normality, where instead of imputing regression estimates, "real" observed values from similar cases are imputed. Methods were also compared by means of a simulated dataset. The simulation showed that the Bayesian approach yielded the most unbiased estimates for imputation. The finding of no increase in consumption levels despite a higher availability remained unaltered. Copyright (C) 2011 John Wiley & Sons, Ltd.

Psychodynamic psychotherapy in newly diagnosed cancer patients: a randomized controlled trial

Background and aims: More than 30% of cancer patients develop a psychiatric disorder during the evolution of their disease. While evidence exists, that psychotherapy can improve psychological distress, questions, such as the prevalence of patients accepting psychotherapy, treatment indications and effectiveness of psychotherapeutic interventions in the oncology setting remain unanswered. The aims were: (1) To assess the prevalence of newly diagnosed cancer patients motivated to engage in psychotherapeutic interventions; (2) to identify those who benefit; and (3) to evaluate their effectiveness. Methods: Every new patient of the Oncology Service at the University Hospital Lausanne was informed of the possibility of benefitting from psychotherapeutic support. Patients who accepted were randomly assigned to individual psychotherapy or to a 4-month waiting list. Psychotherapies were formalized as psychodynamicoriented short interventions (1-4 sessions) or brief psychodynamic psychotherapies (16 sessions). Patients who refused psychotherapy were asked to participate in an observational group. Socio-demographic and medical data, anxiety, depression, alexithymia and quality of life (SCL- 90, HADS, TAS, EORTC) of all participants were evaluated at base line and at 1, 4, 8 and 12 -months Follow- Up. Results: So far 1047 patients have been approached, 20% were included in the study (intervention n=68, observation n=122), 32% were excluded, 22% could not be contacted and 26% refused to participate. At baseline, patients who accepted psychotherapeutic support showed higher depression and anxiety scores (HADS, SCL-90) compared to controls. 56% benefited from 4 sessions of psychological support, 44% engaged in 16 sessions of brief psychodynamic therapy. Conclusions: The preliminary results of this ongoing trial suggest that a minority of newly cancer patients accept psychotherapeutic intervention. These patients are more depressed than controls. Their motivation for short interventions and for brief psychotherapies is comparable.

Counterfactuals and causal inference: Methods and principles for social research

"Most quantitative empirical analyses are motivated by the desire to estimate the causal effect of an independent variable on a dependent variable. Although the randomized experiment is the most powerful design for this task, in most social science research done outside of psychology, experimental designs are infeasible. (Winship & Morgan, 1999, p. 659)." This quote from earlier work by Winship and Morgan, which was instrumental in setting the groundwork for their book, captures the essence of our review of Morgan and Winship's book: It is about causality in nonexperimental settings.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

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.