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Reasons for and against arbitrary objects

Grant number: 19/17407-2
Support type:Scholarships in Brazil - Master
Effective date (Start): January 01, 2020
Effective date (End): February 28, 2021
Field of knowledge:Humanities - Philosophy - Metaphysics
Principal Investigator:Giorgio Venturi
Grantee:Pedro Teixeira Yago
Home Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:16/25891-3 - Arbitrariness and genericity: or on how to speak of the unspeakable, AP.JP

Abstract

Since antiquity philosophers raised questions about the objects of a mathematical theory: is there any such object? what is the nature of such objects? is there a difference between natural objects and mathematical ones? are mathematicalobjects able to ground the certainty of mathematics?Plato was the first to propose that mathematics is about universals. Indeed, platonic ideas represent the first interesting historical example of objects with a character of arbitrariness: objects able to represent the essence of concrete objects of which they are abstraction. Moreover, the history of arbitrary objects, already at the time of Plato and Aristotle, is deeply intertwined with that of logic, because of the universal character of the latter (i.e. the possibility of its application in any field of knowledge). Consequently the study of arbitrary objects follows the evolution of logic along its history.In this research we plan to trace a general history of arbitrary objects making explicit the arguments that philosophers gave in favour or against arbitrary objects and confronting them with the main themes of the modern developmentof logic. (AU)