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 names in Spain are mainly not in vain: Intergenerational mobility and the informational content of surnames

The paper presents a (genetic) model of the joint distribution of surnames and income. It shows that we can infer how important background is by looking at how informative surnames are. Extensions of the model allow for the possibility of assortative mating, and the introduction of ethnic differences in the income process (due to discrimination or any other reason).

The Adoption of agricultural credit cooperativism in Spain (1890-1935) : solidarity from below?

The spread of agrarian credit cooperativism in Spain (1890-1934) was done under a variety of ideological and economic orientations. This article focuses on the construction of a few tools and indicators to explain the characteristics of agricultural credit cooperatives. An analysis of financial operations of rural savings banks is related with socio-political aspects that influenced their development; This analysis helps us to explain the relative success of German credit cooperative models adopted in the context of Spanish agriculture, as happened on European periphery.

Perceptions of Europe in political and economic elites: a geographical compared analysis of Germany, Spain and Poland

Elite perceptions about Europe are a very important point in order to understand the current European integration process, as well as the future perspectives for the continent. This study makes a comparison between the perceptions which political and economical elites in some European countries have about the European Union process and its mechanisms. The main goal is to identify the differences in positions of each type of elites, as well as the variations among three key countries. The database built thanks to the INTUNE (Integrated and United? A quest for Citizenship in an ¨ever closer Europe¨) Project Survey on European Elites and Masses, funded by the Sixth Framework Programme of the EU [Contract CIT 3-CT-2005-513421] have being used. The questionnaire was applied between February and May 2007, in a total of 18 European countries. The national teams got a total of almost 2000 valid responses at European level. In the analysis we have showed some general descriptive statistics about the perception of Europe taking as a reference two dimensions of the INTUNE project: identity (attachment to the national level, the meaning of being a truly national, and the threats from Turkey that EU is facing at this moment) and representation (trust in European and national institutions, preferences for a national or an European army). The results are presented distinguishing between political (national MP’s in low chambers) and economical elites (presidents of corporations, general managers…) and, at the same time, among three countries: Germany as an original member of the European Union; Spain, incorporated in 1986; and a new member, Poland, joining the EU in 2004.

Are parties domocratizing themselves? the evolution of leardership selection in Spain (1977-2008)

The aim of this paper is to verify, for the Spanish case, whether between 1977 and 2008 has increased the internal democracy of the major political parties (PSOE, AP / PP, PCE / IU, PNV and CDC). To do this, we will focus on their leadership selection processes, one of the key elements associated with intra-party democracy. The paper is going to introduce data on four different dimensions of leadership selection: the certification process, the voting procedure, the inclusiveness of the selectorate and, finally, the degree of competitiveness. The results will show that have been few changes in the leadership selection processes of the Spanish political parties since 1977. However, the results of the Spanish case will also be used to suggest some preliminary links between the four dimensions.

Life history of Pygidiopsis crassus n. sp. (Trematoda, Digenea, Heterophyidae) in the neotropical region

The life cycle of Pygidiopsis crassus n. sp. was experimentally reproduced, starting from cercariae from naturally infected Littoridina parchappei collected from Lujan River and different ponds in Buenos Aires Province, Argentina. Metacercariae were found encysted in the body cavity of experimentally and naturally infected fishes Cnesterodon decemmaculatus and naturally infected Jenynsia lineata. Adults were obtained experimentally in chicks and mice. The natural host is unknown. The new species is compared with Pygidiopsis macrostomum Travassos 1928, from Rattus norvegicus and from Noctilio leporinus mastivus, differing in body and egg sizes, in the size relation of oral and ventral sucker and the shape of excretory vesicle.

Mechanisms of agglomeration: Evidence from the location of new manufacturing firms in Spain

El objetivo de esta investigación es aportar evidencia sobre las fuentes de las economías de aglomeración para el caso español. De todas las maneras posibles que se han tomado en la literatura para medir las economías de aglomeración, nosotros lo analizamos a partir de las decisiones de localización de las empresas manufactureras. La literatura reciente ha puesto de relieve que el análisis basado en la disyuntiva localización / urbanización (relaciones dentro de un mismo sector) no es suficiente para entender las economías de aglomeración. Sin embargo, las relaciones entre los diferentes sectores sí resultan significativas al examinar por qué las empresas que pertenecen a diferentes sectores se localizan unas al lado de las otras. Con esto en mente, intentamos explicar que relaciones entre diferentes sectores pueden explicar coaglomeración. Para ello, nos centramos en aquellas relaciones entre sectores definidos a partir de los mecanismos de aglomeración de Marshall, es decir, labor market, input sharing y knowledge spillovers. Trabajamos con el labor market pooling en la medida en que los dos sectores utilizan los mismos trabajadores (clasificación de ocupaciones). Con el segundo mecanismo de Marshall, input sharing, introducimos cómo dos sectores tienen una relación de comprador / vendedor. Por último, nos referimos a dos sectores que utilizan las mismas tecnologías en cuanto a los knowledge spillovers. Con el fin de capturar todos los efectos de los mecanismos de aglomeracion en España, en esta investigación trabajamos con dos ámbitos geográficos, los municipios y los mercados de trabajo locales. La literatura existente nunca se ha puesto de acuerdo en cual es el ámbito geográfico en el que mejor trabajan los mecanismos Marshall, por lo que hemos cubierto todas las unidades geográficas potenciales.

