Formal and diagrammatic reasoning in euclidian proofs by reduction ad absurdum

• Grant number: 14/23191-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2015
• End date: April 02, 2019
• Field of knowledge: Humanities - Philosophy
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Marco Antonio Caron Ruffino
• Grantee: Tamires Dal Magro
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 16/20480-5 - The epistemology of Euclidean diagrams, BE.EP.DR

Abstract

This project purports to investigate the role of diagrams in Euclidean proofs, specifically the relation between diagrammatic entries and textual entries in proofs by reductio ad absurdum. The central question is whether diagrams present only heuristic and pedagogical roles in mathematical proofs or if at least in some cases they play a more significant role, i.e. if there are steps in the proof justified in a legitimate manner by information read off the figures themselves. Such discussion is inserted in the tradition of philosophy of mathematical practice having in the criticisms of Lakatos of the formalist tradition an important exemplar - against a research tradition centered on logical analysis of mathematical theories, this author draws attention to problems that emerge from the analysis of the history and practice of mathematics. Our study is partly historical, because it requires the analyzing of geometrical proofs presented in Euclid's Elements, and partly epistemological, with regards to the role of visualization in mathematical knowledge and the relationship between diagrammatic thought and formal reasoning in Euclidean heterogeneous proofs - that is, those proofs that make substantial use of diagrams. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DAL MAGRO, TAMIRES; VALENTE, MATHEUS. On the representational role of Euclidean diagrams: representing qua samples. SYNTHESE, JAN 2021. (14/23191-9)

DAL MAGRO, TAMIRES; GARCIA-PEREZ, MANUEL J.. On Euclidean diagrams and geometrical knowledge. THEORIA-REVISTA DE TEORIA HISTORIA Y FUNDAMENTOS DE LA CIENCIA, v. 34, n. 2, p. 255-276, MAY 2019. (16/20480-5, 14/23191-9)

DAL MAGRO, TAMIRES; VALENTE, MATHEUS. On the representational role of Euclidean diagrams: representing qua samples. SYNTHESE, v. 199, n. 1-2, p. 22-pg., 2021-01-03. (14/23191-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MAGRO, Tamires Dal. Visual reasoning in Euclidean geometry: the epistemic and representational role of diagrams. 2019. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.