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The investigation of the role of epistemological principals in the historical development of mathematical ideas on the example of the arithmetization of theories of musical proportions

Grant number: 07/02833-9
Support Opportunities:Scholarships abroad - New Frontiers
Effective date (Start): January 31, 2008
Effective date (End): January 30, 2009
Field of knowledge:Humanities - History
Principal Investigator:Oscar João Abdounur
Grantee:Oscar João Abdounur
Host Investigator: Juergen Renn
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: Max Planck Society, Berlin, Germany  

Abstract

This research aims at the arithmetization of the theories of proportion in the theoretical music in the Renaissance as an example to investigate the role of epistemological principals in the understanding of the historical development of mathematical ideas. By means of the study of different structures present in the theories of proportions, of the terminology, of the deductive and analogical arguments, as well as of the axiomatization and the heuristics in the argumentation present in treatises on theoretical music in the Renaissance, this project intends to identify news ideas at this time, that, on the one hand, are related to arithmetization, and on the other hand, deal with structural problems of the music theory. In addition, elements will be identified that indicate the approximation between theoretical music and practical music throughout the Renaissance, when the music comes from a mathematical-speculative conception to assume a mathematical-empirical one. Based on such an investigation, this project intend to evaluate to what extent epistemological reflections of philosophers of science such as Bachelard, Lakatos, Kuhn and Popper are capable of being transferred to a theoeretical framework capable of interpret the development of theoretical music in the period considered above. (AU)

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