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Arbitrariness and definability in the context of non-classical logics

Grant number: 17/23853-0
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): March 01, 2018
Effective date (End): December 31, 2021
Field of knowledge:Humanities - Philosophy
Principal Investigator:Giorgio Venturi
Grantee:Daniel Santiago Jockwich Martinez
Home Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). 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

This project analyses the problematic relationship between arbitrary sets and the intensional notion of sets. Indeed, this distinction can be seen in the two axiomatic developments of a theory of sets as conceived on the one hand by Cantor, Dedekind and Zermelo (who stressed the arbitrariness of sets) and on the other hand by Frege and then Russell (who stressed the possibility of a restricting the existence of sets to types). In this project we plan to analyze the connection of arbitrariness and definability in a set-theoretical context, using both infinitary and paraconsistent logics. (AU)