Abstract
Following J.-Y.Béziau in his pioneer work on nonstandard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries (i.e., both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties (i.e., they must have opposite truth values). In this chapter, we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.
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
Notes
- 1.
In a nutshell, in classical logic, in the presence of a contradiction any proposition whatever may be said derivable, and the resulting system is called trivial. In paraconsistent systems, on the other hand, even if expressions formally representing contradictions are derivable, not every proposition is also derivable, so that the system is not trivial. For the details see [7], and also the discussion in Béziau [3, 5].
- 2.
We have our doubts about the possibility of representing a superposition this way, in particular, in reading the \(+\) sign of a superposition as a conjunction, but we shall do that for the purposes of argumentation in this section (see also [1]).
References
Arenhart, J.R.B., Krause, D.: Contradictions, Quantum Mechanics, and the Square of Oppositions. Preprint available at http://philsci-archive.pitt.edu/10582/ (2014)
Arenhart, J.R.B., Krause, D.: Oppositions and quantum mechanics: Superposition and identity. In: Béziau, J.-Y., Gan-Krzywoszynska, K. (eds.) New Dimensions of the Square of Opposition, Philosophia Verlag, Munich (2015), in press
Béziau, J.-Y.: New Light on the square of oppositions and its nameless corners. Log. Investig. 10, 218–232 (2003)
Béziau, J.-Y.: The Power of the hexagon. Log. Univers. 6(1–2), 1–43 (2012)
Béziau, J.-Y.: Contradiction and Negation. Talk delivered at the XVII EBL 2014 (2014)
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., Bueno, O.: Paraconsistent logic and paraconsistency. In: Jacquette, D. (ed.) Philosophy of Logic, pp. 655–775. Elsevier, Amsterdam (2006)
de Ronde, C.: A Defense of the Paraconsistent Approach to Superpositions (Answer to Arenhart and Krause). Available at http://arxiv.org/abs/1404.5186 (2014)
Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Oxford University Press, Oxford (2011)
Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, London (1996)
Lombardi, O., Dieks, D.: Modal interpretations of quantum mechanics. In: Zalta, E. (ed.) The Stanford Encyclopedia of Philosophy, Spring 2014 Edition. http://plato.stanford.edu/archives/spr2014/entries/qm-modal/ (2014)
Lowe, E.J.: A Survey of Metaphysics. Oxford University Press, Oxford (2002)
Muller, F.A., Saunders, S.: Discerning Fermions. Br. J. Philos. Sci. 59, 499–548 (2008)
Priest, G.: In Contradiction. Nijhoff, Dordrecht, The Netherlands (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to Jean-Yves Béziau on his 50th birthday
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Becker Arenhart, J.R., Krause, D. (2015). Potentiality and Contradiction in Quantum Mechanics. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15368-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-15368-1_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-15367-4
Online ISBN: 978-3-319-15368-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)