Demonstrative knowledge in the Mathematical Sciences on Aristotle's analytics

• Grant number: 22/00781-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2022
• End date: February 28, 2026
• Field of knowledge: Humanities - Philosophy - History of Philosophy
• Principal Investigator: Lucas Angioni
• Grantee: Rafael Cavalcanti de Souza
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Aristotle develops a theory of demonstrative knowledge in posterior analyticc. The present thesis project intends to investigate how this theory connects with the syllogistic theory presented in the prior analytics applied to the Mathematical Sciences. I take the notion of analysis (analysis) as a fundamental concept to understand the Aristotelian thesis that demonstrative knowledge in the Mathematical Sciences was expressed by a syllogistic structure in first figure. I raise as a hypothesis to be investigated that the syllogistic structure in the first figure is adequate to capture the procedure of demonstrative analysis. Such a procedure is expressed by a mediating term, which operates as a previously established principle and, through the conversion relation, explains the connection between the terms of the conclusion. Finally, I intend to investigate the common aspects between Aristotelian theory with the theory of demonstration and the analytical method described by Proclus in A Commentary on the First Book of Euclid's Elements. (AU)