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From Gödel to Kripke: incompleteness, truth and consistency

Grant number: 06/01786-4
Support type:Scholarships in Brazil - Master
Effective date (Start): September 01, 2006
Effective date (End): August 31, 2008
Field of knowledge:Humanities - Philosophy
Principal Investigator:Walter Alexandre Carnielli
Grantee:Anderson Beraldo de Araújo
Home 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).