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.

Emotion, Affect, Sentiment: The Language and Aesthetics of Feeling

Bringing together experts from linguistics, medieval and modern literary studies, this volume offers a transhistorical look at the language and cultural work of emotion in a variety of written, oral and visual texts. Contributors engage with the recent so-called affective turn, but also examine the language and use of emotion from a variety of perspectives, touching on issues such as Romantic and Modernist aesthetics, the history of emotions, melodramatic and the Gothic, reception aesthetics, rudeness, and medicine.

Impact of relative size and language on the attitudes between nations and linguistic groups : The case of Switzerland

This study explores the impact of relative size on the intra- and intergroup attitudes of groups who either share a language or have a different language. For that purpose, we examined international attitudes, comparing a small nation, Switzerland, and two larger nations, Germany and France. We found support for the assumption that large neighbouring nations pose a threat to the smaller nation's identity, especially when they are linguistically similar. Consequently, in line with Tajfel's Social Identity Theory (1978), the smaller nation's inhabitants evaluate those of the larger nation less positively, liking them less and perceiving them to be more arrogant than vice versa. By investigating the special case of the French-speaking and the German-speaking Swiss as linguistic groups within their own nation we were able to demonstrate that these groups seek support with the larger-linguistically-similar nation to defend themselves against the more direct in-country threat to their identity. They acknowledge the similarity with the larger nation, yet keep defending their social identity by expressing a dislike for this perceived similarity.

The role of epilepsy in early language development in a child with a congenital lesion in the right hemisphere

Early epilepsy is known to worsen the developmental prognosis of young children with a congenital focal brain lesion, but its direct role is often very difficult to delineate from the other variables. This requires prolonged periods of follow-up with simultaneous serial electrophysiological and developmental assessments which are rarely obtained. We studied a male infant with a right prenatal infarct in the territory of the right middle cerebral artery resulting in a left spastic hemiparesis, and an epileptic disorder (infantile spasms with transient right hemihypsarrhythmia and focal seizures) from the age of 7 months until the age of 4 years. Pregnancy and delivery were normal. A dissociated delay of early language acquisition affecting mainly comprehension without any autistic features was documented. This delay was much more severe than usually expected in children with early focal lesions, and its evolution, with catch-up to normal, was correlated with the active phase of the epilepsy. We postulate that the epilepsy specifically amplified a pattern of delayed language emergence, mainly affecting lexical comprehension, reported in children with early right hemisphere damage.

Hemispheric language asymmetry in first episode psychosis and schizotypy : the role of cannabis consumption and cognitive disorganization

Cannabis use has been related to an elevated psychosis risk and attenuated cognitive functioning. Cannabis-related cognitive impairments are also observed in populations along the psychosis dimension. We here investigated whether a potential behavioural marker of the psychosis dimension (attenuated functional hemispheric asymmetry) is even further attenuated in individuals using cannabis (CU) versus those not using cannabis (nCU). We tested 29 patients with first episode psychosis (FEP; 11 CU) and 90 healthy controls (38 CU) on lateralized lexical decisions assessing left hemisphere language dominance. In patients, psychotic symptoms were assessed (PANSS). In controls, self-reported schizotypy was assessed (O-LIFE questionnaire). Results indicated that nCU FEP patients had a relative reduced hemispheric asymmetry, as did controls with increasing cognitive disorganisation scores, in particular when belonging to the group of nCU controls. Positive, disorganised and negative PANSS scores in patients and negative and positive schizotypy in controls were unrelated to hemispheric asymmetry. These findings suggest that cannabis use balances rather than exacerbates uncommon hemispheric laterality patterns. Moreover, in healthy populations, the potential stabilisation of typical hemispheric asymmetry in CU might be most relevant to individuals with elevated cognitive disorganisation. We discuss the potential beneficial and harmful effects of cannabis use along the psychosis dimension together with propositions for future studies that should account for the mediating role of additional substances (e.g. nicotine), cannabis composition (e.g. cannabidiol content), and individual differences (e.g. physical health, or absence of significant polysubstance use).

Evaluation de la qualité des sites internet francophones traitant de la dépendance à l'alcool [Assessing the quality of French language web sites pertaining to alcohol dependency]

The objective of this article is to systematically assess the quality of web-based information in French language on the alcohol dependence. The authors analysed, using a standardised pro forma, the 20 most highly ranked pages identified by 3 common internet search engines using 2 keywords. Results show that a total of 45 sites were analysed. The authors conclude that the overall quality of the sites was relatively poor, especially for the description of possible treatments, however with a wide variability. Content quality was not correlated with other aspects of quality such as interactivity, aesthetic or accountability.