Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources

Cuantificadores y compromiso ontológico: hacia una nueva lectura de la paradoja de Carnap

Trabajo de Fin de Máster en Investigación en Lógica y Filosofía de la Ciencia, curso 2014-2015.[ES] Este trabajo constituye un análisis de la llamada paradoja de Carnap, en un intento de desarrollar un enfoque diferente al que ofrece Yablo. En primer lugar, se explicará la distinción carnapiana interno/externo, como parte de la base conceptual que Yablo usa al dar una solución a la paradoja. Se comentará y evaluará el enfoque de Yablo a la cuestión, incluyendo su teoría sobre las partes de contenido. Su perspectiva se completará tomando en consideración algunos enfoques alternativos, como los que desarrollan Hofweber, Azzouni y Priest. Estos no tratan específicamente la paradoja, pero pueden ser de ayuda en una nueva explicación más plausible del problema. Dicha explicación se desarrollará y analizará. El trabajo pone encima de la mesa algunos temas fundamentales en filosofía de la matemática, como el papel de la cuantificación, las alternativas a la lógica clásica, el argumento de la indispensabilidad o la cuestión sobre la existencia de los objetos abstractos, concretamente las entidades matemáticas.[EN] This work constitutes an analysis of the so called Carnap’s Paradox in an attempt to develop a different approach from the one Yablo offers. Firstly, the Carnapian internal/external distinction will be explained, as part of the conceptual basis Yablo uses in order to give an answer to de paradox. Yablo’s approach to the subject will be commented and evaluated, including his theory on content-parts. I will try to overcome some of the problems in his view by taking into account a few alternative approaches, such as the ones developed by Hofweber, Azzouni and Priest. These do not specifically assess the paradox, but their views can help to provide a new and more plausible explanation of the problem. That new explanation will be developed and analysed. The article brings up some fundamental issues on philosophy of mathematics, such as the role of quantification, alternatives to classical logic, the argument of indispensability or the question of the existence of abstract objects, more precisely mathematical entities

Tópicos de marketing

Lograr un equilibrio entre acciones humanas, armonía con la naturaleza, y satisfacer las necesidades del mercado actual sin poner en riesgo aquellos recursos que pudieran precisar las futuras generaciones, es lo importante de impulsar la aplicación del marketing sostenible en las organizaciones. Esto se logra a través de la elaboración de un plan de marketing sostenible que permitirá promover un consumo responsable a través de información clara y oportuna sobre los beneficios personales y sociales que genera la adquisición de productos sostenibles; implantar el reciclado a través de la logística de reversa, procedimiento que origina poca o nula generación de desechos, proporcionar empleos seguros, apoyar al medio ambiente y con responsabilidad social, son algunos beneficios que aporta. El presente capítulo tiene como objetivo proporcionar los principales aspectos que abordan el marketing sostenible, mostrar la importancia de la realización de este marketing para las empresas, así como aportar los pasos para desarrollar un plan de marketing sostenible