From Gödel to Kripke: incompleteness, truth and consistency

• Grant number: 06/01786-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2006
• End date: August 31, 2008
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Walter Alexandre Carnielli
• Grantee: Anderson Beraldo de Araújo
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The present MsC Dissertation project has the aim to examine Kripke's proof of Gödel's Theorems of Incompleteness relative to his Formal Theory of Truth, indicating its consequences for a paraconsistent account of the Incompleteness Phenomenon (according to an expression of Tennant (2002)). An appropriate treatment of that theme will demand, before anything, a comparison of Kripke's and Gödel's proof of the incompleteness of arithmetic, this one syntactic and the other semantic, and without involving diagonalization, as in Putnam (2000) and Kripke's talks (2005) in Brazil. In that sense it is also crucial to analyze the relationship between Kripke's proof and his own Formal Theory of Truth (1975), in which he mentions connections with Gödel's Theorems. Based on this, we intend to present new elements, in opposition to Priest's Dialetheism (1987 and 2002), a paraconsistent approach of the paradoxes that intends to invalidate Gödel's results. This can open possibilities for a new paraconsistent approach about Gödel's results, based on the Logics of the Formal Inconsistency, as systematized in Carnielli et alii (2002 and 2006).