Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...) as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)

In this paper we attempt to provide a physical representation of quantum superpositions. For this purpose we discuss the constraints of the quantum formalism to the notion of possibility and the necessity to consider a potential realm independent of actuality. Taking these insights into account and from the basic principles of quantum mechanics itself we advance towards the definition of the notions of power and potentia. Assuming these notions as a standpoint we analyze the meaning of ‘observation’ and ‘interaction’. As (...) a conclusion we provide a set of axioms which comprise our interpretation of quantum mechanics and argue in favor of a redefinition of the orthodox problems discussed in the literature. (shrink)

In, 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 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 have raised several arguments against this approach. In the present paper we attempt to answer the main (...) questions presented by Arenhart and Krause. We will argue, firstly, that the obstacles presented by them are based on a specific metaphysical stance, which we will characterize in terms of what we call the Orthodox Line of Research. Secondly, that this is not necessarily the only possible line, and that a different one, namely, a Constructive Metaphysical Line of Research provides a different perspective in which the Paraconsistent Approach to Quantum Superpositions can be regarded as a valuable prospect that could be used by different interpretations of quantum mechanics. Finally, we provide a set of specific answers to the main problems raised by Arenhart and Krause in order to clarify our line of research as well as the original perspective introduced by the PAQS. (shrink)

En este artículo, analizamos el significado de las matrices densidad en el formalismo de la mecánica cuántica. Discutimos el problema de los "sistemas cuánticos compuestos" en la lógica cuántica así como también la interpretación de las mezclas impropias. Tomando en cuenta el desarrollo de la lógica cuántica convexa, presentamos un análisis de la estructura formal de la teoría que, argumentaremos, debe ser considerado a la hora de desarrollar un nuevo esquema conceptual para la interpretación de las mezclas cuánticas. In this (...) article, we analyze the meaning of density matrices within the formalism of quantum mechanics. We discuss the problem of compound systems in the context of quantum logic as well as the interpretation of improper mixtures. Taking into account the development of convex quantum logic, we present an analysis of the formal structure of the theory which we will argue, must be taken into account when developing a new conceptual scheme for the interpretation of quantum mixtures. (shrink)

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

In this paper we analyze the definition of quantum superpositions within orthodox Quantum Mechanics and their relation to physical reality. We will begin by discussing how the metaphysical presuppositions imposed by Bohr on the interpretation of QM have become not only interpretational dogmas which constrain the limits of the present Orthodox Line of Research, but also how these desiderata implicitly preclude the possibility of developing a physical representation of quantum superpositions. We will then continue analyzing how most interpretations of QM (...) argue against the existence of superpositions. Firstly, we will focus on those interpretations which attempt to recover a classical representation about ''what there is'', and secondly, we will concentrate on the arguments provided by Dieks and Griffiths who, staying close to the orthodox formalism, also attempt to ''get rid of the ghost of Schrodinger's cat''. Contrary to the OLR, we will argue -based on our definition of Meaningful Physical Statements - that from a representational realist perspective which stays close to the orthodox Hilbert space formalism, quantum superpositions are not only the key to the most important -present and future- technological and experimental developments in quantum information processing but also, they must be considered as the kernel of any interpretation of QM that attempts to provide a physical representation of reality. We will also argue that the price to pay for such representational realist development must be the abandonment of the idea that 'Actuality = Reality'. (shrink)

In [9], 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 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 [1, 2, 3] 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 [14] we defended the Paraconsistent Approach to Quantum Superpositions and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings 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 proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider. (shrink)

We interpret the philosophy of Niels Bohr as related to the so called ''linguistic turn'' and consider paraconsistency in the light of the Bohrian notion of complementarity. Following [16], Jean-Yves Beziau has discussed the seemingly contradictory perspectives found in the quantum mechanical double slit experiment in terms of paraconsistent view-points [7, 8]. This interpretation goes in line with the well known Bohrian Neo-Kantian epistemological account of quantum mechanics. In the present paper, we put forward the idea that one can also (...) consider, within quantum mechanics and departing from the philosophy of the danish physicist, a more radical paraconsistency found within one of the main formal elements of the theory, namely, quantum superpositions. We will argue that, rather than epistemological, the contradictions found within quantum superpositions could be interpreted as ontological contradictions. (shrink)