Innovative use of diagrams and inference in Wallis

• Autores: Ortiz, Erika Rita
• Año de publicación: 2018
• Idioma: inglés
• Tipo de recurso: documento de conferencia
• Materia: Diagrams; Inference; Philosophy of mathematical practice; Wallis, John
• Institución: Universidad Nacional de Córdoba

Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
According to a critical view in philosophy of mathematics, mathematical research is best characterized by problem-solving activities which make use of a variety of modes of representation articulated in deductive and non-deductive arguments in mathematical discourse. Against this background, our aim is to discuss the epistemic value of the appeal to modes of representation other than symbolic notations, as well as ampliative patterns of reasoning in problem-solving activities. Attending to the fact that problem-solving strategies are designed to deal with problems of a particular field of inquiry, they should be considered as actually deployed by the research mathematician in his/her context of work. Therefore, to examine the philosophical aspects at the center of our research we shall proceed by focusing on historical case studies. In our investigation we consider a case study selected from John Wallis´s work onquadrature problems. The main conclusion reached at this stage is that Wallis´s method depends on the employment of non-deductive inferences and the use of different representations among which diagrammatic representations play an essential role. Given the partial conclusions of our work in progress on Wallis´s method, it should be of value for our ongoing research to acquire deeper understanding of the conceptual aspects related to the study of context-sensitive inferences as mixed modes of reasoning based on diagrams.
http://www.diagrams-conference.org/2018/wp-content/uploads/2018/06/Diagrams2018GSProceedings.pdf
Fil: Ortiz, Erika Rita. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Secretaría de Posgrado; Argentina.
Fil: Ortiz, Erika Rita. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Filosofía, Historia y Filosofía de la Ciencia y la Tecnología