Currículo Lattes (UFSC)
Retired as Full Professor of the Department of Mathematics, Federal University of Paraná, Curitiba, PR – Brazil.
From 1978 to 1991, I taught at the Department of Mathematics of the Federal Center of Technological Education of Paraná (CEFET/PR), in Curitiba, PR, Brazil. (today, the Technological Federal University of Paraná).
In 1978, I also taught mathematics at the Faculty of Economy and Administration (FAE) in Curitiba, and in 1986, at the Pontifical Catholic University of Paraná (PUC/PR).
Before my “university” period, I taught physics, mathematics, and geometric drawing in elementary schools.
Department of Philosophy, University of Florence, Italy (1992/1993) School of Philosophy, University of Leeds, UK (1995/1996) Wolfson College, Oxford University, UK (2008)
“Non_reflexivity, Indistinguishability, and Weyl’s Aggregates” (in Portuguese), Department of Philosopy, University of São Paulo (USP), 1990.
Supervisor: Newton C. A. da Costa
In this work, I developed a higher order logic and a mathematical set theory to cope with the general ideas advanced by Erwin Schroedinger concerning the non-individuality of elementary particles in quantum mechanics. According to Schroedinger, the notion of identity does not make sense for elementary particles in quantum physics.
After a general discussion, partially based on Steven French’s papers on the subject, I have extended da Costa’s first order “Schroedinger Logic” to a higher-order logic (a logic of order w, or simple theory of types), and proved a generalized completeness theorem (in Henkin’s sense) for such a logic. This part of the thesis was published (with Newton da Costa) in Studia Logica. The main part of the work was the development of quasi-set theory, a mathematical theory which aims to deal with collections of indistinguishable objects “right from the start” (following a suggestion of Heinz Post). The corresponding chapter was published as a paper in the Notre Dame Journal of Formal Logic. The thesis also contains a general discussion on the logic aspects of quantum mechanics.
Prof. Newton C. A. da Costa, Department of Philosophy, USP - Supervisor
Prof. Jacob Zimbarg, Department of Mathematics, USP
Prof. Antonio Mario Sette, Department of Mathematics, UNICAMP
Dr. Iole de Freitas Druck, Department of Mathematics, USP
Dr. Zara Issa Abut, Department of Mathematics, USP