A study on ontology of numbers

• Grant number: 20/08214-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2020
• End date: August 31, 2021
• Field of knowledge: Humanities - Philosophy - Metaphysics
• Principal Investigator: Giorgio Venturi
• Grantee: Gabriel Andersen Eugênio
• Host 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

Many mathematicians work regularly on the study of mathematical objects, like sets, functions, matrix, etc. However, could we say that these entities exist? It seems a hard question even when we are dealing with the mathematics entities that might be the most fundamental, numbers. Furthermore, assuming one of the positions, that is, saying that such entities exist or not, raise new philosophical complications, because, if numbers exist, what kind of objects they are? If they do not exist, how could we deal with the current development of mathematics, or how could we study it? Should we change the mathematical practice if the numbers do not exist? The present project is a proposal of studying these questions. With it, we will deal with ontology on mathematics, specifically, with the ontology of numbers, and which philosophical consequences are yielded by a defense of one of both theses in this area, that is, realism and anti-realism.