DÉCIO KRAUSE

 


 

Short Profile

Jan  2008

 

Fields of interest: Non classical logics, abstract logics, logical foundations of quantum mechanics, semantic analysis of physical theories, the problem of the objectivity of quantum theories, rationality in science, philosophy of induction, philosophy of science.

 

Born: 01 June 1953, Rio de Janeiro, Brazil. Educated: Catholic University of Paraná, Mathematics,1976; Federal University of Paraná, MSc Education, 1983; University of São Paulo, PhD Philosophy, 1990,  Non-Reflexivity, Indistinguishability, and Weyl’s Aggregates, supervisor: Newton C. A. da Costa.

 

Regular Academic or Research Appointments: Professor of  Logic and Philosophy of Science, Federal University of Santa Catarina since 2000.  Professor of Mathematics, Federal University of Paraná, 1977. Retired as Full Professor, 1998. Professor of Mathematics, Federal Center for Technological Education of Paraná (1978-1991). Previous positions as elementary school teacher.

 

Principal Academic or Research Appointments; Visiting  Scholar, University of Florence, 1992/1993; Visiting Scholar, University of Leeds, 1995/1996.

 

Research Profile: D. Krause has investigated the logical and philosophical foundations of quantum physics. Taking for granted that there is not a just one right way of approaching a wider field of knowledge (like quantum physics), he studies the existence of an adequate mathematical language (logic involved) which would enable us to  speak of the ‘absolutely indiscernible objects’ which form part of the standard discourse of physical theories, even of quantum field theories, and whose objective existence cannot be simple discharged. His approach follows Heinz Post, who in 1963 said that the indistinguishability of quanta should be taken ''right at the start'', as a primitive notion.  The usual way to deal with indiscernible entities (within classical mathematics) is "to confine" them within certain structures whose relations and functions are not sufficient to distinguish them (that is, there are automorphisms of the structure other than the identity function). Thus, the identity initially attached to the objects (by means of coordinates or whatever standard artifice) are blurred by assuming certain symmetry conditions, like the choice for symmetry and anti-symmetric functions (or vectors) to represent the relevant states of the physical systems. Krause studies a way of avoiding these artificial  (philosophically speaking) techniques, which take individuals to start and them assume that they have not individuality. In this vein, he has developed a class of logics termed non-reflexive, where the standard notion of identity is weakened; in particular he presented a quasi-set theory, aiming at to cope with some of the most basic traits of quantum discourse. This case study serves to justify a general philosophical view sketched in the Vision Statement below. His interests go also to abstract logic, the very general approach to logic as developed by Newton da Costa, and in general topics of philosophy of science, like truth in physics, the ontology of physical theories, and the logical structure of scientific theories and their semantical aspects.

 

Main Publications:

 

  1. Identity in Physics: A historical, philosophical and formal analysis, with Steven French, Oxford Un. Press, 2006.
  2. "The logic of complementarity", with Newton C. A. da Costa, in J. van Benthem, G. Heinzmann, M. Rebuschi and H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today, Springer, 2006, 103-120.
  3. "Quantum sortal predicates", with Steven French, Synthese 2007 154 (3), 417-30.  
  4. 'Paraconsistent logic and paraconsistency', with Newton C.A. da Costa and O. Bueno,  in Dale Jacquette (ed.), Handbook of the Philosophy of Science, Volume 5: Philosophy of Logic. Elsevier, 2006, pp. 655-781.
  5. ‘Structures for structural realism’, The Logic Journal of the IGPL 13 (1), 2005, 113-126.
  6. ‘Complementarity and paraconsistency’ (with N. C. A. da Costa), in S. Rahman, J. Symons, D.M. Gabbay and J. -P. van Bendegem (eds), Logic, epistemology, and the unity of science, Vol. 1, Kluwer Ac. Pu., 2004, pp. 557-568.
  7. ‘Quantum vagueness’ (with S. French), Erkenntnis 59 (1), 2003, 97-124.
  8. "Suppes predicate for genetics and natural selection" (with J. C. M. Magalhães), Journal of Theoretical Biology 209 (2) 2001, 141-153.
  9. "Bibel's Matrix Connection Method in Paraconsistent Logic: General Ideas and Implementation", (with E. F. Nobre and M. A. Musicante), Proceedings of the XXI Internacional Conference Chilean Computer Society, Punta Arenas, Chile, 5-9 Nov. 2001 (IEEE Computer Society Press).
  10. "Remarks on quantum ontology", Synthese 125 (1/2), 2000, 155-167.
  11. ‘The logic of quanta’ (with S. French), in Cao, T. Y. (ed.), Conceptual foundations of quantum field theory, Cambridge University Press, 1999, 324-342.
  12. "Quasi set theory for bosons and fermions" (with A. S. Sant'Anna and A. G. Volkov), Foundations of Physics Letters 12 (1), 1999, 67-79.
  13. "Quasi set theories for microobjects: a comparision" (with M. L. Dalla Chiara and R. Giuntini), in E. Castellani (ed), Interpreting bodies: classical and quantum objects in modern physics, Princeton University Press, 1998, 142-152.
  14. "An intensional Schrödinger logic" (with N. C. A. da Costa), Notre Dame Journal of Formal Logic 38 (2), 1997, 179-194.
  15. ‘A formal framework for quantum non-individuality’ (with S. French), Synhese 102, 1995, 195-214.
  16. "Vague identity and quantum non-individuality" (com S. French), Analysis 55 (1), 1995, 20-26.
  17. ‘Schrödinger logics’ (with N. C. A. da Costa), Studia Logica 53 (4), 1994, 533-550.
  18. ‘On a quasi-set theory’, Notre Dame Journal of Formal Logic 33 (3), 1992, 402-411.

 

 

Work in Progress

 

 

 

 

 

 

Service to the Profession: Coordinator of the Research Group on Logic and the Foundations of Science (Brazilian Council for Research and Scientific Development, and Federal University of Santa Catarina, since 2000), Coordinator of the Epistemology and Logic Group of the Federal University of Santa Catarina (2001-2004), General Coordinator of Research, Federal  University of Paraná, 1998-2000, Editor of the Boletim da Sociedade Paranaense de Matemática (1995-2000).

 

Teaching: D. Krause has though various courses in mathematics, logic and philosophy of science to both undergraduate and graduate levels. He has supervised or is supervising Master and PhD thesis on subjects dealing with the foundations of science and mathematical education.

 

Vision Statement: Influenced by Ortega Y Gasset, Krause  used the word perspectivism to speak that a wider domain of knowledge, usually roughly delineated by informal ‘pre-theories’, can be approached from distinct perspectives. Due to the  richness of the field, these approaches  may originate different and even incompatible theories of that domain (the axiomatized of even formalized versions of the informal theories), each one serving to illuminate different aspects of the subject. So, the ‘general logic’ of science, if there is some, might be non-classical, perhaps a paraconsistent one.

 

Honours and Awards:

 

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