| 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) | |
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