A logical analysis of the notion of consistency in set theoretical practice

• Grant number: 14/25342-4
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: July 15, 2015
• End date: June 27, 2016
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Walter Alexandre Carnielli
• Grantee: Giorgio Venturi
• Supervisor: Marco Panza
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Institute for the History and Philosophy of Science and Technology (IHPST), France
• Associated to the scholarship: 13/25095-4 - Set theory and its interal logic, BP.PD

Abstract

In this project I deepen the analysis of the internal logic of set theory - topic of my FAPESP project - proposing a logical analysis of the notion of consistency and its role in the set theoretical practice. This project has a multidisciplinary point of view and tries to combine the philosophical reflection about mathematical practice and the logical description of a mathematical structure. The aim of this project consists in investigating the structure of the multiverse - the collection of all possible universes of set theory provided by the method of forcing - in the search for the more appropriate logic that describes it. I propose to define a new logic that, similar to the case of LFs, includes a logical operator that is meantto formalize the notion of consistency how it is used in set theory. In order to justify the axioms of this logic I propose to use the tools of the philosophy of mathematical practice and to investigate the philosophical problems linked to the use of practice in understanding mathematical phenomena. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GIORGIO VENTURI. A note on the introduction of Hilbert’s Grundlagen der Geometrie. Manuscrito, v. 40, n. 2, p. 5-17, 2017-06-00. (14/25342-4, 13/25095-4)

VENTURI, GIORGIO. A note on the introduction of Hilbert's Grundlagen der Geometrie. Manuscrito, v. 40, n. 2, p. 5-17, APR-JUN 2017. (13/25095-4, 14/25342-4)

GILBERT, DAVID R.; VENTURI, GIORGIO. A note on logics of essence and accident. LOGIC JOURNAL OF THE IGPL, v. 28, n. 5, p. 881-891, OCT 2020. (14/25342-4, 13/25095-4)