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Logic Journal of IGPL Advance Access originally published online on October 12, 2007
Logic Journal of IGPL 2007 15(5-6):421-431; doi:10.1093/jigpal/jzm033
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Logical and Philosophical Remarks on Quasi-Set Theory

Newton C. A. Da Costa

Department of Philosophy, Federal University of Santa Catarina, P.O.Box 476, 88040-900 Florianópolis, SC-Brazil, E-mail: ncacosta{at}terra.com.br

Décio Krause

Department of Philosophy, Federal University of Santa Catarina, P.O.Box 476, 88040-900 Florianópolis, SC-Brazil. E-mail: dkrause{at}cfh.ufsc.br

Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.

Key Words: quasi-sets • logic of quantum mechanics • identity • non-individuality • quantum ontology • quasi-objects.

Received for publication 13 October 2006. Revision received .

References

  1. Cantor G. Contributions to the Founding of the Theory of Transfinite Numbers (1955) New York: Dover.

  2. Cao TY. Introduction: Conceptual issues in quantum field theory. In: Conceptual Foundations of Quantum Feld Theory—Cao TY, ed. (1999) Cambridge: Cambridge Un. Press. 1–27.

  3. da Costa NCA. Ensaio sobre os Fundamentos da Lógica (1980) S. Paulo, Hucitec.

  4. da Costa NCA, Krause D. Schrödinger logics. Studia Logica (1994) 53(4):533–550.[CrossRef]

  5. da Costa NCA, Krause D. An intensional Schrödinger logic. Notre Dame Journal of Formal Logic (1997) 38(2):179–194.[CrossRef]

  6. Dalla Chiara ML, Giuntini R, Krause D. Quasiset theories for microobjects: a comparision. In: Interpreting Bodies: Classical and Quantum Objects in Modern Physics—Castellani E, ed. (1998) Princeton: Un. Press. 142–152.

  7. Domenech G, Holik F. A discussion on particle number and quantum indistinguishability. (2006) peprint.

  8. French S. Identity and Individuality in Quantum Theory. In: The Stanford Encyclopedia of Philosophy—Zalta Edward N, ed. Spring 2006 Edition. http://plato.stanford.edu/archives/spr2006/entries/qt-idind (original from 2000).

  9. French S, Krause D. Quantum vagueness. Erkenntnis (2003) 59:97–124.[CrossRef][ISI]

  10. French S, Krause D. Identity in Physics: A Historical, Philosophical, and Formal Analysis (2006) Oxford: Un. Press.

  11. Krause D. On a quasi-set theory. Notre Dame J. of Formal Logic (1992) 33:402–411.[CrossRef]

  12. Krause D. Axioms for collections of indistinguishable objects. Logique et Analyse (1996) 153–154:69–93.

  13. Krause D. Why quasi-sets? In: Boletim da Sociedade Paranaense de Matemática (2002) 73–92. 20 n. 1/2.

  14. Krause D. The mathematics of non-individuality. In: Coleção Documentos. Série Lógica e Teoria da Ciência n. 46, March 2003: Instituto de Estudos Avançados da Universidade de São Paulo.

  15. Krause D, Sant'Anna AS, Sartorell A. On the concept of identity in Zermelo-Fraenkel-like axioms and its relatioship with quantum statistics. Logique et Analyse (2005) 189–192:231–260.

  16. Krause D, Sant'Anna AS, Volkov AG. Quasi-set theory for bosons and fermions: quantum distributions. Foundations of Physics Letters (1999) 12(1):51–66.[CrossRef][ISI]

  17. Merzbacher E. Quantum Mechanics. (1970) 2nd. ed. New York: John Wiley.

  18. Penrose R. The Emperor's New Mind (1990) London: Vintage.

  19. Post H. Individuality and physics. In: The Listener. October 10. 534–537. reprinted in Vedanta for East and West 132, 1973, 14-22.

  20. Redhead M, Teller P. Particles, particle labels, and quanta: the toll of unacknowledged metaphysics. Foundations of Physics (1991) 21:43–62.[CrossRef][ISI]

  21. Redhead M, Teller P. Particle labels and the theory of indistinguishable particles in quantum mechanics. In: British Journal for the Philosophy of Science (1992) 43:201–218.[Abstract]

  22. Schrödinger E. Science and Humanism (1952) Cambridge: Cambridge Un. Press.

  23. Schrödinger E. ‘What is an elementary particle?’ In: Interpreting bodies: classical and quantum objects in modern physics (1998) Princeton Un. Press. 197–210. reprinted in Castellani, E. (ed.)

  24. Weyl H. Philosophy of Mathematics and Natural Science (1949) Princeton Un. Press.

  25. Wick D. The Infamous Boundary: Seven decades of heresy in quantum physics (1995) Copernicus, Springer-Verlag NY.


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