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.

Altruism - a philosophical analysis

Altruism is a malleable notion that is understood differently in various disciplines. The common denominator of most definitions of altruism is the idea of unidirectional helping behaviour. However, a closer examination reveals that the term altruism sometimes refers to the outcomes of a helping behaviour for the agent and its neighbours - i.e. reproductive altruism - and sometimes to what motivates the agent to help others - i.e. psychological altruism. Since these perspectives on altruism are crucially different, it is important to use a clear terminology to avoid confusion. In particular, we show that the notion of altruism used by biologists profoundly differs from the ones used by philosophers, psychologists and economists in cross-disciplinary debates about human altruism.

Victimization in Childhood of Male Sex Offenders: Relationship between Violence Experienced and Subsequent Offenses through Discourse Analysis

This study aims at better understanding how the form of childhood violence experienced and the type of offense subsequently committed affect how sex offenders recall punishments and difficult events. Fifty-four male perpetrators convicted of sexual offenses against children (SOCs) or against adults (SOAs) were interviewed in France, Belgium, and Switzerland using the Lausanne Clinical Interview (Entretien Clinique de Lausanne or LCI). Almost three-quarters of the sex offenders reported having been victimized during childhood. The correspondence analysis identified several factors that differentiated them. Their appraisal of the distressing event, method of coping with and distancing themselves from it, and how they dealt with emotions varied markedly depending on whether they recognized having experienced various forms of violence during childhood and on what type of offense they subsequently committed. Victimization can be identified as much by the events experienced as by their effect on the sex offender's discourse. Identification of these discursive indicators may lead to an improved therapeutic approach for potentially traumatic childhood experiences.

Patients' spontaneous discourse on the importance of significant others in the course of transplantation: A qualitative study

Background: This study explores significant ones' implication before and after transplantation. Methods: Longitudinal semi-structured interviews were conducted in 64 patients awaiting all-organ transplantation. Among them, 58 patients spontaneously discussed the importance of their significant other in their daily support. Discourse analysis was applied. Findings: During the pre-transplantation period renal patients reported that significant others took part in dialysis treatment and participated to regimen adherence. After transplantation, quality of life improved and the couple dynamics returned to normal. Patients awaiting lung or heart transplantation were more heavily impaired. Significant others had to take over abandoned roles. After transplantation resuming normal life became gradually possible, but after one year either transplantation health benefits relieved physical, emotional and social loads, or complications maintained the level of stress on significant others. Discussion: Patients reported that significant others had to take over various responsibilities and were concerned about long-term stress that should be adequately supported.

The category 'natural' in the discourse of couples who used medically assisted procreation

As a constantly evolving set of complex biotechnologies, medically assisted procreation (MAP) jeopardises a category that seems to be taken for granted: that of 'natural'. What is 'natural' or not when MAP is used to procreate? What are the boundaries between a 'natural' and a 'non-natural' fertilisation? Drawing upon a dialogical approach to language and cognition, our study examined the semantic field of the category 'natural' as expressed in interviews between a psychiatrist and seven couples who resorted to MAP and had to decide whether to keep their frozen pre-embryonic cells (zygotes) for further procreation or to allow them be destroyed. We examined how these couples evoked the category 'natural' and showed that in their argumentation, the category 'natural' encompassed a wide variety of phenomena, which shifted the boundaries between the 'natural' and 'non-natural'. In so doing, the couples 'renaturalised' MAP, normalized it, moved the boundaries between what is legitimate or not, and showed their accountability. Hence, reference to the category 'natural' seemed to act both as an argumentative and a psychological resource in the elaboration of the person's experience in resorting to MAP.