Tax Coordination Between Regions in Spain. The Role of the Courts

Overview of the Tax Coordination of the Regions in Spain from the point of view of the role of the Courts in developing the present system

Tax Coordination Between Regions in Spain - Role of the Courts

Análisis de la jurisprudencia constitucional española sobre la distribución de competencias tributarias entre los distintos niveles de gobierno.

Origins and efficiency of the electric industry regulation in Spain, 1910-1936

The aim of this paper is to discover the origins of utility regulation in Spain, and to analyse, from a microeconomic perspective, its characteristics and the impact of regulation on consumers and utilities. Madrid and the Madrilenian utilities are taken as a case study. The electric industry in the period studied was a natural monopoly2. Each of the three phases of production, generation, transmission and distribution, had natural monopoly characteristics. Therefore, the most efficient form to generate, transmit and distribute electricity was the monopoly because one firm can produce a quantity at a lower cost than the sum of costs incurred by two or more firms. A problem arises because when a firm is the single provider it can charge prices above the marginal cost, at monopoly prices. When a monopolist reduces the quantity produced, price increases, causing the consumer to demand less than the economic efficiency level, incurring a loss of consumer surplus. The loss of the consumer surplus is not completely gained by the monopolist, causing a loss of social surplus, a deadweight loss. The main objective of regulation is going to be to reduce to a minimum the deadweight loss. Regulation is also needed because when the monopolist fixes prices at marginal cost equal marginal revenue there would be an incentive for firms to enter the market creating inefficiency. The Madrilenian industry has been chosen because of the availability of statistical information on costs and production. The complex industry structure and the atomised demand add interest to the analysis. This study will also provide some light on the tariff regulation of the period which has been poorly studied and will complement the literature on the US electric utilities regulation where a different type of regulation was implemented.

How much risk is mitigated by LTC Insurance? A case study of the public system in Spain

We present a methodology that allows to calculate the impact of a given Long-Term Care (LTC) insurance protection system on the risk of incurring extremely large individual lifetime costs. Our proposed methodology is illustrated with a case study. According to our risk measure, the current Spanish public LTC system mitigates individual risk by more than 30% compared to the situation where no public protection were available. We show that our method can be used to compare risk reduction of alternative LTC insurance plans.

Parent-child agreement and prevalence estimates of diagnoses in childhood: direct interview versus family history method.

Diagnostic information on children is typically elicited from both children and their parents. The aims of the present paper were to: (1) compare prevalence estimates according to maternal reports, paternal reports and direct interviews of children [major depressive disorder (MDD), anxiety and attention-deficit and disruptive behavioural disorders]; (2) assess mother-child, father-child and inter-parental agreement for these disorders; (3) determine the association between several child, parent and familial characteristics and the degree of diagnostic agreement or the likelihood of parental reporting; (4) determine the predictive validity of diagnostic information provided by parents and children. Analyses were based on 235 mother-offspring, 189 father-offspring and 128 mother-father pairs. Diagnostic assessment included the Kiddie-schedule for Affective Disorders and Schizophrenia (K-SADS) (offspring) and the Diagnostic Interview for Genetic Studies (DIGS) (parents and offspring at follow-up) interviews. Parental reports were collected using the Family History - Research Diagnostic Criteria (FH-RDC). Analyses revealed: (1) prevalence estimates for internalizing disorders were generally lower according to parental information than according to the K-SADS; (2) mother-child and father-child agreement was poor and within similar ranges; (3) parents with a history of MDD or attention deficit hyperactivity disorder (ADHD) reported these disorders in their children more frequently; (4) in a sub-sample followed-up into adulthood, diagnoses of MDD, separation anxiety and conduct disorder at baseline concurred with the corresponding lifetime diagnosis at age 19 according to the child rather than according to the parents. In conclusion, our findings support large discrepancies of diagnostic information provided by parents and children with generally lower reporting of internalizing disorders by parents, and differential reporting of depression and ADHD by parental disease status. Follow-up data also supports the validity of information provided by adolescent offspring.

Biostratigraphy, mineralogy and geochemistry of the Trabakua Pass and Ermua sections in Spain: Paleocene-Eocene transition

Isotopic, geochemical and bulk mineralogical analyses in the Trabakua and Ermua sections, Basque Basin, reveal major changes across the Paleocene-Eocene transition. Expanded sedimentary records exhibit a gradual decrease of 1.0 parts per thousand in delta(13)C values in the lower part of Zone P5 followed by a more rapid 3 parts per thousand negative excursion. The 3 parts per thousand delta(13)C excursion is associated with an abrupt decrease in carbonate sedimentation, increased detrital flux and decreased grain size which suggest changes in marine/atmospheric currents and/or size and structure of the ocean carbon reservoir. The clays recognized at Trabakua record a deep burial diagenesis as indicated by two generations of chlorite, the presence of mixed-layers chlorite-smectite and illite-smectite, the absence of smectite and the near absence of kaolinite. The very low delta(18)O values (<-3.5 parts per thousand) throughout the Trabakua and Ermua sections reflect diagenetic alteration rather than paleotemperatures. Because of deep burial diagenesis and very poorly preserved microfossils, the Trabakua Pass and Ermua sections are not optimal potential stratotypes for the Paleocene-Eocene boundary.