Abstract
In this paper we review some of the main ideas of two previous papers of ours which deal with an application of a kind of paraconsistent logic to quantum physics [14, 15]. We think that this revision is justified to present once more the richness of paraconsistent logics and suggests a way of dealing with one of most intriguing concepts of quantum theory. We propose and interpretation of complementarity in terms of what we call \(\mathcal {C}\)-theories (theories involving the idea of complementarity, in a sense explained in the text), whose underlying logic is a kind of paraconsistent logic termed paraclassical logic. Roughly speaking, \(\mathcal {C}\)-theories which may have ‘physically’ incompatible theorems (and, in particular, contradictory theorems), but which are not trivial.
The apparently incompatible sorts of information about the behavior of the object under examination which we get by different experimental arrangements can clearly not be brought into connection with each other in the usual way, but may, as equally essential for an exhaustive account of all experience, be regarded as ‘complementary’ to each other.
Niels Bohr (1937), p. 291
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Beller, M.: The birth of Bohr’s complementarity: the context and the dialogues. Stud. Hist. Phil. Sci. 23(1), 147–180 (1992)
Bohr, N.: The quantum postulate and the recent development of atomic theory’ [3], Atti del Congresso Internazionale dei Fisici, 11–20 Sept. 1927, Como-Pavia-Roma, Vol. II, Zanichelli, Bologna, 1928, reprinted in [pp.109–136]boh85
Bohr, N.: The quantum postulate and the recent developments of atomic theory. Nature 121(Suppl.), 580–590 (1928), reprinted in [pp.147-158]boh85
Bohr, N.: ‘Introductory survey’ to Bohr (1929), in [pp. 279–302] boh85
Bohr, N.: Atomic theory and the description of nature. Cambridge University Press, Cambridge (1934). Reprinted in [pp. 279–302]boh85
Bohr, N.: Causality and complementarity. Phil. Sci. 4(3), 289–298 (1937)
Bohr, N.: Natural philosophy of human cultures (1938). In: Atomic physics and human knowledge, pp. 23–31. Wiley, New York (1958) (also in Nature 143, 268–272)
Bohr, N.: Quantum physics and philosophy: causality and complementarity. In: Klibanski, R. (ed.) Philosophy in the Mid-Century I, pp. 308–314. Firenze, La Nuova Italia (1958)
Bohr, N.: Collected works. In: Rüdinger, E. (general ed.), vol. 6: Foundations of Quantum Physics I. (1985) Kolckar, J. (ed.) Amsterdam, North-Holland
Carnap, R.: An Introduction to the Philosophy of Science. Dover Pu, New York (1995)
Cushing, J.T.: Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony. The University of Chicago Press, Chicago and London (1994)
da Costa, N.C.A., Bueno, O.: Paraconsistency: towards a tentative interpretation. Theoria-Segunda Época 16(1), 119–145 (2001)
da Costa, N.C.A., de Ronde, C.: The paraconsistent logic of superpositions. Found. Phys. 43, 854–858 (2013)
da Costa, N.C.A., Krause, D.: Complementarity and paraconsistency. In: Rahman, S., Symons, J., Gabbay, D.M., van Bendegem, J.-P. (eds.) Logic, epistemology, and the Unity of Science, pp. 557–568. Springer (2004)
da Costa, N.C.A., Krause, D.: The logic of complementarity. In: van Benthem, J., Heinzmann, G., Rebushi, M., Visser, H. (eds.) The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today, pp. 103–120. Springer (2006)
da Costa, N.C.A., Vernengo, R.J.: Sobre algunas lógicas paraclássicas y el análisis del razonamiento jurídico. Doxa 19, 183–200 (1999)
da Costa, N.C.A., Krause, D., Bueno, O.: Paraconsistent logics and paraconsistency. In: D. Jacquette, editor of the volume on Philosophy of Logic; Gabbay, D.M., Thagard, P., Woods, J. (eds.) Philosophy of Logic, Elsevier, 2006, in the series Handbook of the Philosophy of Science, vol. 5, pp. 655–781 (2007)
De Février, P.: La structure des théories physiques. Presses Un, de France, Paris (1951)
Englert, B.-G., Scully, M.O., Walther, H.: The duality in matter and light. Sci. Am. 271(6), 56–61 (1994)
French, A.P., Kennedy, P.J. (eds.): Niels Bohr, a Centenary Volume. Harward University Press, Cambridge, MA and London (1985)
Hughes, G.E., Creswell, M.J.: A New Introduction to Modal Logic. Routledge, London (1996)
Jammer, M.: Philosophy of Quantum Mechanics. John Wiley, New York (1974)
Krause, D., Arenhart, J.R.B.: A logical account of quantum superpositions’, forthtcoming. In: Aerts, D., de Ronde, C., Freytes, H., Giuntini, R. (eds.) Probing the Meaning and Structure of Quantum Mechanics: Superpositions, Semantics, Dynamics and Identity. World Scientific, Singapore (2016)
Mendelson, E.: Introduction to Mathematical Logic, 3rd edn. Wadsworth & Brooks/Cole, Monterrey (1987)
Scheibe, E.: The Logical Analisys of Quantum Mechanics. Pergamon Press, Oxford (1973)
Acknowledgments
We would like to thank the organizers of this volume for the opportunity of presenting this paper and dedicate it to Jair Minoro Abe, our friend and colleague of so many years.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
da Costa, N.C.A., Krause, D. (2016). An Application of Paraconsistent Logic to Physics: Complementarity. In: Akama, S. (eds) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-40418-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-40418-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40417-2
Online ISBN: 978-3-319-40418-9
eBook Packages: EngineeringEngineering (R0)