The philosophical foundations of classical "rDzogs chen" in Tibet : investigating the distinction between dualistic mind (sems) and primordial knowing (ye shes)

While the syncretistic Tibetan tradition known as rDzogs chen ("Great Perfection") has attracted considerable attention over the past few decades, its philosophical foundations remain largely unknown to those unacquainted with its primary sources. This thesis looks at the essentials of rDzogs chen philosophy through the lens of two principal distinctions that the tradition has considered indispensable for understanding its distinctive views and practices: dualistic mind (sems) versus primordial knowing (ye shes) and dharmakâya versus the 'ground of all' (kun gzhi) conditioned experience. Arguing that the distinctions provided classical rDzogs chen scholars with a crucial framework for (a) articulating the necessary conditions of nondual primordial knowing, the conditio sine qua non of rNying ma soteriology, and (b) schematizing the relationship between the exoteric and esoteric vehicles of Indian Buddhism within a unifying conception of the Buddhist path as the progressive disclosure of primordial knowing, the thesis shows how the rDzogs chen philosophy of mind has been integral to the tradition's complex soteriology. The thesis consists of two parts: (1) a detailed philosophical investigation of the distinctions and (2) an anthology of previously untranslated Tibetan materials on the distinctions accompanied by critical editions and introductions. The first part systematically invesigates the nature and scope of the distinctions and traces their evolution and complex relationships with Indian Buddhist Cittamâtra, Madhyamaka, Pramàriavàda, and Vajrayâna views. It concludes with an exploration of some soteriological implications of the mind/primordial knowing distinction that became central to rDzogs chen path hermeneutics in the classical period as authors of rDzogs chen path summaries used this distinction to reconcile progressivist sutric and non-progressivist tantric models of the Buddhist path. The translations and texts included in part two of the thesis consist of (a) a short treatise from Klong chen pa's Miscellaneous Writings entitled Sems dang ye shes kyi dris lan (Reply to Questions Concerning Mind and Primordial Knowing), (b) selected passages on the distinctions from this author's monumental summary of the rDzogs chen snying thig system, the Theg mchog mdzod (Treasury of the Supreme Vehicle), and (c) an excerpt on rDzogs chen distinctions taken from 'Jigs med gling pa's (1729-1798) 18th century Klong chen sNying thig path summary entitled Treasury of Qualities (Yon tan mdzod) along with a word-by- word commentary by Yon tan rgya mtsho (b. 19th c.).

'Bio-nano interactions: new tools, insights and impacts': summary of the Royal Society discussion meeting

Bio-nano interactions can be defined as the study of interactions between nanoscale entities and biological systems such as, but not limited to, peptides, proteins, lipids, DNA and other biomolecules, cells and cellular receptors and organisms including humans. Studying bio-nano interactions is particularly useful for understanding engineered materials that have at least one dimension in the nanoscale. Such materials may consist of discrete particles or nanostructured surfaces. Much of biology functions at the nanoscale; therefore, our ability to manipulate materials such that they are taken up at the nanoscale, and engage biological machinery in a designed and purposeful manner, opens new vistas for more efficient diagnostics, therapeutics (treatments) and tissue regeneration, so-called nanomedicine. Additionally, this ability of nanomaterials to interact with and be taken up by cells allows nanomaterials to be used as probes and tools to advance our understanding of cellular functioning. Yet, as a new technology, assessment of the safety of nanomaterials, and the applicability of existing regulatory frameworks for nanomaterials must be investigated in parallel with development of novel applications. The Royal Society meeting 'Bio-nano interactions: new tools, insights and impacts' provided an important platform for open dialogue on the current state of knowledge on these issues, bringing together scientists, industry, regulatory and legal experts to concretize existing discourse in science law and policy. This paper summarizes these discussions and the insights that emerged.

Identification concept and the use of probabilities in forensic odontology--an approach by philosophical discussion.

This paper questions the practitioners' deterministic approach(es) in forensic identification and notes the limits of their conclusions in order to encourage a discussion to question current practices. With this end in view, a hypothetical discussion between an expert in dentistry and an enthusiastic member of a jury, eager to understand the scientific principles of evidence interpretation, is presented. This discussion will lead us to regard any argument aiming at identification as probabilistic.

Discourse Type Clustering using POS n-gram Profiles and High-Dimensional Embeddings

Abstract: To cluster textual sequence types (discourse types/modes) in French texts, K-means algorithm with high-dimensional embeddings and fuzzy clustering algorithm were applied on clauses whose POS (part-ofspeech) n-gram profiles were previously extracted. Uni-, bi- and trigrams were used on four 19th century French short stories by Maupassant. For high-dimensional embeddings, power transformations on the chi-squared distances between clauses were explored. Preliminary results show that highdimensional embeddings improve the quality of clustering, contrasting the use of bi and trigrams whose performance is disappointing, possibly because of feature space sparsity.