Newton da Costa

Newton Carneiro Affonso da Costa (born 16 September 1929 in Curitiba, Brazil) is a Brazilian mathematician, logician, and philosopher. He studied engineering and mathematics at the Federal University of Paraná in Curitiba and the title of his 1961 Ph.D. dissertation was Topological spaces and continuous functions. Da Costa's international recognition came especially through his work on paraconsistent logic and its application to various fields such as philosophy, law, computing, and artificial intelligence. He is one of the founders of this non-classical logic. In addition, he constructed the theory of quasi-truth that constitutes a generalization of Alfred Tarski's theory of truth, and applied it to the foundations of science. The scope of his research also includes model theory, generalized Galois theory, axiomatic foundations of quantum theory and relativity, complexity theory, and abstract logics. Da Costa has significantly contributed to the philosophy of logic, paraconsistent modal logics, ontology, and philosophy of science. He served as the President of the Brazilian Association of Logic and the Director of the Institute of Mathematics at the University of São Paulo. He received many awards and held numerous visiting scholarships at universities and centers of research in all continents. Da Costa and physicist Francisco Antônio Dória axiomatized large portions of classical physics with the help of Patrick Suppes' predicates. They used that technique to show that for the axiomatized version of dynamical systems theory, chaotic properties of those systems are undecidable and Gödel-incomplete, that is, a sentence like X is chaotic is undecidable within that axiomatics. They later exhibited similar results for systems in other areas, such as mathematical economics. Da Costa believes that the significant progress in the field of logic will give rise to new fundamental developments in computing and technology, especially in connection with non-classical logics and their applications.