Abstract
In da Costa and de Ronde (Found Phys 43:845–858, 2013), Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of Quantum Mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause (New dimensions of the square of opposition, Philosophia Verlag, Munich, 2014; Logique et Analyse, 2014; The Road to Universal Logic (volume II), Springer, 2014) have raised several arguments against this approach and claimed that—taking into account the square of opposition—quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In de Ronde ( Los Alamos 2014) we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meaning of modality, potentiality, and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.
This work was partially supported by the following grants: FWO project G.0405.08 and FWO-research community W0.030.06. CONICET RES. 4541-12 (2013–2014).
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Notes
- 1.
The questioning is completely analogous to the one posed by the quantum to classical limit problem: how do we get from contextual weird QM into our safe classical physical description of the world?
- 2.
According to Van Fraassen [39, p. 280]: “The interpretational question facing us is exactly: in general, which value attributions are true? The response to this question can be very conservative or very liberal. Both court later puzzles. I take it that the Copenhagen interpretation—really, a roughly correlated set of attitudes expressed by members of the Copenhagen school, and not a precise interpretation—introduced great conservatism in this respect. Copenhagen scientists appeared to doubt or deny that observables even have values, unless their state forces to say so. I shall accordingly refer to the following very cautious answer as the Copenhagen variant of the modal interpretation. It is the variant I prefer.”
- 3.
For a detailed analysis of the arguments provided by Dieks and Griffiths see: [18].
- 4.
Regarding observation it is important to remark that such contradictory potentialities are observable just in the same way as actual properties can be observed in an object. Potentialities can be observed through actual effectuations in analogous fashion to physical objects—we never observe all perspectives of an object simultaneously, instead, we observe at most a single set of actual properties.
- 5.
As we have discussed in [13] modal interpretations range from empiricist positions such as that of Van Fraassen [39] to realist ones such as the one endorsed in different ways by Dieks [23], Bub [9], and Bacciagaluppi [4]. There are even different strategies and ideas regarding what should be considered to be a coherent interpretation within this group.
- 6.
It is important to notice that there is no difference in this point with the case of entities: we cannot ‘see’ entities—not in the sense of having a complete access to them. We only see perspectives which are unified through the notion of object.
- 7.
For a detailed analysis of the relation between quantum superpositions and physical reality see: [19].
- 8.
A possible development in line with the interpretation presented in this paper will be analyzed in [12].
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de Ronde, C. (2015). Modality, Potentiality, and Contradiction in Quantum Mechanics. In: Beziau, JY., Chakraborty, M., Dutta, S. (eds) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol 152. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2719-9_11
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