From mathematics to dialectic in the Parmenides: the evolution of the concept of hypothesis as turning point of the Platonic epistemology

• Grant number: 14/05437-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2014
• End date: August 31, 2017
• Field of knowledge: Humanities - History - History of Science
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Irineu Bicudo
• Grantee: Gustavo Barbosa
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated scholarship(s): 14/26690-6 - The Plato's Parmenides in the context of the Mathematical Laboratory, BE.EP.PD

Abstract

The aim of this research is to investigate the evolution of the concept of hypothesis in the Plato's Parmenides. Widely accepted as belonging to the transition between the "middle" period and the "late", the dialogue represents an evolution of Plato's thought, mainly because the way it presents the theory of Ideas. Amid self-criticism that determines a revision of Platonic philosophy occurs an epistemological transformation. Before the Parmenides, there is a strong influence of mathematical procedures in the constitution of the Plato's dialectic, and, after that, there is the determination of a classificatory method that proceeds by divisions of logical and linguistic grounds. Both procedures are interlinked in the Parmenides in the way of an Eleatic reformulation, which in it turn reformulates elements from Pythagoreanism. The methodology used set itself up the interpretation of the dialogue from the development of mathematics. This hermeneutic proposal contextualizes the problems and issues inherent in the dialogue parallelly to the history of mathematics, considering its content fragmentary and unfounded. Thus, it is intended to highlight which elements of mathematics and philosophy that undergo transformation under the action of each other, and what they are. The understanding of the details of the reciprocal influence relationship between these two sciences reveals a continuous interaction of process that culminates in the outline of the Platonic dialectic and also in the process of Euclidean formalization. (AU)